source,target
 This gives a dynamical time of 0.8 Cyr. which is an underestimate if he tails do not lie in the plane of the sky: thus the tidal ails are ονOS Cvr old.," This gives a dynamical time of 0.8 Gyr, which is an underestimate if the tails do not lie in the plane of the sky; thus the tidal tails are $>0.8$ Gyr old."
 This lower limit is consistent with he age derived [from the fraction of galaxy light contained within the tails., This lower limit is consistent with the age derived from the fraction of galaxy light contained within the tails.
 The presence of two symmetric tidal tails is generally aken to be a signature of a recent major merger involving wo. approximately equal mass spiral galaxies (see e.g. 2)).," The presence of two symmetric tidal tails is generally taken to be a signature of a recent major merger involving two, approximately equal mass spiral galaxies (see e.g. \pcite{toomre72}) )."
 It the tidal features in Fig., If the tidal features in Fig.
 5. are indeed. genuine tidal tails hen we could. conclude that NGC 1700 has experienced a major merger during its recent history., \ref{fig:resid} are indeed genuine tidal tails then we could conclude that NGC 1700 has experienced a major merger during its recent history.
 Alternatively. if the eatures are merely plumes of tically disturbed material. the situation is less clear.," Alternatively, if the features are merely plumes of tidally disturbed material, the situation is less clear."
 While a major merger could not be ruled. out. the situation of a disc galaxy merging into an existing elliptical would be possible.," While a major merger could not be ruled out, the situation of a disc galaxy merging into an existing elliptical would be possible."
 We present in Fig., We present in Fig.
D δ the D1 colour histogram5 [for NGC 1700 GCs from the Ixeck data., \ref{fig:BIhist} the $B-I$ colour histogram for NGC 1700 GCs from the Keck data.
 Phe histogram appears bimodal with a blue peak at ο£=1.54-£0.05 and a second peak O4440.07 magnitudes recder at Bo4—1.98+£0.05., The histogram appears bimodal with a blue peak at $B-I=1.54\pm0.05$ and a second peak $0.44\pm0.07$ magnitudes redder at $B-I=1.98\pm0.05$.
 This bimodality does not appear to be an artifact of the data onning ancl is still present if the histogram bin boundaries are changed., This bimodality does not appear to be an artifact of the data binning and is still present if the histogram bin boundaries are changed.
 For the subsequent. discussion. anc analysis we define the population as those GC's possessing )s-DdX1.75 and the population with colours l5«D«X0., For the subsequent discussion and analysis we define the population as those GCs possessing $0.8<B-I\leq1.75$ and the population with colours $1.75<B-I<3.0$.
 A statistical analysis using the algorithm (Ashman. Bird ορ 1994). detects xmocdality in the distribution with z99 per cent confidence.," A statistical analysis using the algorithm (Ashman, Bird Zepf 1994) detects bimodality in the distribution with $>99$ per cent confidence."
 The algorithm assigned a colour cut between the blue and red populations of D./=Ls. thus confirming our initial visual estimate.," The algorithm assigned a colour cut between the blue and red populations of $B-I=1.8$, thus confirming our initial visual estimate."
 Phe ο4 distribution of GC's in the Milky Way is also shown in Fig., The $B-I$ distribution of GCs in the Milky Way is also shown in Fig.
 S. (shaded area)., \ref{fig:BIhist} (shaded area).
 The peak of this distribution is at (2ZJ)o~1.5 which is similar to the peak of the blue population of NGC 1700., The peak of this distribution is at $(B-I)_0\sim1.5$ which is similar to the peak of the blue population of NGC 1700.
 Is the bimocality of the D.7 histogram evidence for two distinct. GC populations in NGC 17007, Is the bimodality of the $B-I$ histogram evidence for two distinct GC populations in NGC 1700?
 In order to address this question. one has to consider the expected number of contaminating sources within our final sample.," In order to address this question, one has to consider the expected number of contaminating sources within our final sample."
 As the number of predicted stars colour selection is small. we can immediately conclude that the contamination bv foreground stars in our final sample is negligible.," As the number of predicted stars colour selection is small, we can immediately conclude that the contamination by foreground stars in our final sample is negligible."
 Another source of contamination is background. galaxies., Another source of contamination is background galaxies.
 Our automatic and. visual checks have removed. obvious ealaxies but it is possible that small. unresolved background ealaxies remain.," Our automatic and visual checks have removed obvious galaxies but it is possible that small, unresolved background galaxies remain."
 For our mean D magnitude of 24.5. we expect to be detecting sources oul to à mean redshift: of ~OS (7).," For our mean $B$ magnitude of 24.5, we expect to be detecting sources out to a mean redshift of $z\sim0.8$ \cite{kookron92}."
 At this redshift’ all morphological tvpes of galaxies (with the exception of irregular types) have typical Bf colours in excess of 2.5., At this redshift all morphological types of galaxies (with the exception of irregular types) have typical $B-I$ colours in excess of 2.5.
 This is significantly receler than the peak of the red population and we can thus be fairly, This is significantly redder than the peak of the red population and we can thus be fairly
"C. 1, Odean? The discovery of a possible accelerated expansion of our present uuilverse from ype Ia supernovae (|1])). is perhaps the most remarkable cosmological finding of recent vears.","C. J. $^{2}$ } The discovery of a possible accelerated expansion of our present universe from type Ia supernovae \cite{super1}) ), is perhaps the most remarkable cosmological finding of recent years."
" Furthermore. the flatucss of the universe (O5,= 1) determined w Cosmic Microwave Backeromnd observations (5). togheter with the low natter density (Quarter,< 0.1) inferred from: Large Scale Structure. ([3]}) are sugeesting the presence of a cosmological coustant with high statistical sjeuificauce."," Furthermore, the flatness of the universe $\Omega_{tot}=1$ ) determined by Cosmic Microwave Background observations \cite{flat}) ), togheter with the low matter density $\Omega_{matter}<0.4$ ) inferred from Large Scale Structure \cite{lowmat}) ) are suggesting the presence of a cosmological constant with high statistical significance."
 Towever. the CAIB|LSS result relies ou the assumption of a articular class of models based on adiabatic prinordial fluctuations. cold dark matter and a cosmological constant as dark cucrey compoucut.," However, the CMB+LSS result relies on the assumption of a particular class of models, based on adiabatic primordial fluctuations, cold dark matter and a cosmological constant as dark energy component."
 Iu the ollowing we will refer to this class of model as A-Cold Dark Matter (A-CDAD., In the following we will refer to this class of model as $\Lambda$ -Cold Dark Matter $\Lambda$ -CDM).
 This weak poiut. shared by most of the current studies. should not be overlooked: it wight be possible that a different solution to the dark euerey scenario than a cosmological coustaut cau affect the CMD|LSS determination.," This weak point, shared by most of the current studies, should not be overlooked: it might be possible that a different solution to the dark energy scenario than a cosmological constant can affect the CMB+LSS determination."
 It is therefore Πιο to investigate if the actual CMD data is in complete agrecnent with the A-CDAL sccuario or if we are losing relevaut scientific informations by restricting the current analysis to a subset of models., It is therefore timely to investigate if the actual CMB data is in complete agreement with the $\Lambda$ -CDM scenario or if we are losing relevant scientific informations by restricting the current analysis to a subset of models.
 Tere first we check to what extent modifications to the standard A-CDÀ scenario areneeded by current CMD observations with a model-indepenuden analysis obtained fitting the actual data with a phenomenological fiction au characterizing the observed multiple peaks through a Monte Carlo Markov Chain CMCMXC) algorithm. which allows us to investigate a large uuuber of parameter simultancously (15 im our case).," Here first we check to what extent modifications to the standard $\Lambda$ -CDM scenario are by current CMB observations with a model-independent analysis obtained fitting the actual data with a phenomenological function and characterizing the observed multiple peaks through a Monte Carlo Markov Chain (MCMC) algorithm, which allows us to investigate a large number of parameter simultaneously $15$ in our case)."
 We found a very good agreemenu between the position. relative amplitude aud width of the peaks obtaiue through the model independent approach with the same features expected in a d[-purzuneters model template of A-CDM spectra.," We found a very good agreement between the position, relative amplitude and width of the peaks obtained through the model independent approach with the same features expected in a $4$ -parameters model template of $\Lambda$ -CDM spectra."
 Second. since the A-CDN is a good fit to the CMD data. we then move to other possible candidates for the dark energv component to see what kind of constraint we can obtain.," Second, since the $\Lambda$ -CDM is a good fit to the CMB data, we then move to other possible candidates for the dark energy component to see what kind of constraint we can obtain."
 The common characteristic of alternative scenarios to a cosmological constant.," The common characteristic of alternative scenarios to a cosmological constant,"
reduce the dimensionality of the feature space by combining redundant features. e.g. the equivalent widths of the Balmer lines to a sun of equivalent widths.,"reduce the dimensionality of the feature space by combining redundant features, e.g. the equivalent widths of the Balmer lines to a sum of equivalent widths."
 The remaimine set of features is then evaluated with the iuethods described in Sect. ??.., The remaining set of features is then evaluated with the methods described in Sect. \ref{Sect:Evalu}.
 For supervised classification. a is needed.," For supervised classification, a is needed."
 For our purposes. we define a learuiug sample to be a κο of n; objects for which the feature vectors ave known. and for which it is known to what class they belong.," For our purposes, we define a learning sample to be a set of $n_{l}$ objects for which the feature vectors are known, and for which it is known to what class they belong."
⊺∐↸∖↴∖↴↸∖≼⊳↕⋜↧↴∖∷∖↴↸∖↴∖↴↸⊳⋜⋯↴⋝↸∖≺∐∖↴∐↸∖≺↧∙↸∖∙∶↴↜⊾⋅⋅↴⋝∙↖⇁∶↴∙↕⋅⋯∏≻↕∐∩⋜↧∖↴↸∖↑∪↕ ∙ ∪↴⋝⋅↿≱↸∖↸⊳↑∖↴⋜↧↸⊳↸⊳∪↥⋅≼∐∐∩⊾↑∪↑↕∐∖∐⋅↴∖↴↑↸∖∐⋜∐⋅↻⋜∐⋅⋜↧⋯↸∖↑↸∖↥⋅↴∖↴↸∖∩⊺↥∟↕↕⋜∏⋝↸∖↕≋↸∖↸⊳↑∶↕≻↸∖↸⊳↕↴∖↴↕≺≻∐↕⊰∏↕↸∖↴∖↴ ↕∪∶↴∙⊾∙↙∕⊪⊟∖∐∩∪↥⋝↖⇁⋯⋜↧∐⋯∐↖↽⋜↕∖↴∖↴↕∩⊾∐↕∐∩⊾↸⊳↕⋜↕∖↴∖↴↸∖∖↴↑∪⋜↧∖↴↸∖↑ of spectra by comparison with reference objects.," These classes can be defined, e.g., by grouping a set of objects according to their stellar parameters (e.g. $T_{\mbox{\scriptsize eff}}$, $\log g$, [Fe/H]), or by manually assigning classes to a set of spectra by comparison with reference objects."
 With the help of a learning sample. information on the class- probability deusities plaO;) can be oOgained.," With the help of a learning sample, information on the class-conditional probability densities $p(\vec{x}|\Omega_j)$ can be gained."
 e ∟∕↙∣↨↕∕⋅↕↴∖↴↑∐↸∖⋯⋅≺⋔⋜⋔∐↕↑∙↖↽↑∪∪↴⋝↴∖↴↸∖↥⋅↖↸∖≼↧↕⋟↸∖⋜↕⊓∐⋅↸∖↖↽↸∖↸⊳↑∪↥⋅↕∐⋜↧↥⋅↸∖⋅↿≱↸∖↸⊳↑↕∪↕⊔↴∏↸∖∙ the range ax...z|dx iu the class O;., $p(\vec{x}|\Omega_j)d\!\vec{x}$ is the probability to observe a feature vector in the range $\vec{x}\dots \vec{x}+d\!\vec{x}$ in the class $\Omega_j$.
 We inspected the ouc-dimensional classconditional larisprobability distributions of the classes coveredby the saluples used iu this work. aud qualitatively found their shapes to agree well with Gaussians.," We inspected the one-dimensional class-conditional probability distributions of the classes covered by the learning samples used in this work, and qualitatively found their shapes to agree well with Gaussians."
 We hence model pla]Q;)by multivariate normal distributions. 1.6.. wherej denotes class umber. 44; tho mean feature vector of class O5. aud Xj the covariance matrix. of class Q;. ⊀≚↸⊳↸∖∐," We hence model $p(\vec{x}|\Omega_j)$ by multivariate normal distributions, i.e., where $j$ denotes class number, $\vec{\mu}_j$ the mean feature vector of class $\Omega_j$, and $\Sigma_j$ the covariance matrix of class $\Omega_j$."
⊓⋅⋜↧↕↕↴∖∷∖↴⋯∖↕∐⋜⋯↑∪⋯⋜↧↑↕↸⊳↸⊳↕⋜↕↴∖↴↴∖↴↕∐↸⊳⋜↕⊓∪∐↕↴∖↴↑↕∐∖ construction of a decision rule which is optimal for the given classification problem., A central issue in automatic classification is the construction of a decision rule which is optimal for the given classification problem.
 In the WES. we use three decision rules: the Baves rule. a niuinun cost rule. and," In the HES, we use three decision rules: the Bayes rule, a minimum cost rule, and a rejection rule."
" In the ""pure"" DS phase the star will be puffier for a higher (o0)/m, ratio, as can be seen from the left panel of Fig.4."," In the “pure” DS phase the star will be puffier for a higher $\sv/m_{\chi}$ ratio, as can be seen from the left panel of \ref{radius}."
. This is expected due to the much higher DM heating in that case: a larger radius is required to balance the DM energy production and the radiated luminosity. which scales as /2?.," This is expected due to the much higher DM heating in that case: a larger radius is required to balance the DM energy production and the radiated luminosity, which scales as $R^2$."
" For instance. in the boosted AH4 case the maximum radius is at about 2x 10'cem, whereas for the 100 GeV non-boosted WIMP, the DS will have a maximum radius of 10! cm."," For instance, in the boosted AH4 case the maximum radius is at about $2\times 10^{14}$ cm, whereas for the $100$ GeV non-boosted WIMP, the DS will have a maximum radius of $10^{14}$ cm."
 However. as mentioned before. the KH contraction will set in carlier in the boosted case.," However, as mentioned before, the KH contraction will set in earlier in the boosted case."
 This phase corresponds to the sharp decrease in radius in Fig.4., This phase corresponds to the sharp decrease in radius in \ref{radius}.
". The final radii, as the DS enters the ZAMS are similar in both cases, at around 6x10! em."," The final radii, as the DS enters the ZAMS are similar in both cases, at around $6\times 10^{11}$ cm."
"are no longer in the realm of cosmology. but are dealing with ""messy"" astrophysics.","are no longer in the realm of cosmology, but are dealing with “messy” astrophysics."
 Fortunately. there is an alternative way to study the dark matter distribution.," Fortunately, there is an alternative way to study the dark matter distribution."
 ? already note that the blow-out process can only be effective in dwarf galaxies., \citet{Navarro:1996p192} already note that the blow-out process can only be effective in dwarf galaxies.
 In more massive galaxies. such as spiral galaxies. the potential well is too deep to efficiently remove the gas.," In more massive galaxies, such as spiral galaxies, the potential well is too deep to efficiently remove the gas."
 Finding and investigating more massive dark-matter dominated galaxies may therefore be a more effective way to explore the core/cusp Issue., Finding and investigating more massive dark-matter dominated galaxies may therefore be a more effective way to explore the core/cusp issue.
 These galaxies. fortunately. do exist. and are called Low Surface Brightness (LSB) galaxies.," These galaxies, fortunately, do exist, and are called Low Surface Brightness (LSB) galaxies."
 The term LSB galaxies is used here to indicate late-type. gas-rich. dark-matter-dominated disk galaxies.," The term LSB galaxies is used here to indicate late-type, gas-rich, dark-matter-dominated disk galaxies."
 Their optical component is well-described by an exponential disk with an (extrapolated) inclination-corrected central surface brightness fainter than j/op~23 mag arcsec (???)..," Their optical component is well-described by an exponential disk with an (extrapolated) inclination-corrected central surface brightness fainter than $\mu_{0,B} \sim 23$ mag $^{-2}$ \citep{McGaugh:1994p947,McGaugh:1995p958,deBlok:1995p952}."
 Despite their low surface brightness. their integrated luminosity is a few magnitudes brighter than that of late-type dwarf galaxies (Mp—18 to ~—20 for LSB galaxies. as opposed to Mp=—16 for the dwarf galaxies).," Despite their low surface brightness, their integrated luminosity is a few magnitudes brighter than that of late-type dwarf galaxies $M_B \sim -18$ to $\sim -20$ for LSB galaxies, as opposed to $M_B \ga -16$ for the dwarf galaxies)."
 As noted. they are gas-rich (My/LgZV: 2??22)). and their interstellar medium has a low metallicity (22)...," As noted, they are gas-rich $M_{HI}/L_B \ga 1$; \citealt{Schombert:1992p1053,McGaugh:1997p1066,Schombert:2001p1060}) ), and their interstellar medium has a low metallicity \citep{McGaugh:1994p950,deBlok:1998p1076}."
 Their optical appearance is dominated by an exponential disk with a young. blue population. with little evidence for a dominant old population.," Their optical appearance is dominated by an exponential disk with a young, blue population, with little evidence for a dominant old population."
 Additionally. these galaxies do not have large dominant bulges. and seem to have had a star formation history with only sporadic star formation (???)..," Additionally, these galaxies do not have large dominant bulges, and seem to have had a star formation history with only sporadic star formation \citep{vanderHulst:1993p956,vandenHoek:2000p1081,Gerritsen:1999p1104}."
 Central light concentrations. if present at all. tend to be only fractionally brighter than that of the extrapolated exponential disk.," Central light concentrations, if present at all, tend to be only fractionally brighter than that of the extrapolated exponential disk."
 In terms of their spatial distribution. they are found on the outskirts of the large scale structure filaments (?2)..," In terms of their spatial distribution, they are found on the outskirts of the large scale structure filaments \citep{Bothun:1993p973,Mo:1994p949}."
" In short. most observational evidence indicates that these galaxies have had a quiescent evolution. with little evidence for major merging episodes. interactions. or other processes that might have stirred up the baryonic and dark matter (see also ??.,"," In short, most observational evidence indicates that these galaxies have had a quiescent evolution, with little evidence for major merging episodes, interactions, or other processes that might have stirred up the baryonic and dark matter (see also \citealt{Bothun:1997p937,Impey:1997p1001}."
 As for the term “LSB galaxies”. there is some confusion in the literature about what type of galaxies it applies to.," As for the term “LSB galaxies”, there is some confusion in the literature about what type of galaxies it applies to."
 The type of LSB galaxies most commonly studied. in particular with regards to the core/cusp controversy. are the late-type LSB galaxies whose properties are described above.," The type of LSB galaxies most commonly studied, in particular with regards to the core/cusp controversy, are the late-type LSB galaxies whose properties are described above."
 The other type of LSB galaxies often discussed in the literature are the massive. early-type. bulge-dominated LSB galaxies.," The other type of LSB galaxies often discussed in the literature are the massive, early-type, bulge-dominated LSB galaxies."
 These galaxies have properties entirely different from the late-type LSB galaxies (??)..," These galaxies have properties entirely different from the late-type LSB galaxies \citep{Sprayberry:1995p977,Pickering:1997p988}."
 The massive LSB galaxies are a lot more luminous and their optical appearance is dominated by a bright central bulge with a clearly detectable old population (?).., The massive LSB galaxies are a lot more luminous and their optical appearance is dominated by a bright central bulge with a clearly detectable old population \citep{Beijersbergen:1999p1156}.
 Many of them have low-level AGN activity (?).., Many of them have low-level AGN activity \citep{Schombert:1998p1225}.
 All indications are that the evolution of these galaxies has been entirely different from that of late-type LSB galaxies: if anything. they resemble SO galaxies with extended disks. rather than late-type galaxies.," All indications are that the evolution of these galaxies has been entirely different from that of late-type LSB galaxies: if anything, they resemble S0 galaxies with extended disks, rather than late-type galaxies."
 The presence of the dominant bulge also indicates that their central dynamies are likely to be dominated by the stars. rather than dark matter.," The presence of the dominant bulge also indicates that their central dynamics are likely to be dominated by the stars, rather than dark matter."
 In the following. the term “LSB galaxies” therefore refers to type LSB galaxies only.," In the following, the term “LSB galaxies” therefore refers to late-type LSB galaxies only."
 The first detailed studies of large samples of LSB galaxies soon led to the picture of them being unevolved. gas-rich disk galaxies. as described above.," The first detailed studies of large samples of LSB galaxies soon led to the picture of them being unevolved, gas-rich disk galaxies, as described above."
 The observation that they followed the same Tully-Fisher relation as normal galaxies (2) was intriguing. as this implied they had to be dark-matter dominated.," The observation that they followed the same Tully-Fisher relation as normal galaxies \citep{Zwaan:1995p951} was intriguing, as this implied they had to be dark-matter dominated."
 Follow-up radio synthesis observations in HI (?)) soon confirmed this., Follow-up radio synthesis observations in HI \citep{deBlok:1996p5} soon confirmed this.
" Though the resolution of these early observations was limited. the derived rotation curves clearly resembled those of late-type dwarf and ""normal"" disk galaxies: a slow rise. followed by à gradual flattening."," Though the resolution of these early observations was limited, the derived rotation curves clearly resembled those of late-type dwarf and “normal” disk galaxies: a slow rise, followed by a gradual flattening."
 When expressed in terms of scale lengths. the rotation curves of LSB and HSB galaxies of equal luminosity turned out to be very similar. indicating that LSB galaxies are in general low density objects (?)..," When expressed in terms of scale lengths, the rotation curves of LSB and HSB galaxies of equal luminosity turned out to be very similar, indicating that LSB galaxies are in general low density objects \citep{deBlok:1996p44}."
 Mass models derived using the rotation curves clearly showed that for reasonable assumptions for the stellar mass-to-light ratio. Y.. the dynamics of LSB galaxies had to be dominated by dark matter (?)..," Mass models derived using the rotation curves clearly showed that for reasonable assumptions for the stellar mass-to-light ratio, $\Upsilon_\star$, the dynamics of LSB galaxies had to be dominated by dark matter \citep{deBlok:1997p22}."
 Assuming that the stars had to dominate the dynamics in the inner parts (the so-called maximum disk solution) led to unrealistically high YT. values. and. even when taken at face value. still showed a need for a moderate amount of dark matter at small radii (see also 2)).," Assuming that the stars had to dominate the dynamics in the inner parts (the so-called maximum disk solution) led to unrealistically high $\Upsilon_{\star}$ values, and, even when taken at face value, still showed a need for a moderate amount of dark matter at small radii (see also \citealt{McGaugh:1998p34}) )."
 The distribution of the dark matter at first sight seemed similar to that in gas-rich dwarf galaxies (?).., The distribution of the dark matter at first sight seemed similar to that in gas-rich dwarf galaxies \citep{deBlok:1997p22}.
 Because of the limited resolution of the data. ?— did not attempt fits with the NFW model. but noted that the halos had to be extended. diffuse and low density.," Because of the limited resolution of the data, \citet{deBlok:1997p22} did not attempt fits with the NFW model, but noted that the halos had to be extended, diffuse and low density."
 A first attempt at comparing the HI. data with CDM predictions was made by ?.., A first attempt at comparing the HI data with CDM predictions was made by \citet{McGaugh:1998p34}.
 Rather than making fits to the rotation curve. they simply assumed that the typical velocity Vsoo of the halo had to equal the outer (maximum) rotation velocity of the galaxy.," Rather than making fits to the rotation curve, they simply assumed that the typical velocity $V_{200}$ of the halo had to equal the outer (maximum) rotation velocity of the galaxy."
 The strict cosmological relation between ο and ου then automatically yields a value of ο compatible with ACDM., The strict cosmological relation between $c$ and $V_{200}$ then automatically yields a value of $c$ compatible with $\Lambda$ CDM.
 Adopting these values. the resulting halo rotation curve turned out to be very different from the observed curve. in a similar way as the ? analysis: the NEW curve is too steep and rises too quickly in the inner parts.," Adopting these values, the resulting halo rotation curve turned out to be very different from the observed curve, in a similar way as the \citet{Moore:1994p86} analysis: the NFW curve is too steep and rises too quickly in the inner parts."
 The only way the halo curve could be made to resemble the observed curve. was by abandoning the cosmological (c.σου) relation.," The only way the halo curve could be made to resemble the observed curve, was by abandoning the cosmological $(c,V_{200})$ relation."
 Similar conclusions. were derived by ?.., Similar conclusions were derived by \citet{Cote:2000p77}.
 They presented high-resolution HI observations of dwarfs in the nearby Centaurus and Sculptor groups. and noted that the derived rotation curves did not agree with the NFW model.," They presented high-resolution HI observations of dwarfs in the nearby Centaurus and Sculptor groups, and noted that the derived rotation curves did not agree with the NFW model."
 A possible explanation that was soon put forward was that there were still unrecognized systematic effects in the data. that would give the false impression of a core-like behaviour.," A possible explanation that was soon put forward was that there were still unrecognized systematic effects in the data, that would give the false impression of a core-like behaviour."
 Initially. attention focussed on the resolution of the ?| HI observations.," Initially, attention focussed on the resolution of the \citet{deBlok:1996p5} HI observations."
 These had beam sizes of ~ 15’. resulting in the HI disks of the LSB galaxies investigated having a diameter of between 3 and 18 independent beams.," These had beam sizes of $\sim 15''$ , resulting in the HI disks of the LSB galaxies investigated having a diameter of between 3 and 18 independent beams."
" This limited resolution can potentially affect the shapes of the rotation curves through a process called ""beam smearing”. as also mentioned in ?.."," This limited resolution can potentially affect the shapes of the rotation curves through a process called “beam smearing”, as also mentioned in \citet{deBlok:1996p5}."
 In observations with limited resolution. the beam smearing process decreases the observed velocities (compared to the true velocities). and in extreme cases can turn any steeply rising rotation curve into a slowly rising solid-body one.," In observations with limited resolution, the beam smearing process decreases the observed velocities (compared to the true velocities), and in extreme cases can turn any steeply rising rotation curve into a slowly rising solid-body one."
 This would therefore give the impression of a core being present in the data. while the true distribution could still be cuspy.," This would therefore give the impression of a core being present in the data, while the true distribution could still be cuspy."
 In their paper. ? argued. through modelling of these beam smearing effects. as well as the direct detections of steeply rising rotation curves m the data. that while some beam smearing was indeed present. the effect was not strong enough to completely “hide” the dynamical signature of a cusp. and concluded that the data were consistent with the existence of dark matter cores.," In their paper, \citet{deBlok:1997p22} argued, through modelling of these beam smearing effects, as well as the direct detections of steeply rising rotation curves in the data, that while some beam smearing was indeed present, the effect was not strong enough to completely “hide” the dynamical signature of a cusp, and concluded that the data were consistent with the existence of dark matter cores."
 An alternative interpretation was given in?)who used the ? data. along with high-resolution literature rotation curves," An alternative interpretation was given in \citet{vandenBosch:2000p188} who used the \citet{deBlok:1997p22} data, along with high-resolution literature rotation curves"
et al.,et al.
 Then Chandra follow up observations of the region detected three sources (Tomsick et al., Then Chandra follow up observations of the region detected three sources (Tomsick et al.
" 2008): the same source detected by XRT, a new one located inside the new ISGRI error circle (J174435.4-274453, diamond point) reported in the 4th IBIS catalogue and a third one just at its border (J174427.3-274324 box Within the INTEGRAL/IBIS error circle detects only one source at a position compatible with that of the Chandra source J174435.4-274453 indicating that this could be a possible counterpart."," 2008): the same source detected by XRT, a new one located inside the new ISGRI error circle (J174435.4-274453, diamond point) reported in the 4th IBIS catalogue and a third one just at its border (J174427.3-274324 box Within the INTEGRAL/IBIS error circle detects only one source at a position compatible with that of the Chandra source J174435.4-274453 indicating that this could be a possible counterpart."
" The source spectrum is poorly sampled by XMM as this is only a 4.6 sigma detection but we were able to estimate the 0.2-12 keV observed flux of 8 x 10:14 erg cm? s! fully compatible with that of Chandra of 7 x10!* erg cm? s. However, we note that within the IBIS error box there is also an XMM-Slew source: XMMSL1 J174429.4-274609 (circle point in the figure) whose coordinates are reported in table 2."," The source spectrum is poorly sampled by XMM as this is only a 4.6 sigma detection but we were able to estimate the 0.2-12 keV observed flux of 8 $\times$ $^{-14}$ erg $^{-2}$ $^{-1}$ fully compatible with that of Chandra of $\sim$ 7 $\times$ $^{-14}$ erg $^{-2}$ $^{-1}$ However, we note that within the IBIS error box there is also an XMM-Slew source: XMMSL1 J174429.4-274609 (circle point in the figure) whose coordinates are reported in table 2."
 This source with a 0.2-12 keV flux of 1.64 x 1077? erg cm? s! is the brightest in the high energy error circle and it is also extremely variable as it was seen only once out of four observations of the region made at different epochs., This source with a 0.2-12 keV flux of 1.64 $\times$ $^{-12}$ erg $^{-2}$ $^{-1}$ is the brightest in the high energy error circle and it is also extremely variable as it was seen only once out of four observations of the region made at different epochs.
" This source is associated only to an infrared object (2MASS 17442946-2746114) within the XMM-Slew (5.1"") positional uncertainty with J, H and K magnitudes of 15.13, 12.88 and 12.85 The XMM upper limit on the source flux is 0.4 x 107% erg οπι s! in the same waveband implying a dynamic range of around IGR J17445-2747 is reported in the 4th IBIS catalogue as a transient bursting source since it was significantly detected at ~ 130 level (20-100 keV) only during its outburst activity lasting for a total of ~ 30 days and reaching a peak flux of ~ 30 mCrab or 4.6x 10:10 erg cm s! (20-100 keV)."," This source is associated only to an infrared object (2MASS 17442946-2746114) within the XMM-Slew $^{\prime\prime}$ ) positional uncertainty with J, H and K magnitudes of 15.13, 12.88 and 12.85 The XMM upper limit on the source flux is 0.4 $\times$ $^{-13}$ erg $^{-2}$ $^{-1}$ in the same waveband implying a dynamic range of around IGR J17445-2747 is reported in the 4th IBIS catalogue as a transient bursting source since it was significantly detected at $\sim$ $\sigma$ level (20–100 keV) only during its outburst activity lasting for a total of $\sim$ 30 days and reaching a peak flux of $\sim$ 30 mCrab or $\times$ $^{-10}$ erg $^{-2}$ $^{-1}$ (20–100 keV)."
" On the contrary the source was not ?detected in the total dataset for an on-source exposure time of — 7.3 Ms, providing an upper limit to the flux of 0.1 mCrab (20-40 keV) and resulting in a dynamical range of ~ 300."," On the contrary the source was not detected in the total dataset for an on-source exposure time of $\sim$ 7.3 Ms, providing an upper limit to the flux of 0.1 mCrab (20–40 keV) and resulting in a dynamical range of $\sim$ 300."
" Therefore, given the transient nature of both IGR J17445-2747 and XMMSL1 J174429.4-274609, we conclude that the two sources are very likely associated."," Therefore, given the transient nature of both IGR J17445-2747 and XMMSL1 J174429.4-274609, we conclude that the two sources are very likely associated."
 IGR J18538-0102 is a newly discovered INTEGRAL source listed in the fourth IBIS survey (Bird et al., IGR J18538-0102 is a newly discovered INTEGRAL source listed in the fourth IBIS survey (Bird et al.
 2010)., 2010).
 Recently Stephen et al (2010) provided an improved position for the source using the association with an XMM Slew catalogue source (2XMM J185348.4-010229)., Recently Stephen et al (2010) provided an improved position for the source using the association with an XMM Slew catalogue source (2XMM J185348.4-010229).
 These authors also noted that IGR J18538-0102 is spatially coincident with a hot spot in the supernova remnant candidate G32.1-0.9 detected in X-rays by ROSAT and ASCA (Folgheraiter et al., These authors also noted that IGR J18538-0102 is spatially coincident with a hot spot in the supernova remnant candidate G32.1-0.9 detected in X-rays by ROSAT and ASCA (Folgheraiter et al.
 1997): but it has a much harder spectrum and higher absorption than observed in the supernova remnant., 1997): but it has a much harder spectrum and higher absorption than observed in the supernova remnant.
 This suggests the possibility that IGR J18538-0102 could be a more distant Galactic source or a background AGN and its alignment with G32.1-0.9 is only coincidental., This suggests the possibility that IGR J18538-0102 could be a more distant Galactic source or a background AGN and its alignment with G32.1-0.9 is only coincidental.
 Halpern and Gotthelf (2010) then reported on the XMM observation used here and further discussed a possible infrared/optical counterpart of the source., Halpern and Gotthelf (2010) then reported on the XMM observation used here and further discussed a possible infrared/optical counterpart of the source.
" We re-analysed the XMM data in order to combine them with IBIS ones, performing for the first time a broad band spectral analysis and discussing further the nature of this object."," We re-analysed the XMM data in order to combine them with IBIS ones, performing for the first time a broad band spectral analysis and discussing further the nature of this object."
 The EPIC 0.2-12 keV image shown in figure 9 with the INTEGRAL error circle indicates that there is only one X-ray counterpart., The EPIC 0.2-12 keV image shown in figure 9 with the INTEGRAL error circle indicates that there is only one X-ray counterpart.
" Archival searches within the positional uncertainty finds the infrared object (2MASS 18534847-0102295) discussed by Halpern and Gotthelf which has J, H, and K magnitudes of 14.16, 14 and 12.50 respectively."," Archival searches within the positional uncertainty finds the infrared object (2MASS 18534847-0102295) discussed by Halpern and Gotthelf which has J, H, and K magnitudes of 14.16, 14 and 12.50 respectively."
" It coincides with the USNO-B1 0889-0406090 object (R= 15.2 magnitudes) and with the soft X-ray source 1RXH J185348.2-010228 detected by the Next, we concentrated on broad band spectral"," It coincides with the USNO-B1 0889-0406090 object (R= 15.2 magnitudes) and with the soft X-ray source 1RXH J185348.2-010228 detected by the Next, we concentrated on broad band spectral"
For the MID sample with 35 bandpowers and 5 parameters. V7=21.,"For the MID sample with 35 bandpowers and 5 parameters, $\chi^2 = 21$."
 We find 0.14. in good agreement with the values reported in ?..," We find $k_{BAO} = 0.14$ , in good agreement with the values reported in \citet{eisenstein/seo/white:2007}."
 In Fig., In Fig.
 5 we show that the Path) term accounts for the barvonic features in. {ο(Ας and the polynomial in Á& adequately lits the smooth correction lor the. MID sample.while halolit underestimates the smooth correction by ~4% at &=0.2.," \ref{fig:DMnonlinear3} we show that the $P_{\rm smear}(k)$ term accounts for the baryonic features in $P_{DM}(k)$, and the polynomial in $k$ adequately fits the smooth correction for the MID sample,while halofit underestimates the smooth correction by $\sim 4\%$ at $k=0.2$ ."
 The NEAR and FAR fits are similar., The NEAR and FAR fits are similar.
 In Table 3. we list [its for the NEAR. MID. and FAR power spectra out to a maximum A of 0.2 and 0.4 {Mpeή.," In Table \ref{table:nonlinearfits} we list fits for the NEAR, MID, and FAR power spectra out to a maximum $k$ of 0.2 and 0.4 $h \; {\rm Mpc}^{-1}$."
 When hoe54=0.2 hMpec‘only the first three terms in the polvnomial expansion are necessary [or a good Fig.," When $k_{max,fit} = 0.2$ $h \; {\rm Mpc}^{-1}$, only the first three terms in the polynomial expansion are necessary for a good Fig."
 6 shows diagonal elements of the normalized covariance matrix. Cy;/P(h;)?.," \ref{fig:diagcov} shows diagonal elements of the normalized covariance matrix, $C_{ii}/\bar{P}(k_i)^2$."
 We estimate (he errors from (he diagonal variances (Eqn. 15)):, We estimate the errors from the diagonal variances (Eqn. \ref{cijerrDM}) );
 these may nol capture the (rue errors since off-diagonal elements should be present in the &-point function as well., these may not capture the true errors since off-diagonal elements should be present in the 8-point function as well.
 Nevertheless. when we use these error estimates to compute 4? for the model in Eqn. 13..," Nevertheless, when we use these error estimates to compute $\chi^2$ for the model in Eqn. \ref{cijmodel},"
 we find 4?=1600 for 1296 degrees of freedom (0<hk 0.4): if we restrict the covariance matrix to the 196 elements with both & bands between 0.056 and 0.21. we find 4?=262.," we find $\chi^2 = 1600$ for 1296 degrees of freedom $0 \leq k \leq 0.4$ ); if we restrict the covariance matrix to the 196 elements with both $k$ bands between 0.056 and 0.21, we find $\chi^2 = 262$."
 In (his case there are no [vee parameters and we deem the model a reasonable fit., In this case there are no free parameters and we deem the model a reasonable fit.
 If we allow the amplitude of the beat coupling term to vary. we find a best fit value 0.96 for the [ull matrix (47= 1564) and 0.84 for the 0.056<fh0.21 subsample (47= 218).," If we allow the amplitude of the beat coupling term to vary, we find a best fit value 0.96 for the full matrix $\chi^2 = 1564$ ) and 0.84 for the $0.056 \leq k \leq 0.21$ subsample $\chi^2 = 218$ )."
 We note that for the DC mode realizations of our 42 simulations. thevariance is a factor of 0.83 lower (han the expected variance (in agreement wilh the expected random variation for a single mocle. B-sim1= 15%).," We note that for the DC mode realizations of our 42 simulations, thevariance is a factor of 0.83 lower than the expected variance (in agreement with the expected random variation for a single mode, $N_{sim}^{-1/2} = 15\%$ )."
 We conclude that Eqn., We conclude that Eqn.
 19 is an excellent lit to our dark matter covariance Another point of interest in Fig., \ref{cijmodel} is an excellent fit to our dark matter covariance Another point of interest in Fig.
 G is that the inverse of the diagonal elements of the inverse covariance matrix are nearly equal to the Gaussian expectation (dashed curve)., \ref{fig:diagcov} is that the inverse of the diagonal elements of the inverse covariance matrix are nearly equal to the Gaussian expectation (dashed curve).
 This means (hal while the beat-coupling does not introduce additional errors on the measurement ol the bandpowers. the measured values will be covariant.," This means that while the beat-coupling does not introduce additional errors on the measurement of the bandpowers, the measured values will be covariant."
 However. for a beat-coupling term in (he form of Eqn. 13..," However, for a beat-coupling term in the form of Eqn. \ref{cijmodel},"
 only information on the overall amplitude of P(/) is lost., only information on the overall amplitude of $P(k)$ is lost.
 However. large scale structure analvses traditionally mareinalize over (he;unplitude of (f). since ox and bias are," However, large scale structure analyses traditionally marginalize over theamplitude of $P(k)$ , since $\sigma_8$ and bias are"
Due to tle sensitive dependence of chaotic systems on initial conditions. their yehavior over sufficientv long times is unpredictable in practice. even though the uuderlyiug dyuamics is ceterministic.,"Due to the sensitive dependence of chaotic systems on initial conditions, their behavior over sufficiently long times is unpredictable in practice, even though the underlying dynamics is deterministic."
 Iustead of attempting to accurately describe a phase space trajecto'N over a loug duration. it makes more sense to try to calculate statistical properties of the system. such as equal time moments anc he frequency with which the system coordinates lie within different regions o. phase space.," Instead of attempting to accurately describe a phase space trajectory over a long duration, it makes more sense to try to calculate statistical properties of the system, such as equal time moments and the frequency with which the system coordinates lie within different regions of phase space."
 Typically. statistical )'operties are caleulated by direct numerical simulation.," Typically, statistical properties are calculated by direct numerical simulation."
 The evolution ol the αν1anuical SVsem is observed oLa computer. starting with a particular iuljal condition. al dtle staIntics are σέuputed (ror1 averages over data poliuts generated at reetular time iuΟΥΝεils.," The evolution of the dynamical system is observed on a computer, starting with a particular initial condition, and the statistics are computed from averages over data points generated at regular time intervals."
 It IS assuimed (that the result COLVverges ο tlie exac statistics fast compared to the the ea Wwich nuneric ο) are alljXified by t1ο chaotic iature of the system., It is assumed that the result converges to the exact statistics fast compared to the the rate at which numerical errors are amplified by the chaotic nature of the system.
 FreLLL all aestheti yoint of view. direct. nunjerical simuilation is not an appealing way to πριte staIntIcs. si'e this approacl1 is not foruulated nOev dn terms of the variables oue is “Ulal vd19ο»ed in. amely the statistical quaitities.," From an aesthetic point of view, direct numerical simulation is not an appealing way to compute statistics, since this approach is not formulated solely in terms of the variables one is actually interested in, namely the statistical quantities."
 The'e are equations which deal directly WIitt the statisticM. such as an equation due ic» Hopf [1.2] which governs the genueratlug functiOlla OL edual iue moments.," There are equations which deal directly with the statistics, such as an equation due to Hopf \cite{Hopf,Frisch} which governs the generating functional of equal time moments."
 A better XllOWL equ:lo nopeated to Hopfs equation by Fou‘ier transforjalion. is ——e Fokker-Plauck equajon describin& the time evolutio1 of a probability clistdutiou ove phase space.," A better known equation, related to Hopf's equation by Fourier transformation, is the Fokker-Planck equation describing the time evolution of a probability distribution over phase space."
 Iu sonje specia systelis. icl as the oue described i1 [3].. al ala‘Lic solutio for t lesatistics exists. evel Or na very 'ge nuniaber of degrees of freedom.," In some special systems, such as the one described in \cite{Brad}, an analytic solution for the statistics exists, even for a very large number of degrees of freedom."
 In this article. we will describe au inverse nethoc to CoLstruc chaotic dynanical syslenis. startiig with a iuvaqan »obabilits* distributico) amd a wo-foru having a relatively simple allaNie structure.," In this article, we will describe an inverse method to construct chaotic dynamical systems, starting with an invariant probability distribution and a two-form having a relatively simple analytic structure."
 This uethoc allows oue to generate. it priuciple. iufinite classes of dyiizunical systelis for which some salistical properties are knoWIL exeactly.," This method allows one to generate, in principle, infinite classes of dynamical systems for which some statistical properties are known exactly."
 While we give examples with three aud four cegrees ol reecoinm. we do not anticipae proiive obstructions in applying the inverse inethocl to syselas witl a very large number of «eerees of freedoi.," While we give examples with three and four degrees of freedom, we do not anticipate prohibitive obstructions in applying the inverse method to systems with a very large number of degrees of freedom."
 Our starting point is an analytica exp'ession for au lnvarlit probability distribuion pGr) which is. by construction. a sinooth 1jeastwe inau.W dilueu1al phase space.," Our starting point is an analytical expression for an invariant probability distribution $\rho(\vec x)$ which is, by construction, a smooth measure in an $N$ dimensional phase space."
 H well known that the geometry of a «‘haotic iuvariaut set may be fractal. €aving a fractional information cdimeusio1 less than AN.," It well known that the geometry of a chaotic invariant set may be fractal, having a fractional information dimension less than $N$."
 However. eve1wihb information diinensiou less than JN. an invariant distribution with suppor in JN dimerSlOHS navy still be relevall to the statistics of a chaotic trajectory as a p‘obabili istributio noon the ¢haotic invaγαι1 set upon projection to lower integer «]melnsion.," However, evenwith information dimension less than $N$, an invariant distribution with support in $N$ dimensions may still be relevant to the statistics of a chaotic trajectory as a probability distribution on the chaotic invariant set upon projection to lower integer dimension."
 We eiveοἱ several exalgles where pr) desc‘ibes the statistics of chaotic trajectories αIO »ojection to lower «ΠΗΙΘΗΣΙΟΗ., We give several examples where $\rho(\vec x)$ describes the statistics of chaotic trajectories upon projection to lower dimension.
 There are exaiples for which we hiave fouud 1jumerical eviderce that the initial distribution por). with N«imensioual su)IOI. gives accirate results even fcor connected uoments (cumulauts) which do nol aciilt projecion to lower integer dimeusio[un such as <THE>. dn uv3.," There are examples for which we have found numerical evidence that the initial distribution $\rho(\vec x)$, with N-dimensional support, gives accurate results even for connected moments (cumulants) which do not admit projection to lower integer dimension, such as $<xyz>_c$ in $N=3$."
 This may be ECALse je. information dimensioL which we have 10 vet. calcilated. Is very 1earM7 NV.," This may be because the information dimension, which we have not yet calculated, is very nearly $N$."
 HoweVer. we s»eculate lat the H«pf Luctional Vj)=<<expij-*)> may be 5lieently well )ehaved hat is Foirier transform. wης diis by coustrueion an invariant distribiion. be support in NV clitnensious aud is equal to /)(4).," However, we speculate that the Hopf functional $\Psi(\vec j)= <\exp(i\vec j\cdot
\vec x)>$ may be sufficiently well behaved that its Fourier transform, which is by construction an invariant distribution, has support in $N$ dimensions and is equal to $\rho(\vec x)$."
 IP so. pr) de1uines all polynomial moments eoEiply7e{ 2.1thougl 1rere should be «Iler expectation νιtes of fuuctions ou phase spac whic Lea1 uot be obtained rom pr). «lue ) the fractional iuf‘mation dimension.," If so, $\rho(\vec x)$ determines all polynomial moments $<x^ny^mz^l\cdots>$, although there should be other expectation values of functions on phase space which can not be obtained from $\rho(\vec x)$, due to the fractional information dimension."
 We also fii that. iniLALLY nnstauces. he ratio of frequen«‘ies with which «il'erent regions of phase space ar visited by a chaotic trajectory is determi( by the distribuion pGr). even when the detaileca eeometry of the chaotic 1ivarlant set is euite complicated or LDUISLLOWLL.," We also find that, in many instances, the ratio of frequencies with which different regions of phase space are visited by a chaotic trajectory is determined by the distribution $\rho(\vec x)$ , even when the detailed geometry of the chaotic invariant set is quite complicated or unknown."
M;27 M.,$M_i\gtrsim7\ \Msun$ .
.7 reach a difference of up to 0.4M. in the final masses derived from different metallicities. their study covering a broad metallicity range: Z in between 0.0001. and 0.1.," \citealt{2007arXiv0710.2397M} reach a difference of up to $0.4\ \Msun$ in the final masses derived from different metallicities, their study covering a broad metallicity range: Z in between $0.0001$ and $0.1$."
 They also notice a minimum of the IFAM lor Z=0.04., They also notice a minimum of the IFMR for $Z=0.04$.
 Various semi-empirical linear lits have been derived over the last decade., Various semi-empirical linear fits have been derived over the last decade.
 A few examples are: ? (based on open-cluster data lor the range 2.5—6.5M.: claàming (hat the IEMBR can be modelled by a mean relationship about which there exists some intrinsic scatter. and (hat they ‘cannot justilv the use of any but a linear relationship to model the cluster data): ? (a linear fit to some 27 WDs. menibers of clusters such as the ILvades. Praesepe. M35. NGC2516 and the Pleiades. over initial-mass range of 2.7—6AL. ): T (claiming that the IFAIR is both linear and without anv metallicity dependence): Although the relations obtained. as shown in Fig. 7..," A few examples are: \citet{2005MNRAS.361.1131F} (based on open-cluster data for the range $2.5-6.5\ \Msun$; claiming that the IFMR can be modelled by a mean relationship about which there exists some intrinsic scatter, and that they `cannot justify the use of any but a linear relationship to model the cluster data'): \citet{2006MNRAS.369..383D} (a linear fit to some $27$ WDs, members of clusters such as the Hyades, Praesepe, M35, NGC2516 and the Pleiades, over initial-mass range of $2.7-6\ \Msun$ ): \citet{2007ASPC..372...85W} (claiming that the IFMR is both linear and without any metallicity dependence): Although the relations obtained, as shown in Fig. \ref{fig:ifmr},"
 are quite far [rom linear. the closest linear fit that we can suggest. without using anv artificial anchoring. is which falls slightly above the upper (Pop.," are quite far from linear, the closest linear fit that we can suggest, without using any artificial anchoring, is which falls slightly above the upper (Pop."
II) curve around the lower initial masses ὃν and below the lower (Pop.,"II) curve around the lower initial masses $1.5-2.5\ \Msun$ ), and below the lower (Pop."
I) curve for higher intermediate masses. around 5M...,"I) curve for higher intermediate masses, around $5\ \Msun$."
 This fit is very similar {ο the linear fit of ? (shown in Fig. 7)).," This fit is very similar to the linear fit of \citet{2005MNRAS.361.1131F} (shown in Fig. \ref{fig:ifmr}) ),"
 although the latter is limited io the range 2.5 to 6.5M..., although the latter is limited to the range $2.5$ to $6.5\ \Msun$.
 Clearly. (he. relation obtained represents the set of parameters assumed. mostly those related to the mass-loss recipe.," Clearly, the relation obtained represents the set of parameters assumed, mostly those related to the mass-loss recipe."
 The value of jpg; used here was linearly increasecl from 0.4 at 0.8AL. to 3.0 αἱ 9M..., The value of $\eta_{\rm Reim}$ used here was linearly increased from 0.4 at $0.8\ \Msun$ to 3.0 at $9\ \Msun$.
" A preliminary comparison that we performed. keeping all parameters fixed and changing only mass-loss laws. indeed showed somedifferences in the final WD masses, with a spread of less than 1056."," A preliminary comparison that we performed, keeping all parameters fixed and changing only mass-loss laws, indeed showed somedifferences in the final WD masses, with a spread of less than $10\%$ ."
 More precisely. for our solar model parameters (see 84.3)). selling Are=0.6.Hus50.the derived final WD masses were all in the range 0.53—0.57AL. (or between 0.51—0.56 lor slightly higher mass-loss rates obtained by using Huge;=lOO.Bassus 10).," More precisely, for our solar model parameters (see \ref{canon}) ), setting $\eta_{Rei}=0.6,\ R_{thresh}=50$,the derived final WD masses were all in the range $0.53-0.57\ \Msun $ (or between $0.51-0.56$ for slightly higher mass-loss rates obtained by using $\eta_{Rei}=1.0,\ R_{thresh}=10$ )."
 Performing the same comparison lor 3M.(Z= 0.01). but usingHie;= 2.0. we found final WD masses tobe in the range 0.61—0.67 AZ.," Performing the same comparison for $3\ \Msun\ (Z=0.01)$ , but using$\eta_{Rei}=2.0$ we found final WD masses tobe in the range $0.61-0.67\ \Msun $ ."
contained in them Fieuve 2.,contained in their Figure 2.
 The need for supersolar netallicity is clear for M. dwifs (0.2καιλενUT). where the average metallicity of the planet-hosting stars is [Fe‘TH = 0.1.," The need for supersolar metallicity is clear for M dwarfs $0.2 < M_\ast/M_\sun < 0.7$ ), where the average metallicity of the planet-hosting stars is [Fe/H] = 0.4."
" Metal-rich stars prestunably ounce carried ποτάτοι disks. aud so the planet-metallicity correlation or AL chwarts supports «nr results; aud those of others (Sekix""1998: ¥Youdin&Shu2002: Leeetal.50101: see also Jolausenetal.20090: Bai&Stone201043) hat planectesimals formi much more readily iu inetal-rich enviroments."," Metal-rich stars presumably once carried metal-rich disks, and so the planet-metallicity correlation for M dwarfs supports our results, and those of others \citealt{sekiya98};; \citealt{youdinshu02}; \citealt{leeetal10}; ; see also \citealt{johansenetal09}; \citealt{baistone10}) ) that planetesimals form much more readily in metal-rich environments."
 In particular the data for AI chwarts indicate that a mere factor of 10°!=2.5Γ increase ni nkπαν above soar substantially decreases the probability of planet occmreuce., In particular the data for M dwarfs indicate that a mere factor of $10^{0.4} = 2.5$ increase in metallicity above solar substantially increases the probability of planet occurrence.
 This is consistent with our finding of a super-near trend between maxiuui dust-to-gas ratio aud buk inetallicity refssec:superlinear and Appendix C))., This is consistent with our finding of a super-linear trend between maximum dust-to-gas ratio and bulk metallicity \\ref{ssec:superlinear} and Appendix \ref{app:superlinear}) ).
 However. the planet-uetallicitv correlation weakens svstclnatically with iucreasing stellar mass (Johusonal. 2010).," However, the planet-metallicity correlation weakens systematically with increasing stellar mass \citep{johnsonetal10}."
. For À sars (docAL/M.« 2.0). 10 οςurelation is arenaijv not present.," For A stars $1.4 < M_\ast/M_\sun < 2.0$ ), the correlation is arguably not present."
 This calls iuto uestion the need for supersolar metallicities to form uaeexnaals., This calls into question the need for supersolar metallicities to form planetesimals.
 The observatious of Jolinsonetal.(2010) welt still be reconciles with eravitatioual instability if uore lnassive stars los more lnassive disks. although lish nass would have ο scale with stellar mass in a aster than linear way o lower the threshold Toonue Clsiv (equation 10)).," The observations of \citet{johnsonetal10} might still be reconciled with gravitational instability if more massive stars host more massive disks, although disk mass would have to scale with stellar mass in a faster than linear way to lower the threshold Toomre density (equation \ref{eqn:muToomre}) )."
 The possibility also remains that he observations are no actually a direct or sensitive robe of the theorv., The possibility also remains that the observations are not actually a direct or sensitive probe of the theory.
 Ti6 observations concern stellar notalicity. which might at best correlate with the global notalicity of the disk. 1iteerated over both disk height and disk radius.," The observations concern stellar metallicity, which might at best correlate with the global metallicity of the disk, integrated over both disk height and disk radius."
 By comparison. theory concerns the local Levalicity X fhe. iuteer‘ated over height but uot radius.," By comparison, theory concerns the local metallicity $\Sigmad/\Sigmag$ , integrated over height but not radius."
 This local inetallicitv (not to be confused with the local dust-o-gas ratio pi) cali evolve substautially frou its elobal value. as a consequence of radial particle drifts aud photoevaporation (c.e.. CY10).," This local metallicity (not to be confused with the local dust-to-gas ratio $\mu$ ) can evolve substantially from its global value, as a consequence of radial particle drifts and photoevaporation (e.g., CY10)."
 Rather than look to their parent stars for evidenc for local disk curichment. we can look to the plaucts theniselves.," Rather than look to their parent stars for evidence for local disk enrichment, we can look to the planets themselves."
 If planetesimals cau only form iu metalenriched cnvirouuents. we expect that the resultant planets will also be inetal-enxiched.," If planetesimals can only form in metal-enriched environments, we expect that the resultant planets will also be metal-enriched."
 Caullotetal.(2006) congmitted the bulk metallicities of the first iinue extrasolar planets discovered to be transiting. all of wluch are lie(Xo Jupiters.," \citet{guillotetal06}
 computed the bulk metallicities of the first nine extrasolar planets discovered to be transiting, all of which are hot Jupiters."
 The results are listed in Table .. ogether with the modeled bulk metallicities of Jupiter and Saturn.," The results are listed in Table \ref{tab:metal}, together with the modeled bulk metallicities of Jupiter and Saturn."
 All cleven are indeed metal-euriched. by actors ranging from 2[7 relative to the Sun. aud 220 το]:dive to their host stars.," All eleven are indeed metal-enriched, by factors ranging from 2–47 relative to the Sun, and 2--20 relative to their host stars."
" One caveat behind these results is that models of hot Jupiter iuteriors are sub.ject o the uncertainty over the extra soiree of imternal reat responsible for their unexpectedly large radi {see, e.g.+S. Batvein&Stevenson2010.. who also describe a mousing solution)."," One caveat behind these results is that models of hot Jupiter interiors are subject to the uncertainty over the extra source of internal heat responsible for their unexpectedly large radii (see, e.g., \citealt{batyginstevenson10}, who also describe a promising solution)."
 To inflate planetary radii. Cuillotetal.(2006) iucluded iu each hot Jupiter model al aclditicmal source of power equal to of the received stellar irradiation (Cuullot&Showman2002).," To inflate planetary radii, \citet{guillotetal06}
 included in each hot Jupiter model an additional source of power equal to of the received stellar irradiation \citep{guillotshowman02}."
. The |lk ietallicities inferred from the models depend ou the details of this extra energy source., The bulk metallicities inferred from the models depend on the details of this extra energy source.
 Modulo this caveat. CVCLY planet is euriched iu metals by at least a factor of —2 above solar. which is cousisteut with our fixlue that forming planctesimalsbv gravitational instability requires metal enrichimeuts of this order.," Modulo this caveat, every planet is enriched in metals by at least a factor of $\sim$ 2 above solar, which is consistent with our finding that forming planetesimalsby gravitational instability requires metal enrichments of this order."
 We thank Xuc-Niug Bai. John Joliusou. Eve OstriSOT. Juu Stone. aud Neal Turner for discussions. aud Tristan Caullot for the data in Table 1..," We thank Xue-Ning Bai, John Johnson, Eve Ostriker, Jim Stone, and Neal Turner for discussions, and Tristan Guillot for the data in Table \ref{tab:metal}."
 Nuc-Ning Bai. Anders Johansen. Jim Stone. and Andrew Yordiu provied valuable feedback on a draft version of his paper.," Xue-Ning Bai, Anders Johansen, Jim Stone, and Andrew Youdin provided valuable feedback on a draft version of this paper."
 We are erateful to Stuart Weideuschillius for al iusieliful referees report that put our work iuto beter contest., We are grateful to Stuart Weidenschilling for an insightful referee's report that put our work into better context.
" This research was supported bv the National Scie'6 Foundation. in part through TeraCwid resources provied by Purdue University uuder eraut number TC-AST090079,"," This research was supported by the National Science Foundation, in part through TeraGrid resources provided by Purdue University under grant number TG-AST090079."
 AT.L. acknowledges support frou an NSF σαιate Fellowship., A.T.L. acknowledges support from an NSF Graduate Fellowship.
 For wmuerical estimates in this paper. we adopt the stand disk mode derived in the review by (2010).," For numerical estimates in this paper, we adopt the standard disk model derived in the review by \citet{chiangyoudin10}."
. The disk has surface densities in gas (eg) aud dust (d)., The disk has surface densities in gas (g) and dust (d).
" The dimensionless parameters £ audζω=(N/X,)/0.015. typically of order unity. describe how much total mass the disk has relative to the nininimiuuass solar nebula. aud how metal-rich the disk is compared with a eas of solar abundances. respectively,"," The dimensionless parameters $F$ and$\Zr \equiv (\Sigma/\Sigmag)/0.015$, typically of order unity, describe how much total mass the disk has relative to the minimum-mass solar nebula, and how metal-rich the disk is compared with a gas of solar abundances, respectively."
" The minimnucniass solar nebula CF=1. Zí4= 1) uses a condensate lass fraction for solarabundances of X4/X,=(0.015 (Lodders. 2003)..."," The minimum-mass solar nebula $F=1$, $\Zr=1$ ) uses a condensate mass fraction for solarabundances of $\Sigmad/\Sigmag = 0.015$ \citep{lodders03}. ."
" Values of Ζω>1 correspond to supersolar metallicities X4/X,> 0.015.", Values of $\Zr > 1$ correspond to supersolar metallicities $\Sigmad/\Sigmag > 0.015$ .
 Iuteerated to r=100 AU.equation CÀ1)) vields a total disk mass of 0.037 AL...," Integrated to $r = 100\AU$ ,equation \ref{eq_sigmag})) yields a total disk mass of $0.03 F M_{\odot}$ ."
 At the disk midplane. the gas temperature. scale height. aud density are given by," At the disk midplane, the gas temperature, scale height, and density are given by"
are (at least) viscously coupled.,are (at least) viscously coupled.
 If all of the material that enters the disc at large radii is coplanar. (hen conservation of total angular momentum implies that the total integrated angular momentum about any axis perpendicular to that of the initial co must vanish at all times.," If all of the material that enters the disc at large radii is coplanar, then conservation of total angular momentum implies that the total integrated angular momentum about any axis perpendicular to that of the initial $\boldsymbol \omega$ must vanish at all times."
 This means that if some inner mean annulus of gas tilis in one direction. there will be a corresponding counter-tilt elsewhere.," This means that if some inner mean annulus of gas tilts in one direction, there will be a corresponding counter-tilt elsewhere."
 Turbulent viscosity allows (he radial distribution of (ills to be non-trivial and because jet power is likely dominated by inner annuli. the tilt of the inner-most annuli are particularly relevant for predicting jel wobble because they dominate the accretion power.," Turbulent viscosity allows the radial distribution of tilts to be non-trivial and because jet power is likely dominated by inner annuli, the tilt of the inner-most annuli are particularly relevant for predicting jet wobble because they dominate the accretion power."
 In what follows. we assume that the axis of anv annular section of a jet tracks (he orbital axis of the corresponding disc annulus to which that jet section is anchorecl.," In what follows, we assume that the axis of any annular section of a jet tracks the orbital axis of the corresponding disc annulus to which that jet section is anchored."
 Thus the jet wobble directly tracks the dise wobble., Thus the jet wobble directly tracks the disc wobble.
 llere we apply (he above formulae to thin accretion disces and jet wobble., Here we apply the above formulae to thin accretion discs and jet wobble.
" For a thin. non-sell-gravitating disc in hydrostatic equilibrium where c, is the sound speed. A is the central object mass. and // is (he density scale height."," For a thin, non-self-gravitating disc in hydrostatic equilibrium where $c_s$ is the sound speed, $M$ is the central object mass, and $H$ is the density scale height."
 The Shakura-Sunvaev (Shakura&Sunvaev(1973))) viscosity ν in hyedrostatic equilibriumE. then satislies. v=occcuf>liucoodles. where a is. the viscosity.- parameter.," The Shakura-Sunyaev \cite{ss73}) )viscosity $\nu$ in hydrostatic equilibrium then satisfies $\nu \equiv \alpha c_s H \sim v_{ed}^2/ t_{ed} \sim v_{ed}^2H/c_s$, where $\alpha$ is the viscosity parameter."
" Then (e.g. Blackman 1993) vy~ale, and SO The dise accretion rate can be modeled as Αρ)=μα...y (e.g. (1999))). where My is the accretion rate at the outer edge of the dise. rj, is the radius of the outer edge. and 0«s Iis a parameter."," Then (e.g. Blackman 1998) $v_{ed}\sim \alpha^{1/2}c_s$ and so The disc accretion rate can be modeled as $\dot{M}_a(r) = \dot{M_{o}}(r/r_o)^s$ (e.g. \cite{bb99}) ), where $\dot{M_{0}}$ is the accretion rate at the outer edge of the disc, $r_o$ is the radius of the outer edge, and $0< s< 1$ is a parameter."
 The total mass outflow rate from ry (o r is then M(r)=AL—(rfr;y]., The total mass outflow rate from $r_o$ to $r$ is then $\dot{M}(r) = \dot{M_o}[1-(r/r_o)^s]$.
 Taking the derivative. we obtain the outflow mass loss rate by a small annulus of width dr at radius r to be," Taking the derivative, we obtain the outflow mass loss rate by a small annulus of width $dr$ at radius $r$ to be"
LONE. IRS 16C. and IRS 168W (N97). it could therefore be a transition object just comme out of the LBV phase.,"16NE, IRS 16C, and IRS 16SW (N97), it could therefore be a transition object just coming out of the LBV phase."
 This would be consistent with the e aud M profiles of Garcia-Seeura. Mac Low Langer (1996).," This would be consistent with the $v$ and $\dot\mathrm{M}$ profiles of Garcia-Segura, Mac Low Langer (1996)."
 Ihuuphrevs Davidson (1991) point out that a WN9/Ofpe star appears vorv ιο like au LBV at ninm brightucss and thus the distinction between the two types is often bhurecd., Humphreys Davidson (1994) point out that a WN9/Ofpe star appears very much like an LBV at minimum brightness and thus the distinction between the two types is often blurred.
 However. the large TeἩ of IRS 13EL. compared to a ΠοΤΠ of ~1 for the IRS 16 sources (N97). makes an LBV/WNL determination problematic.," However, the large He/H of IRS 13E1, compared to a He/H of $\sim 1$ for the IRS 16 sources (N97), makes an LBV/WNL determination problematic."
 Observational aud theoretical countcrareuments iuclude the fact that the identity of WR 122. the calibrating WNL source used by NOT. has been called into doubt (Crowther Smith 1999) and recent work (c.g... Langer et al.," Observational and theoretical counterarguments include the fact that the identity of WR 122, the calibrating WNL source used by N97, has been called into doubt (Crowther Smith 1999) and recent work (e.g., Langer et al."
 1999) sugeestsOO nix 1n luassive stars is more efücient than previously thought. resulting ina larger Πο at the start of the WNL phase.," 1999) suggests mixing in massive stars is more efficient than previously thought, resulting in a larger He/H at the start of the WNL phase."
 Hence an LBV/WNL classification is certainly within reason (although see below)., Hence an LBV/WNL classification is certainly within reason (although see below).
 Secoud. we note that there are <27 massive Πο stars in the GC (Bhun. Ramirez. Selleren 1999).Given the observed frequency. ff. of WR binary svstcms (1254Sfος van der Hucht et al.," Second, we note that there are $\simgt 27$ massive HeI stars in the GC (Blum, Ramírrez, Sellgren 1999).Given the observed frequency, $f$ , of WR binary systems $12\% \simlt f \simlt 50\%$; van der Hucht et al."
 1981). it is likely hat some of the GC ΠΟ stars are binaries as well.," 1981), it is likely that some of the GC HeI stars are binaries as well."
 Iu act. IRS 16SW is thought to be an eclipsing binary with a period of ~10 days (Ott. Eckart Cenzel 1999).," In fact, IRS 16SW is thought to be an eclipsing binary with a period of $\sim 10$ days (Ott, Eckart Genzel 1999)."
 Thus it is possible that IRS 13E is also a binary svete. containing ‘or example a WNIO primary with a ZAMS mass of ~100AI; and a somewhat less massive companion that is either an O star or another WR star. or. possibly. a hassive compact object.," Thus it is possible that IRS 13E is also a binary system, containing for example a WN10 primary with a ZAMS mass of $\sim 100~\mathrm{M}_{\sun}$ and a somewhat less massive companion that is either an O star or another WR star, or, possibly, a massive compact object."
 Of the single aud binary scenarios. the latter is preferred.," Of the single and binary scenarios, the latter is preferred."
 As previously mentioned. the model of N97 underprediets the K-baud ΠΟΠ emission for IRS EL by a factor of 3: the colliding winds of a binary will produce more Ile! (Marcheuko et al.," As previously mentioned, the model of N97 underpredicts the K-band HeII emission for IRS 13E1 by a factor of $\sim 3$; the colliding winds of a binary will produce more $^+$ (Marchenko et al."
 1997). poteutially explaining this deficicney.," 1997), potentially explaining this deficiency."
 Also. the ionizing flax from a massive O star would explain why IRS 13E stauds out in Pa-o and [FOIT].," Also, the ionizing flux from a massive O star would explain why IRS 13E stands out in $\alpha$ and [FeIII]."
 An carly-type binary system will also have strone shocks as a result of colliding stellar winds., An early-type binary system will also have strong shocks as a result of colliding stellar winds.
 The N-ray hinunosity of a binary svsteim will be brighter than that fron a solitary star so that in order of increasing X-rav Duninuositv one qualitatively has (with everything else equal) WR. O. O/O. WR/O. WR/WR.," The X-ray luminosity of a binary system will be brighter than that from a solitary star so that in order of increasing X-ray luminosity one qualitatively has (with everything else equal) WR, O, O/O, WR/O, WR/WR."
 Towever. this is mmocdified by the binary separation: if the binaries are too close. absorption will suppress the observed N-ray cluission but if they are too far apart the shocks are largely adiabatic and do not produce significant additional N-ray huuinosity (Pittard Stevens 1997).," However, this is modified by the binary separation: if the binaries are too close, absorption will suppress the observed X-ray emission but if they are too far apart the shocks are largely adiabatic and do not produce significant additional X-ray luminosity (Pittard Stevens 1997)."
 The various WR sources of IRS 16 Gucludiug IRS L6SW) do not appear as yout sources in the observations., The various WR sources of IRS 16 (including IRS 16SW) do not appear as point sources in the observations.
 A solitary WB or even a WR with a DB or later companion may nof ο Visible with due to the large column density between here aud the GC., A solitary WR or even a WR with a B or later companion may not be visible with due to the large column density between here and the GC.
 Using-. aud a Ravinoud-SuuithM thermal plasina mmodel (which assumes optically thin N-rav line aud continu ciuiission: Ravinoud Suüth 1977) iu ionizafion equilibria one can simulate the spectu of a solitary O-star placed at the CC., Using and a Raymond-Smith thermal plasma model (which assumes optically thin X-ray line and continuum emission; Raymond Smith 1977) in ionization equilibrium one can simulate the spectrum of a solitary O-star placed at the GC.
 Assiuuiug an ISM-corrected. N-vay luminosity (0.5-10.0 keV) L4~0.25L: (from κΊων~10'. sec e.g. Waldron. et al.," Assuming an ISM-corrected X-ray luminosity (0.5-10.0 keV) $\mathrm{L_x} \sim 0.25~\mathrm{L}_{\sun}$ (from $L_{x}/L_{bol} 
\sim 10^{-7}$, see e.g. Waldron, et al."
 1998). a characteristic temperature kT~0.5 keV (represcutative of typica solitary O-stars. see Chichowski. et al.," 1998), a characteristic temperature $\mathrm{kT} \sim 0.5$ keV (representative of typical solitary O-stars, see Chlebowski, et al."
 1989). au intervening column deusity Nj~5«107? ? (typical for the GC. see eg. Zrlka et al.," 1989), an intervening column density $_\mathrm{H} 
\sim 5 \times 10^{22}$ $^{-2}$ (typical for the GC, see e.g., Zylka et al."
" 1995), and solu abuudauces hroughout. a 50 ksec observation. spimune the 0.5-10 το. band. would detect Z3 photons. and the O-star would not staud out above the background."," 1995), and solar abundances throughout, a 50 ksec observation, spanning the 0.5-10 keV band, would detect $\simlt 3$ photons, and the O-star would not stand out above the background."
 Thus the IRS 16 sources bleud iuto the diffuse background seen in the central ~5” of the mace in Daganotf et al. (, Thus the IRS 16 sources blend into the diffuse background seen in the central $\sim 5''$ of the image in Baganoff et al. (
1999).,1999).
 Note that this hints that either the ποσα IRS 16SW companion docs not have a siguificaut stellar wind aud thus is of tvpe D or later (and therefore Προς a lower svsten mass than estimated by Ott et al., Note that this hints that either the unseen IRS 16SW companion does not have a significant stellar wind and thus is of type B or later (and therefore implies a lower system mass than estimated by Ott et al.
 1999). or that the circumstellar absorption aud/or binary separation were unfavorable.," 1999), or that the circumstellar absorption and/or binary separation were unfavorable."
 Iu coutrast. Fig.," In contrast, Fig."
 2— shows a theoretical spectrinnfor a hvpothoetica (05L; GC Naav SOUECC simular to the WR/O binary 22 VeL which has a 18.5," \ref{fig:WRO} shows a theoretical spectrumfor a hypothetical $0.5~\mathrm{L}_{\sun}$ GC X-ray source similar to the WR/O binary $\gamma^2$ Vel, which has a 78.5"
component (Robin 1-2 Gyr).,component (Robin 1-2 Gyr).
 Then the best fit FWHM of the Ciaussiaus are (3.2Hy aud (11.5ry5 with fluxes of (2.1840.26)x10.!pholonscm2s Land (5.36£0.5)x101pholonscm2g respectively. the disk flux being (1.83£0.27)xLO?pholonsen7s1. providing a Bulge to Disk ratio of Ο.Τ.," Then the best fit FWHM of the Gaussians are $(3.2_{-1.0}^{+1.0})^\circ$ and $(11.8_{-1.5}^{+1.9})^\circ$ with fluxes of $(2.48 \pm 0.26) \times 10^{-4}~photons~cm^{-2}~s^{-1}$ and $(5.36 \pm 0.5) \times 10^{-4}~photons~cm^{-2}~s^{-1}$ respectively, the disk flux being $ (1.83 \pm 0.27) \times 10^{-3}~photons~cm^{-2}~s^{-1}$, providing a Bulge to Disk ratio of 0.44."
 Usiug the ratio calculated by Ixuóddlseder et al. (, Using the ratio calculated by Knöddlseder et al. (
2005. Table 3) to infer the 511 keV line huninosities aud the factor (6./55411) = 1.61 from Brown Leventhal (1987). we obtaiu annihilation rates of 1.1.xLOMs| in the bulge and 0.8xLOMSs| in the disk.,"2005, Table 3) to infer the 511 keV line luminosities and the factor $e^{+}/\gamma_{511})$ = 1.64 from Brown Leventhal (1987), we obtain annihilation rates of $1.1\times 10^{43} s^{-1}$ in the bulge and $0.8\times 10^{43} s^{-1}$ in the disk."
 We then attempted to describe the exteuded spatial distribution superimposed on the central bulge with various spatial geometries., We then attempted to describe the extended spatial distribution superimposed on the central bulge with various spatial geometries.
 Simple geometric shapes (i.e. two cdimeusional Craussiaus) as well as more pliysical maps (CO. NIB. Robin disk GRobin et ab.," Simple geometric shapes (i.e. two dimensional Gaussians) as well as more physical maps (CO, NIR, Robin disk (Robin et al.,"
 2003)) were Fig., 2003)) were Fig.
 13. stummarizes the result of the correlation map study. with the NA? ( which varies similarly as the reduced masximtun loe-likelihood ratio) plotted for each of the tracer maps.," \ref{fig:traceur511} summarizes the result of the correlation map study, with the $\Delta\chi^2$ ( which varies similarly as the reduced maximum log-likelihood ratio) plotted for each of the tracer maps."
 Best 'esults. are obtained for a Robin disk (in the 0.15-3 Cyr range correspoudiug to au old stellar »opulation) or NIR/DIRBE 107: aud 1.254: maps. which happen to be good tracers of the 7°Al ine emission (Ixnódcdlseder et al..," Best results are obtained for a Robin disk (in the 0.15-3 Gyr range corresponding to an old stellar population) or NIR/DIRBE $\mu$ and $\mu$ maps, which happen to be good tracers of the $^{26}Al$ line emission (Knöddlseder et al.,"
 1999)., 1999).
 Simple bi-climensional Giaussiauns of latitude FWHAL aud longitude FWHM ~250° give also good results., Simple bi-dimensional Gaussians of latitude FWHM $\sim5-7^\circ$ and longitude FWHM $\sim250^\circ$ give also good results.
 We note that the disk exhibits a arger longitude exteusion thau the previoulsy reported values: first by OSSE (Ixiuzer et al..," We note that the disk exhibits a larger longitude extension than the previoulsy reported values: first by OSSE (Kinzer et al.,"
 2001). nut the study is based on a longitudinally truncated data set distribution aud more recently by Weincdeuspointuer et al.," 2001), but the study is based on a longitudinally truncated data set distribution and more recently by Weindenspointner et al.,"
 2008., 2008.
 Even though it is difficult to describe the emission iu greater detail. his result represents a good indication for a bulge/disk structure.," Even though it is difficult to describe the emission in greater detail, this result represents a good indication for a bulge/disk structure."
 Extended disk structure flux (for he most plausible. disks). is. around B1.7-—x10.73photonscm>7?s|! and the Bulge/diskf. ratios. range rom 0.25 to 0.7., Extended disk structure flux (for the most plausible disks) is around $1.7 \times 10^{-3}~photons~cm^{-2}~s^{-1}$ and the Bulge/disk ratios range from 0.25 to 0.7.
 This analysis excludes single halo mocels (inodelled by axisyiumetrie Gaussiaus)., This analysis excludes single halo models (modelled by axisymmetric Gaussians).
 However. in he past. OSSE data have often been compared with bulge models iucludiug some nou-Craussiau Xxoadeniug (wines). featuring a bulge + halo central geometry.," However, in the past, OSSE data have often been compared with bulge models including some non-Gaussian broadening (wings), featuring a bulge + halo central geometry."
 We have tested this kiud of coufiguratiou NN consideriug a stellar halo (or spheroid) moclel proposed by Robin et al. (, We have tested this kind of configuration by considering a stellar halo (or spheroid) model proposed by Robin et al. (
2003).,2003).
 The central regiou »olile is built following the law: N represents a normalisation constant aud x.v.z. the cartesian coordinates iu the bulge reference frame.," The central region profile is built following the law: N represents a normalisation constant and x,y,z, the cartesian coordinates in the bulge reference frame."
" We obtain a good fit to the data with the axis ratio. e = 0.5. in = -2.6. «,—200 pe and Ry=s.5 kpe."," We obtain a good fit to the data with the axis ratio, $\epsilon$ = 0.8, m = -2.6, $a_{c}$ =200 pc and $R_{0}$ =8.5 kpc."
 The 2105 and 1.254 NIR/DIRBE and Robin 1-3 Gyr maps remain the best tracers, The $\mu$ and $\mu$ NIR/DIRBE and Robin 1-3 Gyr maps remain the best tracers
"star, and the Keplerian value is assumed otherwise (Wellstein2001).","star, and the Keplerian value is assumed otherwise \citep{Wellstein01}."
". The change of the orbital period due to mass transfer and stellar wind mass loss is considered according to Podsiadlowski,Joss&Hsu(1992).", The change of the orbital period due to mass transfer and stellar wind mass loss is considered according to \citet{Podsiadlowski92}.
. We follow Brookshaw&Tavani(1993) to determine the amount of the specific angular momentum carried away from the orbit by stellar winds., We follow \citet{Brookshaw93} to determine the amount of the specific angular momentum carried away from the orbit by stellar winds.
 Tidal synchronizationis considered following Wellstein(2001) (seealsoDetmersetal.2008)., Tidal synchronizationis considered following \citet{Wellstein01} \citep[see also][]{Detmers08}.
" We assume a synchronization time scale according to Tassoul(1987,2000) who considered tidally driven meridional circulations as the main mechanism for tidal dissipation: where q denotes the mass ratio and d the orbital separation."," We assume a synchronization time scale according to \citet{Tassoul87, Tassoul00} who considered tidally driven meridional circulations as the main mechanism for tidal dissipation: where $q$ denotes the mass ratio and $d$ the orbital separation."
 This prescription gives a much shorter time scale than that given by Zahn(1977)., This prescription gives a much shorter time scale than that given by \citet{Zahn77}.
". Given that the physics of tidal dissipation is much debated in the literature (Langer2009), we introduce a parameter to investigate how an extremely fast/slow synchronizationfsync may influence the results."," Given that the physics of tidal dissipation is much debated in the literature \citep{Langer09}, we introduce a parameter $f_\mathrm{sync}$ to investigate how an extremely fast/slow synchronization may influence the results."
" In most cases, however, we use fsync=1."," In most cases, however, we use $f_\mathrm{sync} = 1$."
" A few sequences are also computed with Τογπο of (1977) for comparison: where J is the moment of the star, and E» a constant measuring the coupling between the tidal potential and the gravity mode."," A few sequences are also computed with $\tau_\mathrm{sync}$ of \citet{Zahn77} for comparison: where $I$ is the moment of the star, and $E_2$ a constant measuring the coupling between the tidal potential and the gravity mode."
" Using the data of Table 1 in Zahn we constructed a fitting formula for Es as the following:(1977), where Reony is the radius of the convective core."," Using the data of Table 1 in \citet{Zahn77}, we constructed a fitting formula for $E_2$ as the following: where $R_\mathrm{conv}$ is the radius of the convective core."
 Note that both prescriptions by Tassoul and Zahn are not appropriate for a star with a convective envelopeδ., Note that both prescriptions by Tassoul and Zahn are not appropriate for a star with a convective envelope.
". However, the role of tidal synchronization is significant only on the main sequence, and not important in late evolutionary stages as discussed below."," However, the role of tidal synchronization is significant only on the main sequence, and not important in late evolutionary stages as discussed below."
" We computed 45 model sequences for initial masses of the primary star mostly from 12 to 25 Mo at two different metallicities (Z= 0.02 and for different mass ratios, initial orbital periods, and 0.004),WR mass loss rates, as summarized in Table. 1.."," We computed 45 model sequences for initial masses of the primary star mostly from 12 to 25 $\mathrm{M}_\odot$ at two different metallicities $Z=$ 0.02 and 0.004), for different mass ratios, initial orbital periods, and WR mass loss rates, as summarized in Table. \ref{tab1}."
 The initial rotational velocity at the equatorial surface of each star is set to be of the Keplerivan value., The initial rotational velocity at the equatorial surface of each star is set to be of the Keplerivan value.
" We could not calculate more massive systems because of a numerical difficulty encountered during the mass transfer phases, except for Seq."," We could not calculate more massive systems because of a numerical difficulty encountered during the mass transfer phases, except for Seq."
" 26 where a primary star of 60 is considered with a rather large WR mass loss rate Mo(i.e., fwr= 3)."," 26 where a primary star of 60 is considered with a rather large WR mass loss rate (i.e., $f_\mathrm{WR} = 3$ )."
 The adopted initial orbital periods corresponds either to Case A or to Case B mass transfer., The adopted initial orbital periods corresponds either to Case A or to Case B mass transfer.
" In the present study, we do not consider Case C systems, but briefly discuss the possible outcomes of Case C mass transfer in Sect. ??.."," In the present study, we do not consider Case C systems, but briefly discuss the possible outcomes of Case C mass transfer in Sect. \ref{sect:dischydrogen}."
 The evolution of the primary stars is followed up to neon burning in most cases., The evolution of the primary stars is followed up to neon burning in most cases.
" We also present non-rotating single helium star models to discuss SNe Ibe progenitors in binary systems with initial masses larger than 25Mo,, and also to compare them with binary star models (Sect. ??))."," We also present non-rotating single helium star models to discuss SNe Ibc progenitors in binary systems with initial masses larger than 25, and also to compare them with binary star models (Sect. \ref{sect:sn}) )."
" In this section, we focus our discussion on the evolution of primary stars and investigate whether binary evolution via Case A or Case B mass transfer could lead to diverse pre-collapse conditions of SNe Ibc in terms of the amount of core angular momentum."," In this section, we focus our discussion on the evolution of primary stars and investigate whether binary evolution via Case A or Case B mass transfer could lead to diverse pre-collapse conditions of SNe Ibc in terms of the amount of core angular momentum."
" Although the evolution of mass-accreting secondary stars is a matter of extreme interest as discussed in Braun&Langer(1995),, Petrovicetal.(2005a) and Cantielloetal.(2007),, it is beyond the scope of this paper."," Although the evolution of mass-accreting secondary stars is a matter of extreme interest as discussed in \citet{Braun95}, \citet{Petrovic05a} and \citet{Cantiello07}, it is beyond the scope of this paper."
" Here, we first present some results including the Spruit-Tayler dynamo with our fiducial assumption on synchronization time (i.e., fsync= 1), showing that the final amount of angular momentum in the core of the primary star is not much affected by different histories of mass loss (i.e., Case AB or Case B; Sect. ??))."," Here, we first present some results including the Spruit-Tayler dynamo with our fiducial assumption on synchronization time (i.e., $f_\mathrm{sync}=1$ ), showing that the final amount of angular momentum in the core of the primary star is not much affected by different histories of mass loss (i.e., Case AB or Case B; Sect. \ref{sect:fiducial}) )."
" Then, we discuss the influences of different assumptions on tidal synchronization and transport process of angular momentum (Sect. ??))."," Then, we discuss the influences of different assumptions on tidal synchronization and transport process of angular momentum (Sect. \ref{sect:nonfiducial}) )."
 The evolution of the primary star in a close binary system is characterized by the rapid loss of mass due to Roche-lobe overflow., The evolution of the primary star in a close binary system is characterized by the rapid loss of mass due to Roche-lobe overflow.
" As an example, the evolution of the primary star in Seq."," As an example, the evolution of the primary star in Seq."
 14 is described in Figs., 14 is described in Figs.
" 2 and ὃ,, where our fiducial value of fsync=1 is adopted, including"," \ref{fig:kippseq9} and \ref{fig:hrseq9}, , where our fiducial value of $f_\mathrm{sync}=1$ is adopted, including"
station region and the Mach cones orientation at the outer boundaries.,simulation region and the Mach cones orientation at the outer boundaries.
 In 81.3 we discuss both factors., In 4.3 we discuss both factors.
" Ilere. we present results of sinulations for à fixed elougated simulation region Rowe.=θε, Zina,=200r; for three different outer boundary conditions on D,,: (1) a standard “free” boundary condition. (2) avtorce-free™ boundary condition. aud (3) a ""force-balauce boundary concditiou."," Here, we present results of simulations for a fixed elongated simulation region $R_{max}=50 r_i$ , $Z_{max}=200 r_i$ for three different outer boundary conditions on $B_\phi$: (1) a standard “free” boundary condition, (2) a“force-free” boundary condition, and (3) a “force-balance” boundary condition."
" First. we performed simulatious for the simplest standard “free” boundary coudition on ο 0DB,/0n= 0, "," First, we performed simulations for the simplest standard “free” boundary condition on $B_\phi$, $\partial B_\phi/\partial n=0$ ."
We observed that this boundary condition may cive an artificial force on the boundary which iuflueuces the flow within the computational region., We observed that this boundary condition may give an artificial force on the boundary which influences the flow within the computational region.
" For example. if we suppose that on the top boundary 0ID,,/0:=0. then the radial component of the current-density equals to zero. deco(efο =0. which means that the poloidal cureut-deusitv has oulv a z-conipoueut j,jit."," For example, if we suppose that on the top boundary $\partial B_\phi/\partial z=0$, then the radial component of the current-density equals to zero, $j_r=
-(c/4\pi){\partial B_\phi}/{\partial z}$ $=0$, which means that the poloidal current-density has only a $z$ -component ${\bf j}_p=j_z\hat{\bf z}$."
 This meaus that the poloidal curreut-density is not parallel to the poloidal maguetic field , This means that the poloidal current-density ${\bf j}_p$ is not parallel to the poloidal magnetic field ${\bf B}_p$.
"Consequcutlyj,, there is a force (deusity) Jj«B,/ez0 B,.acting in the o direction. opposite to the rotation of the disk."," Consequently, there is a force (density) ${\bf j}_p\times{\bf B}_p/c\neq 0$ acting in the $\phi$ direction, opposite to the rotation of the disk."
" Figure 5 shows the SCOTTY,", Figure 5 shows the geometry.
 These ‘boundary forces act such wav that the flow never reaches a stationary state., These `boundary' forces act such way that the flow never reaches a stationary state.
 To check this fact. aud to be sure that this is not an effect of non-stationarity of our initial configuration. we did simulations for cases which went to a stationary state with other outer boundary conditions.," To check this fact, and to be sure that this is not an effect of non-stationarity of our initial configuration, we did simulations for cases which went to a stationary state with other outer boundary conditions."
" After establishing stationarity. we substituted the outer boundary couditious on B., toa “tree” boundary condition."," After establishing stationarity, we substituted the outer boundary conditions on $B_\phi$ to a “free” boundary condition."
" We observed that the stationary state was destroved for the reasous ientioned above,", We observed that the stationary state was destroyed for the reasons mentioned above.
 Figures Ga.b demonstrate one stage of this destruction. when the poloidal velocity decreased aud became less than fast magnetosonic speed iu all of the computational reeion.," Figures 6a,b demonstrate one stage of this destruction, when the poloidal velocity decreased and became less than fast magnetosonic speed in all of the computational region."
 Even the fluxes of mass and other physical paralucters through the bouncdarics are not constants in this simulation., Even the fluxes of mass and other physical parameters through the boundaries are not constants in this simulation.
 Also. matter with iuaguetie flux euters the region from the rieht-haud side. which is due to the flow being sub-fast maguetosouic.," Also, matter with magnetic flux enters the region from the right-hand side, which is due to the flow being sub-fast magnetosonic."
" To avoid this artificial force. we proposed a “force-free” outer boundary condition ou B,, (Romanova et al."," To avoid this artificial force, we proposed a “force-free” outer boundary condition on $B_\phi$ (Romanova et al."
 1997) which we discuss in the next subsection., 1997) which we discuss in the next subsection.
 Another possibility to consideris that the toroidal component of the magnetic force is zero ou the outer boundaries., Another possibility to consideris that the toroidal component of the magnetic force is zero on the outer boundaries.
" That is. j,|B,=0 on the outer boundaries."," That is, ${\bf j}_p\parallel{\bf B}_p = 0$ on the outer boundaries."
 We can write this condition as We performed simulations with this boundary condition in the elongated region aud observed that the flow reached a stationary state (sce Figures 6 cd).," We can write this condition as We performed simulations with this boundary condition in the elongated region and observed that the flow reached a stationary state (see Figures 6 c,d)."
 This flow las many characteristics of stationary flow., This flow has many characteristics of stationary flow.
 Fluxes of mass. energy. and momentum. mnteerated over different cross-sections. are coustants.," Fluxes of mass, energy, and momentum, integrated over different cross-sections, are constants."
 Iutegrals of motion along magnetic field lines are also constants., Integrals of motion along magnetic field lines are also constants.
 The flow iscollimated iuside the simulation region (see Fieures 6c. d).," The flow is inside the simulation region (see Figures 6c, d)."
 However. more detailed anualvsis (see 8112) shows that this collimation is artificial.," However, more detailed analysis (see 4.2) shows that this collimation is artificial."
" The “force-free” boundary condition for D,, is superior to the “free” boundary condition. because it leads to a stationary state. but it does not give the plysically correct flow."," The “force-free” boundary condition for $B_\phi$ is superior to the “free” boundary condition, because it leads to a stationary state, but it does not give the physically correct flow."
 Iu reality. the magnetic force should not be zero on the boundary.," In reality, the magnetic force should not be zero on the boundary."
 There is a maenetic force pushing matter outward through the outer boundaries., There is a magnetic force pushing matter outward through the outer boundaries.
 One cau see from Fieure 6d that the poloidal current-density (dashed lues) is uot parallel to the poloidal maguetic feld (solid lines)., One can see from Figure 6d that the poloidal current-density (dashed lines) is not parallel to the poloidal magnetic field (solid lines).
 However. ou the bouudaries (Fieure 6d) the two vectors are forced to be parallel aud thus the poloidal force equals zero.," However, on the boundaries (Figure 6d) the two vectors are forced to be parallel and thus the poloidal force equals zero."
 This boundary condition is better than the “free” boundary condition in the sense that there is no strong artificial force at the boundary., This boundary condition is better than the “free” boundary condition in the sense that there is no strong artificial force at the boundary.
 From the other side. when we put the force equal to zero. it is analogous to application of a force equal to the real force but with the opposite sign.," From the other side, when we put the force equal to zero, it is analogous to application of a force equal to the real force but with the opposite sign."
 This is one of the factors which may lead to artificial collimation., This is one of the factors which may lead to artificial collimation.
 Another possible factor (Mach cones orientation) depends on the shape of the simulation region aud ds discussed in 81.2., Another possible factor (Mach cones orientation) depends on the shape of the simulation region and is discussed in 4.2.
" As a next step for improving the outer boundary condition on D,. we take into account the fact that the magnetic field is not force-free aud j, is uot parallel to B,,."," As a next step for improving the outer boundary condition on $B_\phi$, we take into account the fact that the magnetic field is not force-free and ${\bf j}_p$ is not parallel to ${\bf B}_p$."
" We start from equation (16) for B., aud write it iu the forma where we asstune that the density at the boundary is much less than that at the Alfvéun surface. p« for mpDrn."," We start from equation (16) for $B_\phi$ and write it in the form where we assume that the density at the boundary is much less than that at the Alfvénn surface, $\rho \ll \rho_A$ for $r^2 \gg r_A^2$."
 Then. we obtain where we supposed that pr?=FOL aud took iuto account that Ὁ aud p4 are constauts along magnetic feld lines.," Then, we obtain where we supposed that $\rho r^2 = F(\Psi) r^\alpha$ and took into account that $\Omega$ and $\rho_A$ are constants along magnetic field lines."
 Finally. we obtain the outer boundary condition as where à is a parameter.," Finally, we obtain the outer boundary condition as where $\alpha$ is a parameter."
 In this case we got stationary flows which arecollimated iu the simulation region (sce Figures Go. £f).," In this case we got stationary flows which are in the simulation region (see Figures 6e, f)."
 Fluxes through the outer surfaces aud integrals along maguetic field lines are well conserved. as in the case of collinated flow. described in 811.2.," Fluxes through the outer surfaces and integrals along magnetic field lines are well conserved, as in the case of collimated flow, described in 4.1.2."
 The question arises. which boundary condition is correct. “force-free” or “force-balauce”ο," The question arises, which boundary condition is correct, “force-free” or “force-balance”?"
 The Uforee-balance’ coucdition is clearly the physical coudition because it does not generate an artificial force on the boundary., The ``force-balance'' condition is clearly the physical condition because it does not generate an artificial force on the boundary.
 However. it is more dif&cultto apply because there is no direct method for determining the parameter a.," However, it is more difficultto apply because there is no direct method for determining the parameter $\alpha$ ."
 It can only be obtained iteratively using additional simulations. which is very time consunmiug.," It can only be obtained iteratively using additional simulations, which is very time consuming."
 Our analysis, Our analysis
here for simplicity). whose scalings can be derived from simple dimensional considerations (as shown above).,"here for simplicity), whose scalings can be derived from simple dimensional considerations (as shown above)."
" For example. F,4x and FuexΕμμ} for PLSs D and F. respectively. using the notations of Granot&Sari(2002)..."," For example, $F_{\rm\nu,D} \approx F_{\nu,{\rm max}}(\nu/\nu_m)^{1/3}$ and $F_{\rm\nu,F}\approx F_{\nu,{\rm max}} (\nu/\nu_c)^{-1/2}$ for PLSs D and F, respectively, using the notations of \citet{GS02}. ."
" This implies that F2,/F.p.=eal—xl? tay=4/3 and by= -bD and ΕλΕν=UaoSU qas=3/4 and b,= —1/4)."," This implies that $F'_{\nu,D}/F_{\nu,D}
=\zeta^{4/3}\alpha^{-1}\to\kappa\lambda^{1/3}$ $a_D = 4/3$ and $b_D =
-1$ ) and $F'_{\nu,F}/F_{\nu,F}
=\zeta^{3/4}\alpha^{-1/4}\to\kappa^{2/3}\lambda^{1/12}$ $a_F = 3/4$ and $b_F = -1/4$ )."
" As illustrative examples of how the sealings for self-absorbed PLSs may be derived. one can readily obtain that FammUR/EDYQiγιο«R implying FlPap= quyΟΙ=O and by= 2). while foryl PLS A Yin is replaced by y-096O/F [obtained from requiring vosvaa)~ DteBfm,.cyy;]. implying F4«1?“Rep,|* and BIR=icaloanIpICU qu ο."," As illustrative examples of how the scalings for self-absorbed PLSs may be derived, one can readily obtain that $F_{\rm\nu,B} \approx \pi(R/\Gamma D)^2(2\nu^2/c^2)\Gamma\gamma_m m_e
c^2 \propto \nu^2R^2$ implying $F'_{\nu,B}/F_{\nu,B}
=\zeta^{0}\alpha^{2}\to\kappa^{2/3}\lambda^{-2/3}$ $a_B = 0$ and $b_B
= 2$ ), while for PLS A $\gamma_m$ is replaced by $\gamma_e(\nu)
\propto (\nu/\Gamma B)^{1/2}$ [obtained from requiring $\nu\sim \nu_{\rm
syn}(\gamma_e) \sim \Gamma(eB/m_e c)\gamma_e^2$ ], implying $F_{\rm\nu,A} \propto \nu^{5/2}R^2\rho_{\rm u}^{-1/4}$ and $F'_{\nu,A}/F_{\nu,A}
=\zeta^{-1/4}\alpha^{11/4}\to\kappa^{2/3}\lambda^{-11/12}$ $a_A =
-1/4$ and $b_A = 11/4$ )."
 Therefore. these scalings (or a; and bj) do not depend on the external density profile or on the details of the dynamics (and are the same in the relativistic and Newtonian self-similar regimes. when the dynamics are not self-similar. or for the reverse shock).," Therefore, these scalings (or $a_i$ and $b_i$ ) do not depend on the external density profile or on the details of the dynamics (and are the same in the relativistic and Newtonian self-similar regimes, when the dynamics are not self-similar, or for the reverse shock)."
 All of the ditterent scalings are summarized in table 2.., All of the different scalings are summarized in table \ref{tab:PLS}.
 The freedom in the choice of units in the dynamical equations that describe the evolution of ditferent types of physical systems and in their solutions. has been outlined and elucidated.," The freedom in the choice of units in the dynamical equations that describe the evolution of different types of physical systems and in their solutions, has been outlined and elucidated."
 The main results are summarized in Table I.., The main results are summarized in Table \ref{tab:sum}.
 While the emphasis was on numerical solutions of the dynamical equations through simulations. similar scalings hold equally well for analytic solutions of the same equations.," While the emphasis was on numerical solutions of the dynamical equations through simulations, similar scalings hold equally well for analytic solutions of the same equations."
 The number of free parameters N; that describe the family of physical systems that corresponds to a given solution of such a set of equations is given by max(O.3—Αμ) (Eq. 1).," The number of free parameters $N_{\rm f}$ that describe the family of physical systems that corresponds to a given solution of such a set of equations is given by $\max(0,3-N_{\rm udc})$ (Eq. \ref{eq:N_f}] ]),"
 where Nye is the number of independent (in terms of their units) universal dimensional constants (UDCs. such as c. ο. fe m. etc).," where $N_{\rm udc}$ is the number of independent (in terms of their units) universal dimensional constants (UDCs, such as $c$, $G$, $\hbar$, $m_e$, etc.)."
 This corresponds to the three basic physical units Cof mass. length and time) while accounting for the independent constraints on their possible rescalings.," This corresponds to the three basic physical units (of mass, length and time) while accounting for the independent constraints on their possible rescalings."
 Such resealings of the basic units are potentially relevant to many ditferent areas of research. such as plasma physics. astrophysics. cosmology. fluid dynamics or Earth and planetary sciences.," Such rescalings of the basic units are potentially relevant to many different areas of research, such as plasma physics, astrophysics, cosmology, fluid dynamics or Earth and planetary sciences."
 They can prove very useful in numerical studies of various physical systems. and save precious computational resources. especially in systematic numerical studies ofa arge parameter space.," They can prove very useful in numerical studies of various physical systems, and save precious computational resources, especially in systematic numerical studies of a large parameter space."
 The author thanks E. Nakar. F. van den Bosch. F. DeColle. T. Piran. O. Bromberg. E. Ramirez-Ruiz and the anonymous referee for useful discussions. suggestions or comments on the manuscript.," The author thanks E. Nakar, F. van den Bosch, F. DeColle, T. Piran, O. Bromberg, E. Ramirez-Ruiz and the anonymous referee for useful discussions, suggestions or comments on the manuscript."
 This research was supported by the ERC advanced research grant “GRBs”., This research was supported by the ERC advanced research grant “GRBs”.
confidence.,confidence.
 Lower ratios seem to be a characteristic of curichment at 5>2 (Finoguenov ct al., Lower ratios seem to be a characteristic of enrichment at $z>2$ (Finoguenov et al.
 2003). while siauulations sueecst that the WIITM. originates at 2<1 (Con Ostriker 1999).," 2003b), while simulations suggest that the WHIM originates at $z<1$ (Cen Ostriker 1999)."
 Wlile we would rather have more observational evidence on the dispersion of O to alpha clement ratios at different sites. we believe that this is a majorJ source of systelatics in interpreting the clement abuudauce of N-ray laments as a universal value.," While we would rather have more observational evidence on the dispersion of O to alpha element ratios at different sites, we believe that this is a major source of systematics in interpreting the element abundance of X-ray filaments as a universal value."
" To illustrate the point. we calculate the deusity of barvous traced by the OVT absorbers under two sets of assunptious,"," To illustrate the point, we calculate the density of baryons traced by the OVI absorbers under two sets of assumptions."
 Scaling the original value of O4(OQVI)=0013741 of Tripp ct al. (, Scaling the original value of $\Omega_b(OVI) = 0.0043h_{70}^{-1}$ of Tripp et al. (
2000) for ionization equilibrium implied by measurements of Mathlur et al. (,2000) for ionization equilibrium implied by measurements of Mathur et al. (
2003) and using the measurements of the O abundance reported here vields: The formal errorbar is 0.006. mostly froii the uucertainty iu the estimate for iouization.,"2003) and using the measurements of the O abundance reported here yields: The formal errorbar is 0.006, mostly from the uncertainty in the estimate for ionization."
 If. on the other hand. our measurements of Ne abundance are used with the Ne/O ratio for OVI absorbers frou: Nicastro et al. (," If, on the other hand, our measurements of Ne abundance are used with the Ne/O ratio for OVI absorbers from Nicastro et al. ("
"2002) then. Therefore the second set of assunptiouns must be invalid suce the total barvon deusity is Qtoral=0.039, leaving no room for other major components of local burxuvons 1 suchas Lv,Ly, absorbersabsorl (0.012=+0.0020.002) aud starst aud clusters of galaxies (~0.006: ο-ο,, Fiuogueuov et al.","2002) then, Therefore the second set of assumptions must be invalid since the total baryon density is $\Omega_b^{\rm total}=0.039$, leaving no room for other major components of local baryons such as $_\alpha$ absorbers $0.012\pm0.002$ ) and stars and clusters of galaxies $\sim0.006$; e.g., Finoguenov et al."
 2003b and references therein)., 2003b and references therein).
 O depletion outo dust eraius in the OVI absorbers. as suggestedby Nicastroct al. (," O depletion onto dust grains in the OVI absorbers, as suggested by Nicastro et al. ("
2002) as an explanation of the high Ne/O ratio. docs uot explain the unacceptably high barvou abundance iuplied w Eq. (,"2002) as an explanation of the high Ne/O ratio, does not explain the unacceptably high baryon abundance implied by Eq. ("
2). since the solar Ne/O ratio in our observations nav be simply explained by dust sputtering.,"2), since the solar Ne/O ratio in our observations may be simply explained by dust sputtering."
 The observational determination of scaling relatious vetween X-rav properties such as luninositv Ly. eas cluperature TZ. and eutropy is crucial in establishing he phvsieal properties of the ICAL," The observational determination of scaling relations between X-ray properties, such as luminosity $L_X$, gas temperature $T$, and entropy is crucial in establishing the physical properties of the ICM."
 The slopes of he LyT cud inasstemperature relations (e.g. Markevitch 1998: Finoenenoy et al, The slopes of the $L_X-T$ and mass–temperature relations (e.g. Markevitch 1998; Finoguenov et al.
 2001) aud the eas entropy level (e.g. Pouman et al., 2001) and the gas entropy level (e.g. Ponman et al.
 1999: Finoenenov et al., 1999; Finoguenov et al.
 2002) are all at variance with model predictions sed oon pure eravitational heating (INaiser 1986) and require the introduction of extra plivsics to describe the rermmodvnainics of the ICAL (e.g. Evrard Heury 1901: Kaiser 1991)., 2002) are all at variance with model predictions based on pure gravitational heating (Kaiser 1986) and require the introduction of extra physics to describe the thermodynamics of the ICM (e.g. Evrard Henry 1991; Kaiser 1991).
 An often discussed piece of extra physics is preheating of the barvons before they acerete outo ie cluster., An often discussed piece of extra physics is preheating of the baryons before they accrete onto the cluster.
 Most barvous that accrete onto clusters are nought to come from fikumeuts. so we now have au opportunity to compare the ποιοναο properties of 1e filament gas with that of group and cluster eas.," Most baryons that accrete onto clusters are thought to come from filaments, so we now have an opportunity to compare the thermodynamic properties of the filament gas with that of group and cluster gas."
 The (itropy of the N-vay cmitting filament is 150 keV eng. which could be reproduced by heating while falling outo a filament (c.g. Con Ostriker 1999).," The entropy of the X-ray emitting filament is 150 keV $^2$, which could be reproduced by heating while falling onto a filament (e.g. Cen Ostriker 1999)."
 Iu fact. estimating the expected Mach iuuber of the accretion shock when the filament euters the Coma cluster vields à value of Lb. similar to predictions of simmlations by Màiniati et al. (," In fact, estimating the expected Mach number of the accretion shock when the filament enters the Coma cluster yields a value of 4, similar to predictions of simulations by Miniati et al. ("
2000).,2000).
 Reeardless of the origin of the cutropy of the filamentary gas. its entropy is nmeh simaller than the 100 keV cm? implied by ASCA observations of the outskirts of eroups (Fiuoguenov ct al.," Regardless of the origin of the entropy of the filamentary gas, its entropy is much smaller than the 400 keV $^2$ implied by ASCA observations of the outskirts of groups (Finoguenov et al."
 2002). ruling out a universal preheating value.," 2002), ruling out a universal preheating value."
 We note that the euerevoO. of the oOeas (2422=0.36+0.02 keV/particle) is similar. although higher than the SNe energy associated with euricluueut of eas to the observed O abundance (0.22+0.03. keV/particle). so heating by galactic winds is not ruled out.," We note that the energy of the gas ${3\over2}kT=0.36\pm0.02$ keV/particle) is similar, although higher than the SNe energy associated with enrichment of gas to the observed O abundance $0.22\pm0.03$ keV/particle), so heating by galactic winds is not ruled out."
 Although. the temperature of the filament is presently a factor of 10 lower than the Coma virial temperature. as it falls into the cluster it will be shock heated. aud its final adiabat will be higher than iu the selfsimular TL (Dox Santos Doré 2002: Ponnuui et al.," Although, the temperature of the filament is presently a factor of 40 lower than the Coma virial temperature, as it falls into the cluster it will be shock heated, and its final adiabat will be higher than in the self-similar case (Dos Santos Doré 2002; Ponman et al."
 2003)., 2003).
 Since the mass of the fibunent is compirable to that of the Coma cluster. the combined object will also deviate from cluster scaling relatious.," Since the mass of the filament is comparable to that of the Coma cluster, the combined object will also deviate from cluster scaling relations."
 Observations indicate that the gas-to-dark matter distribution will uot be affected (Sauderson et al., Observations indicate that the gas-to-dark matter distribution will not be affected (Sanderson et al.
 2003). but the temperature is hieher for a giveu mass (Finoguenuov ct al.," 2003), but the temperature is higher for a given mass (Finoguenov et al."
 2001)., 2001).
" This process is probably not muniversal, since some groups o: galaxies have “shallow eas profiles. thus possibly poiutiug to adiabatic compression rather than shock heatiug of the prelieated gas. ax proposed by Tozzi Norman (2001)."," This process is probably not universal, since some groups of galaxies have shallow gas profiles, thus possibly pointing to adiabatic compression rather than shock heating of the preheated gas, as proposed by Tozzi Norman (2001)."
 If the structures reported here are oulv associated withi largearee clusters of galaxies.e@alaxics. theirir coutributioutiibutiou fο the barvou budget is negligible (0.1-14)).," If the structures reported here are only associated with large clusters of galaxies, their contribution to the baryon budget is negligible )."
. Of. greater importance is to investigate the accreting environment of the massive groups aud poor clusters that lave a significant cutry in the barvou budget (6560)., Of greater importance is to investigate the accreting environment of the massive groups and poor clusters that have a significant entry in the baryon budget ).
 Tlowever. carly curichiment epoch. suggested by low Ne/O ratio. makes X-ray fibunents a substautial entry iu the ictal budget at high redshifts.," However, early enrichment epoch, suggested by low Ne/O ratio, makes X-ray filaments a substantial entry in the metal budget at high redshifts."
 The thermodvuaiic state of the filamentary gas causes a global feedback effect on the embedded: galaxies by straugliug the eas accretion (Fiuoguenuov et al., The thermodynamic state of the filamentary gas causes a global feedback effect on the embedded galaxies by strangling the gas accretion (Finoguenov et al.
 20032: OL Beuson 2003)., 2003a; Oh Benson 2003).
 The resulting starformation will proceed by consumption of the previously accumulated eas. iu either quicscent mode as in the disk. or mereer-aincdiuced bursts leading to formation of the spheroid (Somerville ct al.," The resulting star-formation will proceed by consumption of the previously accumulated gas, in either quiescent mode as in the disk, or merger-induced bursts leading to formation of the spheroid (Somerville et al."
 2001)., 2001).
 Galaxy ierecrs are frequent inside galaxy groups (Nodama ct al., Galaxy mergers are frequent inside galaxy groups (Kodama et al.
 2001). but in a filament the infall of the eas will primarily be recorded iun the star-formation history of the disk (J&ennieutt et al.," 2001), but in a filament the infall of the gas will primarily be recorded in the star-formation history of the disk (Kennicutt et al."
 1991)., 1994).
 A relevant observation could therefore shed light on the feedback epoch. which is crucial i understanding the relation between the N-rav Glameuts aud OVI absorbers.," A relevant observation could therefore shed light on the feedback epoch, which is crucial in understanding the relation between the X-ray filaments and OVI absorbers."
 The recent Sloan Digital Sky Survey (SDSS) discovery of passive spirals. iu the same filament iu frout of Coma (Coto et al.," The recent Sloan Digital Sky Survey (SDSS) discovery of passive spirals, in the same filament in front of Coma (Goto et al."
 2003). is exactly what is expected from this strangulation process.," 2003), is exactly what is expected from this strangulation process."
 The existence of these passive spirals lends further support to the association of the soft X-ray excess with the Coma filament., The existence of these passive spirals lends further support to the association of the soft X-ray excess with the Coma filament.
 As passive spirals are starting to be found im the outskirts of may, As passive spirals are starting to be found in the outskirts of many
the Lamanu-Werner background. (Machaceketal.Abel2007:O'Shea&Nonuau 2008)..,"the Lyman-Werner background \citep{Mac01, Mac03, Yos03, Sus07, Wis07, O'S08}. ."
 The Lyinan-Werner background thus increases cooling times iu the centers of such halos., The Lyman-Werner background thus increases cooling times in the centers of such halos.
 Asa result. the minima niass of a star-forming halo increases with the Lyuiui-Werner backeround intensity.," As a result, the minimum mass of a star-forming halo increases with the Lyman-Werner background intensity."
 The Lxiuau-Werner backgrouud becomes less of an issue iu atomic line cooling halos as Lya cooling provides wuple amounts of free clectrous for Πο cooling. and they become seltshiclding to this raciatio- (O'Shea&Norman2008:SusaWiseAbeaa2008:Wise&Cen 2009).," The Lyman-Werner background becomes less of an issue in atomic line cooling halos as $\alpha$ cooling provides ample amounts of free electrons for ${\rm H}_{2}$ cooling, and they become self-shielding to this radiation \citep{O'S08, Sus08, Wis08, Wis09}."
. Tn the later epoch. dust ejected bv stars in ealaxies is effective to shield the Lyian-Werner backeroundC» and acts as an effective. catalyst for Il» molecule production ou the dust grains.," In the later epoch, dust ejected by stars in galaxies is effective to shield the Lyman-Werner background and acts as an effective catalyst for ${\rm H}_{2}$ molecule production on the dust grains."
 Iu smaunulatious with star formation inodels based ou nolecular lvdrogen (Robertson&IEuavtsov2008:(ποσαetal. 2009).. once the eas enriched up to Z~0.011Z.. the subsequent star formation aud enrichment of metal anc dust can be απο more accelerated.," In simulations with star formation models based on molecular hydrogen \citep{Rob08, Gne09}, once the gas enriched up to $Z\sim0.01-0.1\ {Z_{\odot}}$, the subsequent star formation and enrichment of metal and dust can be much more accelerated."
 Cuedietal.(2000) show that the transition from atomic to molecular hydrogen depends primarily on metallicity. asstunineg that the dust abundance is directly related to metallicity.," \citet{Gne09} show that the transition from atomic to molecular hydrogen depends primarily on metallicity, assuming that the dust abundance is directly related to metallicity."
 Dus plavs a crucial role iu the star formation: (1) molecular bydrogen is produced more efficiently ou dust erains than m gas plase. (i) dust shiclds dissociating UV. radiation. and (3) dust allows the formation of low-mass stars in low-1uetallicitv chviromlments. aud hence affects the initial mass function (IME) (Oxninkaietal.2005:Schneider 2010).," Dust plays a crucial role in the star formation: (i) molecular hydrogen is produced more efficiently on dust grains than in gas phase, (ii) dust shields dissociating UV radiation, and (iii) dust allows the formation of low-mass stars in low-metallicity environments, and hence affects the initial mass function (IMF) \citep{Omu05, Sch06, Sch10, Omu10}."
. Iu theoretical studies on the molecular abuudauce in the interstellar medium (ISM). dust abuudanuce i» often scaled with the metallicity and dust erain properties are assuned to be the same as iu the local ISAL," In theoretical studies on the molecular abundance in the interstellar medium (ISM), dust abundance is often scaled with the metallicity and dust grain properties are assumed to be the same as in the local ISM."
 However. the composition of dust is likely to be differcut in early galaxies.," However, the composition of dust is likely to be different in early galaxies."
 The observational evidence is that the dust extinction curves of the broad absorption line quasars at ;Dom Lare likely to be due to the type II SN (SN ID dust (Maiolinoetal.2001:Callerani 2010).," The observational evidence is that the dust extinction curves of the broad absorption line quasars at $z>4$ are likely to be due to the type II SN (SN II) dust \citep{Mai04, Gal10}."
. Since the lifetime of SN II progenitor is short. SN II can be the dominant production source of dust erünus in voune («1 Cor) galaxies.," Since the lifetime of SN II progenitor is short, SN II can be the dominant production source of dust grains in young $<1$ Gyr) galaxies."
 Primeval SNe produced by Population III stars (Brounetal.2008) may contribute the dust production (Nozawactal.2003:Schneideret2001).," Primeval SNe produced by Population III stars \citep{Bro03, Kit05, Wha08} may contribute the dust production \citep{Noz03, Sch04}."
. The winds of evolved low-mass stars contribute to dust formation considerably in nearby galaxies. but the cosmic time is uot long enough for such stars to evolve at hieh redshift (2=5) where all galaxies should have ages vounecr than z1 Civ.," The winds of evolved low-mass stars contribute to dust formation considerably in nearby galaxies, but the cosmic time is not long enough for such stars to evolve at high redshift $z>5$ ) where all galaxies should have ages younger than $\simeq 1$ Gyr."
 Contribution of dust production by low-1ass stars is not donünant iu such vouug galaxies., Contribution of dust production by low-mass stars is not dominant in such young galaxies.
 Iun addition. dust is destroved bv SN. shocks.," In addition, dust is destroyed by SN shocks."
 Thus. the modeling of dust evolution in galaxies requires an accurate treatineut of production and destruction of dust eraius together with star formation activities (Ilirashita&Ferrara2002).," Thus, the modeling of dust evolution in galaxies requires an accurate treatment of production and destruction of dust grains together with star formation activities \citep{Hir02}."
. Iun this paper. we investigate uot only the evolution of dust mass but also the time evolution of dust size distribution.," In this paper, we investigate not only the evolution of dust mass but also the time evolution of dust size distribution."
 The dust size distribution evolves rapidly because of the destruction by sputtering in the high-velocitv shocks driven bx SNe., The dust size distribution evolves rapidly because of the destruction by sputtering in the high-velocity shocks driven by SNe.
 Collision of the expauding SN cjecta with the surrounding ISM. creates a forward shock at the interface between the ejecta and the ISM (Nozawactal.2006).. and a reverse shock that penetrates into the ejecta (Bianchi&Schucideretal. 2010).," Collision of the expanding SN ejecta with the surrounding ISM creates a forward shock at the interface between the ejecta and the ISM \citep{Noz06}, and a reverse shock that penetrates into the ejecta \citep{Bia07, Noz07, Nat08, Sil10}."
. Since the erosion rate by sputtering does not stronely depeud on the erain size. s122ll erains are predoniünantlv destroved regardless of erain species.," Since the erosion rate by sputtering does not strongly depend on the grain size, small grains are predominantly destroyed regardless of grain species."
 Therefore. the fraction of small size erains relatively decreases with galaxy evolution.," Therefore, the fraction of small size grains relatively decreases with galaxy evolution."
 We focus on the effects of molecular hydrogen abundance ou the SER in the carly stage of galaxy evolution. talking iuto account molecular formation on dust. «nee IH» formation on dust surface is very effective (Iirashita&Ferrara2002:Cazaux&Spaans200 [).," We focus on the effects of molecular hydrogen abundance on the SFR in the early stage of galaxy evolution, taking into account molecular formation on dust, since ${\rm H}_{2}$ formation on dust surface is very effective \citep{Hir02, Caz04}."
. IDirashita&Ferrara(2002) slow that this effect causes an eublauceioeut of the SER by an order of magnitude on a timescale of 3/5 ealactic dynamical time., \citet{Hir02} show that this effect causes an enhancement of the SFR by an order of magnitude on a timescale of $3-5$ galactic dynamical time.
 Iowever. they assuued a single dust eraiu size (~1.03 pau).," However, they assumed a single dust grain size $\sim0.03\ \mu{\rm m}$ )."
 We adopt more accurate analytic forilac for theformation of molecular hydrogeu ou ¢ust eraius than Iirashita by usiic the results of dust size distribution by Nozawactal(2006.2007 )..," We adopt more accurate analytic formulae for theformation of molecular hydrogen on dust grains than \citet{Hir02} by using the results of dust size distribution by \citet{Noz06, Noz07}. ."
 This is the first stidv ongalaxy evolution considering dust size evolution for halo masses above 108? in the high-redshift (5«+ 10). whose interiors we expect to be roughly," This is the first study ongalaxy evolution considering dust size evolution for halo masses above $10^{8-9}$ in the high-redshift $5<z<10$ ), whose interiors we expect to be roughly"
as m each night images of the wide binaries 442758. 445072. HIP446657. HIP550602.,"as in each night images of the wide binaries 42758, 45072, 46657, 50602."
 The instrument. Is found to be stable within the individual nights in May 2010., The instrument is found to be stable within the individual nights in May 2010.
" In addition. to our K-band observations we also obtained images in the J-. and H-band to determine the infrared photometry of BB. The magnitude difference between BB and its primary is measured always after the subtraction of the PSF of the bright star in all NACO images. and is summarized in reftable,froro.."," In addition, to our $\rm K_{s}$ -band observations we also obtained images in the J-, and H-band to determine the infrared photometry of B. The magnitude difference between B and its primary is measured always after the subtraction of the PSF of the bright star in all NACO images, and is summarized in \\ref{table_photo}."
" As AA is saturated in our deep NACO images. taken in September 2009. only a lowerlimit for the difference in the K.-band could be derived (AK,>3.0+0.1 mmag)."," As A is saturated in our deep NACO images, taken in September 2009, only a lowerlimit for the magnitude-difference in the $\rm K_{s}$ -band could be derived $\Delta K_{s} > 5.0\pm0.1$ mag)."
 The determined limit agrees with the photometry of BB obtained in all other observing epochs. in which NACO's neutral density filter σι was used in the case that AA would have saturated the NACO detector.," The determined limit agrees with the photometry of B obtained in all other observing epochs, in which NACO's neutral density filter $\rm ND_{Short}$ was used in the case that A would have saturated the NACO detector."
" The photometric measurements from the individual observing epochs are all consistent with each other within their uncertainties,", The photometric measurements from the individual observing epochs are all consistent with each other within their uncertainties.
" The apparent magnitudes of BB and its primary can be derived with the obtained magnitude-differences. as well as the accurate photometry of the TTel system 6.856+0.021] mmag. H=6.486+0.049 mmag. K,=6.366+0.024HL mmag). which is listed in the 2MASS point source catalogue (?).."," The apparent magnitudes of B and its primary can be derived with the obtained magnitude-differences, as well as the accurate photometry of the Tel system $J = 6.856 \pm 0.021$ mag, $H = 6.486 \pm 0.049$ mag, $K_{s} = 6.366 \pm 0.024$ mag), which is listed in the 2MASS point source catalogue \citep{skrutskie2006}."
" Finally. the precise Hipparcos parallax of TTelNd d distance modulus E=3.48040.127 mmag. which is usec05 derive the absolute magnitudes of BB 0.]2mmag. Mj;=8.52+40.13 mmag. and My=82440.10 mmag). assuming that the NACO and 2MASS JHK, color systems are identical."," Finally, the precise Hipparcos parallax of Telyields a distance modulus $E=3.480\pm0.127$ mag, which is used to derive the absolute magnitudes of B $M_{J}=9.05\pm0.12$ mag, $M_{H}=8.52\pm0.13$ mag, and $M_{K_{s}}=8.24\pm0.10$ mag), assuming that the NACO and 2MASS $K_{s}$ color systems are identical."
" We obtained deep NACO observations of AA and its companion in September 2009 in the K,-band.", We obtained deep NACO observations of A and its companion in September 2009 in the $\rm K_{s}$ -band.
 The achieved detection limit of our NACO image with and without PSF subtraction is shown in reflimit together with the expected magnitudes of substellar objects with different masses at an assumed age of MMyr. derived with the ? evolutionary models and the well know1 distance of the TTel system.," The achieved detection limit of our NACO image with and without PSF subtraction is shown in \\ref{limit} together with the expected magnitudes of substellar objects with different masses at an assumed age of Myr, derived with the \cite{baraffe2003} evolutionary models and the well known distance of the Tel system."
 After PSF subtraction. all brown dwarf companions (mass>12 M4) are detectable in our NACO image beyond aaresec (or ~ AAU of projected separation) arounc AA up to about aaresee (~ AAU) at the outer edge of the field of view. fully covered by NACO's S13 optics (Jitter-width. taken into account).," After PSF subtraction, all brown dwarf companions $>12\,M_{Jup}$ ) are detectable in our NACO image beyond arcsec (or $\sim$ AU of projected separation) around A up to about arcsec $\sim$ AU) at the outer edge of the field of view, fully covered by NACO's S13 optics (jitter-width taken into account)."
" In the background noise limited region. beyond a separation of about aaresec (~ AAU). a sensitivity of K,=19.6 mmag ts reached i1 average. Which allows the detection of planetary mass objects down to a mass of about 2M,,,,, around AA. Beside BB. one further very funt (AK,> mmag) companion-candidate is detected in. our deep NACO image at sep=3.818+0.006 aarcsec. and PA= 0.117."," In the background noise limited region, beyond a separation of about arcsec $\sim$ AU), a sensitivity of $K_{s} = 19.6$ mag is reached in average, which allows the detection of planetary mass objects down to a mass of about $2\,M_{Jup}$ around A. Beside B, one further very faint $\Delta K_{s}>10.2$ mag) companion-candidate is detected in our deep NACO image at $sep = 3.818\pm0.006$ arcsec, and $PA=166.21\pm0.11^{\circ}$ ."
 This candidate was already detected by ?.. who proposed that it is most probably à background source (Epoch:," This candidate was already detected by \cite{chauvin2010}, , who proposed that it is most probably a background source (Epoch:"
but speeds of ~2 km/s are found already in the inner penumbra.,but speeds of $\sim 2$ km/s are found already in the inner penumbra.
 Phenomena strikingly similar to the overturning motion in the penumbral filaments presented in the previous section are seen in high-resolution observations of convection around the small magnetic elements that make up most of a young active region., Phenomena strikingly similar to the overturning motion in the penumbral filaments presented in the previous section are seen in high-resolution observations of convection around the small magnetic elements that make up most of a young active region.
" An example is shown in Fig. 4,,"," An example is shown in Fig. \ref{oslo},"
 taken on 10 May 2004 with the SST., taken on 10 May 2004 with the SST.
" The magnetic field in such elements reduces the gas pressure, so they are more transparent and appear as ‘dips’, or depressions in the observed surface of the Sun (Spruit 1976, 1977)."," The magnetic field in such elements reduces the gas pressure, so they are more transparent and appear as `dips', or depressions in the observed surface of the Sun (Spruit 1976, 1977)."
 This is particularly clear in observations near the limb of the Sun., This is particularly clear in observations near the limb of the Sun.
 The limb-side rim of such a dip is seen as a brightening while the proximal boundary is obscured., The limb-side rim of such a dip is seen as a brightening while the proximal boundary is obscured.
 Radiative cooling of gas surrounding the boundary increases its density; as a consequence the element is surrounded by convective downflows., Radiative cooling of gas surrounding the boundary increases its density; as a consequence the element is surrounded by convective downflows.
" Given sufficient spatial resolution, these flows can be observed directly in time sequences of images such as Fig. 4.."," Given sufficient spatial resolution, these flows can be observed directly in time sequences of images such as Fig. \ref{oslo}."
 The phenomenology seen in such observations has been reproduced in detail by radiative magnetohydrodynamic simulations (Carlsson et al., The phenomenology seen in such observations has been reproduced in detail by radiative magnetohydrodynamic simulations (Carlsson et al.
" 2004, Keller et al 2004, De Pontieu et al."," 2004, Keller et al 2004, De Pontieu et al."
" 2006, see also Steiner 2005)."," 2006, see also Steiner 2005)."
 We can thus be confident of the interpretation given above: we have a good understanding of what overturning convection along a magnetic boundary in the solar photosphere looks like., We can thus be confident of the interpretation given above: we have a good understanding of what overturning convection along a magnetic boundary in the solar photosphere looks like.
" The boiling, overturning impression given by the penumbral movie of Fig."," The boiling, overturning impression given by the penumbral movie of Fig."
 1 is similar to the flows seen on the limb side of the pores in Fig. 4.., \ref{stria} is similar to the flows seen on the limb side of the pores in Fig. \ref{oslo}.
" Apart from the overall impression, the time scales and length scales as well as the ‘striated’ substructure are common properties."," Apart from the overall impression, the time scales and length scales as well as the `striated' substructure are common properties."
 'The main difference is the orientation of the striation., The main difference is the orientation of the striation.
 In the magnetic structures in refoslo the striation is parallel to the downward flow; in the penumbral filament it is at an angle., In the magnetic structures in \\ref{oslo} the striation is parallel to the downward flow; in the penumbral filament it is at an angle.
 For isolated magnetic elements we know that the striation follows magnetic field lines: it is a corrugation of the surface bounding the magnetic structure from the surrounding convection zone. [, For isolated magnetic elements we know that the striation follows magnetic field lines: it is a corrugation of the surface bounding the magnetic structure from the surrounding convection zone. [
"This is demonstrated by comparison with the MHD simulations, DDe Pontieu et al.","This is demonstrated by comparison with the MHD simulations, De Pontieu et al."
 2006]., 2006].
" The striation in the penumbral filament, on the other hand, is inclined at angles expected for the field at such a position in the penumbra."," The striation in the penumbral filament, on the other hand, is inclined at angles expected for the field at such a position in the penumbra."
" The obvious interpretation is thus that the striation is a corrugation of the magnetic surface surrounding the filament, outlining the direction of the field lines."," The obvious interpretation is thus that the striation is a corrugation of the magnetic surface surrounding the filament, outlining the direction of the field lines."
" The downflow along the boundary, carrying the corrugation with it, causes an apparent outward motion of the striation."," The downflow along the boundary, carrying the corrugation with it, causes an apparent outward motion of the striation."
 It is likely that a real outward fluid motion along the gap also contributes to the motion of the striation., It is likely that a real outward fluid motion along the gap also contributes to the motion of the striation.
 The numerical simulations of Heinemann et al. (, The numerical simulations of Heinemann et al. (
"2007) show an outward flow in the gaps, along the boundary with the magnetic field.","2007) show an outward flow in the gaps, along the boundary with the magnetic field."
 Scharmer et al. (, Scharmer et al. (
"2008) discuss its origin,","2008) discuss its origin,"
visible at 10” from the center.,visible at $\arcsec$ from the center.
" Both from the VDP and from the RC of NGC 1427 there is evidence for kinematically distinct components at the inner 2"" and inside 10” from the center; NGC 1427 shows also anti-correlated wiggles in both the RC and the VDP.", Both from the VDP and from the RC of NGC 1427 there is evidence for kinematically distinct components at the inner $\arcsec$ and inside $\arcsec$ from the center; NGC 1427 shows also anti-correlated wiggles in both the RC and the VDP.
 In summary: it seems that more than half of the galaxies in the present sample are. at least from the kinematical point of view. misclassified S(A-B)Os.," In summary: it seems that more than half of the galaxies in the present sample are, at least from the kinematical point of view, misclassified S(A-B)0s."
" Morphological classification by visual inspection of images. apparently results in a dramatic over-estimate of the true number of ""dynamically hot’ stellar systems."," Morphological classification by visual inspection of images, apparently results in a dramatic over-estimate of the true number of `dynamically hot' stellar systems."
 The catalog of Ferguson (1989) lists 58 Fornax galaxies with 7 «15.0 mag. from the 14 listed as having morphological type E. only 3 turn out to be true elliptical galaxies in the classical sense of the word: indicating that these objects are in fact quite rare.," The catalog of Ferguson (1989) lists 58 Fornax galaxies with $B_T$$<$ 15.0 mag, from the 14 listed as having morphological type E, only 3 turn out to be true elliptical galaxies in the classical sense of the word; indicating that these objects are in fact quite rare."
 Most of the objects. moreover. show complex kinematical profiles. like kinematically distinct components. wiggles. and asymmetries.," Most of the objects, moreover, show complex kinematical profiles, like kinematically distinct components, wiggles, and asymmetries."
If a star is gravitationally microlensed by a lens system composed of two masses. the resulting light curve can dramatically deviate from the smooth and symmetric one of a single-lens event.,"If a star is gravitationally microlensed by a lens system composed of two masses, the resulting light curve can dramatically deviate from the smooth and symmetric one of a single-lens event."
 This deviation is caused by the formation of caustics for binary-lens systems., This deviation is caused by the formation of caustics for binary-lens systems.
 The caustics represent the source positions at which the lensing magnification of a point source becomes infinite., The caustics represent the source positions at which the lensing magnification of a point source becomes infinite.
 The set of caustics forms one. two. or three close curves each of which is composed of concave curves that meet at points.," The set of caustics forms one, two, or three close curves each of which is composed of concave curves that meet at points."
 By analyzing the light curve of a binary-lens event. it is possible to obtain information about the lens system because the structure of the caustic system and the resulting light curve vary depending on the mass ratio and the projected separation between the components of binary lenses.," By analyzing the light curve of a binary-lens event, it is possible to obtain information about the lens system because the structure of the caustic system and the resulting light curve vary depending on the mass ratio and the projected separation between the components of binary lenses."
 Since the pioneering work by Chang&Refsdal(1980. 1984).. binary lensing has been a subject of intense theoretical studies.," Since the pioneering work by \citet{chang80, chang84}, binary lensing has been a subject of intense theoretical studies."
 Schneider&Weiss(1986) made a comprehensive study of binary lenses in order to learn about caustics in quasar macrolensing., \citet{schneider86} made a comprehensive study of binary lenses in order to learn about caustics in quasar macrolensing.
 Witt(1990) developed a simple algorithm for finding caustics of binary lenses., \citet{witt90} developed a simple algorithm for finding caustics of binary lenses.
 Witt&Mao(1995) studied lensing magnification inside caustic and found that the minimum magnification when the source Is inside a caustic is greater than 3., \citet{witt95} studied lensing magnification inside caustic and found that the minimum magnification when the source is inside a caustic is greater than 3.
 Rhie(1997) found that the maximum number of images for multiple-lens systems., \citet{rhie97} found that the maximum number of images for multiple-lens systems.
 With the beginning of microlensing surveys. theoretical studies became even more active.," With the beginning of microlensing surveys, theoretical studies became even more active."
 Gaudi&Gould(1997) pointed out that microlensing is an efficient method to detect close binaries., \citet{gaudi97} pointed out that microlensing is an efficient method to detect close binaries.
 DiStefano&Perna(1997). mentioned. various channels of detecting binaries including repeating events., \citet{distefano97} mentioned various channels of detecting binaries including repeating events.
 Dominik(1999b) studied the lensing behavior in the extreme cases of binary separations and mass ratios., \citet{dominik99b} studied the lensing behavior in the extreme cases of binary separations and mass ratios.
 Dominik(1999a) and Albrowetal.(1999b) mentioned possible degeneracies in modeling light curves of binary-lens events., \citet{dominik99a} and \citet{albrow99b} mentioned possible degeneracies in modeling light curves of binary-lens events.
 Han.Chun.&Chang(1999) and Han(2001) studied the astrometric behavior of binary-lens events., \citet{han99} and \citet{han01} studied the astrometric behavior of binary-lens events.
 Bozza(2000.2001) derived analytic expressions for the location of causties and studied the motion of images of microlensed stars.," \citet{bozza00,bozza01} derived analytic expressions for the location of caustics and studied the motion of images of microlensed stars."
 investigated the photometric and astrometric behaviors m the region very close to caustics., investigated the photometric and astrometric behaviors in the region very close to caustics.
 Graff&(2002) devised a method to measure the mass of the system from the analysis of light curves of crossing events., \citet{graff02} devised a method to measure the mass of the binary-lens system from the analysis of light curves of caustic-crossing events.
" In addition to the theoretical studies. binary- events were actually detected from various. surveys (Udalskietal.1994,1998:Alcock1999:Alard.Mao&Cassanetal.2004:Jaroszynski2005. 2006)."," In addition to the theoretical studies, binary-lens events were actually detected from various surveys \citep{udalski94, udalski98, 
alcock99, alard95, afonso00, albrow99a, albrow00, albrow01, 
an02, smith02, albrow02, abe03, kubas05, jaroszynski04, cassan04, 
jaroszynski05, jaroszynski06}."
. With the active researches in. both. theoretical and observational fields. binary microlensing has developed into a useful tool to study stellar astrophysics.," With the active researches in both theoretical and observational fields, binary microlensing has developed into a useful tool to study stellar astrophysics."
 The most active field of application is the stellar atmosphere for which microlensing is used to probe detailed structures on the surface of source stars by using the high resolution of caustic-crossing events (Albrowetal.1999a.2001:Abe2003).," The most active field of application is the stellar atmosphere for which microlensing is used to probe detailed structures on the surface of source stars by using the high resolution of caustic-crossing events \citep{albrow99a, albrow01, 
abe03}."
. Microlensing can also be used to probe the distributions of binary companions of Galactic stars as functions of mass ratio and separation., Microlensing can also be used to probe the distributions of binary companions of Galactic stars as functions of mass ratio and separation.
 These binary distributions provide important observational constraints on theories of star formation., These binary distributions provide important observational constraints on theories of star formation.
 Since microlensing 1s sensitive to low-mass companions that are difficult to be detected by other methods. it is in principle possible to make complete distribution down to the lower mass limit of binary companions.," Since microlensing is sensitive to low-mass companions that are difficult to be detected by other methods, it is in principle possible to make complete distribution down to the lower mass limit of binary companions."
 Despite the importance. the progress of this application of binary lensing has been stagnant.," Despite the importance, the progress of this application of binary lensing has been stagnant."
 There are two main reasons for this., There are two main reasons for this.
 The first reason is caused by the difficulty in estimating the detection efficiency of binary-lens events., The first reason is caused by the difficulty in estimating the detection efficiency of binary-lens events.
 In previous lensing surveys. most binary-lens events were discovered through the channel of caustic-crossing events. in which the caustic crossings were accidently discovered from the sudden rise of the source star flux.," In previous lensing surveys, most binary-lens events were discovered through the channel of caustic-crossing events, in which the caustic crossings were accidently discovered from the sudden rise of the source star flux."
 Due to the haphazard nature of caustic crossings. it was difficult to estimate the detection efficiency that is essential for the statistical studies of binary companions.," Due to the haphazard nature of caustic crossings, it was difficult to estimate the detection efficiency that is essential for the statistical studies of binary companions."
 The second reason is that microlensing is mainly sensitive to binaries over a narrow range of projected separations., The second reason is that microlensing is mainly sensitive to binaries over a narrow range of projected separations.
 This limits especially, This limits especially
Once the state on the interface is determined. the fluxes can be computed and the conservative quantities can be updated.,"Once the state on the interface is determined, the fluxes can be computed and the conservative quantities can be updated."
 The gravitational potential is obtained though the classical algorithm used by Particle-Mesh codes., The gravitational potential is obtained though the classical algorithm used by Particle-Mesh codes.
 We solve Poisson’s equation with Fourter-transformations and Green's function (2)., We solve Poisson's equation with Fourier-transformations and Green's function \citep{Hockney88}.
 Then. the conservative quantities are updated with the gravitational source terms.," Then, the conservative quantities are updated with the gravitational source terms."
 To perform the needed Fourter-transformations we use the public available FFTW library (?).., To perform the needed Fourier-transformations we use the public available FFTW library \citep{FFTW}.
 The evolution of the number densities and the heating and cooling originate in the same physical processes and have similar timescales., The evolution of the number densities and the heating and cooling originate in the same physical processes and have similar timescales.
 It is therefore necessary to compute their evolution in à similar way., It is therefore necessary to compute their evolution in a similar way.
 In the IE case a solution to =;=0 can be found by iteration., In the IE case a solution to $\Xi_i = 0$ can be found by iteration.
 The situation is more difficult in the on-IE case., The situation is more difficult in the non-IE case.
 Here. the integration of the system of ordinary moaifferential equations 7==; is performed.," Here, the integration of the system of ordinary differential equations $\dot{n} = \Xi_i$ is performed."
 These are stiff ordinary differential equations. and therefore most codes use nplicit methods for their solution.," These are stiff ordinary differential equations, and therefore most codes use implicit methods for their solution."
 In our code. we use a Cifferent approach and adopt the C.eveloped in biochemical oceanography (?)..," In our code, we use a different approach and adopt the developed in biochemical oceanography \citep{Burchard03}."
" Although it is αxplicit it ensures the positivity of temperature and number ""Sensities and conserves total amount of hydrogen and helium.", Although it is explicit it ensures the positivity of temperature and number densities and conserves total amount of hydrogen and helium.
 The modified Euler-Patankar scheme reads: where pa is the production matrix contaming the rates producing species { from species Κ. while dj is the destruction matrix containing the rates that transform species / into species κ.," The modified Euler-Patankar scheme reads: where $p_{ik}$ is the production matrix containing the rates producing species $i$ from species $k$, while $d_{ik}$ is the destruction matrix containing the rates that transform species $i$ into species $k$."
 That implies pg=dj; and all diagonal coefficients are zero., That implies $p_{ik} = d_{ki}$ and all diagonal coefficients are zero.
 We obtain: The other components vanish., We obtain: The other components vanish.
 If we define Eq. (B9)), If we define Eq. \ref{eModpatankar}) )
 can be further performed to This ts an easy solvable system of linear equations., can be further performed to This is an easy solvable system of linear equations.
 Since the 2x block matrix for hydrogen and 3x matrix for helium are not coupled. this system can be solved for them independently.," Since the $2 \times 2$ block matrix for hydrogen and $3 \times 3$ matrix for helium are not coupled, this system can be solved for them independently."
 In the IE as well as in the non-IE case the update of the pressure is performed using original Patankar-Trick (2):: The algorithm for the thermal conduction ts carried out similar to the hydrodynamie scheme., In the IE as well as in the non-IE case the update of the pressure is performed using original Patankar-Trick \citep{Patankar80}: The algorithm for the thermal conduction is carried out similar to the hydrodynamic scheme.
 After the thermal fluxes between the cells are computed. those fluxes are used to update the energy density and modified entropy density.," After the thermal fluxes between the cells are computed, those fluxes are used to update the energy density and modified entropy density."
 Like the hydrodynamic scheme this is done in an unsplit fashion., Like the hydrodynamic scheme this is done in an unsplit fashion.
" In order to compute the thermal flux. first the temperature gradient is computed: where ἐν""+1/2 denotes the positionm of7 the interfacen7 and i, and ἐν+I the cell left and right of the interface."," In order to compute the thermal flux, first the temperature gradient is computed: where $i_x+1/2$ denotes the position of the interface and $i_x$ and $i_x+1$ the cell left and right of the interface."
" Then. the conduction coefficient « and the fraction of mean free path and temperature 2,/7 are computed in cell ἐν and ἐν+1 and then extrapolated to the interface 7,+1/2 by simple averaging."," Then, the conduction coefficient $\kappa$ and the fraction of mean free path and temperature $\lambda_e / T$ are computed in cell $i_x$ and $i_x+1$ and then extrapolated to the interface $i_x+1/2$ by simple averaging."
 The heat flux is then, The heat flux is then
"resolved at their mass resolution (2.8x 10°Mo), prohibiting a self-consistent treatment of subhaloes.","resolved at their mass resolution $2.8\times 10^8
\Ms$ ), prohibiting a self-consistent treatment of subhaloes."
" Consequently, they only include haloes above 1.6x10'°Mo in the conditional mass function."," Consequently, they only include haloes above $1.6\times10^{10}\Ms$ in the conditional mass function."
 ? also apply their analysis to an analytic Sheth-Tormen mass function obtained by ?.., \citeauthor{Moster-2009} also apply their analysis to an analytic Sheth-Tormen mass function obtained by \cite{Vale-2006}.
" In this non- model, a halo mass of 10!°Mo corresponds to a stellar mass of 1.9x10°Mo, more similar to the value of ?.."," In this non-parametric model, a halo mass of $10^{10}\Ms$ corresponds to a stellar mass of $1.9\times10^6\Ms$, more similar to the value of \cite{Guo-2010}."
" In Figure 4,, we plot the stellar mass — halo mass relation of ? for haloes between 10° and 10!7Mo."," In Figure \ref{M/L-Qi}, we plot the stellar mass – halo mass relation of \cite{Guo-2010} for haloes between $10^{9}$ and $10^{12}\Ms$."
 The solid section of the line shows the relation in the region directly derived from SDSS DR-7 data where the uncertainties are very small., The solid section of the line shows the relation in the region directly derived from SDSS DR-7 data where the uncertainties are very small.
" The dashed section denotes an extrapolation to stellar masses below 10°°Mo, assuming faint-end slope of a=—1.15 for the stellar mass function,a as reported by ?.."," The dashed section denotes an extrapolation to stellar masses below $10^{8.3}\Ms$ assuming a faint-end slope of $\alpha = -1.15$ for the stellar mass function, as reported by \cite{Li-2009}."
" Studies of the faint-end of the stellar mass function are either limited to nearby regions or galaxy clusters, or require corrections for incompleteness and, in the case of photometric redshifts, background subtraction, which introduce considerable uncertainties (e.g.?).."," Studies of the faint-end of the stellar mass function are either limited to nearby regions or galaxy clusters, or require corrections for incompleteness and, in the case of photometric redshifts, background subtraction, which introduce considerable uncertainties \citep[e.g.][]{Christlein-2009}."
" As a result, different values for oin the range of —1.1 to —1.6 are found in the recent literature (e.g.????).."," As a result, different values for $\alpha$in the range of $-1.1$ to $-1.6$ are found in the recent literature \citep[e.g.][]{Trentham-2005, Blanton-2005, Carrasco-2006,
 Baldry-2008}."
" The dark grey area in Figure 4 shows the effect of a steepening of the faint-end slope up to a=—1.58, the value reported by ?.."," The dark grey area in Figure \ref{M/L-Qi} shows the effect of a steepening of the faint-end slope up to $\alpha = -1.58$, the value reported by \cite{Baldry-2008}."
" While this has a strong effect on the lowest mass haloes, we note that it cannot account for the discrepancy we find in haloes of 10!°Mo."," While this has a strong effect on the lowest mass haloes, we note that it cannot account for the discrepancy we find in haloes of $10^{10} \Ms$."
" In order to fit the constraints of SDSS DR-7, the maximal dispersion at fixed halo mass is 0.2 dex in M,, indicated by the light-grey area."," In order to fit the constraints of SDSS DR-7, the maximal dispersion at fixed halo mass is 0.2 dex in $_\star$, indicated by the light-grey area."
" We overplot the results of our six simulations as red squares and add other z=0 predictions from the studies listed in Table 1,, correcting all halo masses for baryonic effects, as described below."," We overplot the results of our six simulations as red squares and add other $z=0$ predictions from the studies listed in Table \ref{table:other}, correcting all halo masses for baryonic effects, as described below."
 It is apparent that all these hydrodynamical simulations overproduce stellar mass for their respective halo mass by at least an order of magnitude., It is apparent that all these hydrodynamical simulations overproduce stellar mass for their respective halo mass by at least an order of magnitude.
" In Table 3,, we compare the properties of our six simulations to the abundance matching predictions."," In Table \ref{table:compare}, we compare the properties of our six simulations to the abundance matching predictions."
" We note that, due to the outflow of baryons, the total mass of our six haloes is almost a factor of 1—Q,/Qm smaller than the masses of the corresponding haloes from the pure dark matter simulation."," We note that, due to the outflow of baryons, the total mass of our six haloes is almost a factor of $1-\Omega_b/\Omega_m$ smaller than the masses of the corresponding haloes from the pure dark matter simulation."
 This effect is expected at such low star formation efficiency., This effect is expected at such low star formation efficiency.
" For consistency with ?,, we therefore use the (higher) peak masses of the pure dark matter simulations in deriving the stellar mass predicted for each of our haloes by the abundance matching argument."," For consistency with \cite{Guo-2010}, we therefore use the (higher) peak masses of the pure dark matter simulations in deriving the stellar mass predicted for each of our haloes by the abundance matching argument."
" For all galaxies listed in Table 1 whose peak halo mass cannot be defined or is not given, we increase the halo mass in Figure by 22/Qm~2096, the maximally expected correction."," For all galaxies listed in Table \ref{table:other} whose peak halo mass cannot be defined or is not given, we increase the halo mass in Figure \ref{M/L-Qi} by $\Omega_b/\Omega_m\sim20\%$, the maximally expected correction."
" Comparing the results of our simulations to the predictions, we find that the hydrodynamical simulations overproduce stellar mass by a median factor of ~ 50."," Comparing the results of our simulations to the predictions, we find that the hydrodynamical simulations overproduce stellar mass by a median factor of $\sim 50$ ."
" Alternatively, abundance matching predicts that galaxies of 10°°Mo, the median stellar mass produced in our hydrodynamical simulations, should reside in haloes with typical masses of ~4.5x10!°Mo, rather than 10'°Mo."," Alternatively, abundance matching predicts that galaxies of $10^{7.9}\Ms$, the median stellar mass produced in our hydrodynamical simulations, should reside in haloes with typical masses of $\sim 4.5\times10^{10}\Ms$, rather than $10^{10}\Ms$."
" If 10!?M, haloes really hosted galaxies with M,=10?M, a ACDM universe would overpredict their abundance by a factor of ~4."," If $10^{10}\Ms$ haloes really hosted galaxies with $M_\star=10^{7.9}\Ms$, a $\Lambda$ CDM universe would overpredict their abundance by a factor of $\sim 4$."
 This discrepancy is too large to be attributed solely to incompleteness in the observed stellar mass function., This discrepancy is too large to be attributed solely to incompleteness in the observed stellar mass function.
 ? have used the stellar mass — surface brightness relation of SDSS galaxies in order to estimate the completeness at the faint end., \cite{Baldry-2008} have used the stellar mass – surface brightness relation of SDSS galaxies in order to estimate the completeness at the faint end.
" Based on this analysis, ? estimate the completeness at 105?Mg to be well above 70%."," Based on this analysis, \cite{Li-2009}
 estimate the completeness at $10^{8.3}\Ms$ to be well above $70\%$."
" Following ?,, the uncertainty in the number of 10?M galaxies is much smaller than the discrepancy we report."," Following \citeauthor{Baldry-2008}, the uncertainty in the number of $10^{7.9}\Ms$ galaxies is much smaller than the discrepancy we report."
" The difference is also unlikely to be attributable to numerical errors in our hydrodynamical simulations, or to the specific parametrisation of star formation and feedbackin our model."," The difference is also unlikely to be attributable to numerical errors in our hydrodynamical simulations, or to the specific parametrisation of star formation and feedbackin our model."
" From Table 1,, it is clear that all other current hydrodynamical models,while succeeding in reproducing many of the observed features of individual"," From Table \ref{table:other}, , it is clear that all other current hydrodynamical models,while succeeding in reproducing many of the observed features of individual"
"High-z studies (as far as z2.4 ) have found a significant number of massive. passively evolving galaxies (stellar mass M..>I0""M, ) with relatively small effective radii Ες<2kpe (see.amongothers.Trujilloetal.2006;Cimatti2008;etal. 2009).. sometimes named galaxies (SDGs).","High-z studies (as far as $z\sim2.4$ ) have found a significant number of massive, passively evolving galaxies (stellar mass $\sm>10^{10}\rm{M_{\odot}}$ ) with relatively small effective radii $\re<2\rm{kpc}$ \citep[see, among
others,][]{trujillo06,cimatti08,vandokkum08,vanderwel09,saracco09}, sometimes named galaxies (SDGs)."
 The general claim by various authors is that local galaxies are three to six times larger in size when compared to high-z ones. at the same stellar mass.," The general claim by various authors is that local galaxies are three to six times larger in size when compared to high-z ones, at the same stellar mass."
 In addition. Trujilloetal.(2009) found a complete absence of massive. old and extremely compact galaxies in the local universe.," In addition, \citet{trujillo09} found a complete absence of massive, old and extremely compact galaxies in the local universe."
" However. Valentinuzzietal.(2010) (hereafter V10) have shown that of local cluster members in the WINGS sample with M..>3«10'M, and Xs;23\10°M..kpe have the same characteristies of the high-z SDGs reported in the literature by various authors."," However, \citet{valentinuzzi10} (hereafter V10) have shown that of local cluster members in the WINGS sample with $\sm>3\per10^{10}\msol$ and $\Sigma_{50}\geq3\per10^{9}\msol kpc^{-2}$ have the same characteristics of the high-z SDGs reported in the literature by various authors."
 In the same paper. the authors found that selecting galaxies with old stellar populations is equivalent to selecting the smaller ones. for a given stellar mass.," In the same paper, the authors found that selecting galaxies with old stellar populations is equivalent to selecting the smaller ones, for a given stellar mass."
 Since a large number of galaxies have stopped forming stars at relatively low redshift ἐς« 1.4). and these tend to be the largest. it is not valid to compare high-z passive galaxies with all low-z passive ones.," Since a large number of galaxies have stopped forming stars at relatively low redshift $z<1.4$ ), and these tend to be the largest, it is not valid to compare high-z passive galaxies with all low-z passive ones."
 To avoid selection effects when making comparisons with passive galaxies at high redshift. one needs to select locally those galaxies which at the cosmic time the high-z data correspond to.," To avoid selection effects when making comparisons with passive galaxies at high redshift, one needs to select locally those galaxies which at the cosmic time the high-z data correspond to."
 More recently. Tayloretal.(2009). revisited the search of SDGs in SDSS-DR7 and found a relatively small but significant number of SDGs.," More recently, \citet{taylor09} revisited the search of SDGs in SDSS-DR7 and found a relatively small but significant number of SDGs."
 Following the same criterion used in VIO. they find a fraction of SDGs.," Following the same criterion used in V10, they find a fraction of SDGs."
 The issue is much debated., The issue is much debated.
 Mancinietal.(2010). have analyzed a sample of 12 galaxies at 0.5<<<1.9 in the Cosmos field. finding masses and sizes compatible with the local SDSS ones.," \citet{mancini09} have analyzed a sample of 12 galaxies at $0.5<z<1.9$ in the Cosmos field, finding masses and sizes compatible with the local SDSS ones."
 Furthermore. by using a set of simulated early-type galaxies. they have shown that the low signal-to-noise of high-z images can cause measured effective-radii to be lower than the intrinsic. values.," Furthermore, by using a set of simulated early-type galaxies, they have shown that the low signal-to-noise of high-z images can cause measured effective-radii to be lower than the intrinsic values."
 In a recent paper vanDokkumetal.(2010) select galaxies with a constant number density at different cosmic times.," In a recent paper \citet{vandokkum10}
 select galaxies with a constant number density at different cosmic times."
 They use all galaxies instead of only passive ones. and find that galaxies have grown in size by a factor of from z—2 to z—-0.," They use all galaxies instead of only passive ones, and find that galaxies have grown in size by a factor of 4 from $z\sim2$ to $z\sim0$."
 Even more 4recently. while Szomoruetal.(2010) confirm the extreme compactness of a z21.9 galaxy with the HST-WFC3. Saraccoetal.(2010) show that the comoving number density of compact ETGs over the volume of about I0Mpe? sampled by the GOODS area between 0.9«z1.92 is compatible even with the local lower limits given in VIO.," Even more recently, while \citet{szomoru10} confirm the extreme compactness of a $z=1.9$ galaxy with the HST-WFC3, \citet{saracco10} show that the comoving number density of compact ETGs over the volume of about $4.4\per10^5\rm{Mpc}^3$ sampled by the GOODS area between $0.9<\rm{z}< 1.92$ is compatible even with the local lower limits given in V10."
 In this Letter we present the results of a search for SDGs in the ESO Distant Clusters Survey (EDISCS)) at z—0.7. and we report the comparison of the mass-size relation (MSR) with the same relation in WINGS clusters at z~0.," In this Letter we present the results of a search for SDGs in the ESO Distant Clusters Survey ) at $z\sim0.7$, and we report the comparison of the mass-size relation (MSR) with the same relation in WINGS clusters at $z\sim0$."
 We further discuss selection effects which may introduce a spurious size evolutionwith redshift if not properly taken into account., We further discuss selection effects which may introduce a spurious size evolutionwith redshift if not properly taken into account.
 The high-z cluster sample is extracted from EDisCS.. a multiwavelength photometric and spectroscopicsurvey of galaxies in 20 fields containing galaxy clusters at 0.4< (Whiteetal. 2005)...," The high-z cluster sample is extracted from , a multiwavelength photometric and spectroscopicsurvey of galaxies in 20 fields containing galaxy clusters at $0.4<z<1$ \citep[][]{white05}. ."
" We will use a sub-sample of 8which have HST-ACS images for high- size Measurements (Desaietal. 2007).. and cluster central velocity dispersions (0,44,2400km s!"," We will use a sub-sample of 8which have HST-ACS images for high-precision size measurements \citep[][]{desai07}, , and cluster central velocity dispersions $\sigma_{clus}\geq400\rm{km\;s^{-1}}$ ,"
In (his mass-traces-light analvsis. (he CI? parameter changes by a [factor of 3.10 (depending upon the fit used) between (he inner and outer regions of the M33 disk.,"In this mass-traces-light analysis, the $CP$ parameter changes by a factor of 3–10 (depending upon the fit used) between the inner and outer regions of the M33 disk."
 In this illustrative example the CP) behavior appears inconsistent with the MOND scenario., In this illustrative example the $CP(r)$ behavior appears inconsistent with the MOND scenario.
 The sense of the discrepancy. wilh CP? values less than one. corresponds to ji.>pep. so Chat matter appears to be overaccelerating in the radial direction more than in the vertical direction.," The sense of the discrepancy, with $CP$ values less than one, corresponds to $\mu_z>\mu_r$, so that matter appears to be overaccelerating in the radial direction more than in the vertical direction."
 The exponential scale length of the \133 disk emission depends upon the passband used {ο measure the surlace brightness. ranging from 1.56 kpe in the Ix band to 2.5 kpe in the V band.," The exponential scale length of the M33 disk emission depends upon the passband used to measure the surface brightness, ranging from 1.56 kpc in the K band to 2.5 kpc in the V band."
 Stepping back from the light-traces-mass approach. is interesting to explore what combinations of fy and 2) would produce a CP(r) closest to unity.," Stepping back from the light-traces-mass approach, is interesting to explore what combinations of $R_0$ and $z_0$ would produce a $CP(r)$ closest to unity."
 Allowing both Ay ancl τη as free parameters. with no constraints and with no assumption about (he galaxys niass-to-light ratio. the values that best mateh CP?=1 are Ry=5.4 kpc and 24=0.035 kpe.," Allowing both $R_0$ and $z_0$ as free parameters, with no constraints and with no assumption about the galaxy's mass-to-light ratio, the values that best match $CP=1$ are $R_0=5.4$ kpc and $z_0=0.035$ kpc."
 This corresponds (o a remarkably Chin disk. with a verlical scale heieht ol only 35 pe.," This corresponds to a remarkably thin disk, with a vertical scale height of only 35 pc."
 The CP(+) profile from this more general fit is shown in Figure 2., The $CP(r)$ profile from this more general fit is shown in Figure 2.
 This provides a better fit to the kinematic observations. but. CP still varies bv over a [actor of two across the [ace ol M33.," This provides a better fit to the kinematic observations, but $CP$ still varies by over a factor of two across the face of M33."
 Also. the value of 2)//2)=0.006 is over an order of magnitude less than typical aspect ratios.," Also, the value of $z_0/R_0=0.006$ is over an order of magnitude less than typical aspect ratios."
 Although we can achieve improved MOND-inspired fits to the kinematic data. these models imply strong racial aid vertical eradients in (he galaxys mass-to-light ratio.," Although we can achieve improved MOND-inspired fits to the kinematic data, these models imply strong radial and vertical gradients in the galaxy's mass-to-light ratio."
 This is al variance with the elegant what-vou-see-is-all-t here-isMOND scenario., This is at variance with the elegant what-you-see-is-all-there-is MOND scenario.
 Our objective is to propose a general techiiieque for testing the sell-consistency of MOND. using the existing M33 data as an illustrative example.," Our objective is to propose a general technique for testing the self-consistency of MOND, using the existing M33 data as an illustrative example."
 The vertical aud circular motions of a galaxy can be jointly used for Chis test., The vertical and circular motions of a galaxy can be jointly used for this test.
 Potential weaknesses in (he argument presented above include i) the assertion that the vertical scale height of galaxies is racius-independent. ii) modeling the galaxy. with the form shown in equation (1). and iii) the implicit assertion that either objects overaccelerate. or Chey dont.," Potential weaknesses in the argument presented above include i) the assertion that the vertical scale height of galaxies is radius-independent, ii) modeling the galaxy with the form shown in equation (1), and iii) the implicit assertion that either objects overaccelerate, or they don't."
 The first issue can be addressed with better observations and more statistics. and the second by a more comprehensive treatinent of the svslems kinematics.," The first issue can be addressed with better observations and more statistics, and the second by a more comprehensive treatment of the system's kinematics."
"The Yale code (Demarque&Percy1964;1992) uses as an outer boundary condition the empirically derived fit of KrishnaSwamy(1966) to the T'—7 relation for the Sun, € Eridani, and Gmb 1830.","The Yale code \citep{demarque,gdkp92} uses as an outer boundary condition the empirically derived fit of \cite{ks66} to the $T-\tau$ relation for the Sun, $\epsilon$ Eridani, and Gmb 1830."
" Empirical fits have the flaw that they are suspect if extrapolated; these stars are on the main sequence, and of G and K spectral type (G2V, K2V, and G8Vp, respectively)."," Empirical fits have the flaw that they are suspect if extrapolated; these stars are on the main sequence, and of G and K spectral type (G2V, K2V, and G8Vp, respectively)."
" Gmb 1830 is a halo star of 0.60M with a metalicity of about 0.1 of solar (AllendePrieto,etal.2000),, while ε Eridani is a solar metalicity star of about 0.85Mo."," Gmb 1830 is a halo star of $0.64\rm M_\odot$ with a metalicity of about 0.1 of solar \citep{apetal00}, while $\epsilon$ Eridani is a solar metalicity star of about $0.85\rm M_\odot$."
" If applied to stars of the same stage of evolution and the same abundance, such empirical boundary condidtions are at their best."," If applied to stars of the same stage of evolution and the same abundance, such empirical boundary condidtions are at their best."
 Unfortunately the “calibration” approach may hide mistakes in the assumed physics., Unfortunately the “calibration” approach may hide mistakes in the assumed physics.
" The Garching code (Schlatt]1996) was modified (Schlattl,Weiss&Ludwig1997) to use synthetic atmospheres fitted to the interior solution at optical depth (r— 20)."," The Garching code \citep{schlattl}
 was modified \citep{swl97} to use synthetic atmospheres fitted to the interior solution at optical depth $\tau = 20$ )."
" In addition a spatially varying mixing length was employed to reproduce the pressure- stratification calculated by 2D- models (Freytag,Ludwig,& 1996)..", In addition a spatially varying mixing length was employed to reproduce the pressure-temperature stratification calculated by 2D-hydrodynamic models \citep{fls96}. .
 T'his involved the interpolation, This involved the interpolation
belore il enters the gas subshock.,before it enters the gas subshock.
" S0 we use the subscripts “O°. ""I. and 72 to denote the conditions [ar upstream. immediate upstream and downstream of shock. respectively."," So we use the subscripts “0"", “1"", and “2"" to denote the conditions far upstream, immediate upstream and downstream of shock, respectively."
 Ol course. in the (est-particle limit. the distinction between [ar and immediate upstream quantities disappears. e.g.. py=f».," Of course, in the test-particle limit, the distinction between far and immediate upstream quantities disappears, e.g., $\rho_0=\rho_1$."
 In the limit of large AJ (0224) and large M4 (020). the maximum energv of CR protons can be approximated bv The CR proton spectrum limited by the shock agec» is expected to have a cutoff at around eDuas) (see Section 3.3 lor further discussion).," In the limit of large $M$ $\sigma \approx 4$ ) and large $M_A$ $\delta \approx 0$ ), the maximum energy of CR protons can be approximated by The CR proton spectrum limited by the shock age is expected to have a cutoff at around $\sim p_{\rm max}(t)$ (see Section 3.3 for further discussion)."
 As noted in Introduction. it seems natural to assume that ICMs and cluster outskirts contain pre-existing CRs.," As noted in Introduction, it seems natural to assume that ICMs and cluster outskirts contain pre-existing CRs."
 But their nature is not well constrained. except that P.S0. the pressure of CR protons is less that ~10% of the gas thermal pressure (e.g..Abdoet 2010).," But their nature is not well constrained, except that $P_c \la 0.1 P_g$, the pressure of CR protons is less that $\sim 10$ of the gas thermal pressure \citep[e.g.,][]{abdo10,ddcb10}."
. With pre-existing CRs ofspectrum fo(p) upstream of shock. the steady-state. test-particle solution of Equation (1)) for the downstream CR distribution can be written as where q is the test-particle power-law slope given in Equation (2)) (Drury.1983).," With pre-existing CRs ofspectrum $f_0(p)$ upstream of shock, the steady-state, test-particle solution of Equation \ref{diffcon}) ) for the downstream CR distribution can be written as where $q$ is the test-particle power-law slope given in Equation \ref{qtp}) ) \citep{dru83}."
. Here. Pinj Is Lhe lowest momentum boundary above which particles can cross the shock. the injection momentunm (see the next subsection).," Here, $p_{\rm inj}$ is the lowest momentum boundary above which particles can cross the shock, the injection momentum (see the next subsection)."
 Dv this delinition of pij. the CR distribution unction. fp=0 and fo=0 lor p<pi.," By this definition of $p_{\rm inj}$, the CR distribution function, $f_0=0$ and $f_2=0$ for $p<p_{\rm inj}$."
 The first term in the right-hand-side of Equation (6)) represents the re-accelerated population of pre-existing CRs. while the second term represents the population of CRs freshly injected at the shock and will be discussed in the rext subsection.," The first term in the right-hand-side of Equation \ref{drury}) ) represents the re-accelerated population of pre-existing CRs, while the second term represents the population of CRs freshly injected at the shock and will be discussed in the next subsection."
 We adopt a power-law form. fap)=fyc:G/pij). with the slope s=4— 5. as the nodel spectrum lor pre-existing CR protons.," We adopt a power-law form, $f_0(p)=f_{\rm pre}\cdot (p/p_{\rm inj})^{-s}$, with the slope $s = 4 - 5$ , as the model spectrum for pre-existing CR protons."
 If pre-existing CRs were generated at previous shocks. the slope of s=4—5 is achieved for M>V5 with 9=0 (see Equation (2))).," If pre-existing CRs were generated at previous shocks, the slope of $s = 4 - 5$ is achieved for $M \geq \sqrt{5}$ with $\delta = 0$ (see Equation \ref{qtp}) ))."
 On the other hand. if (hey are mainly the outcome of turbulent acceleration. the slope should be close los~4 (see.e.g..Chandran 2005)..," On the other hand, if they are mainly the outcome of turbulent acceleration, the slope should be close to$s \sim 4$ \citep[see, e.g.,][]{chan05}. ."
 Then. the spectrum of re-accelerated CRs is," Then, the spectrum of re-accelerated CRs is"
"flux ος.70.3TeV)~44-10I""phem7s! (Grindlavetal.1997).. what made Centaurus A the very first (although not confirmed) detected extragalactic source of the VILE radiation.","flux $S(\varepsilon_{\gamma} \geq 0.3 \, {\rm TeV}) \sim 4.4 \cdot
 10^{-11} \, {\rm ph \, cm^{-2} \, s^{-1}}$ \citep{gri75}, what made Centaurus A the very first (although not confirmed) detected extragalactic source of the VHE radiation."
 Recent upper limit suggests that this emission can be variable on a timescale of vears. in analogy to the low- and high-states of activity known from the TeV blazar observations ," Recent upper limit suggests that this emission can be variable on a timescale of years, in analogy to the low- and high-states of activity known from the TeV blazar observations \citep[but see also][for the X-ray
 variability of the large scale jet emission in M 87]{har97,har03}."
Existence of a hidden BL Lae core in the Centaurus A nucleus. as expected in a framework of unification scheme. was wiclely discussed over the last decade (Baileyetal.al. 2000).," Existence of a hidden BL Lac core in the Centaurus A nucleus, as expected in a framework of unification scheme, was widely discussed over the last decade \citep{bai86,mor91,haw93,pac96,ste98,cap00}."
. Most. recently. Chiabergeetal.(2001) reconstructed broad-band spectrum of Centaurus A nucleus. [rom radio to 5-rav. [requencies. and found spectacular similarities to the characteristic double-peaked blazar spectral energy distribution.," Most recently, \citet{chi01}
 reconstructed broad-band spectrum of Centaurus A nucleus, from radio to $\gamma$ -ray frequencies, and found spectacular similarities to the characteristic double-peaked blazar spectral energy distribution."
 The svuchrotron component of (his radiation was found to peak al far infra-red energy. range. Verte~107— Hz. with the observed Iuminosity ο...104101 ere/s. The Compton break energv was placed near ~01. MeV. with the observed. power comparable io (he svnchrotron one.," The synchrotron component of this radiation was found to peak at far infra-red energy range, $\nu_{bl, \, br} \sim 10^{12} - 10^{13}$ Hz, with the observed luminosity $[\nu L_{\nu}]_{bl, \, br} \sim 10^{41} - 10^{42}$ erg/s. The inverse-Compton break energy was placed near $\sim 0.1$ MeV, with the observed power comparable to the synchrotron one."
 Chiabergeetal. fitted the SSC! model to the multiwavelength Centaurus A nucleus emission. and found that all (except one) intrinsic parameters are similar to those of the low-Iuminous blazar sources.," \citeauthor{chi01} fitted the SSC model to the multiwavelength Centaurus A nucleus emission, and found that all (except one) intrinsic parameters are similar to those of the low-luminous blazar sources."
 The only difference. as compared to the‘typical’ BL Lac broad-band spectrum. was a small value of the required Doppler factor. dy1.6.," The only difference, as compared to the`typical' BL Lac broad-band spectrum, was a small value of the required Doppler factor, $\delta_{bl} \sim 1.6$."
 Chiabergeetal. interpreted their results as (hie evidence for the jet radial velocity structure al pc-scales. consisting of a fast central spine surrounded by a slower boundary laver (seealsoChiabergeetal.2000).," \citeauthor{chi01} interpreted their results as the evidence for the jet radial velocity structure at pc-scales, consisting of a fast central spine surrounded by a slower boundary layer \citep[see
 also][]{chi00}."
. Assiuming that the physical properties (i.e. electron enerev distribution. magnetic field intensity. etc) are the same in both jet components. the observed multiwavelength spectrum of the Centaurus A nucleus can then be regarded as a representation of a (vpical low-Iuminous blazar emission. but originating within the slower jet boundary laver and (therefore less beamed as compared to the ‘classical’ BL Lacs.," Assuming that the physical properties (i.e. electron energy distribution, magnetic field intensity, etc) are the same in both jet components, the observed multiwavelength spectrum of the Centaurus A nucleus can then be regarded as a representation of a typical low-luminous blazar emission, but originating within the slower jet boundary layer and therefore less beamed as compared to the `classical' BL Lacs."
" It is consistent with the jet inclination ~70"".", It is consistent with the jet inclination $\sim 70^0$.
" Most probably. Centaurus Aobserved at small angles to the jet axis would be therefore classified as LBL. with the observed luminosity LOY—10"" ere/s and with the observed break frequency ~LOM—1011 Hz."," Most probably, Centaurus Aobserved at small angles to the jet axis would be therefore classified as LBL, with the observed luminosity $\sim 10^{45} - 10^{46}$ erg/s and with the observed break frequency $\sim 10^{13} - 10^{14}$ Hz."
 Note. that in such a casethe Centaurus A nucleus is not expected to radiate at the VIIE range 2001).," Note, that in such a casethe Centaurus A nucleus is not expected to radiate at the VHE range \citep[cf.][]{bai01}."
". For the estimates below. we assume [|z/L,]y,ο~0.3. vy4400.01. Το10 and ὃμ~1.6."," For the estimates below, we assume $[\nu L_{\nu}]_{bl, \, 42} \sim 0.3$, $\nu_{bl, \,
 14} \sim 0.01$, $\Gamma_{bl} \sim 10$ and $\delta_{bl} \sim 1.6$."
 In order to diseuss (he 5-rav emission of the large scale jet in Centaurus A. let us consider its brightest part in N-ravs and at radio frequencies. the ensemble of the knots Al - At.," In order to discuss the $\gamma$ -ray emission of the large scale jet in Centaurus A, let us consider its brightest part in X-rays and at radio frequencies, the ensemble of the knots A1 - A4."
 The N-ray observations (Ixraftοἱal.2002) suggest Chat for this region A4~ 0.8. ppi0 Od B.1 O06 ay~1.5 and Ly~4-10 erg/s. The synchrotron break frequency is unknown. as there is no observation of the jet svnchrotron emission at LR/optical frequencies.," The X-ray observations \citep{kra02} suggest that for this region $R_{-1} \sim 0.8$ , $r_1 \sim 0.4$ , $B_{-4} \sim 0.6$ , $\alpha_X \sim 1.5$ and $L_X \sim 4 \cdot 10^{39}$ erg/s. The synchrotron break frequency is unknown, as there is no observation of the jet synchrotron emission at IR/optical frequencies."
 (Crawford&Kraft1956)..., \citep{1956ApJ...123...44C}.
 ~107—M. e.g.]|andreferencestherein|2008cIno.book.....B..," $\sim 10^{-5} - 10^{-4} \msun$ \\citep[see, e.g.][and references therein]{2008clno.book.....B}."
 (Warner2008) x107—109 (Truran&Livio1986).. (Gaposchkin1957).. 1992;DellaValle&Livio1998).. (Starrfield2005). (Anupama2008)..," \citep{2008clno.conf....1W} $\times\;10^{3}-10^{6}$ \citep{1986ApJ...308..721T}. \citep{1957gano.book.....G}, \citep{1992AJ....104..725W}. \citep{1990LNP...369...34D,1992A&A...266..232D,1998ApJ...506..818D}. \citep{1985ApJ...291..136S,2005ApJ...623..398Y}. \citep{2008ASPC..401...31A}."
 Recurrent nova systems have been sub-divided into three general sub-classes (Anupama2008) via a combination of the properties of the eruption and via the properties of the progenitor system whilst at quiescence: (hereafter the RS Oph-class) are observed to contain red giant secondaries and hence have much longer orbital periods (~ a year). and typically smaller outburst amplitudes than CNe.," Recurrent nova systems have been sub-divided into three general sub-classes \citep{2008ASPC..401...31A} via a combination of the properties of the eruption and via the properties of the progenitor system whilst at quiescence: (hereafter the RS Oph-class) are observed to contain red giant secondaries and hence have much longer orbital periods $\sim$ a year), and typically smaller outburst amplitudes than CNe."
 Their outbursts exhibit rapid declines from maximum. with large ejection velocities (34000kms! y.," Their outbursts exhibit rapid declines from maximum, with large ejection velocities $\ge 4000\;\mathrm{km\;s}^{-1}$ )."
 These systems show evidence of an interaction between the ejecta and material from the pre-existing red giant wind., These systems show evidence of an interaction between the ejecta and material from the pre-existing red giant wind.
 The ejected mass from these systems 1s typically two orders of magnitude less than that observed from CN systems (seepaperswithinEvansetal.2008)..syste, The ejected mass from these systems is typically two orders of magnitude less than that observed from CN systems \citep[see papers within][]{2008ASPC..401.....E}.
ms are observed to contain. evolved main sequence or sub-giant secondaries. with orbital periods closer to those of CNe (hours up to of order a day).," are observed to contain evolved main sequence or sub-giant secondaries, with orbital periods closer to those of CNe (hours up to of order a day)."
 They again exhibit rapid declines. being amongst the fastest declining novae observed. with very high ejection velocities (up to 10000km s7!).," They again exhibit rapid declines, being amongst the fastest declining novae observed, with very high ejection velocities (up to $10000\;\mathrm{km\;s}^{-1}$ )."
 Their post-outburst spectra resemble those of the He/N sub-class of CNe (Williams1992).., Their post-outburst spectra resemble those of the He/N sub-class of CNe \citep{1992AJ....104..725W}.
 These systems eject a similar mass of material as RS Oph systems., These systems eject a similar mass of material as RS Oph systems.
 Thesystems (also CI Aql and IM Nor) are much more akin to CNe., The (also CI Aql and IM Nor) are much more akin to CNe.
 They exhibit short orbital. periods. and spectroscopically resemble Fe II CNe (Williams1992).., They exhibit short orbital periods and spectroscopically resemble Fe II CNe \citep{1992AJ....104..725W}.
 Their optical decline rate classifies them as moderately fast or slow novae., Their optical decline rate classifies them as moderately fast or slow novae.
 The ejected mass in these systems Is consistent with the range observed in CNe (Μα107 Μ.Ο., The ejected mass in these systems is consistent with the range observed in CNe $\mathrm{M}_{\mathrm{ej}}\sim 10^{-5}\msun$ ).
 These systems are generally only distinguishable from CNe due to their shorter recurrence times. not by the properties of the progenitor system or the outburst.," These systems are generally only distinguishable from CNe due to their shorter recurrence times, not by the properties of the progenitor system or the outburst."
 The short inter-outburst time observed in RNe is likely due to some combination of a higher mass WD and an aecretion rate greater than the typical for CN systems., The short inter-outburst time observed in RNe is likely due to some combination of a higher mass WD and an accretion rate greater than the typical for CN systems.
 Indeed. both RS Oph and U Sco (amongst others from these classes) appear to have WDs close to the Chandrasekhar limit.," Indeed, both RS Oph and U Sco (amongst others from these classes) appear to have WDs close to the Chandrasekhar limit."
 A number of authors (seee.g.Hachisuetal.2007;Osborne2011: have indicated that the WD mass may be increasing over time and these systems have been proposed as a Type lasupernova (SN) progenitor candidate (seee.g.Ko- 2008)..," A number of authors \cite[see e.g.][]{2007ApJ...659L.153H,2011ApJ...727..124O,SumnerConf} have indicated that the WD mass may be increasing over time and these systems have been proposed as a TypeIa supernova (SN) progenitor candidate \citep[see e.g.][]{2008ASPC..401..150K}."
However.Mason(2011) reported that U Sco could contain an O-Ne WD. rather than a C-O WD. and hence may," .However,\citet{2011arXiv1107.4013M} reported that U Sco could contain an O-Ne WD, rather than a C-O WD, and hence may"
between z;2O.4 and z;=1.4.,between $z_i=0.4$ and $z_i=1.4$.
 Thus we include by default only tomographic measures for every fifth bin /. but all j>i. in the S/N. The absolute value of the S/N depends of course on how many power spectra are incorporated. but we are only interested 1n the ratio of S/N for the nulled datasets over the set of original power spectra.," Thus we include by default only tomographic measures for every fifth bin $i$ , but all $j>i$, in the S/N. The absolute value of the S/N depends of course on how many power spectra are incorporated, but we are only interested in the ratio of S/N for the nulled datasets over the set of original power spectra."
 Note that for every z; one can make use of N.—i power spectra Οἱ(0)., Note that for every $z_i$ one can make use of $N_z-i$ power spectra $Q^{(ij)}(\ell)$.
 The very same number of modes is available in the standard nulling approach although one mode is discarded to perform the actual nulling (for details2009)., The very same number of modes is available in the standard nulling approach although one mode is discarded to perform the actual nulling <cit.>[for details.
 Transformed auto-correlation power spectra with /=j do not enter the S/N. but by construction the P'MOL) do contribute to all Οἱ) via the ATI). Whereas in standard nulling auto-correlations are completely discarded.," Transformed auto-correlation power spectra with $i=j$ do not enter the S/N, but by construction the $P^{(ii)}(\ell)$ do contribute to all $Q^{(ij)}(\ell)$ via the $\Pi_Q^{(i)}(\ell)$, whereas in standard nulling auto-correlations are completely discarded."
 However. due to the dense redshift binning. we expect the amount of independent information contained in auto-correlation power spectra to be small.," However, due to the dense redshift binning, we expect the amount of independent information contained in auto-correlation power spectra to be small."
 We have given the resulting. ratios. of the S/N for the nulled data set over the S/N for the original one in Table5., We have given the resulting ratios of the S/N for the nulled data set over the S/N for the original one in Table.
 The considerable loss of information can be confirmed. the S/N for both nulling methods yielding less than 20% of the original S/N. We find that these numbers are very robust against changes in the number and values of redshift bins / included in the S/N by varying the size of steps in bin numbers / and the range of redshifts considered.," The considerable loss of information can be confirmed, the S/N for both nulling methods yielding less than $20\,\%$ of the original S/N. We find that these numbers are very robust against changes in the number and values of redshift bins $i$ included in the S/N by varying the size of steps in bin numbers $i$ and the range of redshifts considered."
 It is quite remarkable that the ratios for both nulling methods are very similar., It is quite remarkable that the ratios for both nulling methods are very similar.
 The slightly bigger number for the nulling as devised in this work could be related to the inclusion of auto-correlation power spectra. but is not very significant anyway.," The slightly bigger number for the nulling as devised in this work could be related to the inclusion of auto-correlation power spectra, but is not very significant anyway."
 In the standard nulling case the information loss 1s causec by discarding part of the signal. namely one mode per bi i whereas the variant suggested here features à signal that deviates by at most about 20% from the untransformed one.," In the standard nulling case the information loss is caused by discarding part of the signal, namely one mode per bin $i$ whereas the variant suggested here features a signal that deviates by at most about $20\,\%$ from the untransformed one."
 I the latter case the loss ts caused by an increase in the covariance due to the subtraction of signals in (33)., In the latter case the loss is caused by an increase in the covariance due to the subtraction of signals in ).
 We conjecture at this point that the agreement in the amount of informatior lost. 1 spite of the largely different mechanisms of the two methods. hints at a fundamental limit of how far GI and GG signals ca be distinguished by only relying on the redshift dependence of the two contributions.," We conjecture at this point that the agreement in the amount of information lost, in spite of the largely different mechanisms of the two methods, hints at a fundamental limit of how far GI and GG signals can be distinguished by only relying on the redshift dependence of the two contributions."
 In this paper we presented à method which extracts shear-ellipticity correlations (the GI signal) from a tomographie cosmic-shear data set., In this paper we presented a method which extracts shear-ellipticity correlations (the GI signal) from a tomographic cosmic-shear data set.
 The approach relies neither on models of intrinsic alignments nor on knowledge of the cosmological parameters that characterise the cosmic shear (GG) signal. making only use of the typical and well-understood redshift dependencies of both the GI and GG term.," The approach relies neither on models of intrinsic alignments nor on knowledge of the cosmological parameters that characterise the cosmic shear (GG) signal, making only use of the typical and well-understood redshift dependencies of both the GI and GG term."
" We derived constraints which a linear transformation of second-order cosmic shear measures has to fulfil in order to boost the GI signal and simultaneously suppress the lensing contribution,", We derived constraints which a linear transformation of second-order cosmic shear measures has to fulfil in order to boost the GI signal and simultaneously suppress the lensing contribution.
 We studied in depth a particular parametrisation of the weights entering this transformation and analysed the performance of the resulting GI boosting technique for three representative survey models., We studied in depth a particular parametrisation of the weights entering this transformation and analysed the performance of the resulting GI boosting technique for three representative survey models.
 Applying the GI boosting to future all-sky cosmic shear surveys. it should be possible to isolate the GI signal with subdominant biases due to a residual GG term. and with constraints that are comparable to current results from indirect measurements of shear-ellipticity correlations2010).," Applying the GI boosting to future all-sky cosmic shear surveys, it should be possible to isolate the GI signal with subdominant biases due to a residual GG term, and with constraints that are comparable to current results from indirect measurements of shear-ellipticity correlations."
" If one restricts the analysis to galaxies with photometric redshift information of good quality. i.e. a redshift scatter of not more than c(l+5) with cy,=0.03. one can achieve | o-errors on the GI signal amplitude A in the parametrisation of (27) of better than 0.2when varying only the amplitude. and a marginalised error of approximately 0.7 when fitting an additional redshift dependence."," If one restricts the analysis to galaxies with photometric redshift information of good quality, i.e. a redshift scatter of not more than $\sigma_{\rm ph}(1+z)$ with $\sigma_{\rm ph}=0.03$, one can achieve $1\,\sigma$ -errors on the GI signal amplitude $A$ in the parametrisation of ) of better than 0.2when varying only the amplitude, and a marginalised error of approximately 0.7 when fitting an additional redshift dependence."
A. , 
New clues ave emerging that long GRB are associated with supernovae (Galamaοἱal.Bloometal.1999:Kulkarni2000:Reichart 2001).,"New clues are emerging that long GRB are associated with supernovae \citep{gal98,blo99,kul00,rei01}."
. This is illustrated most recently bv oplical emissions lines in the late-time light-ecurve of the HETE-II burst GRB 030329 (Stanekοἱal.2003).. which are remarkably similar to those observed in GRDB930425/8N1993bw (Galamaetal.1993).," This is illustrated most recently by optical emissions lines in the late-time light-curve of the HETE-II burst GRB 030329 \citep{sta03}, which are remarkably similar to those observed in GRB980425/SN1998bw \citep{gal98}."
.. A GRB-supernova assocation provides important support for the collapsar model of GIDs. representing a violent death of evolved massive stars 1998).," A GRB-supernova assocation provides important support for the collapsar model of GRBs, representing a violent death of evolved massive stars \citep{woo93,pac98}."
. The short lifespan of tens of Myrs of massive stars implies that GRBs take place in star-orming regions (Pacevuski1998:Fruchterοἱal.1999).. and hence more broadly points towards an association to molecular clouds.," The short lifespan of tens of Myrs of massive stars implies that GRBs take place in star-forming regions \citep{pac98,fru99}, and hence more broadly points towards an association to molecular clouds."
 The event rate of GRBs per unit cosmological volume is hereby. expected (o be correlated (to the cosmic stau-Iormation rate (e.g.. Blain&Natarajan(2000):Bergeretal.(2002):ChouclhurySrianand (2002))).," The event rate of GRBs per unit cosmological volume is hereby expected to be correlated to the cosmic star-formation rate (e.g., \citet{bla00,ber03,cho02}) )."
 Because observations bv past and current experiments (see Table I) are f[lux-Iimited. the observed CIRD-event rate is strongly biased towards events at lower redshilts.," Because observations by past and current experiments (see Table I) are flux-limited, the observed GRB-event rate is strongly biased towards events at lower redshifts."
are constrained using recent observations of disc fractions in nearby clusters (Mamajek 2009).,are constrained using recent observations of disc fractions in nearby clusters (Mamajek 2009).
 We require a viscosity coefficient of approximately a=2.5x107? to match the observational constraints., We require a viscosity coefficient of approximately $\alpha = 2.5\times10^{-3}$ to match the observational constraints.
 OOur main conclusions can be briefly summarised as follows:, Our main conclusions can be briefly summarised as follows:
source average count rate). were then computed according to the method described in Vaughanetal.(1994).,"source average count rate), were then computed according to the method described in \citet{vaughan94}."
. In OBSI. upper limits at à level of30%..20%.. and were inferred in the ss. ss. and ss period range. respectively.," In OBS1, upper limits at a level of, and were inferred in the s, s, and s period range, respectively."
 In OBS2. we derived upper limits at a level of20%%..30%.. and for periods 1n the range 0.03-20 s. 20-50 s. and s. respectively.," In OBS2, we derived upper limits at a level of, and for periods in the range 0.03-20 s, 20-50 s, and 0.02-0.03 s, respectively."
 oobserved oon 2007 May 29. with the Epic-PN camera operating in full frame.," observed on 2007 May 29, with the Epic-PN camera operating in full frame."
 To identify the high background time intervals we followed the same technique described for (see Sect., To identify the high background time intervals we followed the same technique described for (see Sect.
 4.2. and Fig. 1))., \ref{sec:igrresults} and Fig. \ref{fig:backselection}) ).
 We extracted the Epic-PN lightcurve for the full field of view (FOV) in the 10-12 keV energy band. and set a threshold on the full-FOV count rate in this energy band of 0.45 cts/s. The total effective exposure time after the good time interval selection for wwas 26 ks.," We extracted the Epic-PN lightcurve for the full field of view (FOV) in the 10-12 keV energy band, and set a threshold on the full-FOV count rate in this energy band of 0.45 cts/s. The total effective exposure time after the good time interval selection for was 26 ks."
 From the lighteurve of the observation (Fig. 100).," From the lightcurve of the observation (Fig. \ref{fig:igrb}) ),"
 it is apparent that the variability in the quiescent state of this source was rather similar to that of Un particular. the lower panel of Fig.," it is apparent that the variability in the quiescent state of this source was rather similar to that of In particular, the lower panel of Fig."
 10. shows that the hardness ratio of increased with the source count rate., \ref{fig:igrb} shows that the hardness ratio of increased with the source count rate.
 Figure 11. shows the hardness-intensity diagram of oobtained with the same technique described m Sect. 4.1.., Figure \ref{fig:igrbhardness} shows the hardness-intensity diagram of obtained with the same technique described in Sect. \ref{sec:xteresults}.
 In this case. the scatter of the points is somehow less evident than in the case of παπά a linear fit to the data required a slope of 1.9-40.2.," In this case, the scatter of the points is somehow less evident than in the case of and a linear fit to the data required a slope of $\pm$ 0.2."
 To investigate the origin of the variability in the hardness ratio of we extracted three different spectra during the time intervals of the observation in which the source count rate was 70.2. 0.1-0.2. and «0.1 (hereafter spectra A. B. C).," To investigate the origin of the variability in the hardness ratio of we extracted three different spectra during the time intervals of the observation in which the source count rate was $>$ 0.2, 0.1-0.2, and $<$ 0.1 (hereafter spectra A, B, C)."
 A fit to these spectra with a simple absorbed BB or PL model provided unacceptable results am .5-5.0. d.o.£.228-44).," A fit to these spectra with a simple absorbed BB or PL model provided unacceptable results $\chi^2_{\rm red}$$\gtrsim$ 1.5-5.0, d.o.f.=28-44)."
" A CUTOFFPL model with a fixed £44,211 keV (see Sect. 1))", A CUTOFFPL model with a fixed $E_{\rm cut}$ =11 keV (see Sect. \ref{sec:intro}) )
 provided tighter fits to the three spectra (AZ 1.2-1.6. d.o.f=28-44).," provided tighter fits to the three spectra $\chi^2_{\rm red}$$\sim$ 1.2-1.6, d.o.f=28-44)."
 However. the - was still significantly larger than |. the value of the absorption column density measured from the spectra B and C was unreasonably low (compatible with zero). and some structures were apparent in the residuals from the fits at energies «2 keV (see Fig. 12).," However, the $\chi^2_{\rm red}$ was still significantly larger than 1, the value of the absorption column density measured from the spectra B and C was unreasonably low (compatible with zero), and some structures were apparent in the residuals from the fits at energies $<$ 2 keV (see Fig. \ref{fig:igrbcountrate}) )."
 A CUTOFFPL model with a free to vary ων improved only the fit to spectrum A (X2. /d.o.f21.03/39). whereas the results of the," A CUTOFFPL model with a free to vary $E_{\rm cut}$ improved only the fit to spectrum A $\chi^2_{\rm red}$ /d.o.f=1.03/39), whereas the results of the"
"resonant for a particle of a given cnere AB, (07mee ky. where hy,= 22r). one can refer to a qualitative discussion of energetic particle diffusion presented by Drury (1983)","resonant for a particle of a given energy, $\delta B_r$ $\delta B_r^2 / 8 \pi \approx F(k_r) 
\cdot k_r$ , where $k_r = 2 \pi / r_g$ ), one can refer to a qualitative discussion of energetic particle diffusion presented by Drury (1983)."
" With his sealing 5jx(0D,/D) and 5&1x(0D,./ D). the amplitude for resonance waves can. be evaluated as 6B,/BzRE."," With his scaling $\kappa_\| \propto (\delta B_r / B)^{-2}$ and $\kappa_\perp \propto (\delta B_r / B)^2$ , the amplitude for resonance waves can be evaluated as $\delta B_r / B \approx \aleph^{1/4}$."
" The respective values o£8—81/5 were derived in auxiliary simulations involving the spatially uniform. background magnetic field with the induction of 1.510.* ""T and particles with energies equal to the initial energy fy=2 MeV. ""Trajectories of a large number of particles were followed with the imposed. scattering process involving the momentum angular scattering. uniform. within a cone of half opening angle equal to 11 and with the cone axis directed. along the original momentum vector."," The respective values of $\aleph \equiv \kappa_\perp / \kappa_\|$ were derived in auxiliary simulations involving the spatially uniform background magnetic field with the induction of $1.5 \cdot 10^{-3}$ T and particles with energies equal to the initial energy $E_0 = 2$ MeV. Trajectories of a large number of particles were followed with the imposed scattering process involving the momentum angular scattering, uniform within a cone of half opening angle equal to $11^\circ$ and with the cone axis directed along the original momentum vector."
 The only parameter varving between the simulations was the time interval between successive scattering events. Af.," The only parameter varying between the simulations was the time interval between successive scattering events, $\Delta t$."
 The resulting cillusion cocllicicnts were derived. from growing particle dispersions along the background field (64) and along two orthogona axes perpendicular to the backeround field (= along the 1- or 2-axis)., The resulting diffusion coefficients were derived from growing particle dispersions along the background field $\kappa_\|$ ) and along two orthogonal axes perpendicular to the background field $\equiv$ along the $1$ - or $2$ -axis).
 The results of such computations are presented in Pig., The results of such computations are presented in Fig.
 2., 2.
 Presentation of two derived values ofa.fr) and 82/58 allows one to evaluate the accuracy of these computations., Presentation of two derived values of $\kappa_1 / \kappa_\|$ and $\kappa_2 / \kappa_\|$ allows one to evaluate the accuracy of these computations.
" The values used in the paper are fits to the asvmptotic QUox) value of 8=0.5(58,|we)fay."," The values used in the paper are fits to the asymptotic $(T \to \infty)$ value of $\aleph = 0.5 \, 
(\kappa_1 + \kappa_2) / \kappa_\|$."
 For a sequence of scattering tines M — 10P. 10. 7. 10. Land 10.7 we derive the respective values of N = 1 7.6:10.7. 6-107. anc 6-10.," For a sequence of scattering times $\Delta t$ = $10^{-6}$, $10^{-5}$ , $10^{-4}$ and $10^{-3}$ we derived the respective values of $\aleph$ = $1.2 \cdot 10^{-2}$, $6 \cdot 10^{-3}$, $6 \cdot 
10^{-5}$, and $6 \cdot 10^{-7}$."
 The results derived without applying any scattering are indicated by N=0., The results derived without applying any scattering are indicated by $\aleph = 0$.
 In order to provide qualitative evaluations of turbulence ellects in the volume of reconnecting magnetic Ποια. but considering it only as a factor introducing rancom motion component to particle trajectories. we performed simulations of energetic proton spectra with a varving amount of turbulence (= scattering).," In order to provide qualitative evaluations of turbulence effects in the volume of reconnecting magnetic field, but considering it only as a factor introducing random motion component to particle trajectories, we performed simulations of energetic proton spectra with a varying amount of turbulence $\equiv$ scattering)."
 As explained. above. this approach assumes the existence of short wave magnetic Ποιά perturbations to be present in the limited volume — the black rectangle in Fig.," As explained above, this approach assumes the existence of short wave magnetic field perturbations to be present in the limited volume – the black rectangle in Fig."
 1... near the central neutral point. but we do not consider the influence of the turbulence on the reconnection process.," 1 – near the central neutral point, but we do not consider the influence of the turbulence on the reconnection process."
 Thus it is a complementary approach to that using MIID moelling of the turbulent reconnection including wave perturbations from a narrow wave vector range. as discussed in section 1.," Thus it is a complementary approach to that using MHD modelling of the turbulent reconnection including wave perturbations from a narrow wave vector range, as discussed in section 1."
" We performed simulations of particle evolution starting ab the same ""injection energv. Ly=2 MeV. avoiding consideration of the real injection process at. much. lower energies (cf."," We performed simulations of particle evolution starting at the same `injection' energy $E_0 = 2$ MeV, avoiding consideration of the real injection process at much lower energies (cf."
 Miller et al., Miller et al.
 1997)., 1997).
 For each set. of. particles we derived. the spectrum. of particles escaping from the reconnection volume. as illustrated in Fig.," For each set of particles we derived the spectrum of particles escaping from the reconnection volume, as illustrated in Fig."
 3., 3.
 In the non-»erturbed: model (CS=0. curve A) protons can increase heir initial energy. by approximately 70%.," In the non-perturbed model $\aleph = 0$, curve A) protons can increase their initial energy by approximately $70$."
 One should note that the injected energetic particles can gain as well as oose energy., One should note that the injected energetic particles can gain as well as loose energy.
 Introducing trajectory perturbations results in substantial modification of the acceleration process (curves D. €. D. Iz in Fig.," Introducing trajectory perturbations results in substantial modification of the acceleration process (curves B, C, D, E in Fig."
 3)., 3).
 The spectrum energy. eut-olf shifts to ugher values and the spectrum becomes harder when the amount of scattering (turbulence amplitude) is increased., The spectrum energy cut-off shifts to higher values and the spectrum becomes harder when the amount of scattering (`turbulence amplitude') is increased.
 In our simulations the resulting Hat spectra extend. up to 50 MeV. for models with strong turbulence (Model D and 19). and a steeper part of the spectrum is recorded. at energies above LOO MeV. This behaviour results from. the act that the dilfusive component introduced in to particle rajectorics by the scattering enables some particles to stay in the reconnection region much longer and dilfuse back close to the null point from outside.," In our simulations the resulting flat spectra extend up to $50$ MeV for models with strong turbulence (Model D and E), and a steeper part of the spectrum is recorded at energies above $100$ MeV. This behaviour results from the fact that the diffusive component introduced in to particle trajectories by the scattering enables some particles to stay in the reconnection region much longer and diffuse back close to the null point from outside."
 As illustrated. this can lave a pronounced influence on the acceleration process by substantially increasing the particlemean energy eain aud »ovidine much larecr energies of individual particles.," As illustrated, this can have a pronounced influence on the acceleration process by substantially increasing the particlemean energy gain and providing much larger energies of individual particles."
 There, There
dark matter oudegree scales.,dark matter on scales.
" As with the weak leusiug of faint galaxies. dmaee distortions manifest on simall augular scales aro used to reconstruct the mass on a much larger scale,"," As with the weak lensing of faint galaxies, image distortions manifest on small angular scales are used to reconstruct the mass on a much larger scale."
 Mapping the dark matter distribution therefore requires high resolution. high signal-to-noise maps of the CMB auisotropics themselves.," Mapping the dark matter distribution therefore requires high resolution, high signal-to-noise maps of the CMB anisotropies themselves."
" Conversely, though a wide Held of at least several degrees on the side is required to nap the full extent of the structures expected. the statistic essentially high pass filters the input. CMB maps."," Conversely, though a wide field of at least several degrees on the side is required to map the full extent of the structures expected, the statistic essentially high pass filters the input CMB maps."
 A true nap that retaius correlations across these scales is not lCCOSSUIPY., A true map that retains correlations across these scales is not necessary.
 To see how au observing strategy might be optimized or napping the dark matter. let us consider the trade-offs between sky coverage. mstruneutal noise aud beau.," To see how an observing strategy might be optimized for mapping the dark matter, let us consider the trade-offs between sky coverage, instrumental noise and beam."
 Because this statistic isa quadratic function of the temperature Huctuation data. the balance differs from the usual case.," Because this statistic is a quadratic function of the temperature fluctuation data, the balance differs from the usual case."
 Iu Fig. L.," In Fig. \ref{fig:sensitivity},"
 we show the total signal-to-noise in the measurement of the deflection power spectrum: (πιο in quadrature over L) of an experiment as a function of these parameters., we show the total signal-to-noise in the measurement of the deflection power spectrum (summed in quadrature over $L$ ) of an experiment as a function of these parameters.
 We consider separately the case of noise variance from the Gaussian random primary auisotropies and detector noise alone aud combined with tle sample variance of the lensing Ποια»., We consider separately the case of noise variance from the Gaussian random primary anisotropies and detector noise alone and combined with the sample variance of the lensing fields.
⋅ When- the former: exceeds the latter. a high. sigual-.TUE ot; : structures ∖↴⋅⊳1c ↴sults," When the former exceeds the latter, a high signal-to-noise map of the structures results."
",Be≱∖⋈ (othisijo de; at oCoorax. statistic.map thethi characteristic sigual-to-noise CaliforIs Goldberg. features is nich. higher (see Fig. 1))."," Because this is an integrated statistic, the characteristic signal-to-noise for large-scale features is much higher (see Fig. \ref{fig:defl}) )."
 Ile. arethe steep Increaseinerease 1ni he signasienal ο...EN llu.Πας detector noise is reduced with the shallow increase asKaiser. sky. coverage 2 oQUgló2, Compare the steep increase in the signal-to-noise as the detector noise is reduced with the shallow increase with sky coverage of $f_{\rm sky}^{1/2}$.
" Upτ eU?maili 1/2 ©2↽10(1(10 Μοτο,(-Ixiox. x.observing tineof isf. best spent goiug deep10 rather Seljak. wide."," Up until $w^{-1/2} \sim 10$ $(10^{-6}$ -arcmin), observing time is best spent going deep rather than wide."
 Bevoud. this point.. the. iutriusie noise. variance. Reljak.teli by⋅ the primary CAIBj anisotropiesκ⋅ themselves.Tyson. Zaldarriaga. to dominate and saturate the signal-to-noise.," Beyond this point, the intrinsic noise variance provided by the primary CMB anisotropies themselves begins to dominate and saturate the signal-to-noise."
 If the Zaldarriaga. eoal is to produce a high signal-to-nolse nap of structures. heu gomme down tow17?1: (10. arcuin) can achieve substantially improved maps of the finer scale structures iu the map.," If the goal is to produce a high signal-to-noise map of structures, then going down to $w^{-1/2} \sim 1$ $(10^{-6}$ -arcmin) can achieve substantially improved maps of the finer scale structures in the map."
 Another crucial factor is the beam size., Another crucial factor is the beam size.
 To resolve the structures thatbest trace the lensing. a beam of o«B5 is required aud it is not uutilo~1'2 that the eains saturate.," To resolve the structures thatbest trace the lensing, a beam of $\sigma < 5'$ is required and it is not until $\sigma \sim 1'-2'$ that the gains saturate."
 If foregrounds are not removed from the map through their spatial coherence and/or frequency dependence then this balance cau shift to larecr aneular scales and more skv coverage., If foregrounds are not removed from the map through their spatial coherence and/or frequency dependence then this balance can shift to larger angular scales and more sky coverage.
" For the 1.5’. 10 (10.arcmin) baseline experiment. iuchisiou of Gaussian random noise from the Suuvaev-Zeldovich aud Vishuiac effects iu CT"" imply a relative degradation in sigual-to-noise of ~105€ and ~L4 (for 7=0.1) respectivelv aud so do not require substantial reoptimization."," For the $1.5'$, $10$ $(10^{-6}$ -arcmin) baseline experiment, inclusion of Gaussian random noise from the Sunyaev-Zel'dovich and Vishniac effects in $C_l^{\rm tot}$ imply a relative degradation in signal-to-noise of $\sim 10\%$ and $\sim 1\%$ (for $\tau=0.1$ ) respectively and so do not require substantial reoptimization."
 A high sigual-to-noise map of the dark matter in projection can also be used to pull out tracers of the larec-scale structure of the universe in other maps through cross-correlation., A high signal-to-noise map of the dark matter in projection can also be used to pull out tracers of the large-scale structure of the universe in other maps through cross-correlation.
 Examples include secondary. aulsotropies suc[um as the integrated. Sachs-Wolte aud Suuyyaecv-Zeldovich effects (Goldberg&Sperecl 1999: Seljak&Zaldarriaga 1998: Cooray&Thi 2000)., Examples include secondary anisotropies such as the integrated Sachs-Wolfe and yaev-Zel'dovich effects \cite{GolSpe99} 1999; \cite{SelZal98} 1998; \cite{CooHu00a} 2000).
 Oue cau show that the statistic employed here retains all of the information iu the full bispectin of the secoucdary-lensine-primary correlation and sois the optimal statistic to measure these correlations., One can show that the statistic employed here retains all of the information in the full bispectrum of the secondary-lensing-primary correlation and so is the optimal statistic to measure these correlations.
 ⊺↕↓↸∖∏↕↾↸∖↕⋅↴⇖∏∖∩↧↾∪↕⋅↸∖↸↾∪∐↴∖↴∏⋅⋯↾↾↾↕↓↸∖↸↧⋮↕∏∖⊽↕⊔⋮↕⊺↾↸∖↕⋅↕⊔⋮↕⋟: ⋅ ↕≯∪∐∐⋜↧∐⋅↖⊽↥⋅↸∖≺∣∏∏⋅↸∖⋜↧↴∖↴↕∐↻∏↑∐↸∖↻∪∖∏∖↥⋅↴∖↴↻↸∖↸⊳∏↴∐, The filters used to reconstruct the dark matter map formally require as input the power spectrum of the CMB lensing.
⊔∪↕⋟∏∐∖≼⊲⋀∖∐≩ ≀⇂∣↕⋮↗∠∎∪∣⋏↕↕↸∖∐↴∖↴↕∐∶↴⋁∙⊺∐↸∖↕↸∖∐↴∖↴↸∖≼⊔⊲⋀∖∐≧↻∪↖↖↽↸∖↥⋅↴∖↴↻↸∖↸⊳⊓⋅⋯⊔↖↖⇁↕∐∪↕≯ ≼⊳≺∏∐⋅↴∖↴↸∖↴⋈∖∐∐∖⋜↧↴∖↴↿∐⋅↸∖≼↧↑∪↸∖⊼≺∏∏↴∖↴↕↑↸∖↻↥⋅↸∖↸⊳↕↴∖↴↕∪∐↴, The lensed CMB power spectrum will of course be measured to exquisite precision by CMB satellites and by the input temperature map themselves.
⋝∙↖⇁≼⊲⋀∖∐≧↴∖↴⋜↧↑↸∖∐↕↑↸∖↴∖↴ ⋜⋯≺⊓⋝∙↖↽↑↕∐∖↕↕∏⋯↑↑↸∖∐∏⋉∖↥⋅⋜↧↿∐⋅↸∖∐↓⋜∏≻∐↸∖↕⊔↴∖↴↸∖↕↖⇁↸∖↴∖↴∙⊏∐∏≻↕∪⋅↖↽↕∐∶↴⋁ he lensed οΠΟ power spectrin in the filter or an otherwise slightly incorrect assuiptiou simply degrades the sigual-o-hoise by a correspoudingly siuiall amount but does not introduce spurious structures in the enusenible-averaged recovery., Employing the lensed CMB power spectrum in the filter or an otherwise slightly incorrect assumption simply degrades the signal-to-noise by a correspondingly small amount but does not introduce spurious structures in the ensemble-averaged recovery.
 They appear as a calibration error for tle mass nap., They appear as a calibration error for the mass map.
 Indeed in the context of a parameterized cosmology he unlensed CAB power spectrum may itself be reconstructed Your the observed spectrum., Indeed in the context of a parameterized cosmology the unlensed CMB power spectrum may itself be reconstructed from the observed spectrum.
 For a non-uniform survey econmetrv. with perhaps foreground-contanminated reeious renmnioved. more sophisticated techniques than the Fouricr-ransforiu flteriug scheme enploved here will have to © developed.," For a non-uniform survey geometry, with perhaps foreground-contaminated regions removed, more sophisticated techniques than the Fourier-transform filtering scheme employed here will have to be developed."
 These complications should uot preseut au insumuouutable obstacle to the goal of mapping the dark hatter iu projection at intermediate redshifts., These complications should not present an insurmountable obstacle to the goal of mapping the dark matter in projection at intermediate redshifts.
 Y acknowledge useful conversations with A.R. Cooray and M. Zaldarriaga as well as support your NASA NAG5-10810. DOE OJI aud au Alfred D. Sloan Foundation Fellowship.," I acknowledge useful conversations with A.R. Cooray and M. Zaldarriaga as well as support from NASA NAG5-10840, DOE OJI and an Alfred P. Sloan Foundation Fellowship."
Gamma-Ray Bursts (GRBs) are explosions which release roughly 10°! erg in the form of kinetic energy of highly relativistic material (Frail et al.,Gamma-Ray Bursts (GRBs) are explosions which release roughly $^{51}$ erg in the form of kinetic energy of highly relativistic material (Frail et al.
 2001. Panaitescu Kumar2001011.," 2001, Panaitescu Kumar."
.. Many GRBs appear to be highly non-spherical explosions. as evidenced by a nearly-achromatie break im the light-curve (e.g. Harrison et al.," Many GRBs appear to be highly non-spherical explosions, as evidenced by a nearly-achromatic break in the light-curve (e.g. Harrison et al."
 1999; Stanek et al., 1999; Stanek et al.
 1999)., 1999).
" Highly relativistic jets are ""visible"" when our line of sight is within the jet aperture (0,4,< Oy). otherwise. because of relativistic beaming of photons away from our line-of-sight. the object is too dim."," Highly relativistic jets are “visible” when our line of sight is within the jet aperture $\theta_{\rm obs}<\theta_0$ ), otherwise, because of relativistic beaming of photons away from our line-of-sight, the object is too dim."
 As the jet decelerates. the relativistic beaming becomes less severe and the emission from the jet becomes detectable to observers at larger viewing angles.," As the jet decelerates, the relativistic beaming becomes less severe and the emission from the jet becomes detectable to observers at larger viewing angles."
" In this Letter we study the afterglow light-curves for off-axis locations (0,7 0). focusing on observers lying outside of the initial jet opening angle (0,4,7 09)."," In this Letter we study the afterglow light-curves for off-axis locations $\theta_{\rm obs}>0$ ), focusing on observers lying outside of the initial jet opening angle $\theta_{\rm obs}>\theta_0$ )."
 Granot et al. (, Granot et al. (
"2001) have shown that the light curve seen by an observer located within the initial jet aperture (0,5, 0) is very similar to that for an on-axis observer (η.= 0).",2001) have shown that the light curve seen by an observer located within the initial jet aperture $\theta_{\rm obs}<\theta_0$ ) is very similar to that for an on-axis observer $\theta_{\rm obs}=0$ ).
 Dalal et al. (, Dalal et al. (
2002) and Rossi et al. (,2002) and Rossi et al. (
2002) have presented simple models to calculate the flux in this case.,2002) have presented simple models to calculate the flux in this case.
 We reanalyze these models in $22.1 and consider more realistic models in $22.2 822.3., We reanalyze these models in 2.1 and consider more realistic models in 2.2 2.3.
 Moderski. Sikora and Bulik (2000) have calculated off-axis light-curves with a more In ," Moderski, Sikora and Bulik (2000) have calculated off-axis light-curves with a more complex model, similar to that presented in 2.2."
"$33 we calculate the temporal evolution of the linear polarization for various @,,,.", In 3 we calculate the temporal evolution of the linear polarization for various $\theta_{\rm obs}$.
 In $44 we analyze the prospects of using the detection rate of orphan afterglows to estimate the collimation of GRB jets., In 4 we analyze the prospects of using the detection rate of orphan afterglows to estimate the collimation of GRB jets.
 In 855 we analyze the suggestion of Woosley. Eastman. Schmidt (1999) that a relativistic Jet emanating from the SN explosion and pointing away from us could explain the observations.," In 5 we analyze the suggestion of Woosley, Eastman, Schmidt (1999) that a relativistic jet emanating from the SN explosion and pointing away from us could explain the observations."
 In this section we calculate the afterglow light curves of jetted GRBs. as seen by observers at different viewing angles. Oop. Wat the symmetry axis of the jet.," In this section we calculate the afterglow light curves of jetted GRBs, as seen by observers at different viewing angles, $\theta_{\rm obs}$, w.r.t the symmetry axis of the jet."
 For simplicity. we consider only a jet propagating into a homogeneous medium.," For simplicity, we consider only a jet propagating into a homogeneous medium."
 In order to improve our understanding of the underlying physics and in order to check how general the results are. we explore three different models with an increasing level of complexity.," In order to improve our understanding of the underlying physics and in order to check how general the results are, we explore three different models with an increasing level of complexity."
 We begin with a simple model. where for 4).=0 the light curve follows the results of simple jet models (Rhoads 1999: Sari. Piran Halpern 1999. hereafter R-SPH99). and for Oy.20 the light curves are calculated assuming the emission is from a point source that moves along the jet axis.," We begin with a simple model, where for $\theta_{\rm obs}=0$ the light curve follows the results of simple jet models (Rhoads 1999; Sari, Piran Halpern 1999, hereafter R-SPH99), and for $\theta_{\rm obs}>0$ the light curves are calculated assuming the emission is from a point source that moves along the jet axis."
 The on-axis light curve exhibits a jet break at (R-SPH99): where £5» is the isotropic equivalentenergy in units of 107? erg. y is the ambient density inci° and : is the cosmological redshift of the source.," The on-axis light curve exhibits a jet break at (R-SPH99): where $E_{52}$ is the isotropic equivalentenergy in units of $10^{52}$ erg, $n_0$ is the ambient density in ${\rm cm}^{-3}$ and $z$ is the cosmological redshift of the source."
 Att<fia. Ενθω0) is taken from Sari. Piran and Narayan (1998). while at #>fj4 the temporal scalings of the break frequencies and peak flux change according to R-SPH99.," At $t<t_{\rm jet}$, $F_{\nu}(\theta_{\rm obs}=0)$ is taken from Sari, Piran and Narayan (1998), while at $t>t_{\rm jet}$ the temporal scalings of the break frequencies and peak flux change according to R-SPH99."
" The observed flux density from a point source Is where L'/, and 7 are the spectral luminosity and frequency in the local rest frame of the jet. 4| and d; are the angular and luminosity distances to the source. (LF)H3 is the Lorentz factor of the source and 0 is the angle between the direction of motion of the source and the direction to the observer in the observer frame (in our case 0.= 0)."," The observed flux density from a point source is where $L'_{\nu'}$ and $\nu'$ are the spectral luminosity and frequency in the local rest frame of the jet, $d_{A}$ and $d_{L}$ are the angular and luminosity distances to the source, $\gamma=(1-\beta^2)^{-1/2}$ is the Lorentz factor of the source and $\theta$ is the angle between the direction of motion of the source and the direction to the observer in the observer frame (in our case $\theta=\theta_{\rm obs}$ )."
 Since tUzmdtfdt=vfvυ-ἷ- Jeos0). where f and v are the observed time and frequency. owe obtain that," Since $t/t'\approx dt/dt'=\nu'/\nu=(1+z)\gamma(1-\beta\cos\theta)$ , where $t$ and $\nu$ are the observed time and frequency, we obtain that"
"Fitting two-dimensional Gaussians to the SMA images, leads to flux densities of 16.8+1.5 mJy and 8.52.0 mJy for MM1 and MM14, respectively.","Fitting two-dimensional Gaussians to the SMA images, leads to flux densities of $16.8\pm1.5$ mJy and $8.5\pm2.0$ mJy for MM1 and MM14, respectively."
" The MM14 detection is tentative since, as we shall see below, it could not be reliably identified with any significant counterpart at other wavelengths."," The MM14 detection is tentative since, as we shall see below, it could not be reliably identified with any significant counterpart at other wavelengths."
" The Gaussian fit indicates that both sources are unresolved with a maximum deconvolved FWHM size of 1.8""x1.0"" and 2.0""x0.6"", respectively, consistent with the sizes found for high-redshift SMGs, which are typically unresolved at ~2” resolution (Ionoetal.etal. 2009)."," The Gaussian fit indicates that both sources are unresolved with a maximum deconvolved FWHM size of $1.8\arcsec\times1.0\arcsec$ and $2.0\arcsec\times0.6\arcsec$, respectively, consistent with the sizes found for high-redshift SMGs, which are typically unresolved at $\sim2\arcsec$ resolution \citep{Iono2006,Younger2007, Wang2007,Younger2009}."
. This also yields from the flatness of the real visibility amplitudes as a function of the projected baseline length., This also yields from the flatness of the real visibility amplitudes as a function of the projected baseline length.
" The measured SMA position for MM1 is a(J2000)=1000""15.6125, 5(J2000)=+02°15’49.00”, with a positional error in theGaussian fit of 0.09"", while for MM14 it is a(J2000)=10""00™47.329°, 5(J2000)= --02?10'21.44"", with a positional error in the fit of 0.15”."," The measured SMA position for MM1 is $\alpha(\mathrm{J2000})=10^\mathrm{h}00^\mathrm{m}15.612^\mathrm{s}$, $\delta(\mathrm{J2000})=+02\degr15\arcmin49.00\arcsec$, with a positional error in theGaussian fit of $0.09\arcsec$, while for MM14 it is $\alpha(\mathrm{J2000})=10^\mathrm{h}00^\mathrm{m}47.329^\mathrm{s}$, $\delta(\mathrm{J2000})=+02\degr10\arcmin21.44\arcsec$ , with a positional error in the fit of $0.15\arcsec$."
" This positional accuracy in the fit is consistent with the one expected for the beam and S/N of the observations: 0.09""and 0.2""for MM1 and MM14, respectively."," This positional accuracy in the fit is consistent with the one expected for the beam and S/N of the observations: and for MM1 and MM14, respectively."
" From the comparison of the reference (Browneetal.1998) and measured (this work) positions of the test quasar J1008+063, we find a positional uncertainty of 0.18""."," From the comparison of the reference \citep{Browne1998} and measured (this work) positions of the test quasar $+$ 063, we find a positional uncertainty of $0.18\arcsec$."
" 'This, added in quadrature to the positional error in the Gaussian fit to the MM1 and MM14 images, gives a positional uncertainty of 0.2"" and 0.27"", respectively."," This, added in quadrature to the positional error in the Gaussian fit to the MM1 and MM14 images, gives a positional uncertainty of $0.2\arcsec$ and $0.27\arcsec$, respectively."
MM1. The SMA peak position coincides with the position of a ~3.50 radio peak (Fig. 1))., The SMA peak position coincides with the position of a $\sim3.5\sigma$ radio peak (Fig. \ref{fig:allphot}) ).
" A bright and elongated source with photometric redshift z—1.4 (bertetal.2009) is located at —2.1""north-west from the SMA position.", A bright and elongated source with photometric redshift $z=1.4$ \citep{Ilbert2009} is located at $\sim$ north-west from the SMA position.
" The radio peak lies within 0.3"" from the SMA position, however given the beam of the radio image (~ 2""), we do not discard that part of the emission comes from this bright optical source."," The radio peak lies within $0.3\arcsec$ from the SMA position, however given the beam of the radio image $\sim2\arcsec$ ), we do not discard that part of the emission comes from this bright optical source."
 From Fig., From Fig.
" 2 (left), we identify a very faint K-band source, located at z0.3"" from the SMA position, as the likely counterpart."," \ref{fig:closeup} (left), we identify a very faint $K$ -band source, located at $\approx0.3\arcsec$ from the SMA position, as the likely counterpart."
" The bright optical source strongly contaminates theSpitzer images, making it difficult to reliably measure the faint emission of MM1."," The bright optical source strongly contaminates the images, making it difficult to reliably measure the faint emission of MM1."
 We extracted photometry in the IRAC bands by subtracting this bright source based on the K-band image convolved with the IRAC PSF (Table 1))., We extracted photometry in the IRAC bands by subtracting this bright source based on the K-band image convolved with the IRAC PSF (Table \ref{table:1}) ).
 We do not attempt to extract photometry of this source in the 24 wm images., We do not attempt to extract photometry of this source in the 24 $\mu$ m images.
" No emission is detected at 70 and 160 um. The deep K-band images show two peaks, separated by about0.6"", or a physical scale of ~4.3 kpc at z~8 (Fig. 2))."," No emission is detected at 70 and 160 $\mu$ m. The deep $K$ -band images show two peaks, separated by about, or a physical scale of $\sim4.3$ kpc at $z\sim3$ (Fig. \ref{fig:closeup}) )."
" The fainter peak appears to be the one associated with the submm emission, suggesting a possible double system, similar to the case of the SMG AzTECII (Youngeretal.2009)."," The fainter peak appears to be the one associated with the submm emission, suggesting a possible double system, similar to the case of the SMG AzTEC11 \citep{Younger2009}."
.MM14. The radio maps do not show any peak close to the position of the SMA source down to a 3c level of 30 LJ y., The radio maps do not show any peak close to the position of the SMA source down to a $3\sigma$ level of 30 $\mu$ Jy.
" At ~1.2"" to the north of the SMA position we find a faint optical source that appears diffuse and faint in the K-band (Fig. 1)).", At $\sim1.2\arcsec$ to the north of the SMA position we find a faint optical source that appears diffuse and faint in the $K$ -band (Fig. \ref{fig:allphot}) ).
 This source has a likely photometric redshift of ~3.4 (Mobasheretal.2007)., This source has a likely photometric redshift of $\sim3.4$ \citep{Mobasher2007}.
". From Fig. 1,,"," From Fig. \ref{fig:allphot},"
" the northern optical source appears to be composed by several “clumps” that extend over ~1.5"", or 11 kpc at z~3.5."," the northern optical source appears to be composed by several “clumps” that extend over $\sim1.5\arcsec$, or $\sim11$ kpc at $z\sim3.5$."
" We also find a very faint K-band emission peak (c-3e in the smoothed image), located tto the south of the SMA position (Fig. 2))."," We also find a very faint $K$ -band emission peak $\sim$ $\sigma$ in the smoothed image), located to the south of the SMA position (Fig. \ref{fig:closeup}) )."
" This peak has ~2σ significance in the original K-band image (without smoothing; Fig. 1)),"," This peak has $\sim2\sigma$ significance in the original $K$ -band image (without smoothing; Fig. \ref{fig:allphot}) ),"
 implying the source is spatially extended., implying the source is spatially extended.
" Due to its proximity to the SMA position, it appears to be the most likely counterpart to the submm emission despite its faintness."," Due to its proximity to the SMA position, it appears to be the most likely counterpart to the submm emission despite its faintness."
" Hereafter, we refer to this source as MM14S (south), while for the northern optical source we refer as MM14N. However, since we could not reliably identify any significant multi-wavelength counterpart for this source and given the relatively low significance of the SMA detection, we label this source (MM14S) as a tentative detection."," Hereafter, we refer to this source as MM14S (south), while for the northern optical source we refer as MM14N. However, since we could not reliably identify any significant multi-wavelength counterpart for this source and given the relatively low significance of the SMA detection, we label this source (MM14S) as a tentative detection."
" The spatial configuration between MM14S and MMIAN could resemble a system, where the submm emission comesmerger/interaction from a highly obscured source (MM14S), but could also correspond toan extended galaxy with the submm emission located in an obscured spiral arm."," The spatial configuration between MM14S and MM14N could resemble a merger/interaction system, where the submm emission comes from a highly obscured source (MM14S), but could also correspond toan extended galaxy with the submm emission located in an obscured spiral arm."
" The offset between the MM14N and the submm position (MM14S) is 9 kpc, assuming z~3.5, similar to the case of the high-redshift SMG GN20 (Jonoetal. 2006),, where the submm and the optical peaks are separated by ~0.8”, or ~6 kpc."," The offset between the MM14N and the submm position (MM14S) is $\sim9$ kpc, assuming $z\sim3.5$, similar to the case of the high-redshift SMG GN20 \citep{Iono2006}, , where the submm and the optical peaks are separated by $\sim0.8\arcsec$, or $\sim6$ kpc."
" Based on the local density of sources with z>3, n=0.002 arcsec-?, we find that the probability that a z>3 optical source brighter than MM14N is located by chance within a distance of ffrom the SMA position is only P—0.996, thus supporting a physical association."," Based on the local density of sources with $z>3$, $n=0.002$ $^{-2}$, we find that the probability that a $z>3$ optical source brighter than MM14N is located by chance within a distance of from the SMA position is only $P=0.9\%$, thus supporting a physical association."
" photometry was performed with SExtractor Optical/IR(Bertin&Arnouts1996) in a aaperture, using the K-band images for detection."," Optical/IR photometry was performed with SExtractor \citep{Bertin1996} in a aperture, using the $K$ -band images for detection."
" None of our targets was detected in the Spitzer MIPS bands, and we thus provide 3e upper limits based on their local noise level within one beam."," None of our targets was detected in the MIPS bands, and we thus provide $3\sigma$ upper limits based on their local noise level within one beam."
" The measured flux densities at several wavelengths for MM1, MM14S and MM14N are listed in Table 1.."," The measured flux densities at several wavelengths for MM1, MM14S and MM14N are listed in Table \ref{table:1}. ."
 MMI and MM14S were not detected in the COSMOS catalogs (Capaketal.2007;Ilbert and thus there is no previous estimate for theirredshift.," MM1 and MM14S were not detected in the COSMOS catalogs \citep{Capak2007, Ilbert2009} and thus there is no previous estimate for theirredshift."
2009) Assuming that the correlation between the far-IR and, Assuming that the correlation between the far-IR and
specific predictions about how center ancl satellite galaxies of the same luminosity ciffer: this dillerence is the subject of Section. ??..,specific predictions about how center and satellite galaxies of the same luminosity differ; this difference is the subject of Section \ref{compareM2L}.
 These predictions can also be tested. by studying how stellar and total mass-to-light ratios depend on environment: how the luminosity function. of clusters (alter removing the BCC) depends on cluster richness: and how the amount of intracluster light depends on. cluster richness., These predictions can also be tested by studying how stellar and total mass-to-light ratios depend on environment; how the luminosity function of clusters (after removing the BCG) depends on cluster richness; and how the amount of intracluster light depends on cluster richness.
 The connections between these tests and the halo niodel are discussed in a final section which summarizes our findings., The connections between these tests and the halo model are discussed in a final section which summarizes our findings.
" Fhroughout. we assume a spatially Hat cosmology withQO, 20.3. Ag=1.Qo and ex=0.9. and we write the ILubble constant as Ly=1005 km | |."," Throughout, we assume a spatially flat cosmology with$\Omega_0=0.3$ , $\Lambda_0=1-\Omega_0$ and $\sigma_8=0.9$, and we write the Hubble constant as $H_0=100h$ km $^{-1}$ $^{-1}$."
 An Appenclix presents a few inconsistencies between the halo mocel of Zehavi et al. (, An Appendix presents a few inconsistencies between the halo model of Zehavi et al. (
2005) and the group catalog of Jerlind et al. (,2005) and the group catalog of Berlind et al. (
2006).,2006).
 Ht argues that while these may be due to Zehavi et al., It argues that while these may be due to Zehavi et al.
's assumption that ax=0.9. they are unlikely to invalidate our findings.,"'s assumption that $\sigma_8=0.9$, they are unlikely to invalidate our findings."
 The halo model decomposition provides a prescription for how the ealaxy population in a halo depends. on halo mass., The halo model decomposition provides a prescription for how the galaxy population in a halo depends on halo mass.
 In practice. halo mass is not an observable. so comparison of this prediction with the objects in à eroup catalog is not straightforward.," In practice, halo mass is not an observable, so comparison of this prediction with the objects in a group catalog is not straightforward."
 Llowever. the halo model decomposition can be re-written so that observable cquantities are predicted: these include the number density of groups containing IN galaxies more luminous than some threshold Luminosity. as well as the average Iuminosities of the central ancl satellite galaxies as a function. of NV.," However, the halo model decomposition can be re-written so that observable quantities are predicted: these include the number density of groups containing $N$ galaxies more luminous than some threshold luminosity, as well as the average luminosities of the central and satellite galaxies as a function of $N$."
 Specifically. and where dn(AID)/dÀAL is the halo mass function. (we use the parametrization given by Sheth Tormen 1999). and the distribution pCN|AZ) has mean with Noy drawn from a Poisson distribution (Zehavi et al.," Specifically, and where $dn(M)/dM$ is the halo mass function (we use the parametrization given by Sheth Tormen 1999), and the distribution $p(N|M)$ has mean with $N_{\rm sat}$ drawn from a Poisson distribution (Zehavi et al."
 2005)., 2005).
" ere AZ,CL)zz23Αμ). where μμ denotes the minimum mass required to host a galaxy of luminosity L or greater. and àz1."," Here $M_1(L)\approx 23\,M_{\rm min}(L)$, where $M_{\rm min}$ denotes the minimum mass required to host a galaxy of luminosity $L$ or greater, and $\alpha\approx 1$."
 Phe minimum mass scales with i;-band £ (our r-band is actually the SDSS r filter shifted to z=0.1. sometimes denoted. ULL 77r) as (Skibba et al.," The minimum mass scales with $r$ -band $L$ (our $r$ -band is actually the SDSS $r$ filter shifted to $z=0.1$, sometimes denoted $^{0.1}r$ ) as so (Skibba et al."
" 2006). assuming Al.,=4.76 (Blanton et al."," 2006), assuming $M_{\odot r}=4.76$ (Blanton et al."
 2003)., 2003).
 Note that the luminosity of the central object is predicted to increase linearly. with halo mass when AL107 TAL. but the increase is only logarithmic at larger Ad (also see Tinker et al.," Note that the luminosity of the central object is predicted to increase linearly with halo mass when $M\ll 10^{12}\,h^{-1}M_\odot$ , but the increase is only logarithmic at larger $M$ (also see Tinker et al."
 2005)., 2005).
 This is qualitatively consistent with the findings of Lin Mohr (2004). Yang et al. (," This is qualitatively consistent with the findings of Lin Mohr (2004), Yang et al. ("
2005b) and Cooray (2006).,2005b) and Cooray (2006).
 The mean satellite luminosity is given hy Figure 2 of Skibba et al. (, The mean satellite luminosity is given by Figure 2 of Skibba et al. (
2006) shows that this is a much weaker function of A than is Leon.,2006) shows that this is a much weaker function of $M$ than is $L_{\rm cen}$.
 To see why. notice that if a(L) were independent of L. then the mean satellite Iuminosity would. be independent of Al.," To see why, notice that if $\alpha(L)$ were independent of $L$, then the mean satellite luminosity would be independent of $M$."
 This suggests that the Z-dependenee of à reflects the mass dependence of satellite luminosities: the halo model prediction. tha satellite luminosities depend. only weakly on halo mass is a consequence of the fact that a is only weakly dependen on L., This suggests that the $L$ -dependence of $\alpha$ reflects the mass dependence of satellite luminosities: the halo model prediction that satellite luminosities depend only weakly on halo mass is a consequence of the fact that $\alpha$ is only weakly dependent on $L$ .
" ligure1 compares equation (3)) with the mean satellite luminosity in the M,19.9 eroup catalog of Berlind e al. (", Figure\ref{berlindLsat} compares equation \ref{LsatN}) ) with the mean satellite luminosity in the $M_r\le -19.9$ group catalog of Berlind et al. (
2006).,2006).
 This catalog is drawn from the SDSS Fourth Data Release (DR4. Adelman-MeCarthy ct al.," This catalog is drawn from the SDSS Fourth Data Release (DR4, Adelman-McCarthy et al."
 2006): i, 2006); it
"find clear trends in the detailed radio morphologies with the properties of the stellar populations. it is notable that all but one (36305) of the 7 CSS/GPS sources in our sample have nuclear spectra that are consistent with relatively voung ages for their YSP (js,0.1 Gyr).","find clear trends in the detailed radio morphologies with the properties of the stellar populations, it is notable that all but one (3C305) of the 7 CSS/GPS sources in our sample have nuclear spectra that are consistent with relatively young ages for their YSP $t_{ysp} < 0.1$ Gyr)."
 At optical wavelengths most of the objects in our sample of starburst radio galaxies show morphological peculiaritics compared with quiescent elliptical galaxies: 17 (S0%)) show tidal tails. fans. or highly. asvnimetric/clumpy outer envelopes at. relatively high surface. brightness. levels: 14 (67'4)) show dust. features: 5 (23:43) have double. nuclei or close companions within 15 kpe: and 20 (95%)) show one or more of these optical peculiarities.," At optical wavelengths most of the objects in our sample of starburst radio galaxies show morphological peculiarities compared with quiescent elliptical galaxies: 17 ) show tidal tails, fans, or highly asymmetric/clumpy outer envelopes at relatively high surface brightness levels; 14 ) show dust features; 5 ) have double nuclei or close companions within 15 kpc; and 20 ) show one or more of these optical peculiarities."
 This rate of incidence is much higher than in the general. population of massive elliptical galaxies observed: with similar surface brightness sensitivity (c.g.Malin&Carter1983).., This rate of incidence is much higher than in the general population of massive elliptical galaxies observed with similar surface brightness sensitivity \citep[e.g.][]{malin83b}.
 However. at this relatively erude level of morphological classification. a similar rate of morphological disturbance has recently been found in the general population of powerful 2J. racio ealaxies at intermediate recshilts (including non-starburst objects: Ranios Almeida et al.," However, at this relatively crude level of morphological classification, a similar rate of morphological disturbance has recently been found in the general population of powerful 2Jy radio galaxies at intermediate redshifts (including non-starburst objects: Ramos Almeida et al."
 2010)., 2010).
 The ages of the YSP detected in radio galaxies can provide Κων information about the order-of-events and the triggering of the AGNjet activity., The ages of the YSP detected in radio galaxies can provide key information about the order-of-events and the triggering of the AGN/jet activity.
 Therefore it is interesting to examine the distribution of luminositv-weighted YSP ages determined. from the two component fits to the optical spectra of the full sample of starburst radio. galaxies described. in section 2., Therefore it is interesting to examine the distribution of luminosity-weighted YSP ages determined from the two component fits to the optical spectra of the full sample of starburst radio galaxies described in section 2.
 The top panel of Figure 1. shows the cistribution of luminositv-welghted ages for the nuclear of the starburst radio galaxies., The top panel of Figure 1 shows the distribution of luminosity-weighted ages for the nuclear of the starburst radio galaxies.
 For comparison we also show the YSP age distribution for a complete sample of ULIItCGs with redshifts 2<0.13.— representing the extreme starburst population in the local Universe which have been modelled: using identical techniques by RodriguezZaurinctal.(2009)., For comparison we also show the YSP age distribution for a complete sample of ULIRGs with redshifts $z < 0.13$ – representing the extreme starburst population in the local Universe -- which have been modelled using identical techniques by \citet{zaurin09}.
. Note that. in some apertures of some starburst radio galaxies it proved. possible to mocel the optical spectra with YSP covering a wide range of ages.," Note that, in some apertures of some starburst radio galaxies it proved possible to model the optical spectra with YSP covering a wide range of ages."
 In such cases we have used the mean age over the range of models that provided. good fits., In such cases we have used the mean age over the range of models that provided good fits.
 Since the upper limiting ages in the latter group were often large (C16 vr). this will tend to skew the age distribution to larger ages.," Since the upper limiting ages in the latter group were often large $>$ 1Gyr), this will tend to skew the age distribution to larger ages."
 Several features are apparent [rom Table 2 and Figure, Several features are apparent from Table 2 and Figure 1.
Toexplain theX—polarizat,asymmetry parameters as
Toexplain theX—polarizati,asymmetry parameters as
Toexplain theX—polarizatio,asymmetry parameters as
Toexplain theX—polarization,asymmetry parameters as
Toexplain theX—polarization.,asymmetry parameters as
be dense. compact aud massive enough to be au eccentric disk progenitor. however they are probably too diffuse to account for the laree disk mass in M31 within a few parsecs of its black hole.,"be dense, compact and massive enough to be an eccentric disk progenitor, however they are probably too diffuse to account for the large disk mass in M31 within a few parsecs of its black hole."
 Dense bulges such as found i AL31 itself. aud iu lower huninosity ellipticals galaxies such as M32. are dense aud conrpact enough that they could be similar to progenitors for ΑΟκ and NGC 1186D's ecceutzic disks.," Dense bulges such as found in M31 itself, and in lower luminosity ellipticals galaxies such as M32, are dense and compact enough that they could be similar to progenitors for M31's and NGC 4486B's eccentric disks."
 Nuclear star clusters. such as found in M33. may also be deuse aud conrpact cnough to be progenitors.," Nuclear star clusters, such as found in M33, may also be dense and compact enough to be progenitors."
 Though the mass of AI3B3¢s cluster (a few uulliou A.) is too small to he a progenitor for MDs eccentric disk. the nuclear stellar clusters observed by (Bokerotal.2002) iu late-tvpe ealaxies have half light radii of order Spec. rauge in their estimated nmiasses from LO°105A... aud so could be xoesenitors for eccentric disks following disruption by a nassive black hole.," Though the mass of M33's cluster (a few million $M_\odot$ ) is too small to be a progenitor for M31's eccentric disk, the nuclear stellar clusters observed by \citep{boker2002}
 in late-type galaxies have half light radii of order 5pc, range in their estimated masses from $10^6-10^8 M_\odot$, and so could be progenitors for eccentric disks following disruption by a massive black hole."
 Because of the large mass of bulges and nuclear star clusters at simall radii. it would be easier ) account for the lieh masses of the two known eccentric aeisks by cisvupting them. thin possible by disrupting a elobular cluster.," Because of the large mass of bulges and nuclear star clusters at small radii, it would be easier to account for the high masses of the two known eccentric disks by disrupting them, than possible by disrupting a globular cluster."
 While the massive black hole in ΑΣ welt prevent a progenitor simular to M2 from forming i eccentric disk. unclear clusters such as found iu M33 can lack massive black holes iud so might provide better xoesenitor candidates.," While the massive black hole in M32 might prevent a progenitor similar to M32 from forming an eccentric disk, nuclear clusters such as found in M33 can lack massive black holes and so might provide better progenitor candidates."
 To date the high augular resolution of TST has resolved extremely high stellar densities or order 109A7.pe7 in only the nearest ealaxv bulges., To date the high angular resolution of HST has resolved extremely high stellar densities or order $10^6 M_\odot{\rm pc}^{-3}$ in only the nearest galaxy bulges.
 Until higher augular resolution observatious are available. we wil uot know if such high deusitv galaxy cores are COMMON.," Until higher angular resolution observations are available, we will not know if such high density galaxy cores are common."
 The two galaxies with double nuclei. M31 and NCC 115610. exhibit only moderate color variatious in their nuclei (Laueretal.1996.1998).. a situation that could be a natural consequence of a scenario that involves the mereing of galaxy bulges (proposed here). aud is more difficult to explain with a scenario that forms a vounecr disk iu situ (an iueredieut of the formation scenarios discussed by Baconetal.2001:Toma2002:TagaJacobs&Selawood1999}).," The two galaxies with double nuclei, M31 and NGC 4486B, exhibit only moderate color variations in their nuclei \citep{lauer96,lauer98}, a situation that could be a natural consequence of a scenario that involves the merging of galaxy bulges (proposed here), and is more difficult to explain with a scenario that forms a younger disk in situ (an ingredient of the formation scenarios discussed by \citealt{bacon,touma,taga,jacobs}) )."
 The scenario proposed here is based on a simple tidal disuption aremuent aud can be most quickly tested with N-body simmilations such as have heen carried out bv Merritt&Cruz(2002):Bekla(20002):ITollev-Bockelinanu&Richstone(2000).," The scenario proposed here is based on a simple tidal disruption argument and can be most quickly tested with N-body simulations such as have been carried out by \citet{merritt,bekki,holley}."
.. The simulations of Doekki(20002) established that the disruption of a cluster could. result in the formation of au eccentric disk. aud Merritt&Cruz(2002):EHTollevy-Dockeluiuun&Richstone(2000) have carried out simulations based on realistic galaxy profiles aud with massive black holes.," The simulations of \citet{bekki} established that the disruption of a cluster could result in the formation of an eccentric disk, and \citet{merritt,holley}
 have carried out simulations based on realistic galaxy profiles and with massive black holes."
 Hollev-Bockeliuaun&Rich-stone(2000) established that a spinning nuclear stellar disk can be a remnant., \citet{holley} established that a spinning nuclear stellar disk can be a remnant.
 It remains to be seen whether the merecr of two galaxy cores ean result in the creation of au eccentric stellar disk., It remains to be seen whether the merger of two galaxy cores can result in the creation of an eccentric stellar disk.
 We suspect that the mereer of a primary galaxy containing a very massive black hole with a secondary with accore-type or shallow central surface brielitucss profile. and significantly lower mass black hole. would be most likely to form: an ecceutric disk with N-body simulations.," We suspect that the merger of a primary galaxy containing a very massive black hole with a secondary with a `core-type' or shallow central surface brightness profile, and significantly lower mass black hole, would be most likely to form an eccentric disk with N-body simulations."
 For the core-tvpe galaxies. the break radius and density at this radius provide au equivaleut for the Nine or core radius and ceutral deusity used in Figure 1 and so cau be used to estimate the Bkelibood that the core can disrupt to form an eccentric disk.," For the core-type galaxies, the break radius and density at this radius provide an equivalent for the King or core radius and central density used in Figure 1 and so can be used to estimate the likelihood that the core can disrupt to form an eccentric disk."
 Tf the mereecr of galaxy bulges cau result in tle formation of an eccentric disk. then their formation would be a natural cousequence of licrarchical galaxy. formation. aud can also be used to probe the properties of the parcuts of ealaxies which coutain tho.," If the merger of galaxy bulges can result in the formation of an eccentric disk, then their formation would be a natural consequence of hierarchical galaxy formation, and can also be used to probe the properties of the parents of galaxies which contain them."
 This work was initiated by discussions with Joel Creenu and Bob Cortermuth in the class Astronomy 552 at the University of Rochester during the fall of 2002., This work was initiated by discussions with Joel Green and Rob Gutermuth in the class Astronomy 552 at the University of Rochester during the fall of 2002.
 We thank Chien Peng. Ari Laor and Eric Eisellem for helpful discussions and correspondence.," We thank Chien Peng, Ari Laor and Eric Emsellem for helpful discussions and correspondence."
generally to surveys of isotropic distributions of tracers with uncertain radial positions.,generally to surveys of isotropic distributions of tracers with uncertain radial positions.
" In summary, the presented method is a flexible and numerically efficient addition to the analysis toolbox for large scale galaxy surveys."," In summary, the presented method is a flexible and numerically efficient addition to the analysis toolbox for large scale galaxy surveys."
 It improves accuracy of galaxy redshifts and three dimensional density fields from photometric galaxy redshift surveys and therefore has the potential to add substantial value to their scientific output., It improves accuracy of galaxy redshifts and three dimensional density fields from photometric galaxy redshift surveys and therefore has the potential to add substantial value to their scientific output.
" We thank Francisco S. Kitaura, Torsten A. Enflin and Simon D. White for useful discussions and encouraging us to pursue the project described in this work."," We thank Francisco S. Kitaura, Torsten A. lin and Simon D. White for useful discussions and encouraging us to pursue the project described in this work."
" Further, we thank Cristiano Porciani for providing us with the simulated density field and Nina Roth for providing us with required reading routines and information on how to handle the simulation data."," Further, we thank Cristiano Porciani for providing us with the simulated density field and Nina Roth for providing us with required reading routines and information on how to handle the simulation data."
 Particular thanks go to Rainer Moll and Bjórrn M. Schiffer for useful discussions and, Particular thanks go to Rainer Moll and Björrn M. Schäffer for useful discussions and
shorter orbital periods. reducing the mass below the hydrogen burning limit at the minimum period. after which evolution proceeds slowly back to longer periods (Kolb1993:Kolb&Baratte 1999).,"shorter orbital periods, reducing the mass below the hydrogen burning limit at the minimum period, after which evolution proceeds slowly back to longer periods \citep{Kolb93aa,KolbBaraffe99mn}."
" Whilst a number of CV secondary stars with sub-stellar masses have been identified hear the minimum period (Littlefairetal.2006.2008).. there is yet no unimpeachable detection of the predicted ""post-bounce"" population."," Whilst a number of CV secondary stars with sub-stellar masses have been identified near the minimum period \citep{Littlefair+06sci,Littlefair+08mn}, there is yet no unimpeachable detection of the predicted “post-bounce” population."
 The expected characteristics of post-bounce CVs are a very low accretion rate. a low WD temperature. a very low secondary star mass. and a brown-dwarf secondary spectral type.," The expected characteristics of post-bounce CVs are a very low accretion rate, a low WD temperature, a very low secondary star mass, and a brown-dwarf secondary spectral type."
 The ability to differentiate between pre- and post-bounce CVs increases with longer orbital periods. because of the greater difference in secondary spectral type and mass transfer rate between the two types of systems.," The ability to differentiate between pre- and post-bounce CVs increases with longer orbital periods, because of the greater difference in secondary spectral type and mass transfer rate between the two types of systems."
 Among the SDSS CVs that have white-dwarf dominated optical spectra. JJ0039 exhibits currently the best credentials to be a post-bounce system. as it has an extremely late-type companion star (2L2) and an orbital period clearly beyond the mmin period spike.," Among the SDSS CVs that have white-dwarf dominated optical spectra, J0039 exhibits currently the best credentials to be a post-bounce system, as it has an extremely late-type companion star $\ga$ L2) and an orbital period clearly beyond the min period spike."
 The post-bounce nature of our object can be tested by near-infrared photometry. which would provide a stronger constraint on the spectral type of the companion star.," The post-bounce nature of our object can be tested by near-infrared photometry, which would provide a stronger constraint on the spectral type of the companion star."
 Doppler maps of the Ha. Il aand II eemission lines were computed using the maximum entropy method (Marsh&Horne1988)..," Doppler maps of the $\alpha$, I and I emission lines were computed using the maximum entropy method \citep{MarshHorne88mn}."
 We have overlaid a basic interpretation of JJ0039 onto the Doppler maps reftig:0039:map))., We have overlaid a basic interpretation of J0039 onto the Doppler maps \\ref{fig:0039:map}) ).
 The centre of mass of the system is shown with a cross. and the expected position of the surface of the secondary star m velocity space is shown with an unbroken line.," The centre of mass of the system is shown with a cross, and the expected position of the surface of the secondary star in velocity space is shown with an unbroken line."
 The dots and dotted lines indicate the velocity of the accretion stream and the Keplerian velocity of the disc along the path of the stream., The dots and dotted lines indicate the velocity of the accretion stream and the Keplerian velocity of the disc along the path of the stream.
 The emission characteristics apparent in the trailed spectra of JJ0039 translate into unusual features in the Doppler maps., The emission characteristics apparent in the trailed spectra of J0039 translate into unusual features in the Doppler maps.
 The first of these is the intense inner emission feature. which is clearly visible at Ha but totally absent in the II lines.," The first of these is the intense inner emission feature, which is clearly visible at $\alpha$ but totally absent in the I lines."
 The maps have been rotated to bring this feature onto the line passing through the centres of mass of the two stars. the standard configuration for Doppler maps.," The maps have been rotated to bring this feature onto the line passing through the centres of mass of the two stars, the standard configuration for Doppler maps."
 In the next section we consider and reject the possibility that the inner emission feature arises from the surface of either the WD or secondary star., In the next section we consider and reject the possibility that the inner emission feature arises from the surface of either the WD or secondary star.
 The Doppler maps bring out another extraordinary feature of 0039 which is less obvious in the data than the central S-wave., The Doppler maps bring out another extraordinary feature of J0039 which is less obvious in the data than the central S-wave.
 The outer disc in Ha appears to be extremely non-circular. given that circular motion leads to symmetry around the centre of mass of the WD. located just below the centre of mass of the system.," The outer disc in $\alpha$ appears to be extremely non-circular, given that circular motion leads to symmetry around the centre of mass of the WD, located just below the centre of mass of the system."
 The non-circularity is extreme: the bright region in the lower-right quadrant has a velocity a factor of two lower than that of the upper-left quadrant., The non-circularity is extreme: the bright region in the lower-right quadrant has a velocity a factor of two lower than that of the upper-left quadrant.
 A Keplerian velocity profile (V.ος/7'7) then implies that the outer disc varies in radius by a factor of four!, A Keplerian velocity profile $V \propto r^{-1/2}$ ) then implies that the outer disc varies in radius by a factor of four!
 The behaviour of the II lines ts very different and more symmetric. which suggests that the lower-right quadrant of Ha is in some way unusual.," The behaviour of the I lines is very different and more symmetric, which suggests that the lower-right quadrant of $\alpha$ is in some way unusual."
 We can only interpret this feature in the Doppler maps as evidence of non-Keplerian flow., We can only interpret this feature in the Doppler maps as evidence of non-Keplerian flow.
" The inner emission feature is unusual in normal CVs and reminiscent of the “central spike"" seen in some CCVn (ultracompact binary) stars. where it is ascribed to the WD CCom: Morales-Ruedaetal.2003))."," The inner emission feature is unusual in normal CVs and reminiscent of the “central spike” seen in some CVn (ultracompact binary) stars, where it is ascribed to the WD Com; \citealt{Morales+03aa}) )."
 To investigate this we developed a six-Gaussian model to fit the observed Ha: line profiles., To investigate this we developed a six-Gaussian model to fit the observed $\alpha$ line profiles.
 The two wide emission peaks from the accretion disc are each modelled with one wide and one narrow Gaussian. the central spike with a fifth Gaussian. and the bright spot with a sixth.," The two wide emission peaks from the accretion disc are each modelled with one wide and one narrow Gaussian, the central spike with a fifth Gaussian, and the bright spot with a sixth."
 Each Gaussian was allowed to vary sinusoidally in both radial velocity and brightness on the orbital period., Each Gaussian was allowed to vary sinusoidally in both radial velocity and brightness on the orbital period.
 The fit is plotted in reffig:0039:fitplot.., The fit is plotted in \\ref{fig:0039:fitplot}.
" We find a velocity amplitude of A,=202+3 ffor the central spike. which immediately rules out the CCVn explanation’ as it is too high to be associated with the WD."," We find a velocity amplitude of $K_{\rm spike} = 202 \pm 3$ for the central spike, which immediately rules out the CVn explanation' as it is too high to be associated with the WD."
 On the other hand it is much too low to be from the bright spot region on the accretion disc. which the Doppler maps show to have a velocity of aboutkms7!.," On the other hand it is much too low to be from the bright spot region on the accretion disc, which the Doppler maps show to have a velocity of about."
. The only stable feature of the system left is the secondary star. so we now consider this possibility.," The only stable feature of the system left is the secondary star, so we now consider this possibility."
 It is very unlikely that the central spike originates from the whole surface of the secondary. because Άρης is very low given that the velocity amplitude of the accretion dise emission peaks is Vap=631 !.," It is very unlikely that the central spike originates from the whole surface of the secondary, because $K_{\rm spike}$ is very low given that the velocity amplitude of the accretion disc emission peaks is $V_{\rm AD} = 631$ ."
. Consider the following relations: under the Rapassumption of Keplerian velocities., Consider the following relations: under the assumption of Keplerian velocities.
 The orbital angular frequency. Q. is given by where a and i are the orbital separation and inclination. Mwp and M» are the masses of the component stars. K> is the velocity amplitude of the centre of mass of the secondary star. and Rap is the radius of the outer accretion disc.," The orbital angular frequency, $\Omega$, is given by where $a$ and $i$ are the orbital separation and inclination, $M_{\rm WD}$ and $M_2$ are the masses of the component stars, $K_2$ is the velocity amplitude of the centre of mass of the secondary star, and $R_{\rm AD}$ is the radius of the outer accretion disc."
 From this we find which for the values quoted above gives where g=Ms/Mwp isthe mass ratio and a is. the semimajor axis., From this we find which for the values quoted above gives where $q = {M_2}/{M_{\rm WD}}$ isthe mass ratio and $a$ is the semimajor axis.
 This value can be compared with the minimum, This value can be compared with the minimum
core dynamo hypothesis suggested by |Charbonneau&MacGregor)(2001) because the core must create magnetic fields that are much stronger than equipartition values in order to reach to the surface.,core dynamo hypothesis suggested by \citet{char2001} because the core must create magnetic fields that are much stronger than equipartition values in order to reach to the surface.
 (1999) argues that a principle ingredient of dynamo operation in a star is rapid rotation., \citet{spruit1999} argues that a principle ingredient of dynamo operation in a star is rapid rotation.
 This is certainly available in massive stars., This is certainly available in massive stars.
" While the driving mechanism of magnetic field generation is based on hydrodynamical instabilities in solar type stars, similar instabilities in the radiative stars may be produced by the magnetic fields themselves."," While the driving mechanism of magnetic field generation is based on hydrodynamical instabilities in solar type stars, similar instabilities in the radiative stars may be produced by the magnetic fields themselves."
 Examples are the Parker and Tayler instabilities ∙∙ ," Examples are the Parker and Tayler instabilities \citep{parker1979, tayler1973}."
formulated a dynamo mechanism for a differentially rotating star in which Tayler instability replaces the role of convection in closing the field amplification loop.," \citet{spruit2002}
 formulated a dynamo mechanism for a differentially rotating star in which Tayler instability replaces the role of convection in closing the field amplification loop."
 The azimuthal component of the magnetic field grows until it reaches a critical strength by winding up an initially very small radial component in a non-convective zone., The azimuthal component of the magnetic field grows until it reaches a critical strength by winding up an initially very small radial component in a non-convective zone.
" At that point the Tayler instability operates on a very short time-scale, of the order of Alfvénn crossing time, to regenerate the radial field."," At that point the Tayler instability operates on a very short time-scale, of the order of Alfvénn crossing time, to regenerate the radial field."
 The result is a predominantly toroidal field and a closed dynamo loop., The result is a predominantly toroidal field and a closed dynamo loop.
 Recent numerical simulations by and showed that a stable configuration can be reached within a non-convective star on an Alfvénn time-scale from an arbitrary initial magnetic field., Recent numerical simulations by \citet{brait2004} and \citet{brait2006} showed that a stable configuration can be reached within a non-convective star on an Alfvénn time-scale from an arbitrary initial magnetic field.
 The Spruit-Tayler mechanism is not the only one that operates in non-convective material., The Spruit-Tayler mechanism is not the only one that operates in non-convective material.
 |Balbus&Hawley](1994) have proposed a magneto-rotational instability which works well for accretion discs without convection., \citet{balbus1994} have proposed a magneto-rotational instability which works well for accretion discs without convection.
 reffiggainer shows the internal structure of the gainer during the mass transfer for our system with initial masses of 5 and 3Mo.," \\ref{figgainer} shows the internal structure of the gainer during the mass transfer for our system with initial masses of $5$ and $3\,\rm{M}_{\odot}$."
 The gainer has a substantial convective core and an almost constant mass radiative envelope throughout the mass accretion., The gainer has a substantial convective core and an almost constant mass radiative envelope throughout the mass accretion.
" As pointed out, differential rotation in single stars provides a finite amount of energy for generating magnetic fields so we might expect that the dynamo to cease once the rotation profile has been smoothed out."," As \citet{spruit2002} pointed out, differential rotation in single stars provides a finite amount of energy for generating magnetic fields so we might expect that the dynamo to cease once the rotation profile has been smoothed out."
" In the case of our semi-detached binary stars with discs, the energy in differential rotation can be continuously supplied from the disc material which has high specific angular momentum relative to the star as we discussed in section BJ]."," In the case of our semi-detached binary stars with discs, the energy in differential rotation can be continuously supplied from the disc material which has high specific angular momentum relative to the star as we discussed in section \ref{models}."
" Hence, if a Spruit-Tayler type dynamo operates in this case, magnetic fields are regenerated as long as mass transfer continues."," Hence, if a Spruit-Tayler type dynamo operates in this case, magnetic fields are regenerated as long as mass transfer continues."
 According to our assumption that the wind is accelerated to the stellar escape velocity (equation [12)) and leaves the system at the, According to our assumption that the wind is accelerated to the stellar escape velocity (equation \ref{meq5}) ) and leaves the system at the
In the fireball model. Gamma-Ray Burst (CRB) afterglows are thought to be the result. of svnchrotron. radiation eencrated by electrons during the interaction of a strongly collimated relativistic jet [rom a compact source with its environment (for recent reviews. see Piran2005:Alészaros 2006)).,"In the fireball model, Gamma-Ray Burst (GRB) afterglows are thought to be the result of synchrotron radiation generated by electrons during the interaction of a strongly collimated relativistic jet from a compact source with its environment (for recent reviews, see \citealt{Piran2005, Meszaros2006}) )."
 Initially the resulting spectra and light curves have been modelled: using only the shock front. of a spherical explosion ancl a simple power law approximation for the svnchrotron radiation (e.g. Wijers.Rees&Aészaros1997:Alészáros&Rees1997:Sarietal.1998:Rhoacls 1999)).," Initially the resulting spectra and light curves have been modelled using only the shock front of a spherical explosion and a simple power law approximation for the synchrotron radiation (e.g. \citealt{Wijers1997, Meszaros1997, Sari1998, Rhoads1999}) )."
 One or more spectral and temporal breaks were used to connect regimes with dillerent. power law slopes., One or more spectral and temporal breaks were used to connect regimes with different power law slopes.
 For the dynamics the self similar approximation of a relativistic explosion was used (Blandford&Melxee1976)., For the dynamics the self similar approximation of a relativistic explosion was used \citep{Blandford1976}.
.. These models have been refined. continuously., These models have been refined continuously.
 More. details of the shock structure were included (e.g. Guanotetal.1999:Gruzinov&Waxman 1999)). more accurate formulae for the svnchrotron radiation were used (e.g. Wijers&Calama 1999)) and. efforts have been made to implement collimation using various analytical approximations to the jet structure and lateral spreacing behaviour (see Cranot2005.r for an overview).," More details of the shock structure were included (e.g. \citealt{Granot1999, Gruzinov1999}) ), more accurate formulae for the synchrotron radiation were used (e.g. \citealt{Wijers1999}) ) and efforts have been made to implement collimation using various analytical approximations to the jet structure and lateral spreading behaviour (see \citealt{Granot2005} for an overview)."
 On top of that. there have been studies focussing on arrival time effects (c.g. Hluangetal. 2007)) and some numerical simulations (e.g. Salmonson2003:Ciranotetal.2001:Nakar& 2007)).," On top of that, there have been studies focussing on arrival time effects (e.g. \citealt{Huang2007}) ) and some numerical simulations (e.g. \citealt{Salmonson2003, Granot2001, Nakar2007}) )."
 The aim of this paper is twofold., The aim of this paper is twofold.
" ""The first aim is to introduce a new method to cerive light curves and spectra by post-processing relativistic hvdrodyvnamic (RILD) jet simulations of arbitrary dimension. properly taking into account all beaming ancl arrival time cllects. as well as the precise shape of the svnchrotron spectrum. and electron cooling (in this paper we will ignore self-absorption. although it can in principle be included in our method)."," The first aim is to introduce a new method to derive light curves and spectra by post-processing relativistic hydrodynamic (RHD) jet simulations of arbitrary dimension, properly taking into account all beaming and arrival time effects, as well as the precise shape of the synchrotron spectrum and electron cooling (in this paper we will ignore self-absorption, although it can in principle be included in our method)."
 This is done in sections 2. ancl 3.., This is done in sections \ref{peak_section} and \ref{cooling_section}.
 The second aim is to present a set of scaling coelTicients [or the slow-cooling case for a density profile p—po-(RIBI) [or general values of &., The second aim is to present a set of scaling coefficients for the slow-cooling case for a density profile $\rho = \rho_0 \cdot (R/R_0)^{-k}$ for general values of $k$.
 Fits to alterglow data using & as a [ree fitting parameter have vielded: values markedly cillerent from both &=0 and &=2 (Starlingetal. 2007).. although with error bars not excluding either option.," Fits to afterglow data using $k$ as a free fitting parameter have yielded values markedly different from both $k=0$ and $k=2$ \citep{Starling2007}, although with error bars not excluding either option."
 The scaling coellicients have been obtained. by application of our post-process code not to ai full. hydrocdsynamic simulation but to an emulation of this., The scaling coefficients have been obtained by application of our post-process code not to a full hydrodynamic simulation but to an emulation of this.
 From the spherical Dlandford Melxee (BM) analytical solution for the blast wave for the impulsive energy injection scenario. snapshots containing the state of the [uid at given emission times were constructed. ancl stored to. provide the input for the post-xYocess code.," From the spherical Blandford McKee (BM) analytical solution for the blast wave for the impulsive energy injection scenario, snapshots containing the state of the fluid at given emission times were constructed and stored to provide the input for the post-process code."
 The use of the BAL solution provides us with an opportunity to check the results and. the consistency. of he code in an environment where we already have a ot of analytical control and understanding., The use of the BM solution provides us with an opportunity to check the results and the consistency of the code in an environment where we already have a lot of analytical control and understanding.
 Phe scaling cocllicients are presented. in section 4.., The scaling coefficients are presented in section \ref{coefficients_section}.
 Thes. can be used w observers to obtain the physical parameters for the blast wave (c.g. explosion cnerey and cireumburst censity) from. he values for the peak flux ancl break frequencies that have xen Obtained from fits to the data., They can be used by observers to obtain the physical parameters for the blast wave (e.g. explosion energy and circumburst density) from the values for the peak flux and break frequencies that have been obtained from fits to the data.
 Reacers interested only, Readers interested only
photon index of the incident. power law spectrum with an exponential cutoll at fo: R= O25. where 9 is the solid angle subtended by the optically thick material: sp—cost. where @ is the angle between the line of sight and the normal vector of the optically thick laver: zd. the iron abundance of the optically thick material.,"photon index of the incident power law spectrum with an exponential cutoff at $E_c$ ; $R=\Omega/2\pi$ , where $\Omega$ is the solid angle subtended by the optically thick material; $\mu=cos\theta$, where $\theta$ is the angle between the line of sight and the normal vector of the optically thick layer; $A_{\rm Fe}$, the iron abundance of the optically thick material."
 Element abundances besides iron are assumed to be the solar values., Element abundances besides iron are assumed to be the solar values.
 In the following [itting. ££. is fixed at 200 Κον (practically a single power law in the observed range).," In the following fitting, $E_c$ is fixed at 200 keV (practically a single power law in the observed range)."
 qi is fixed at 0.45 so that the model spectrum is closest to that averaged over all viewing angles as described in. \lagedziarz Zelziarski (1995)., $\mu$ is fixed at 0.45 so that the model spectrum is closest to that averaged over all viewing angles as described in Magdziarz Zdziarski (1995).
 Combining with the thermal component and the line emission. the overall fitting model is given by where [ree parameters are shown in. parentheses.," Combining with the thermal component and the line emission, the overall fitting model is given by where free parameters are shown in parentheses."
 The normalization factors of the rellection component. Iac. [or the and.ANTE spectra are left. [ree from each other for possible time variation of the AGN luminosity.," The normalization factors of the reflection component, $K_{\rm AGN}$, for the and spectra are left free from each other for possible time variation of the AGN luminosity."
 The flux ratio between the Fe Ix-line. and the AGN continuum {νενοκ ds assumed to be constant., The flux ratio between the Fe K-line and the AGN continuum $K_l/K_{\rm AGN}$ is assumed to be constant.
 ALL other parameters are also assumed to be the same between the two observations., All other parameters are also assumed to be the same between the two observations.
 Another power-law with a photon index of 1.56 that represents the contamination sources is acdcdec to the model for the PCA and LIENTE spectrum., Another power-law with a photon index of 1.56 that represents the contamination sources is added to the model for the PCA and HEXTE spectrum.
 As shown in Figure 7 and ‘Table 4. this mode can account for the 0.5200 keV wide-band spectrum satisfactorily.," As shown in Figure \ref{fig:reffit} and Table 4, this model can account for the 0.5–200 keV wide-band spectrum satisfactorily."
 The lux of the contamination sources in theXE spectrum determined from the fit is in goo agreement with that obtained with the CIS within ~I0., The flux of the contamination sources in the spectrum determined from the fit is in good agreement with that obtained with the GIS within $\sim10\%$.
 The two normalization. factors of the AGN componen obtained from the andRAND spectra respectively happened to be very close (AESTEfyMC29 991.26). as were the Fe Ix-line. intensities nearly equal in these two observations.," The two normalization factors of the AGN component obtained from the and spectra respectively happened to be very close $K^{\rm RXTE}/K^{\rm ASCA}$ =0.92–1.26), as were the Fe K-line intensities nearly equal in these two observations."
 “Phe equivalent width: of the iron line with respect to the rellection continuum. is OS keV. which is à typical value for the Duorescence line associated. with the Compton-rellection.," The equivalent width of the iron line with respect to the reflection continuum is 0.8 keV, which is a typical value for the fluorescence line associated with the Compton-reflection."
 Llowever. the best-fit photon index E of the incident AGN spectrum is. 1.2640.18. which is unusually small compared to the typical values for AGNs (e.g. Mushotzky. Done. Pounds 1993).," However, the best-fit photon index $\Gamma$ of the incident AGN spectrum is $\pm$ 0.13, which is unusually small compared to the typical values for AGNs (e.g. Mushotzky, Done, Pounds 1993)."
 In this fit. the viewing angle cos@ was fixed at 0.45.," In this fit, the viewing angle $\mu = cos \theta$ was fixed at 0.45."
 Even if we allow fi to vary (Table 4). photon index larger than 1.54 is not acceptable.," Even if we allow $\mu$ to vary (Table 4), photon index larger than 1.54 is not acceptable."
 Phe intrinsic luminosity. of the AGN is estimated to be larger than 4.3..10°13 ergs/s. the value correspondingH to the maximum. solid angle. Le. 42=O25. of 1.0.," The intrinsic luminosity of the AGN is estimated to be larger than $4.3\times10^{43}$ ergs/s, the value corresponding to the maximum solid angle, i.e. $R=\Omega/2\pi$, of 1.0."
 Although. the above vellection-only model gives a satisfactory fit to theANTE | data. the small photon index derived in 4.2 still remains to be problem.," Although, the above reflection-only model gives a satisfactory fit to the + data, the small photon index derived in 4.2 still remains to be problem."
 As shown below. this is resolved by adding an absorbed AGN continuum that is transmitted through a thick absorber on the line of sight. (," As shown below, this is resolved by adding an absorbed AGN continuum that is transmitted through a thick absorber on the line of sight. ("
Here we do not consider the extent of the absorber. hence we assume no scattering of X-rays into the line of sight.),"Here we do not consider the extent of the absorber, hence we assume no scattering of X-rays into the line of sight.)"
 The transmitted ACGN component is given by where epi is theThomsonscattering cross-section. and ;Ngcy ds the hvdrogen-column density along line of sight.," The transmitted AGN component is given by where $\sigma_{\rm Th}$ is theThomsonscattering cross-section, and $N_{\rm H,AGN}$ is the hydrogen-column density along line of sight."
 The attenuation by the Thomson scattering becomes, The attenuation by the Thomson scattering becomes
This research was supported by the Agenzia Spaziale Italiana (ASI) and the Ministero dellIstruzione. Univversita e della Ricerca.,"This research was supported by the Agenzia Spaziale Italiana (ASI) and the Ministero dell'Istruzione, versità e della Ricerca."
and 4.. the former cisplaving how they change with viewing angle v at fixed i. the latter how thev changee with accretion rate mmn at fixed J.,"and \ref{fig:light-curves-mdot}, the former displaying how they change with viewing angle $\vartheta$ at fixed $\dot m$, the latter how they change with accretion rate $\dot m$ at fixed $\vartheta$."
 Changingexe inclination does relatively little io alter longe time-scale fluctuations. but can lead to differences on short time-scales.," Changing inclination does relatively little to alter long time-scale fluctuations, but can lead to differences on short time-scales."
 On the other hand. changingoOe the opacity ean lead to substantial differences in the lighte eurve even while the viewinge angleex remains the same.," On the other hand, changing the opacity can lead to substantial differences in the light curve even while the viewing angle remains the same."
 Remarkably. however. the exgross shape of the power spectrum is almost invariant to both sorts of changes: the best-fit power-law index is ~—2 [or all but the highest accretion rates and inclinations (Fig. 5)).," Remarkably, however, the gross shape of the power spectrum is almost invariant to both sorts of changes: the best-fit power-law index is $\simeq -2$ for all but the highest accretion rates and inclinations (Fig. \ref{fig:power-law-exponents-pspace}) )."
 The strongest effects influencing the inclination dependence of variations are relativistic beaming and boosting. which become more important as the orbital velocity becomes larger and more nearly parallel to the outgoing geodesics.," The strongest effects influencing the inclination dependence of variations are relativistic beaming and boosting, which become more important as the orbital velocity becomes larger and more nearly parallel to the outgoing geodesics."
 They therefore have the greatest. effect on radiation issuing from the smallest radii when viewed at high inclination., They therefore have the greatest effect on radiation issuing from the smallest radii when viewed at high inclination.
 Because those same inner radii have the highest dynamical frequency. one might (then expect a boost in the hieh-lrequeney portion of the power spectrum αἱ large J.," Because those same inner radii have the highest dynamical frequency, one might then expect a boost in the high-frequency portion of the power spectrum at large $\vartheta$."
 Ii relative terms. this does occuras we have seen. (he slope of the power spectrum depends only weakly on inclination. except when i» is «quite large (see further discussion later in this subsection).," In relative terms, this does occur—as we have seen, the slope of the power spectrum depends only weakly on inclination, except when $\dot m$ is quite large (see further discussion later in this subsection)."
 Nonetheless. although the relative variance changes little with inclination. the absolute variance. as well as the absolute luminosity. does increase when (he disk becomes more edge-on. as has also been seen in previous calculations (??)..," Nonetheless, although the relative variance changes little with inclination, the absolute variance, as well as the absolute luminosity, does increase when the disk becomes more edge-on, as has also been seen in previous calculations \citep{AR03,2006ApJ...651.1031S}."
 Because we explore only relative variability. (he absolute Iuminositvs proportionality lo 1» is irrelevant to our discussion.," Because we explore only relative variability, the absolute luminosity's proportionality to $\dot{m}$ is irrelevant to our discussion."
 The accretion rate influences the light eurves in our caleulations only bv setting Che opacity scale., The accretion rate influences the light curves in our calculations only by setting the opacity scale.
 The accretion rate is therefore degenerate with our choice of 7. and we can speak equivalently in (terms of accretion rate or optical depth.," The accretion rate is therefore degenerate with our choice of $\tau_\circ$, and we can speak equivalently in terms of accretion rate or optical depth."
 When the opacity is dominated by electron scattering. the disk is completely transparent for accretion rates re=0.001 or lower.," When the opacity is dominated by electron scattering, the disk is completely transparent for accretion rates $\dot m = 0.001$ or lower."
 Increasing rn» moves the photosphere Luther from the disks midplane. and emission from high latitudes becomes more dominant because our disk follows a nearly constant ///r prolile.," Increasing $\dot{m}$ moves the photosphere farther from the disk's midplane, and emission from high latitudes becomes more dominant because our disk follows a nearly constant $H/r$ profile."
 At (ihe same time. increasing 1 leads to a relative suppression of light [rom outer radii because the disk surface density. aud hence its optical depth. increases rapidly oulwarcl.," At the same time, increasing $\dot m$ leads to a relative suppression of light from outer radii because the disk surface density, and hence its optical depth, increases rapidly outward."
 For (his reason. the largest accretion rates select out [Inctuations from (he innermost ancl uppermost regions of the (bound) accretion low.," For this reason, the largest accretion rates select out fluctuations from the innermost and uppermost regions of the (bound) accretion flow."
 This pruning of the coronal volume with increasing 7? is the most likely explanation for the [act that the relative variance of the light curves monotonically increases with accretion rale. [rom 0.04 at i»=0.001 to 0.09 at m=1.," This pruning of the coronal volume with increasing $\dot m$ is the most likely explanation for the fact that the relative variance of the light curves monotonically increases with accretion rate, from $0.04$ at $\dot{m}=0.001$ to $0.09$ at $\dot{m}=1$."
 As the region above the photosphere shrinks in racial and vertical extent with rv. it contains fewer independently-fhictuating volumes. so that their summed emission has larger fractional fluctuations.," As the region above the photosphere shrinks in radial and vertical extent with $\dot{m}$ , it contains fewer independently-fluctuating volumes, so that their summed emission has larger fractional fluctuations."
in giants (angular momeutui deposited in the core is retained or all angular iiomentum is in the convective envelope). aud internal augular moinentum trausport on the liorizontal brauch. (solid body rotation or local conservation of augular momeutuim between the glaut branch tip aud the horizontal branch).,"in giants (angular momentum deposited in the core is retained or all angular momentum is in the convective envelope), and internal angular momentum transport on the horizontal branch (solid body rotation or local conservation of angular momentum between the giant branch tip and the horizontal branch)."
 In section 2. we outline the method we used to construct our stellar moclels.," In section 2, we outline the method we used to construct our stellar models."
 We present the results in section 3. ancl discuss the implications in section L," We present the results in section 3, and discuss the implications in section 4."
 A παν of our conclusions is given in section 5., A summary of our conclusions is given in section 5.
 We used the Yale Rotating Evolution Code (YREC. see Sills.Piusonneault&Terudrup (1999))) o calculate a standard non-rotati[n]ο stellar model from the main sequence up the giant branch to the ieliuiu core flash.," We used the Yale Rotating Evolution Code (YREC, see \cite{SPT99}) ) to calculate a standard non-rotating stellar model from the main sequence up the giant branch to the helium core flash."
 This model was chosen to have parameters appropriate for stars in. M13: M=0.8 L.. Z=0.0006 ([Fe/H]—-1.5) and Y=0.23.," This model was chosen to have parameters appropriate for stars in M13: M=0.8 $_{\odot}$, Z=0.0006 ([Fe/H]=-1.5) and Y=0.23."
 The turnolf age of this star is LL7 Gyr., The turnoff age of this star is 14.7 Gyr.
 The mixing eneth parameter. set by calibrating a solar model. was 1.7.," The mixing length parameter, set by calibrating a solar model, was 1.7."
 We used OPAL opacities (Iglesias& [or temperatures greater than logT=LO. Alexauder&Ferguson(1991) opacities or lower temperatures. the Sala equation of state. and grey Exldington atmospheres.," We used OPAL opacities \citep{IR96} for temperatures greater than $\log T = 4.0$, \cite{AF94} opacities for lower temperatures, the Saha equation of state, and grey Eddington atmospheres."
 The choice of he equation of state aud atmospheres was mace necessary by the rauge of evolutiouary stages that we are Investigatiug., The choice of the equation of state and atmospheres was made necessary by the range of evolutionary stages that we are investigating.
 The more recent. aud more accurate. equatious of state (Rogers.Swenson.&1996:Saumon.Chabrier.&VanHorn1995) aud atmospheres (Allard&Hauschildt1995) uufortunately do uot yet exteud to the temperatures aud deusities required for stellar models near the tip of the giant branch.," The more recent, and more accurate, equations of state \citep{RSI96,SCV95} and atmospheres \citep{AH95} unfortunately do not yet extend to the temperatures and densities required for stellar models near the tip of the giant branch."
 However. since this work is an initial study of rotational evolutiou iu these advanced phases. the qualitative results presented bere will not be affected by minor chauges in the position of the evolutionary track in the HR diagram.," However, since this work is an initial study of rotational evolution in these advanced phases, the qualitative results presented here will not be affected by minor changes in the position of the evolutionary track in the HR diagram."
 Helioseisinology cau be used to infer the internal rotation profile of the Sun by observing the rotational splitting of solar p-miodes., Helioseismology can be used to infer the internal rotation profile of the Sun by observing the rotational splitting of solar p-modes.
 The results imply that the Stu's radiative core is rotating as a solid body down to about #=0.22.. with some disagreement about deeper layers (Chaplinetal.al.1996:Corbardet 1998).," The results imply that the Sun's radiative core is rotating as a solid body down to about $R=0.2 R_{\sun}$, with some disagreement about deeper layers \citep{Chap99,Laz96,Cor98}."
.. The angular velocity of the solar surface convection zone is dependent on latitude but not on radius (Thompsonetal.1996)., The angular velocity of the solar surface convection zone is dependent on latitude but not on radius \citep{T96}.
. Old metal-poor stars do not have similar direct coustraints on their internal rotation. but the solar case is certaluly a eood first approximation.," Old metal-poor stars do not have similar direct constraints on their internal rotation, but the solar case is certainly a good first approximation."
 We therefore assume solid body rotation throughout the interior of the ain sequence turnolf progenitor and examine whether it is possible to retain sufficient. angular momentum to explain the rapid observed horizontal brauch rotation rates., We therefore assume solid body rotation throughout the interior of the main sequence turnoff progenitor and examine whether it is possible to retain sufficient angular momentum to explain the rapid observed horizontal branch rotation rates.
 Qur initial conditions therefore reduce to the total moment of inertia at the main sequence, Our initial conditions therefore reduce to the total moment of inertia at the main sequence
"Finally, the power spectrum is averaged over all segments.","Finally, the power spectrum is averaged over all segments."
 The power spectrum obtained with an artificial light curve is shown on figure 2.., The power spectrum obtained with an artificial light curve is shown on figure \ref{mc_fps}.
 The artificial light curve was produced by summing three simulated components., The artificial light curve was produced by summing three simulated components.
" The light curve of PKS 1830-211 shown on figure 1 does not exhibit any easily recognizable features, but has a rather random-like aspect."," The light curve of PKS 1830-211 shown on figure \ref{lc} does not exhibit any easily recognizable features, but has a rather random-like aspect."
" The first component was thus simulated as a white noise, with a Poisson distribution."," The first component was thus simulated as a white noise, with a Poisson distribution."
" It would be more realistic to use red noise instead of white noise but the latter is sufficient for most of our purposes, such as computing D,. The second component is obtained from the first by shifting the light curve with a 28 days time lag."," It would be more realistic to use red noise instead of white noise but the latter is sufficient for most of our purposes, such as computing $D_{a}.$ The second component is obtained from the first by shifting the light curve with a 28 days time lag."
 The effect of differential magnification of the images has also been included., The effect of differential magnification of the images has also been included.
 The background photon noise was taken into account by adding a third component with a Poisson distribution., The background photon noise was taken into account by adding a third component with a Poisson distribution.
 The mean number of counts per 2 day bin for PKS is 5.42 counts., The mean number of counts per 2 day bin for PKS 1830-211 is 5.42 counts.
 This value was used for the simulation of the artificial light curve., This value was used for the simulation of the artificial light curve.
 The first and second component contribute of the simulated count rate and the rest is contributed by the noise component., The first and second component contribute of the simulated count rate and the rest is contributed by the noise component.
" To get a simulated flux similar to the observed flux, the simulated count rate is divided by the average exposure from observations ( 2.8557107s cm’)."," To get a simulated flux similar to the observed flux, the simulated count rate is divided by the average exposure from observations ( $2.8557\ 10^{7}\ s\ cm^{2}$ )."
" The methods of time delay determination use the power spectrum P, obtained as described in the previous section.", The methods of time delay determination use the power spectrum $P_{\nu}$ obtained as described in the previous section.
" The simulated P, presented on figure 2 shows a very clear periodic pattern.", The simulated $P_{\nu}$ presented on figure \ref{mc_fps} shows a very clear periodic pattern.
 From equation 1 we know that the period of the observed wobbles corresponds to inverse of the time delay between the images., From equation \ref{Powereq} we know that the period of the observed wobbles corresponds to inverse of the time delay between the images.
" Our preferred approach was to calculate the double power spectrum D,.", Our preferred approach was to calculate the double power spectrum $D_{a}$.
" As in section 3.2,, the power spectrum P, has to be prepared before undergoing a Fourier transform to the ""time delay"" domain."," As in section \ref{FPSsubs}, the power spectrum $P_{\nu}$ has to be prepared before undergoing a Fourier transform to the “time delay” domain."
" The low frequency part (v«1/55day|!) of P, is cut off.", The low frequency part $\nu < 1/55 \mbox{day}^{-1}$ ) of $P_{\nu}$ is cut off.
 This cut arises because of the large power observed low frequencies in the power spectrum of PKS 1830-211., This cut arises because of the large power observed low frequencies in the power spectrum of PKS 1830-211.
" The high frequency part of the spectrum P, is also removed because the power at high frequency is small (it goes to O at the Nyquist frequency).", The high frequency part of the spectrum $P_{\nu}$ is also removed because the power at high frequency is small (it goes to 0 at the Nyquist frequency).
" The calculation of D, proceeds like in section 3.2,, except that the P, data are bend to zero by multiplication with a cosine bell."," The calculation of $D_{a}$ proceeds like in section \ref{FPSsubs}, except that the $P_{\nu}$ data are bend to zero by multiplication with a cosine bell."
" This eliminates spurious high frequencies, when zeros are added to the P, series."," This eliminates spurious high frequencies, when zeros are added to the $P_{\nu}$ series."
" The D, distribution is estimated from 5 segments of the light curve.", The $D_{a}$ distribution is estimated from 5 segments of the light curve.
" In every bin of the D, distribution, the estimated double power spectrum is given by the average over the 5 segments."," In every bin of the $D_{a}$ distribution, the estimated double power spectrum is given by the average over the 5 segments."
" The errors bars on D, are estimated from the dispersion of bin values divided by 2 (since there are 5 segments).", The errors bars on $D_{a}$ are estimated from the dispersion of bin values divided by 2 (since there are 5 segments).
" Due to the random nature of the sampling process, some of the error bars obtained are much smaller than the typical dispersion in the D, points."," Due to the random nature of the sampling process, some of the error bars obtained are much smaller than the typical dispersion in the $D_{a}$ points."
" To take this into account, a small systematic error bar was added quadratically to all points."," To take this into account, a small systematic error bar was added quadratically to all points."
 The result (with statistical error bars only) is presented on figure 3.., The result (with statistical error bars only) is presented on figure \ref{mc_sps}.
" As described in section 3.2,, we simulated light curves with atime delay of 28 days."," As described in section \ref{FPSsubs}, we simulated light curves with a time delay of 28 days."
" A peak is apparent near a time delay of 28 days on the D, distribution shown on figure 3..", A peak is apparent near a time delay of 28 days on the $D_{a}$ distribution shown on figure \ref{mc_sps}.
 The points just outside the peak are compatible with a flat distribution., The points just outside the peak are compatible with a flat distribution.
 Including also the points in the peak gives a distribution which is incompatible with a flat distribution at the 10 sigma level., Including also the points in the peak gives a distribution which is incompatible with a flat distribution at the 10 sigma level.
 The parameters of the peak were determined by fitting the sum of a linear function for the background plus a Gaussian function for the signal., The parameters of the peak were determined by fitting the sum of a linear function for the background plus a Gaussian function for the signal.
" In the case shown on figure 3,, the time delay estimated from D, is 27.94+0.61 days."," In the case shown on figure \ref{mc_sps}, the time delay estimated from $D_{a}$ is $27.94\pm0.61$ days."
" As mentioned in section 3.1,, the usual approach for the time delay estimation is to compute the autocorrelation of the light curve."," As mentioned in section \ref{idea}, the usual approach for the time delay estimation is to compute the autocorrelation of the light curve."
" The auto-covariance is obtained by taking the real part of the inverse Fourier transform of P,.", The auto-covariance is obtained by taking the real part of the inverse Fourier transform of $P_{\nu}$ .
 The auto-covariance is normalized (divided by the value at zero time lag) to get the autocorrelation., The auto-covariance is normalized (divided by the value at zero time lag) to get the autocorrelation.
 The autocorrelation function of an artificial light curve simulated as in section 3.2 is presented on figure 4.., The autocorrelation function of an artificial light curve simulated as in section \ref{FPSsubs} is presented on figure \ref{mc_ac}.
 A peak with a significance of roughly 16 o is present at 27.85+0.14 days., A peak with a significance of roughly 16 $\sigma$ is present at $27.85\pm0.14$ days.
 However the significance of this peak is overestimated since light curves are simulated with white noise instead of red noise., However the significance of this peak is overestimated since light curves are simulated with white noise instead of red noise.
" The autocorrelation function of a light curve driven by red noise is given by e"", In the case of our simulated light curves, A=0, so that the peak is a little affected by the background of the AGN."," The autocorrelation function of a light curve driven by red noise is given by $e^{-a/ \lambda}.$ In the case of our simulated light curves, $\lambda = 0$, so that the peak is a little affected by the background of the AGN."
" For the simulated light curves, both approaches of time delay determination give reasonable and compatible results."," For the simulated light curves, both approaches of time delay determination give reasonable and compatible results."
 The results for real data were obtained with the same procedure as was presented for the simulated light curves., The results for real data were obtained with the same procedure as was presented for the simulated light curves.
" Figure 8 shows the power spectrum P, calculated from the light curve of PKS 1830-211.", Figure \ref{pks1830_fps} shows the power spectrum $P_{\nu}$ calculated from the light curve of PKS 1830-211.
 A periodic pattern is obvious onthe distribution of, A periodic pattern is obvious onthe distribution of
many cases the distance estimates that we can clerive are quite Inprecise.,many cases the distance estimates that we can derive are quite imprecise.
 T Leo. BZ UAla. D8490. SW δία. and V405 Peg have high-quality. parallax distance measurements ((Thorstensen 2003: Thorstensenetal.2006: Thorstensenctal. 2008:: ''horstensenetal. 2009)).," T Leo, BZ UMa, RBS490, SW UMa, and V405 Peg have high-quality parallax distance measurements \citealt{Thorstensen03}; ; \citealt{ThorstensenLepineShara06}; \citealt{ThorstensenLepineShara08}; \citealt{Thorstensen09}) )."
 Other reliable estimates of CV distances are found. by photometric parallax. in cases where the white carl or the onor star ds detected in a way that makes it possible to iscntanele its [lux contribution from that of other light sources.," Other reliable estimates of CV distances are found by photometric parallax, in cases where the white dwarf or the donor star is detected in a way that makes it possible to disentangle its flux contribution from that of other light sources."
 We use such estimates for PP Ari anc EXDra7., We use such estimates for TT Ari and EX.
. TT Ari has a distance measurement based on the donor star Es»eetrum (Gansickeetal.1999:: this is also consistent with 1e distance derived from the white dwarf spectrum)., TT Ari has a distance measurement based on the donor star spectrum \citealt{GansickeSionBeuermann99}; this is also consistent with the distance derived from the white dwarf spectrum).
 Based on the photometric parallax of the secondary. the distance to EX Dra is 240zope (see Shafter&Holland2003: Baptistaςal. 2000:: Pretoriusetal. 2007b:: we have revised. this to be slightly less conservative than the estimate we used previously).," Based on the photometric parallax of the secondary, the distance to EX Dra is $240^{+68}_{-52}\,\mathrm{pc}$ (see \citealt{ShafterHolland03}; \citealt{BaptistaCatalanCosta00}; \citealt{NEPrho}; we have revised this to be slightly less conservative than the estimate we used previously)."
 There. are a few well-known. less. direct (ancl less reliable) methods of estimating distances to CVs.," There are a few well-known, less direct (and less reliable) methods of estimating distances to CVs."
 We use methodsbased. on dwarf nova (DN) outburst. maximum (Warner1987: sec also Harrisonetal.2004 and Patterson 20112). the near-LR apparent brightness for svstems in whichthe donor star is not directly detected (the method of 1981.. but as prescribed by Ixnigee2006 and. Ixnigge 2011)). and the strength. of L5 emission lines 1984: see also Patterson 2011)).," We use methodsbased on dwarf nova (DN) outburst maximum \citealt{brian87}; see also \citealt{HarrisonJohnsonMcArthur04} and \citealt{Patterson11}) ), the near-IR apparent brightness for systems in whichthe donor star is not directly detected (the method of \citealt{Bailey81}, but as prescribed by \citealt{Knigge06} and \citealt{KBP11}) ), and the strength of $\beta$ emission lines \citealt{Patterson84}; see also \citealt{Patterson11}) )."
" The relation between the absolute magnitude at DN outburst maximum and. 2, was most recently studied. by Patterson(2011).. who confirms that the scatter is relatively small. and that there are no large outliers."," The relation between the absolute magnitude at DN outburst maximum and $P_{orb}$ was most recently studied by \cite{Patterson11}, who confirms that the scatter is relatively small, and that there are no large outliers."
 We therefore use this relation as Far as possible (for CC Sel. VW Livi. WA Ivi. SU UMa. PY PsA. WW. Cet. SDSS J1730. and EE Tuc).," We therefore use this relation as far as possible (for CC Scl, VW Hyi, WX Hyi, SU UMa, TY PsA, WW Cet, SDSS J1730, and EF Tuc)."
 ]t should. be noted that SU UMa has a parallax distance estimate that agrees very well with the distance based. on outburst maximum. but which is less precise: we choose in this case to use the estimate based on outburst. rather than the parallax (see Phorstensen2003. and. Patterson 2011)).," It should be noted that SU UMa has a parallax distance estimate that agrees very well with the distance based on outburst maximum, but which is less precise; we choose in this case to use the estimate based on outburst, rather than the parallax (see \citealt{Thorstensen03} and \citealt{Patterson11}) )."
 ‘Two systems. SDSS J1730 and EE Tuc. do not have orbital inclination measurements (although it is known that they are not eclipsing). and have less well determined. maximum oparent magnitudes. leading to more imprecise distance estimates from this method.," Two systems, SDSS J1730 and EF Tuc, do not have orbital inclination measurements (although it is known that they are not eclipsing), and have less well determined maximum apparent magnitudes, leading to more imprecise distance estimates from this method."
 For RA J1831 we use the prescription of Ixnigee(2006) (as updated. by IxXnigeeetal. 901109)., For RX J1831 we use the prescription of \cite{Knigge06} (as updated by \citealt{KBP11}) ).
 This is based. on a semi-empirical donor sequence for CVs. ancl the olfsets between this sequence and the absolute 444A. magnitudes m La sample of CVs with parallax distances.," This is based on a semi-empirical donor sequence for CVs, and the offsets between this sequence and the absolute $JHK$ magnitudes of a sample of CVs with parallax distances."
 Apparent near-IR. magnitudes for RX JISA31 were obtained [rom the Two Micron All Sky Survey (2ALASS: Skrutskieetal. 2006))., Apparent near-IR magnitudes for RX J1831 were obtained from the Two Micron All Sky Survey (2MASS; \citealt{2mass}) ).
 Finally. although there clearly exists an. empirical relation between MW(13) and the absolute magnitude of the disc. this relation contains large scatter (see Patterson2011. for an updated plot).," Finally, although there clearly exists an empirical relation between $EW(H\beta)$ and the absolute magnitude of the disc, this relation contains large scatter (see \citealt{Patterson11} for an updated plot)."
 We therefore use it as à ast resort. in those four cases where the data required » the other two methods. are not available (LW Pic. IQ Iri. RA J1715. and 129111).," We therefore use it as a last resort, in those four cases where the data required by the other two methods are not available (TW Pic, IQ Eri, RX J1715, and RBS1411)."
 For RN J1715. and tDS141I. we have no data to allow us to check. whether he absolute magnitudes we find are reasonable (other than hat RA J1715 is known to be a short-period CV. and that tDS1411I has an optical spectrum resembling that of a short-xeriod. CV).," For RX J1715 and RBS1411, we have no data to allow us to check whether the absolute magnitudes we find are reasonable (other than that RX J1715 is known to be a short-period CV, and that RBS1411 has an optical spectrum resembling that of a short-period CV)."
 For the remaining 2 svstems. we find absolute magnitudes that are in reasonable agreement with what we would find from outhurst (in the case of LQ Evi). and the method. of Ixnigge (in the case of TW Pic). if we mace reasonable assumptions about orbitalperiod”.," For the remaining 2 systems, we find absolute magnitudes that are in reasonable agreement with what we would find from outburst (in the case of IQ Eri), and the method of Knigge (in the case of TW Pic), if we made reasonable assumptions about orbital."
 Interstellar extinction is expected to be low for our systems. since they are at high Galactic latitude. and since most of them are quite nearby.," Interstellar extinction is expected to be low for our systems, since they are at high Galactic latitude, and since most of them are quite nearby."
 For those systems. with distances below 200 pe. we neglect. interstellar extinction.," For those systems with distances below 200 pc, we neglect interstellar extinction."
 For the more distant objects. we use chy estimates from Patterson(2011).. where available. and for a few more. we fine estimates in Bruch&Engel(1904).," For the more distant objects, we use $A_V$ estimates from \cite{Patterson11}, where available, and for a few more, we find estimates in \cite{BruchEngel94}."
. In the cases where no more direct estimate of extinction is available. we use the model of Amores&Lépine(2005).. with a few iterations. so that the value we finally adopt in the distance caleulation is that given by the model at the estimated distance to the object.," In the cases where no more direct estimate of extinction is available, we use the model of \cite{AmoresLepine05}, with a few iterations, so that the value we finally adopt in the distance calculation is that given by the model at the estimated distance to the object."
 Lo convert from visual extinction to extinction in the PALASS bands. we use ely=0282.1. ly=0.175... and eli=OLD (Cambrésyetal.2002).," To convert from visual extinction to extinction in the 2MASS bands, we use $A_J = 0.282 A_V$, $A_H=0.175 A_V$ , and $A_{K_S} = 0.112 A_V$ \citep{CambresyBeichmanJarrett02}."
. We conservatively assume errors of in the extinction values., We conservatively assume errors of in the extinction values.
 We then find the probability distribution. for the distance to each source. assuming Gaussian errors in all the input parameters (apparent. magnitudes. inclination. EW(123). extinction)," We then find the probability distribution for the distance to each source, assuming Gaussian errors in all the input parameters (apparent magnitudes, inclination, $EW(H\beta)$, extinction)."
 The distances estimates. listed in column 3 of Table 1.. are in all cases the median. together with the 1-7 confidence interval corresponding to the 16th and S4th percentile points.," The distances estimates, listed in column 3 of Table \ref{tab:distances}, are in all cases the median, together with the $\sigma$ confidence interval corresponding to the 16th and 84th percentile points."
 Distance estimates may suller from. two well-knownbiases. namelyMalmeuist (Malmeuist1924). and Lutz-Ixelker bias (Lutz&Ixelker 1973)..," Distance estimates may suffer from two well-knownbiases, namelyMalmquist \citep{Mbias} and Lutz-Kelker bias \citep{LKbias}. ."
 These biases. the relation between them. and how to correct for them have been the subject of many papers Smith 2003)).," These biases, the relation between them, and how to correct for them have been the subject of many papers \\citealt{GonzalezFaber97}; ; \citealt{Smith03}) )."
 Llere να will examine whether our clistance estimates could be biased., Here we will examine whether our distance estimates could be biased.
"To constrain the slope of the BM down to the lowest masses in "" cluster we derive the ratio of verv low-mass stars (0.076 n- 0.1 AL.) to brown dwarls (0.02 -Ma 0.076 NL. ) in our survey.",To constrain the slope of the IMF down to the lowest masses in the cluster we derive the ratio of very low-mass stars (0.076 - 0.1 $_\odot$ ) to brown dwarfs (0.02 - 0.076 $_\odot$ ) in our survey.
 We calculate this ratio to be R==0.230x0.20 assuming a (os. isochrone. with the errors computed due to Poisson statistics.," We calculate this ratio to be $R = 3/10 = 0.30 \pm 0.20$ assuming a 0.3 Myr isochrone, with the errors computed due to Poisson statistics."
 For al Myr isochrone ralio increases to Ro = 5/8 — 0.625 dL- 0.356., For a 1 Myr isochrone this ratio increases to R = 5/8 = 0.625 $\pm$ 0.356.
 Both cluster ages give5 ratios consistent with having been drawn from a Chabrier(2003) svstem IME. which gives a most likely ratio (mode) of Ro = 0.30.," Both cluster ages give ratios consistent with having been drawn from a \citet{ch03} system IMF, which gives a most likely ratio (mode) of R = 0.30."
 This corresponds to a slope of dN/dM x FF over this range., This corresponds to a slope of dN/dM $\propto$ $^{-1.1}$ over this range.
 For the older isochrone there are a larger number of low-mass stars but still more brown dwarls due to the hvdrogen burning limit shifting to a fainter magnitude for a higher cluster age., For the older isochrone there are a larger number of low-mass stars but still more brown dwarfs due to the hydrogen burning limit shifting to a fainter magnitude for a higher cluster age.
 Both ratios are lower limits. since the low-mass bin has objects for which we do not have spectra and thus contamination by field stars may lead us to overestimate the number of brown chwarls relative to low mass stars in (he sample.," Both ratios are lower limits, since the low-mass bin has objects for which we do not have spectra and thus contamination by field stars may lead us to overestimate the number of brown dwarfs relative to low mass stars in the sample."
 Above 0.076 AL. all objects but one have assigned spectral types which allow us (o assess their cluster membership., Above 0.076 $_\odot$ all objects but one have assigned spectral types which allow us to assess their cluster membership.
 The object. without a spectral tvpe is ASRGa which is a previously identified cluster member (Aspinetal.1994). which we have resolved to be a binary., The object without a spectral type is ASR9a which is a previously identified cluster member \citep{as94} which we have resolved to be a binary.
 Below 0.076 M. however. apart fron ASR 9b. there are [our objects without spectral tvpes. which could be possible field stars.," Below 0.076 $_\odot$ however, apart from ASR 9b, there are four objects without spectral types, which could be possible field stars."
" Thus these ratios imply pn limits for the slope of the cluster mass spectrum belowQ.1 M. of a x Ld anda x» 0.55MM lor 0.3slope. Myr and 1 Myr isochrones respectively. where dN/dAl x M.P"" aad a = 2.35 is "," Thus these ratios imply upper limits for the slope of the cluster mass spectrum below 0.1 $_\odot$ of $\alpha$ $\leq$ 1.1 and $\alpha$ $\leq$ 0.55 for 0.3 Myr and 1 Myr isochrones respectively, where dN/dM $\propto$ $^{-\alpha}$ and $\alpha$ = 2.35 is the Salpeter slope."
Where does our result stand with regard to comparable clusters and studies?, Where does our result stand with regard to comparable clusters and studies?
 have explored the mass spectrum of NGC 1333 ms an extinction limited sample down to»0.04 AL. finding ralio of sub-stellar (0.04- 0.1 AL.) to stellar objects (0.1- 1 M.) to Rey= 1.11 +0.8/-0.4., \citet{wil03} have explored the mass spectrum of NGC 1333 using an extinction limited sample down to 0.04 $_\odot$ finding the ratio of sub-stellar (0.04 - 0.1 $_\odot$ ) to stellar objects (0.1 - 1 $_\odot$ ) to be $_{SS}$ = 1.11 +0.8/-0.4.
(he; functionThey used this to estimate an upper limit for the slope of the lower endof the mass of a < 1.6., They used this to estimate an upper limit for the slope of the lower endof the mass function of $\alpha$ $\leq$ 1.6.
 This compares well with slopes in the solar neighborhood below the hvdrogen-burning limit. whieh Reidetal.(1999). found tobe l <a «2.," This compares well with slopes in the solar neighborhood below the hydrogen-burning limit, which \citet{rei98} found to be 1 $<$ $\alpha$ $<$ 2."
 Allenetal.(2005) have further attempted to constrain the shape of the field star IME below 0.1 AL. and found -0.6 <a < 0.6 with confidence and a best fit of o — 0.3., \citet{al05} have further attempted to constrain the shape of the field star IMF below 0.1 $_\odot$ and found -0.6 $<$ $\alpha$ $<$ 0.6 with confidence and a best fit of $\alpha$ = 0.3.
 To derive a broader estimate of the cluster mass function we attempted to combine this survey with that of Wilkingetal.(2004) to make the cluster mass function more easily comparable to ratios published for other regions., To derive a broader estimate of the cluster mass function we attempted to combine this survey with that of \citet{wil03} to make the cluster mass function more easily comparable to ratios published for other regions.
" We combined all objects between 0.1 - 1 AL. from veeetal.(2004) with an extinction limit of A, < 12.8” with the LIST objects between 0.03 - 0.1 AL. with an extinetion limit of A, < 21.1"". scaling the number of LIST objects bv ""ratios of (he survey areas. which is 26.3. as well as the extinctions. which is"," We combined all objects between 0.1 - 1 $_\odot$ from \citet{wil03} with an extinction limit of $_v$ $\leq$ $^m$ with the HST objects between 0.03 - 0.1 $_\odot$ with an extinction limit of $_v$ $\leq$ $^m$ , scaling the number of HST objects by the ratios of the survey areas, which is 26.3, as well as the extinctions, which is"
In the context of stellar-mass compact objects. resolved. radio-emitting relativistic ejection events are typically associated. with periods of high rates of accretion and transitions in the state of the accretion flow (e.g. Fender. Belloni Gallo 20043.,"In the context of stellar-mass compact objects, resolved radio-emitting relativistic ejection events are typically associated with periods of high rates of accretion and transitions in the state of the accretion flow (e.g. Fender, Belloni Gallo 2004)."
 The case of SGR 1806-20 is clearly rather different: the object is probably not accreting (Kouveliotou et al., The case of SGR 1806-20 is clearly rather different: the object is probably not accreting (Kouveliotou et al.
 1998) and the apparent steady growth of the radio source is rather different from the jets associated with X-ray binaries. which typically have small (<107) opening angles (Miller-Jones. Fender Nakar 2005).," 1998) and the apparent steady growth of the radio source is rather different from the jets associated with X-ray binaries, which typically have small $\leq 10^{\circ}$ ) opening angles (Miller-Jones, Fender Nakar 2005)."
 Several aspects of this behaviour may be associated with the probable lower bulk Lorentz factor of this event. L'acg~1.4 (Granot et al.," Several aspects of this behaviour may be associated with the probable lower bulk Lorentz factor of this event, $\Gamma_{\rm SGR} \sim 1.4$ (Granot et al."
 2005: compare with Lo2 for X-ray binary jets)., 2005; compare with $\Gamma \geq 2$ for X-ray binary jets).
 We can also compare this event with the jet-like outflows from isolated neutron stars such as the Crab (Hester et al., We can also compare this event with the jet-like outflows from isolated neutron stars such as the Crab (Hester et al.
 2002). Vela (Pavlov et al.," 2002), Vela (Pavlov et al."
 2003) and PSR Β1500-55 (DeLaney et al., 2003) and PSR B1509-58 (DeLaney et al.
 2005)., 2005).
" In these radio pulsars and SGR 1806-20 it seems that the the ""escape velocity principle’. in which outflows have velocities comparable to the escape velocity at their launch point (e.g. Livio 1999 and references therein) is maintained. while it is is blatantly violated by the jets from the accreting neutron stars Sco X-1 (Fomalont. Geldzahler Bradshaw 2001) and Circinus X-| (Fender et al."," In these radio pulsars and SGR 1806-20 it seems that the the 'escape velocity principle', in which outflows have velocities comparable to the escape velocity at their launch point (e.g. Livio 1999 and references therein) is maintained, while it is is blatantly violated by the jets from the accreting neutron stars Sco X-1 (Fomalont, Geldzahler Bradshaw 2001) and Circinus X-1 (Fender et al."
 2004). which are much more relativistic. suggesting the necessity of a disc in forming the most relativistic flows.," 2004), which are much more relativistic, suggesting the necessity of a disc in forming the most relativistic flows."
 Nevertheless. the radio source is still associated with the ejection of matter in a preferred direction in space. and probably the resultant in-situ particle acceleration.," Nevertheless, the radio source is still associated with the ejection of matter in a preferred direction in space, and probably the resultant in-situ particle acceleration."
 The observed synchrotron emission is likely to have the highest surface brightness close to regions of particle acceleration. and it may be these regions which are producing the brightest regions of radio flux measured on the longest baselines by MERLIN and the VLBA.," The observed synchrotron emission is likely to have the highest surface brightness close to regions of particle acceleration, and it may be these regions which are producing the brightest regions of radio flux measured on the longest baselines by MERLIN and the VLBA."
 Obvious sites for the particle acceleration are at the leading edge of the ejecta (external shocks). internal shocks distributed along the flow itself (easier to achieve the more collimated the initial flow was) and possibly at the site of the magnetar itself.," Obvious sites for the particle acceleration are at the leading edge of the ejecta (external shocks), internal shocks distributed along the flow itself (easier to achieve the more collimated the initial flow was) and possibly at the site of the magnetar itself."
 In this scenario any radio emission associated with more diffuse components would be due to leptons which have diffused away from the particle acceleration site., In this scenario any radio emission associated with more diffuse components would be due to leptons which have diffused away from the particle acceleration site.
 To conclude. we have observed at high angular resolution the early stages of the evolution of the radio counterpart to the giant flare of SGR 1806-20 on 2004 Dec 27.," To conclude, we have observed at high angular resolution the early stages of the evolution of the radio counterpart to the giant flare of SGR 1806-20 on 2004 Dec 27."
 Despite many difficulties with analysing and interpreting the MERLIN and VLBA datasets. we tind evidence for significant substructure on angular scales =100 mas. associated with about of the total radio flux.," Despite many difficulties with analysing and interpreting the MERLIN and VLBA datasets, we find evidence for significant substructure on angular scales $\la 100$ mas, associated with about of the total radio flux."
 The compact radio structure is likely to be associated with sites of particle acceleration. which may be external or internal shocks in the outflow. or somehow associated with the environment close to the magnetar itself.," The compact radio structure is likely to be associated with sites of particle acceleration, which may be external or internal shocks in the outflow, or somehow associated with the environment close to the magnetar itself."
 MERLIN is a National Facility operated by the University of Manchester at Jodrell Bank Observatory on behalf of the UK Particle Physics and Astronomy Research Council., MERLIN is a National Facility operated by the University of Manchester at Jodrell Bank Observatory on behalf of the UK Particle Physics and Astronomy Research Council.
 The US National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities. Inc. We thank the referee for detailed and constructive criticism.," The US National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. We thank the referee for detailed and constructive criticism."
velocity V and. its. dispersion σι. in radial bins.,velocity $V$ and its dispersion $\sigma_V^{\phantom2}$ in radial bins.
 The niiddle left. panels of Figs. 6-, The middle left panels of Figs. \ref{M12_kin}-
" 9 the quantity (fo,jhe versus radius. for some of the remnants."," \ref{M13_kin} the quantity $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}$ versus radius, for some of the remnants."
 In all simulations. we find (AVfay2.1/22l for the voung population. indicating that this population forms a massive. rotationally. supported. dise.," In all simulations, we find $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}>1$ for the young population, indicating that this population forms a massive, rotationally supported disc."
 Ehe only exception. is simulation M12z. where (Ve27«] between radii 3 and Gkpe.," The only exception is simulation M12z, where $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}<1$ between radii 3 and $6\,\rm kpc$."
 As the top panel of Fig., As the top panel of Fig.
 7 shows. this region corresponds to the discontinuitv between the inner disc and the counter- outer ring.," \ref{M12z_kin} shows, this region corresponds to the discontinuity between the inner disc and the counter-rotating outer ring."
" Simulations M12. MlI2orb. MI2z. and MII all have {170,72«L indicating the presence of a “hot cise” supported by internal motions rather than rotation."," Simulations M12, M12orb, M12z, and M11 all have $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}<1$, indicating the presence of a “hot disc” supported by internal motions rather than rotation."
 Simulation MI3 has (Y07L7zmo] oat oradii r«προ and (AVYayo-Lat larger radii.," Simulation M13 has $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}<1$ at radii $r<3\,{\rm kpc}$ and $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}>1$ at larger radii."
 Simulations AI290.. rMI2. and MIIO all have (VVfayyhooLE. indicating that the old population is also rotationally supported. but in all three cases the rotational support. 1s significantly smaller for the old. population. tvpically by a [actor of order 5.," Simulations M1290, rM12, and M110 all have $\langle(V/\sigma^{\phantom2}_V)^2\rangle^{1/2}>1$, indicating that the old population is also rotationally supported, but in all three cases the rotational support is significantly smaller for the old population, typically by a factor of order 5."
 In the case of simulation rMI2. this result is consistent with the fact that retrograde orbits are less destructive than proegrade orbits.," In the case of simulation rM12, this result is consistent with the fact that retrograde orbits are less destructive than prograde orbits."
 The middle right panels of Pigs. 6-, The middle right panels of Figs. \ref{M12_kin}-
 9 show the velocity dispersion versus formation epoch. with the cash vertical lines indicating the starburst.," \ref{M13_kin} show the velocity dispersion versus formation epoch, with the dash vertical lines indicating the starburst."
 In 5 of the S simulations. the velocity. dispersion is larger for stars formed. prior to the collision. and smaller for stars born after the collision.," In 5 of the 8 simulations, the velocity dispersion is larger for stars formed prior to the collision, and smaller for stars born after the collision."
 Εις is consistent with the statement that old stars have a smaller rotational support than voung stars., This is consistent with the statement that old stars have a smaller rotational support than young stars.
" “Phe exceptions are the simulations with high mass ratios. MIS and MAIO. for which a, peaks during the starburst. and M12z. for which σι peaks after the starburst (Fig. 7))."," The exceptions are the simulations with high mass ratios, M13 and M110, for which $\sigma^{\phantom2}_V$ peaks during the starburst, and M12z, for which $\sigma^{\phantom2}_V$ peaks after the starburst (Fig. \ref{M12z_kin}) )."
 The bottom left panels of Figs. 6-, The bottom left panels of Figs. \ref{M12_kin}-
 9 show histograms of the stellar mass versus rotation velocity., \ref{M13_kin} show histograms of the stellar mass versus rotation velocity.
 For simulations MI2. AlPork. MI290. rMI2. ancl ALIS. the voung population is concentrated in a narrow region of the histogram. while he old. population is spread in velocity. from the positive o the negative side (though it is concentrated mostly on the positive side for rMI2).," For simulations M12, M12orb, M1290, rM12, and M13, the young population is concentrated in a narrow region of the histogram, while the old population is spread in velocity, from the positive to the negative side (though it is concentrated mostly on the positive side for rM12)."
 The voung component. is counter-rotating for simulation MIL., The young component is counter-rotating for simulation M11.
 For simulations MI2z. xwts of the voung component are Counter-rotating. and the otal distribution is centered. near zero.," For simulations M12z, parts of the young component are counter-rotating, and the total distribution is centered near zero."
 Simulation MIIO (the minor merger) dillers from. all others in that the old »»pulation is concentrated at positive velocities., Simulation M110 (the minor merger) differs from all others in that the old population is concentrated at positive velocities.
 Notice hat this is the only case for which the old population is rotationally supported., Notice that this is the only case for which the old population is rotationally supported.
 One wav to ciscriminate between kinematically dilferent star populations is the use of the Toomre Diagram (Sandage&Fouts1987)., One way to discriminate between kinematically different star populations is the use of the Toomre Diagram \citep{sf87}.
. By comparing V. (circular velocity) with CLAM (radial and perpendicular velocity respectively). we can have a clearer picture of the kinematic distribution of the voung ancl old. population.," By comparing $V$ (circular velocity) with $U+W$ (radial and perpendicular velocity respectively), we can have a clearer picture of the kinematic distribution of the young and old population."
 A thin disc will be mostly formed by. stars with low C|WM and a large V component since all stars will be in nearly coplanar orbits., A thin disc will be mostly formed by stars with low $U+W$ and a large $V$ component since all stars will be in nearly coplanar orbits.
 The bottom right. panels of Figs. 6-, The bottom right panels of Figs. \ref{M12_kin}-
 9. show the Toone diagram for cach simulations., \ref{M13_kin} show the Toomre diagram for each simulations.
 For MI2. the voung stars are concentrated in a small region of the diagram. centered around 1|—400kms and (C7|W7)/7?=Okms which is characteristic of a thin disc since these stars are mainly on fast rotating planar orbits.," For M12, the young stars are concentrated in a small region of the diagram, centered around $V=400\,{\rm km\,s^{-1}}$ and $(U^2+W^2)^{1/2}=0\,{\rm km\,s^{-1}}$, which is characteristic of a thin disc since these stars are mainly on fast rotating planar orbits."
 Phe old stars are distributed throughout the diagram. indicating that these stars follow. orbits with significant. racial ancl orthogonal velocities. characteristic of systems supported. by velocity dispersion.," The old stars are distributed throughout the diagram, indicating that these stars follow orbits with significant radial and orthogonal velocities, characteristic of systems supported by velocity dispersion."
 These stars are located mostly in the thick disc ancl halo., These stars are located mostly in the thick disc and halo.
 The Toomre diagrams for the other simulations show similarities. and also interesting cillerences. with the diagram for simulation MI2.," The Toomre diagrams for the other simulations show similarities, and also interesting differences, with the diagram for simulation M12."
 Some simulations present a cliscontinuity between the positive ancl negative region. of the diagram., Some simulations present a discontinuity between the positive and negative region of the diagram.
 For example. simulation rMI2 produces. two different population of old stars. one forming a thick disc and another one forming a counter-rotating thick clisc/halo.," For example, simulation rM12 produces two different population of old stars, one forming a thick disc and another one forming a counter-rotating thick disc/halo."
 Simulation All22 and ALLL have a cüllerent Foomre diagram than the other simulations., Simulation M12z and M11 have a different Toomre diagram than the other simulations.
 For \ll2z (Fig. 7)).," For M12z (Fig. \ref{M12z_kin}) ),"
 there is no, there is no
noise due to the low number density of galaxies in. each tomographic galaxy sample. apart from only the smallest angular frequencies.,"noise due to the low number density of galaxies in each tomographic galaxy sample, apart from only the smallest angular frequencies."
 As can be seen from (30). the errors scale inversely with the total number of galaxies in the survey If cosmic variance is negligible.," As can be seen from ), the errors scale inversely with the total number of galaxies in the survey if cosmic variance is negligible."
 Thus. if in the future larger number densities of galaxies with highly accurate photometric redshifts than assumed in this work are attainable. the constraints on GI correlations via the boosting technique will improve accordingly.," Thus, if in the future larger number densities of galaxies with highly accurate photometric redshifts than assumed in this work are attainable, the constraints on GI correlations via the boosting technique will improve accordingly."
 If we re-run the analysis for survey S with the galaxy number density assumed for survey PI. 1e. a factor of 10 higher. all the statistical errors indeed decrease by almost an order of magnitude.," If we re-run the analysis for survey S with the galaxy number density assumed for survey P1, i.e. a factor of 10 higher, all the statistical errors indeed decrease by almost an order of magnitude."
 If one is able to extract the GI signal from cosmic shear data. the question arises whether this could also be used to remove the GI contamination from the data and thus make cosmic shear analyses robust against biases due to intrinsic alignments.," If one is able to extract the GI signal from cosmic shear data, the question arises whether this could also be used to remove the GI contamination from the data and thus make cosmic shear analyses robust against biases due to intrinsic alignments."
 Intuitively. one can simply subtract an isolated GI signal from the original measures. and indeed we are going to devise such a procedure.," Intuitively, one can simply subtract an isolated GI signal from the original measures, and indeed we are going to devise such a procedure."
 Afterwards we will again propose a simple. parametric weight function to construct a boosting method. whose outcome will then be used to eliminate the GI signal.," Afterwards we will again propose a simple, parametric weight function to construct a boosting method, whose outcome will then be used to eliminate the GI signal."
" These steps are not optimised and merely serve to demonstrate the link between GI boosting and its removal. as well as to compare the performance of the latter to the standard nulling technique of in a simple scenario,"," These steps are not optimised and merely serve to demonstrate the link between GI boosting and its removal, as well as to compare the performance of the latter to the standard nulling technique of in a simple scenario."
 As an alternative to the procedure in 2.2. one can choose the lower integration boundary in (6) às μήν—y; ," As an alternative to the procedure in $\,$, one can choose the lower integration boundary in ) as $\chi_{\rm min}=\chi_i$."
As is evident from (7). in this case only the first term of the transformed GI signal remains.," As is evident from ), in this case only the first term of the transformed GI signal remains."
 Hence. it is likely that Yinin=O produces a larger amplitude of the modified GI power spectrum. but yin=y; results in a cleaner signal insofar as it contains only contributions from intrinsic alignments generated by matter at distance y;.," Hence, it is likely that $\chi_{\rm min}=0$ produces a larger amplitude of the modified GI power spectrum, but $\chi_{\rm min}=\chi_i$ results in a cleaner signal insofar as it contains only contributions from intrinsic alignments generated by matter at distance $\chi_i$."
 Consequently. we are going to use the latter choice of yi for constructing a method to remove the GI signal at y;.," Consequently, we are going to use the latter choice of $\chi_{\rm min}$ for constructing a method to remove the GI signal at $\chi_i$."
 The transformed lensing signal for yq;=y; 15 derived in analogy to (9) and reads Now suppose we are able to constructa boosting technique with à significant signal MG)) while nasrescaled(CO=0., The transformed lensing signal for $\chi_{\rm min}=\chi_i$ is derived in analogy to ) and reads Now suppose we are able to constructa boosting technique with a significant signal $\Pi_{\rm GI}^{(i)}(\ell)$ while $\Pi_{\rm GG}^{(i)}(\ell) \approx 0$.
 Noting again that the remaining first term in (7) is a version of the original GI signal (2.1). we define a further set of power spectra and likewise for the individual GG and GI signals.," Noting again that the remaining first term in ) is a rescaled version of the original GI signal ), we define a further set of power spectra and likewise for the individual GG and GI signals."
 This definition holds for all i«j., This definition holds for all $i < j$.
 The auto-correlations QU(/) would simply correspond to the original auto-correlation power spectra PP(£)., The auto-correlations $Q^{(ii)}(\ell)$ would simply correspond to the original auto-correlation power spectra $P^{(ii)}(\ell)$.
 As we are still working in the approximation of very narrow redshift bins. auto-correlations are hardly affected by Gl correlations at all.," As we are still working in the approximation of very narrow redshift bins, auto-correlations are hardly affected by GI correlations at all."
 In practice. auto-correlations are likely to be excluded or specially treated anyway due to the presence of intrinsic ellipticity correlations. see the discussion in 7.," In practice, auto-correlations are likely to be excluded or specially treated anyway due to the presence of intrinsic ellipticity correlations, see the discussion in $\,$ ."
 Assuming that the GI boosting works effectively. nas(ώς 0. so that one expects that UOxTUENTUR ie. the transformed cosmic shear signalQr is close to the original GG term.," Assuming that the GI boosting works effectively, $\Pi_{\rm GG}^{(i)}(\ell) \approx 0$ , so that one expects that $Q_{\rm GG}^{(ij)}(\ell) \approx P_{\rm GG}^{(ij)}(\ell)$, i.e. the transformed cosmic shear signal is close to the original GG term."
 Switching to the notation of narrow redshift bins again. we find for the transformed GI signal where we have inserted (2.1) and the first term of (7). and made use of the transition ο)—οίnyj). see (5).," Switching to the notation of narrow redshift bins again, we find for the transformed GI signal where we have inserted ) and the first term of ), and made use of the transition $g^{(j)}(\chi_i) \rightarrow g(\chi_j,\chi_i)$, see )."
 As a consequence. QUU)EPol)-fHWeg=POL.," As a consequence, $Q_{\rm obs}^{(ij)}(\ell) \approx P_{\rm GG}^{(ij)}(\ell) - f_{ij}\, \Pi^{(i)}_{\rm GG}(\ell) \approx P_{\rm GG}^{(ij)}(\ell)$."
 Hence. if we can devise an effective booting nique USINE yj. We immediately have a means of GI removal at our disposal via (33).," Hence, if we can devise an effective boosting technique using $\chi_{\rm min}=\chi_i$ , we immediately have a means of GI removal at our disposal via )."
 Note that the standard nulling technique as presented in also makes use of the definition (6) with yq;=y;., Note that the standard nulling technique as presented in also makes use of the definition ) with $\chi_{\rm min}=\chi_i$.
 The central condition in their approach ts recovered in our formalism by requiring G(y;)=0. which eliminates the GI signal under the same assumption of narrow redshift bins. see (7).," The central condition in their approach is recovered in our formalism by requiring $G^{(i)}(\chi_i)=0$, which eliminates the GI signal under the same assumption of narrow redshift bins, see )."
 For practical purposes we also switch to the discretised form of the signal transformation (10). using NOW fai=&," For practical purposes we also switch to the discretised form of the signal transformation ), using now $j_{\rm min}=i$."
 We begin by developing again a boosting technique. now for the changed condition yin=y;.," We begin by developing again a boosting technique, now for the changed condition $\chi_{\rm min}=\chi_i$."
 Due to the associated change in the lower boundary of integration in. (6). the condition to remove the GG signal is altered as well.," Due to the associated change in the lower boundary of integration in ), the condition to remove the GG signal is altered as well."
 Keeping the same approximations as used to derive ). we now obtain from (32) where we executed the integration over y and defined Inserting (11) into the foregoingdefinition and integrating by parts. one arrives at the useful relations," Keeping the same approximations as used to derive ), we now obtain from ) where we executed the integration over $\chi$ and defined Inserting ) into the foregoingdefinition and integrating by parts, one arrives at the useful relations"
that the dark matter problems on the galactic and cosmological scales have a common resolution. this need not necessarily be the case.,"that the dark matter problems on the galactic and cosmological scales have a common resolution, this need not necessarily be the case."
 Our focus in this paper will be on the ealactic dark matter problem as manifested in the ubiquitous observation of flat. rotation Curves., Our focus in this paper will be on the galactic dark matter problem as manifested in the ubiquitous observation of flat rotation curves.
 A number of ideas have been put forth to account for flat rotation curves., A number of ideas have been put forth to account for flat rotation curves.
 All require some form of new physics., All require some form of new physics.
 These ideas include: The communitw consensus al present prefers the dark matter hypothesis. but galactic dark matter has (hus lar evaded all attempts to detect it.," These ideas include: The community consensus at present prefers the dark matter hypothesis, but galactic dark matter has thus far evaded all attempts to detect it."
 We should strive to test. whenever possible. alternatives to the dark matter scenario.," We should strive to test, whenever possible, alternatives to the dark matter scenario."
 Motivated by the observed spiral galaxy rotation curves. Milgrom|(1983) proposecl a modification of the dvnamies of non-relativistie matter.," Motivated by the observed spiral galaxy rotation curves, \citet{Milgrom83} proposed a modification of the dynamics of non-relativistic matter."
 This modified behavior. termed MOND [or Modification of Newtonian Dynamics. is conjectured (o arise only in the regime of low accelerations.," This modified behavior, termed MOND for Modification of Newtonian Dynamics, is conjectured to arise only in the regime of low accelerations."
 MOND is a proposed modification to an objects acceleration under an applied force. such that à=g/pCr) where g is the acceleration expected under Newtonian physics. and a=e/e depends upon the MOND acceleration scale ay~1.2x10.m/s?. with pir>1)ceLtr«c cs ," MOND is a proposed modification to an object's acceleration under an applied force, such that $a=g/\mu(x)$ where $g$ is the acceleration expected under Newtonian physics, and $x=a/a_0$ depends upon the MOND acceleration scale $a_0 \sim 1.2 \times 10^{-10} m/s^2$, with $\mu(x \gg 1) \simeq
 1, \mu(x \ll 1) \simeq x$ ."
A commonly adopted form is pr)=ήν1-24227.," A commonly adopted form is $\mu(x) =
 {{x}/{\sqrt{1+x^2}}}$."
 In general a eravilaling svstem's behavior under MOND can be described by (taking the Newtonian description and replacing C. the coupling constant. by Cj. with the understanding that the dvnamies is being altered rather than the nature of the gravitational interaction.," In general a gravitating system's behavior under MOND can be described by taking the Newtonian description and replacing $G$, the coupling constant, by $G/\mu$, with the understanding that the dynamics is being altered rather than the nature of the gravitational interaction."
 In this scenario the mass of a galaxy. resides in (he ordinary. astrononical components that we can detect by their emission or absorption of electromagnetic radiation. and the ealaxy’s light distribution traces out its mass distribution.," In this scenario the mass of a galaxy resides in the ordinary astronomical components that we can detect by their emission or absorption of electromagnetic radiation, and the galaxy's light distribution traces out its mass distribution."
 A review of MONDas an alternative to dark matter ispresented in Sanders&AMeGaugh (2002).., A review of MONDas an alternative to dark matter ispresented in \citet{Sanders02}. .
poMEAM;,$\mu\equiv M/M_i$.
 Vor clarity. we provide below a brief description of these processes.," For clarity, we provide below a brief description of these processes."
 Since we are dealing essentially with cisk clusters. we adopt the Solar-metallicity. approximation given by Lamers&Gicles (2006).. which is based. on single-stellar population GALENV mocdels (CAnders&Eritze-v.Alvensleben 2003)) and a Salpeter-like (Salpeter 1955)) mass function: with qqΞlog(/)1.0. e—0.255. and b=1.805.," Since we are dealing essentially with disk clusters, we adopt the Solar-metallicity approximation given by \citet{LG06}, which is based on single-stellar population GALEV models \citealt{GALEV}) ) and a Salpeter-like \citealt{Salp55}) ) mass function: with $qq = \log(t)-1.0$, $a=0.255$, and $b=-1.805$."
 This process is relevant for |/o>10 Myr., This process is relevant for $t>10$ Myr.
" We adopt the semi-analvtical description of the niass-Ioss of clusters on a steadvy-tidal field of Lamers.Baumgardt&CGieles (2010).. which is expected to apply to a broad range of cluster conditions and orbit environments: with /,-—HEU""(1yf[Haum 2nm MMvr for clusters with an initial concentration [actor of the density Wing profile Woy=5. and £j=3.5 MMyr for ο 0:5=0.65 for Mi=5 and 5=OS for Mu=7. hus. both > and /j are not independent. parameters. since hey can be expressed as a function of Wo: ο is the cluster orbit eccentricity: the average stellar mass at time / is given » the interpolation formula :(/)=0.6193.—0.036270148177| 0.002277. where r=log(/): Rey is the cluster's Galactocentric distance. ancl ec; is the (assumed. constant) rotation velocity."," We adopt the semi-analytical description of the mass-loss of clusters on a steady-tidal field of \citet{Lamers10}, which is expected to apply to a broad range of cluster conditions and orbit environments: with $t_o = t_R\left(\frac{1-\epsilon}{\bar m^\gamma}\right)\left(\frac{R_G}{8.5kpc}
\right)\left(\frac{v_G}{220\kms}\right)^{-1}$, $t_R=13.3$ Myr for clusters with an initial concentration factor of the density King profile $W_0=5$, and $t_R=3.5$ Myr for $W_0=7$; $\gamma=0.65$ for $W_0=5$ and $\gamma=0.8$ for $W_0=7$, thus, both $\gamma$ and $t_R$ are not independent parameters, since they can be expressed as a function of $W_0$; $\epsilon$ is the cluster orbit eccentricity; the average stellar mass at time $t$ is given by the interpolation formula $\bar m(t) = 0.6193-0.0362\tau-0.01481\tau^2+0.0022\tau^3$ , where $\tau=\log(t)$; $R_G$ is the cluster's Galactocentric distance, and $v_G$ is the (assumed constant) rotation velocity."
 In what follows we take ec;=200kmis or orbits around the Solar neighbourhood.," In what follows we take $v_G=200\,\kms$ for orbits around the Solar neighbourhood."
 The energv gain and the mass loss due to the clisruptive οσο of spiral-armi passages of star clusters with planar ane circular orbits around the centres of galaxies has been thoroughly studied by Cicles.Athanassoula&PortegicsZwart (2007)., The energy gain and the mass loss due to the disruptive effect of spiral-arm passages of star clusters with planar and circular orbits around the centres of galaxies has been thoroughly studied by \citet{GAP07}.
. In. particular. for the Solar neighbourhood. Ciclos.Athanassoula&PortegiesZwart(2007). and Lamers&Gieles(2006). find: Similarly to the spiral arms. Lamers&Cicles(2006) estimate the energy. gain ancl mass loss due to encounters between clusters and GAICs.," In particular, for the Solar neighbourhood, \citet{GAP07} and \citet{LG06} find: Similarly to the spiral arms, \citet{LG06} estimate the energy gain and mass loss due to encounters between clusters and GMCs."
 Assuming GALC parameters typical of the Solar neighbourhood. they find: ‘Phe mass loss due to GAIC's is thus 10 times higher than that of the spiral armis.," Assuming GMC parameters typical of the Solar neighbourhood, they find: The mass loss due to GMCs is thus 10 times higher than that of the spiral arms."
 Stars can also escape from a cluster by. means of ejection and evaporation., Stars can also escape from a cluster by means of ejection and evaporation.
 jection occurs when. after a single. close encounter with another star. à member ends up with excess velocity with respect to the escape velocity.," Ejection occurs when, after a single, close encounter with another star, a member ends up with excess velocity with respect to the escape velocity."
 Evaporation. on the other hand. is related to a series of more distant encounters that eracually increase a stars energy. eventually leacing it to escape from the cluster.," Evaporation, on the other hand, is related to a series of more distant encounters that gradually increase a star's energy, eventually leading it to escape from the cluster."
" With the respective time scales taken from Ixhalisi. Amaro-Seoane Spurzenm. (2007. and references therein). the mass loss associated with both processes are. respectively: and where the half-mass radius is given by A, (Larsen 2004). τν=0.11 is the Coulomb factor. (1/103)N=Απ) is the number of stars at time £. and C is the gravitational constant."," With the respective time scales taken from Khalisi, Amaro-Seoane Spurzem (2007, and references therein), the mass loss associated with both processes are, respectively: and where the half-mass radius is given by $R_{hm} = 3.75\left(M/10^4\right)^{0.1}$ \citealt{Larsen04}) ), $\gamma_c=0.11$ is the Coulomb factor, $N=M(t)/\bar m(t)$ is the number of stars at time $t$ , and $G$ is the gravitational constant."
 In summary. given a cluster of initial mass M;. and a set of model parameters(Rec. Wo. 5.6. Eg). Eq.," In summary, given a cluster of initial mass $M_i$, and a set of model parameters, $W_0$, $\gamma$, $\epsilon$, $t_R$ ), Eq."
 1 should be solved to find the mass still bound to the cluster at a later time /. M= M(). The Solar neighbourhood ADE has been subject to previous investigation.," \ref{eq1} should be solved to find the mass still bound to the cluster at a later time $t$ , $M=M(t)$ The Solar neighbourhood ADF has been subject to previous investigation."
 In particular. Lamersetal.(2005)— and Lamers&Gicles(2006) employed. the cluster dissolution processes 1.4 (Sect. 3))," In particular, \citet{Lamers05} and \citet{LG06} employed the cluster dissolution processes 1—4 (Sect. \ref{TCADF}) )"
 to study. the ADE of 114: OC's closer than d.= Q.Gkkpe taken from Ixharchenkoctal. (2005)., to study the ADF of 114 OCs closer than $\ds=0.6$ kpc taken from \citet{Kharchenko05}.
. Their ADF can be reasonably well described. by a nearlv-constant. SER. (in bound clusters of mass 107.<ARM.)<3. 104) of SPR=40041.Myr corresponding to a surface formation rate ενzBOOAL.Myr5kpe which is considerably lower than the νε=τοῦ1000AL.Myr5kpe? inferred. from ECs (Lada.&/Lada 2003)). andthe Xsp=3000.7000M.Myr!kpe? from ficld stars (Miller&Sealo 1979)).," Their ADF can be reasonably well described by a nearly-constant SFR (in bound clusters of mass $10^2<M(\ms)<3\times10^4$ ) of $SFR=400\,\mmy$, corresponding to a surface formation rate $\ssfr\approx350\,\mmk$, which is considerably lower than the $\ssfr=700-1000\,\mmk$ inferred from ECs \citealt{LL2003}) ), and the $\ssfr=3000-7000\,\mmk$ from field stars \citealt{MS79}) )."
 They. also find evidence of a local burst of star formation that took place between MNSr ago (also present inPiskunovetal. 2006)).Yosicdes cluster dissolution. observational completeness is also important for the ADI shape.," They also find evidence of a local burst of star formation that took place between Myr ago (also present in\citealt{Piskunov06}) ).Besides cluster dissolution, observational completeness is also important for the ADF shape."
 Ligh absorption aud crowding. usually associated with fieldsdominated by clise ancl bulge stars. alfect. cluster detectability. especially. the faint and/or poorly-populated ones.," High absorption and crowding, usually associated with fieldsdominated by disc and bulge stars, affect cluster detectability, especially the faint and/or poorly-populated ones."
observed (V-I) color of the Pleiades) would result in an age of 126 4 11 Mvr for the Pleiacles. where the error includes the observational and theoretical uncertainty only (see Table 2)).,"observed (V-I) color of the Pleiades) would result in an age of 126 $\pm$ 11 Myr for the Pleiades, where the error includes the observational and theoretical uncertainty only (see Table \ref{obstab}) )."
 Alternative ages and errors of the other open clusters adopting the 0.3 magnitude change in the I-band bolometrie correction are given in parenthesis in Table 2.., Alternative ages and errors of the other open clusters adopting the 0.3 magnitude change in the I-band bolometric correction are given in parenthesis in Table \ref{obstab}.
 Our LDB age for the Pleiades is even older than the original LDB age estimate of 125 Ayr given in Stamler.Schultz.&Wirkpatrick(1998)., Our LDB age for the Pleiades is even older than the original LDB age estimate of 125 Myr given in \citet{sta98}.
. In deriving the Pleiades age. Slautler.Schultz.&Nirkpatrick(1998) emplov the caleulations of Baralleοἱal.(1998). ," In deriving the Pleiades age, \citet{sta98} employ the calculations of \citet{bar98}. ."
As discussed in Sections ?? and ??.. the lithium depletion calenlations of at the lowest Iuminosities/oldest ages are vounger by15%.," As discussed in Sections \ref{interrbudget} and \ref{exterrbudget}, the lithium depletion calculations of \citet{bar98} at the lowest luminosities/oldest ages are younger by."
.. The vounger age is a 2-8 deviation from our reference model based on our examination of the theoretical errors in the LDB ages., The younger age is a $\sigma$ deviation from our reference model based on our examination of the theoretical errors in the LDB ages.
 Using identical input physics as close as possible to Baralleetal.(1998). we are unable to reproduce their voung LDB ages at the lowest Iuminosities.," Using identical input physics as close as possible to \citet{bar98}, we are unable to reproduce their young LDB ages at the lowest luminosities."
 Until other independent calculations are available. including an additional error to the LDB ages nav be warranted.," Until other independent calculations are available, including an additional error to the LDB ages may be warranted."
 This svstematic error is discussed in Section ?? and is not included in our error budget as it does not materially affect any conclusions., This systematic error is discussed in Section \ref{exterrbudget} and is not included in our error budget as it does not materially affect any conclusions.
 For the Pleiades cluster. the LDD age technique is dominated by uncertainties in the bolometric correction and the observational LDB location.," For the Pleiades cluster, the LDB age technique is dominated by uncertainties in the bolometric correction and the observational LDB location."
 If the bolometric correction and LDB location error sources are eliminated. (hen our calculations show the LDB age technique could provide absolute ages for open clusters accurate to for 200 Myr clusters increasing to for 20 Myr clusters.," If the bolometric correction and LDB location error sources are eliminated, then our calculations show the LDB age technique could provide absolute ages for open clusters accurate to for 200 Myr clusters increasing to for 20 Myr clusters."
 We want to thank I. Daralfe. J. Stauffer. and D. Τοπνο for useful discussions.," We want to thank I. Baraffe, J. Stauffer, and D. Terndrup for useful discussions."
 Thiswork was supported by NSF erant. AST-0206003., Thiswork was supported by NSF grant AST-0206008.
measurements.,measurements.
 An important aspect of our conversion to the Lick svstem is the adoption of standard index values [rom Schiavon(2007).. rather than those of Worthevetal.(1994).," An important aspect of our conversion to the Lick system is the adoption of standard index values from \cite{s07}, rather than those of \cite{wo94}."
.. We proceeded (his way because of (he higher accuracy of the Schiavon(2007)/ indices., We proceeded this way because of the higher accuracy of the \cite{s07} indices.
 Because (μον are based on [lux-calibrated CCD spectra. they are free Irom the uncertainties associated with diflieulties in calibrating data obtained with the Lick Image Dissector Scanner. upon which the Worthevetal.(1994). indices are based.," Because they are based on flux-calibrated CCD spectra, they are free from the uncertainties associated with difficulties in calibrating data obtained with the Lick Image Dissector Scanner, upon which the \cite{wo94} indices are based."
 For more details. see discussion in Schiavon (2007).. ancl particularly Figures 1 ancl 2 of that. paper.," For more details, see discussion in \cite{s07}, and particularly Figures 1 and 2 of that paper."
 Insirumental and standard Lick indices are compared in Figures d. and 2. [or the Tololo data. and in Figures 3. and [ον the IHHectospec data. where residuals ave plotted as a function of index strength.," Instrumental and standard Lick indices are compared in Figures \ref{zeroa}
 and \ref{zerob} for the Tololo data, and in Figures \ref{zm31a}
 and \ref{zm31b} for the Hectospec data, where residuals are plotted as a function of index strength."
 Error bars were calculated based on propagation of photon noise. readout noise. and sky-subtraction errors into index measurements. following elal. (1998).," Error bars were calculated based on propagation of photon noise, readout noise, and sky-subtraction errors into index measurements, following \cite{ca98}."
. In the ease of the Tololo data. thev are smaller than the svmbol sizes. and are (hus not plotted.," In the case of the Tololo data, they are smaller than the symbol sizes, and are thus not plotted."
 The IDs of the standard stars observed. as well as the instrumental nmeasurenienis are provided in Tables 4. through 7..," The IDs of the standard stars observed, as well as the instrumental measurements are provided in Tables \ref{std_m31a}
 through \ref{std_mwb}."
 The standard values were taken from Schiavon(2007).. for the indices modeled in that paper.," The standard values were taken from \cite{s07}, for the indices modeled in that paper."
 The residuals are in general small. and so are the zero point corrections lor all indices in both sets of observations. which is a result. of the data being based on flux calibrated. hieh-S/N spectra. as discussed by Schiavon (2007).," The residuals are in general small, and so are the zero point corrections for all indices in both sets of observations, which is a result of the data being based on flux calibrated, high-S/N spectra, as discussed by \cite{s07}."
. We note that. due mostly to unfavorable weather. we unfortunately were unable to collect data for a large number of Lick standards. particularly during the observing run in Cerro Tololo. where the Galactic GCs were observed.," We note that, due mostly to unfavorable weather, we unfortunately were unable to collect data for a large number of Lick standards, particularly during the observing run in Cerro Tololo, where the Galactic GCs were observed."
 Therefore. as seen in those Figures. (he conversion to the standard Lick svstem is sometimes based on a handful of data points. in most cases spanning an insullicient range of index strengths. resulting in somewhat uncertain. (hough small. zero point corrections.," Therefore, as seen in those Figures, the conversion to the standard Lick system is sometimes based on a handful of data points, in most cases spanning an insufficient range of index strengths, resulting in somewhat uncertain, though small, zero point corrections."
 Most importantly. lor the purposes of (hiis paper. we note that (he residuals of the CN indices in both data sets are," Most importantly, for the purposes of this paper, we note that the residuals of the CN indices in both data sets are"
s) regular outbursts is a key test of the correct. viscosity parameterization.,s) regular outbursts is a key test of the correct viscosity parameterization.
 Another type of the thermal - viscous instability occurs due to the partial ionization of hvdrogen ancl helium., Another type of the thermal - viscous instability occurs due to the partial ionization of hydrogen and helium.
 The unstable zone is twpically present in the outer part of the disc. where the effective temperature is of order of 6000 Ix. The ionization instability was first found by Alever& and Smak(1984). in the clisks surrounding white ciwarls and it is at present the accepted explanation of the dwarl novae ancl X-ray novae outbursts.," The unstable zone is typically present in the outer part of the disc, where the effective temperature is of order of 6000 K. The ionization instability was first found by \cite{meyer81} and \cite{smak84} in the disks surrounding white dwarfs and it is at present the accepted explanation of the dwarf novae and X-ray novae outbursts."
 The numerical models presented in a number of works (ce... Dubusetal.(2001). Janiuketal. (2004):: for a review. see Lasota (2001))) stuclied the one or two (111) dimensional models of the global evolution of accretion disces under the thermal and viscous instability and confirmed the possibility of the limit evcle behaviour.," The numerical models presented in a number of works (e.g., \cite{dubus01}, \cite{janiuk04}; ; for a review, see \cite{Lasota01}) ) studied the one or two (1+1) dimensional models of the global evolution of accretion discs under the thermal and viscous instability and confirmed the possibility of the limit cycle behaviour."
 The hydrogen ionization instability is thus an example ofa firm agreement between the observations and theory., The hydrogen ionization instability is thus an example of a firm agreement between the observations and theory.
 A recent example is SU UAla-type dwarf nova V344 Lyr observed. by. Ixepler. satellite. for which its outbursts and supcroutbursts have been modeled with this instability (Cannizzoetal. (2010))).," A recent example is SU UMa-type dwarf nova V344 Lyr observed by Kepler satellite, for which its outbursts and superoutbursts have been modeled with this instability \cite{can10}) )."
 This instability also likely applies to active galaxies (Lin&Shields (1986).. Mineshige&Shields (1990))) although this is still uncertain.," This instability also likely applies to active galaxies \cite{lin86}, \cite{mineshige90}) ) although this is still uncertain."
 The models of the outbursts were further developed by Sicmiginowskaetal. (1996)... Janiuk (2004).. and they were applied to statistics of ACN by Sicmiginowska&Elvis(1997).," The models of the outbursts were further developed by \cite{siem96}, , \cite{janiuk04}, and they were applied to statistics of AGN by \cite{sie97}."
. Menou&Quataert(2001) ancl Llameuryctal.(2009) argued that the amplitude of such outbursts will be small but the evaporation of the inner disk enhances the amplitude considerably al.(2004) and prolongs the qiescent state Llameury (2009)., \cite{MenQ01} and \cite{hameury09} argued that the amplitude of such outbursts will be small but the evaporation of the inner disk enhances the amplitude considerably \cite{janiuk04} and prolongs the qiescent state \cite{hameury09}.
. 1n this case the situation is much similar to the above. as the disc eveles between two states.," In this case the situation is much similar to the above, as the disc cycles between two states."
 The hot and. mostly ionized state of a [large local accretion rate is intermittent with a cold. neutral state of a small local accretion rate.," The hot and mostly ionized state of a large local accretion rate is intermittent with a cold, neutral state of a small local accretion rate."
 Again. the quantitative outcome of the model is governed bv the assumed external (mean) accretion rate. viscosity and mass of the central object.," Again, the quantitative outcome of the model is governed by the assumed external (mean) accretion rate, viscosity and mass of the central object."
 We calculated the steady-state. models. of the accretion clise structure. for two exemplary values of the black hole mass. characteristic for Galactic sources (10 AZ.) and AGN (1O°AL.).," We calculated the steady-state models of the accretion disc structure, for two exemplary values of the black hole mass, characteristic for Galactic sources (10 $M_{\odot}$ ) and AGN $10^{8} M_{\odot}$ )."
 Phe mocels are based on the vertically averaged equations for the energy balance between the viscous heating and radiative as well as advective cooling ancl hyclrostatic equilibrium., The models are based on the vertically averaged equations for the energy balance between the viscous heating and radiative as well as advective cooling and hydrostatic equilibrium.
 The heating term. governed. by the viscosity »xwameter à. is in the radiation pressure dominated region assumed. proportional to either the total pressure. or to the square root of the total times the gas pressure.," The heating term, governed by the viscosity parameter $\alpha$, is in the radiation pressure dominated region assumed proportional to either the total pressure, or to the square root of the total times the gas pressure."
 In the gas oessure dominated region. located at larger distances. t realing is assumed proportional only to the gas pressure.," In the gas pressure dominated region, located at larger distances, the heating is assumed proportional only to the gas pressure."
 We caleulate here the vertical profiles of temperature. density ancl pressure. using the opacity tables that cover the cmperature range relevant for partial hydrogen ionization. inclucling the presence of dust and molecules (see details in Rozatiskaetal.(1999))).," We calculate here the vertical profiles of temperature, density and pressure, using the opacity tables that cover the temperature range relevant for partial hydrogen ionization, including the presence of dust and molecules (see details in \cite{roz99}) )."
 The basic parameter of cach stationary mocel is the elobal (external) accretion rate. through which we determine the total energy. Hux dissipated in the dise at every racius r.," The basic parameter of each stationary model is the global (external) accretion rate, through which we determine the total energy flux dissipated in the disc at every radius $r$."
 Once the cllective temperature ancl surface density are determined at every dise raclius. we find the stable solutions. Le. the accretion rates for which the slope of {οX (or AQ) relation is positive. and the unstable solutions. with he negative slopes.," Once the effective temperature and surface density are determined at every disc radius, we find the stable solutions, i.e. the accretion rates for which the slope of $T-\Sigma$ (or $\dot M -\Sigma$ ) relation is positive, and the unstable solutions, with the negative slopes."
" In other words. the ""S-curve is plotted ocallv at a number of disk. racii and we search for the critical ii points at which the curve is bending."," In other words, the “S-curve” is plotted locally at a number of disk radii, and we search for the critical $\dot m$ points at which the curve is bending."
 These points imit the maximum and minimum. values of accretion rates or which at a given radius the disk will be unstable., These points limit the maximum and minimum values of accretion rates for which at a given radius the disk will be unstable.
 In turn. we determine the range of radii. for which at a given global accretion rate the disc is unstable first due to the radiation oessure and then to the ionization instability.," In turn, we determine the range of radii, for which at a given global accretion rate the disc is unstable first due to the radiation pressure and then to the ionization instability."
 For the latter. the unstable strip is located at the outskirts of the disk.," For the latter, the unstable strip is located at the outskirts of the disk."
 Obviously. if the instability. arises at he outer disk. the front will then propagate inwarels to much smaller racic," Obviously, if the instability arises at the outer disk, the front will then propagate inwards to much smaller radii."
 However. if the disk size is smaller than he inner edge of the unstable strip plotted. in Figure 1.. no ionization instability. outbursts should take place.," However, if the disk size is smaller than the inner edge of the unstable strip plotted in Figure \ref{fig:topo}, no ionization instability outbursts should take place."
 Our results. based on the detailed vertical structure caleulations. are consistent with the simplified. formulae. given. in the Appendix of Lasota—(2001). with respect to the inner xundary. of the ionisation instability strip.," Our results, based on the detailed vertical structure calculations, are consistent with the simplified formulae given in the Appendix of \cite{Lasota01}, with respect to the inner boundary of the ionisation instability strip."
 Lhe outer edge we determined is somewhat larger. due to a dilferent opacity ables in our model which include absorption on molecules. e.g. molecular hydrogen. as described in (1999).," The outer edge we determined is somewhat larger, due to a different opacity tables in our model which include absorption on molecules, e.g. molecular hydrogen, as described in \cite{roz99}."
. In Figure 1. we show the maps of the disc instabilities or the to chosen black hole masses. on the plane radius vs. elobal accretion rate (in dimensionless units).," In Figure \ref{fig:topo} we show the maps of the disc instabilities for the two chosen black hole masses, on the plane radius vs. global accretion rate (in dimensionless units)."
 In. addition. we distinguish the two possible stabilizing mechanisms for he radiation pressure instability: the heating prescription and the possibility of energy outflow to the jet.," In addition, we distinguish the two possible stabilizing mechanisms for the radiation pressure instability: the heating prescription and the possibility of energy outflow to the jet."
 The latter is parameterized by the following function: and the jet outllow actsas a source of additional cooling (Navakshinetal.(2000)... Janiuketal... (2002))).," The latter is parameterized by the following function: and the jet outflow actsas a source of additional cooling \cite{nayak00}, \cite{janiuk02}) )."
 The jet outllow: reduces the size of the unstable zone for large accretion rates. as well as limits the instability to operate below some threshold maximum ri.," The jet outflow reduces the size of the unstable zone for large accretion rates, as well as limits the instability to operate below some threshold maximum $\dot m$."
 This rate is of course sensitive to our adopted: parameter for the jet streneth., This rate is of course sensitive to our adopted parameter for the jet strength.
 Phe Figure 1. shows the case of a very strong jet. with of=25 and in this case the limiting accretion rate is about of the Exidington rate.," The Figure \ref{fig:topo} shows the case of a very strong jet, with $A=25$ and in this case the limiting accretion rate is about of the Eddington rate."
 For a LO times weaker jet the limiting accretion rate is about 3 times larger., For a 10 times weaker jet the limiting accretion rate is about 3 times larger.
 The viscosity parameter. a. only moderately alfects the results for the radiation pressure instability. apart from the timescales of the μμ evele.," The viscosity parameter, $\alpha$, only moderately affects the results for the radiation pressure instability, apart from the timescales of the limit cycle."
 Phe Figure Ll presents the conservative case of a very small viscosity. a=0.01. for which the extension of the unstable zone is small.," The Figure \ref{fig:topo} presents the conservative case of a very small viscosity, $\alpha=0.01$, for which the extension of the unstable zone is small."
 If the viscosity is larger. the unstable zone size is also increased. for instance for a=0.1 the outer radius of the instability is larger by a factor of ~ 1.25.," If the viscosity is larger, the unstable zone size is also increased, for instance for $\alpha=0.1$ the outer radius of the instability is larger by a factor of $\sim 1.25$ ."
 This also means that the minimum. accretion rate for which the cise isunstable. is slightly smaller.," This also means that the minimum accretion rate for which the disc isunstable, is slightly smaller."
However. in this smallest accretion rates the unstable zone is very narrow.,"However, in this smallest accretion rates the unstable zone is very narrow."
 For a very narrow width of the, For a very narrow width of the
that. with perfect knowledge of the shear field. a good reconstruction is achieved with our method.,"that, with perfect knowledge of the shear field, a good reconstruction is achieved with our method."
 For the cluster at 2=0.25. the error is <0.1 of the signal within a radius of 0.2 degrees of the cluster. except for the core pixel where the error isH1.," For the cluster at $z=0.25$, the error is $<0.4$ of the signal within a radius of 0.2 degrees of the cluster, except for the core pixel where the error is."
554.. For the cluster at τ=0.5. the error is <5% of the sienal within a radius of 0.1 degrees of the cluster. except for the core pixel where the error is.," For the cluster at $z=0.5$, the error is $<5\%$ of the signal within a radius of 0.1 degrees of the cluster, except for the core pixel where the error is."
 This is again due to the cusp at the cluster ceutre. which cannot be followed well by our averaged shear field.," This is again due to the cusp at the cluster centre, which cannot be followed well by our averaged shear field."
 Nevertheless. it is clear that our method is successful in reconstructing cluster eravitatioual poteutials iu the absence of noise.," Nevertheless, it is clear that our method is successful in reconstructing cluster gravitational potentials in the absence of noise."
 Having demonstrated that the inversions of the shear field to obtain the gravitational poteutial is viable iu the absence of noise. we now wish to add the two primary sources of noise present in leusiug experiments: Poisson noise due to only sampling the field at a finite set of galaxy positions. and additional noise due to galaxies’ non-zero cllipticitics.," Having demonstrated that the inversions of the shear field to obtain the gravitational potential is viable in the absence of noise, we now wish to add the two primary sources of noise present in lensing experiments: Poisson noise due to only sampling the field at a finite set of galaxy positions, and additional noise due to galaxies' non-zero ellipticities."
 As an example we use umber deusities for plausible space-based experiments (100 per sq arcmin). aud an appropriate umber of objects at cach redshift slice.," As an example we use number densities for plausible space-based experiments (100 per sq arcmin), and an appropriate number of objects at each redshift slice."
 Figure 5 (LIIS) shows the dark matter potential measurements for our notional space-based survey after Wiener filtering., Figure \ref{simspace} (LHS) shows the dark matter potential measurements for our notional space-based survey after Wiener filtering.
 We measure the +=0.25 chister with v=L2 at the peak (trough) pixel of its eravitational potential well. with v=2.1 at the eravitational potential trough of the ~=0.1 cluster.," We measure the $z=0.25$ cluster with $\nu=4.2$ at the peak (trough) pixel of its gravitational potential well, with $\nu=2.1$ at the gravitational potential trough of the $z=0.4$ cluster."
 We also find a substantial noise peak in the foreground at 2=0.1., We also find a substantial noise peak in the foreground at $z=0.1$.
 While the recovery of the cluster eravitational potentials therefore constitutes a challenging measuremoenut. we are indeed able to reconstruct useful iuformation in the eravitational potential Beld itself. (," While the recovery of the cluster gravitational potentials therefore constitutes a challenging measurement, we are indeed able to reconstruct useful information in the gravitational potential field itself. ("
The significance of these clusters is ιο higher than the measurement 7 at a eiven point in the cluster).,The significance of these clusters is much higher than the measurement $\nu$ at a given point in the cluster).
 Iu this section. we will use these methods to calculate the dark matter potential for the COMDOLT? supercluster A901/2 (See Cray et al 2002 for a 2-D shear analysis}.," In this section, we will use these methods to calculate the dark matter potential for the COMBO17 supercluster A901/2 (See Gray et al 2002 for a 2-D shear analysis)."
 For more details of the 3-D dark. latter reconstruction see Tavlor et al (2003)., For more details of the 3-D dark matter reconstruction see Taylor et al (2003).
 Fi, Fig.
s.5 (RIS) shows a cross-section through the final Φ feld., \ref{simspace} (RHS) shows a cross-section through the final $\Phi$ field.
 Note several siguificaut features of this field., Note several significant features of this field.
 Firstly. we see that the eravitational potential trough associated with supercluster at 2=0.16 is clearly recovered at the bottom ofthe plot. with a peak pixel S/N of 2.9.," Firstly, we see that the gravitational potential trough associated with supercluster at $z=0.16$ is clearly recovered at the bottom of the plot, with a peak pixel S/N of 2.9."
 Secondly. further analysis shows that the gravitational potential displavs troughs at approximately the positions of the three component," Secondly, further analysis shows that the gravitational potential displays troughs at approximately the positions of the three component"
comparable to the spectral resolution. to reduce the artificial per-pixel errors and error correlations.,comparable to the spectral resolution to reduce the artificial per-pixel errors and error correlations.
 In this paper. all Stokes parameters were rebinned to a iinterval.," In this paper, all Stokes parameters were rebinned to a interval."
 The binning was done by calculating the average polarization within a bin weighted bv the number of detected photons within each pixel (Wang.Wheeler.&ΠΟΙΟ1997)., The binning was done by calculating the average polarization within a bin weighted by the number of detected photons within each pixel \citep{WWH:1997}.
. The 15À bbinning was chosen so (hat it is slightly larger than spectral resolution of the data (12.7 A)) to eliminate sampling errors of the resolution element., The 15 binning was chosen so that it is slightly larger than spectral resolution of the data (12.7 ) to eliminate sampling errors of the resolution element.
 The rebinning is equivalent to calculating the degree of polarization of all photons integrated in each bin: when the bin size is larger than the resolution element. the errors of the Stokes Parameters in each wavelength bin are uncorrelated.," The rebinning is equivalent to calculating the degree of polarization of all photons integrated in each bin; when the bin size is larger than the resolution element, the errors of the Stokes Parameters in each wavelength bin are uncorrelated."
 Typical photon statistical errors in (he Q and U vector after binnine io the 15 interval are around [or all of these observations and are not a major source of error in (he discussion of (hese data., Typical photon statistical errors in the Q and U vector after binning to the 15 interval are around for all of these observations and are not a major source of error in the discussion of these data.
 During the commissioning of FOBRS1 in 1993/1999 (he svstematic instrumental polarization of FORSI was found to be less than (Szeilert 1999. private communication).," During the commissioning of FORS1 in 1998/1999 the systematic instrumental polarization of FORS1 was found to be less than (Szeifert 1999, private communication)."
 Errors during data reduction are expected to be small as well (<0.02%) as (he data are reduced in double precision., Errors during data reduction are expected to be small as well $<0.02\%$ ) as the data are reduced in double precision.
 Figure 2 shows the spectral evolution of SN 2001el., Figure 2 shows the spectral evolution of SN 2001el.
 The date of 2 maximum of SN 2001el was found to be Sept 31 by Ixrisciunasetal...(2003).. from which we found (hat our spectra were taken al -4. +1. —10. +19. and +41 days from D maximum. respectively.," The date of $B$ maximum of SN 2001el was found to be Sept 31 by \citet{Krisciunas:2003}, from which we found that our spectra were taken at -4, +1, +10, +19, and +41 days from $B$ maximum, respectively."
 SN 2001el would be a spectroscopically normal supernova had the wavelengths bevond 750 nm nol been observed in the pre-maximum phase., SN 2001el would be a spectroscopically normal supernova had the wavelengths beyond 750 nm not been observed in the pre-maximum phase.
 The match of spectral features (ο SN 1994D is extremely good except for the vicinitv of the Ca II IR. triplet., The match of spectral features to SN 1994D is extremely good except for the vicinity of the Ca II IR triplet.
 The Ca IL IR triplet is clearly detected in all our spectra of SN 2001el with a strength Chat grows in (ime al a velocity around -10.000 km J|. close to the velocities given by other photospheric lines such as Si I] 635.5 nm.," The Ca II IR triplet is clearly detected in all our spectra of SN 2001el with a strength that grows in time at a velocity around -10,000 km $^{-1}$, close to the velocities given by other photospheric lines such as Si II 635.5 nm."
 The feature that distinguishes SN 2001el is a distinctively strong absorption αἱ around 300 nm., The feature that distinguishes SN 2001el is a distinctively strong absorption at around 800 nm.
 As argued below. we interpret this as a kinematically ancl geometrically separate filaanent or shell of caleium-rich material.," As argued below, we interpret this as a kinematically and geometrically separate filament or shell of calcium-rich material."
 SN 1994D and other SN Ia have shown weak features corresponding to the Ca II IR triplet at. hieh velocities with a double-hunmped absorption minimum (Ilatanoetal.1999)., SN 1994D and other SN Ia have shown weak features corresponding to the Ca II IR triplet at high velocities with a double-humped absorption minimum \citep{Hatano:1999}.
. Alodels of SN 1994D showed that the Ca II IR: triplet can form a feature with a two- absorption minimum (lIlolfilich 1995b: IHófllich. Wheeler Thielemann 1993. their Figure 9). but that the double minimum structure is primarily dictated by the density and temperature through the ionization in such a way that the feature should recede in," Models of SN 1994D showed that the Ca II IR triplet can form a feature with a two-component absorption mimimum (Höfflich 1995b; Höfflich, Wheeler Thielemann 1998, their Figure 9), but that the double minimum structure is primarily dictated by the density and temperature through the ionization in such a way that the feature should recede in"
In the previous section. we stunmarizecl (he circumstellar gas evolution during the TP-AGD phase and related it with the stellar wind behavior.,"In the previous section, we summarized the circumstellar gas evolution during the TP-AGB phase and related it with the stellar wind behavior."
 The dvnoamical evolution ol the cireiumstellar gas is highly non-linear. and although the stellar wind on the experiences huge modulations. the circumstellar gas structure does not retain this inlormation.," The dynamical evolution of the circumstellar gas is highly non-linear, and although the stellar wind on the TP-AGB experiences huge modulations, the circumstellar gas structure does not retain this information."
 The subsequently formed shells are either accelerated during the evolution. or decelerated by the ISM. most of them disappearing when thev merge wilh other shells or when they reach pressure equilibrium with the surroundings.," The subsequently formed shells are either accelerated during the evolution, or decelerated by the ISM, most of them disappearing when they merge with other shells or when they reach pressure equilibrium with the surroundings."
 The shells formed bv a shock in (he interaction region between (wo subsequentis enhancements of mass-loss ancl velocity are the most stable structures. and remain visible at the end of the AGB phase.," The shells formed by a shock in the interaction region between two subsequents enhancements of mass-loss and velocity are the most stable structures, and remain visible at the end of the AGB phase."
 In (able 2 we have summarized. for each of the shells marked in Figs.," In table 2 we have summarized, for each of the shells marked in Figs."
 2. 4. 5. 6. 7. 3 and 9 the radius (determined at the position of the densitv peak). density ancl velocity for the limes shown in the figures.," 2, 4, 5, 6, 7, 8 and 9 the radius (determined at the position of the density peak), density and velocity for the times shown in the figures."
 The formation process of the shell and its life-time (1) ave also eiven. where “x means that the shell remains until the end of the TP-AGB evolution.," The formation process of the shell and its life-time $L_t$ ) are also given, where $\infty$ ” means that the shell remains until the end of the TP-AGB evolution."
 The largest radius corresponds to Che shells with the longest lifetime., The largest radius corresponds to the shells with the longest lifetime.
 It should be noted that although shellsab for both the 1 and 1.5 models have the largest radii. thev are not the main observable feature.," It should be noted that although shells for both the 1 and 1.5 models have the largest radii, they are not the main observable feature."
 Shellx is the main observable feature due to its highest densitv., Shell is the main observable feature due to its highest density.
 The radii show a range between 70.07pc. for shells that have just been formed. up to 71.8 for evolved shells at the end of the AGB.," The radii show a range between $\sim$ 0.07, for shells that have just been formed, up to $\sim$ 1.8 for evolved shells at the end of the AGB."
 The shells velocities range between 2 up io 19|., The shells velocities range between 2 up to 19.
.. Although the maximum wind velocity was 15 we can see how many ol these shells have been accelerated by. thermal pressure., Although the maximum wind velocity was 15 we can see how many of these shells have been accelerated by thermal pressure.
 In Fig., In Fig.
 10 we show the cireumstellar gas deusitv and velocity structure at the end of the AGB for all the initial masses considered., 10 we show the circumstellar gas density and velocity structure at the end of the AGB for all the initial masses considered.
 For the 1 model. the bottom panel of Fig.," For the 1 model, the bottom panel of Fig."
 2 was selected very close to the end of the ACB stage. and therefore the gas radial profiles are very similar (to the ones shown in Fig.," 2 was selected very close to the end of the AGB stage, and therefore the gas radial profiles are very similar to the ones shown in Fig."
 10., 10.
 In the case of the 1.5 moclel only one external thick shell remains visible which is formed when shell merges with shellab., In the case of the 1.5 model only one external thick shell remains visible which is formed when shell merges with shell.
 A double-peaked structure can be seen in the outermost shell of the 2 model where the outermost peak correspond to shell (see Fig., A double-peaked structure can be seen in the outermost shell of the 2 model where the outermost peak correspond to shell (see Fig.
 6) and the innermost peak is produced by a shock region which develops when (he matter ejected later on from (he star reaches shellx., 6) and the innermost peak is produced by a shock region which develops when the matter ejected later on from the star reaches shell.
 Therefore this double-peaked structure is not caused by an expansion due to à pressure difference., Therefore this double-peaked structure is not caused by an expansion due to a pressure difference.
 The density structure of the rest of the models has not changed significantly since ihe times shown in Figs., The density structure of the rest of the models has not changed significantly since the times shown in Figs.
 7. 8. aud 9.," 7, 8, and 9."
 It has been widely assumed in the literature that a law of the tvpe p.xr7 describes the gas structure resulted [rom the AGB evolution (e.g. Okorokov et al., It has been widely assumed in the literature that a law of the type $\rho~\propto~r^{-2}$ describes the gas structure resulted from the AGB evolution (e.g. Okorokov et al.
 1985: Sehmiclt- Ixópppen 1987a. I937b: Marten. Schónnberner 1991: Alellema 1994; Frank Alellema 1994).," 1985; Schmidt-Voigt Köpppen 1987a, 1987b; Marten Schönnberner 1991; Mellema 1994; Frank Mellema 1994)."
 In order to compare our density structures wilh a constant mass-loss rate, In order to compare our density structures with a constant mass-loss rate
of the relaxed and unrelaxed components was simulated following a Hernquist. distribution (seeHernquist1990;Mahdavietal.1990:Rines&Diaferio 2006).,"of the relaxed and unrelaxed components was simulated following a Hernquist distribution \cite[see][]{hernquist90, mahdavi99, rines06}."
.. The relaxed galaxies were located within a radius of r/rsoo€2. while the unrelaxed component represents à compact galaxy group with radius r/rsoo€0.2. being the centre of the unrelaxed component randomly chosen.," The relaxed galaxies were located within a radius of $_{200} \leq 2$, while the unrelaxed component represents a compact galaxy group with radius $_{200}\leq0.2$, being the centre of the unrelaxed component randomly chosen."
 The velocity distribution of the relaxed and unrelaxed components is Gaussian with different meai and sigma., The velocity distribution of the relaxed and unrelaxed components is Gaussian with different mean and sigma.
" We have selected 7 different values per simulated cluster for the relative velocity of cluster and group: (vo—V.e)/o = O. 0.5. 1.0. 1.5.2.0. 2.5. and 3.0. v, and c, being the nean velocity and velocity dispersion of the relaxed component. and v, the mean velocity of the unrelaxed galaxy population."," We have selected 7 different values per simulated cluster for the relative velocity of cluster and group: $(v_{c}-v_{g})/\sigma_{c}$ = 0, 0.5, 1.0, 1.5,2.0, 2.5, and 3.0, $_{c}$ and $\sigma_{c}$ being the mean velocity and velocity dispersion of the relaxed component, and $_{g}$ the mean velocity of the unrelaxed galaxy population."
 We also varied the ratios between the velocity dispersion of the relaxed and unrelaxed components. choosing w/o.=0.3.0.5 and 0.8 for our simulations.," We also varied the ratios between the velocity dispersion of the relaxed and unrelaxed components, choosing $\sigma_{g}/\sigma_{c}=0.3, 0.5$ and 0.8 for our simulations."
 We simulated two sets of clusters with different numbers of galaxies (50 and 100)., We simulated two sets of clusters with different numbers of galaxies (50 and 100).
 The unrelaxed component in each of these clusters represents 10% and 30% of the total galaxy population respectively., The unrelaxed component in each of these clusters represents $\%$ and $\%$ of the total galaxy population respectively.
" Thus. for a fixed total number of galaxies we have simulated 42 different clusters varying v,—v. σος and the percentage of substructure."," Thus, for a fixed total number of galaxies we have simulated 42 different clusters varying $v_{g}-v_{c}$, $\sigma_{g}/\sigma_{c}$ and the percentage of substructure."
 Each of these simulated clusters was simulated 100 times changing the centre of the unrelaxed component., Each of these simulated clusters was simulated 100 times changing the centre of the unrelaxed component.
 In total. 4400 different clusters were simulated.," In total, 400 different clusters were simulated."
 We computed the fraction of simulated clusters with substructure provided by the DS test., We computed the fraction of simulated clusters with substructure provided by the DS test.
" Figure | shows this fraction as a function. of (v.—v,)/o..", Figure \ref{f1} shows this fraction as a function of $(v_{c}-v_{g})/\sigma_{c}$.
 Note that the DS test is not very efficient for detecting substructure in clusters when the relaxed and unrelaxed components have similar mea velocities., Note that the DS test is not very efficient for detecting substructure in clusters when the relaxed and unrelaxed components have similar mean velocities.
" In contrast. the efficiency is very high (more thai 80%) for clusters with (v—v,)/o,>1-1.5."," In contrast, the efficiency is very high (more than $\%$ ) for clusters with $(v_{c}-v_{g})/\sigma_{c}>1-1.5$."
" Note also that. for a given value of (v.—v)/o,. the substructure is detected more eficiently when it is located in cooler groups. and represents a larger fraction of the galaxies in the cluster."," Note also that, for a given value of $(v_{c}-v_{g})/\sigma_{c}$, the substructure is detected more eficiently when it is located in cooler groups, and represents a larger fraction of the galaxies in the cluster."
 These constraints were also pointed out by Pinkney et al. (, These constraints were also pointed out by Pinkney et al. (
1996) i1 their numerical simulations.,1996) in their numerical simulations.
 We applied the DS test to our galaxy cluster sample., We applied the DS test to our galaxy cluster sample.
 We analysed the substructure of the clusters. taking into account the galaxies inside two apertures: ο«700 (inner cluster regions) and mon«r<2r» (outer cluster regions).," We analysed the substructure of the clusters, taking into account the galaxies inside two apertures: $r<r_{200}$ (inner cluster regions) and $r_{200}<r<2r_{200}$ (outer cluster regions)."
 In the inner cluster regions. [ος of our galaxy clusters showed substructure at the 95% significance level.," In the inner cluster regions, $\%$ of our galaxy clusters showed substructure at the $\%$ significance level."
 This value is compatible with other results obtained previously using the same statistics., This value is compatible with other results obtained previously using the same statistics.
 Thus. Solanes et al. (," Thus, Solanes et al. ("
"1999), Biviano et al. (","1999), Biviano et al. ("
1997). Escalera et al. (,"1997), Escalera et al. ("
1994). Bird (1994). and Biviano et al. (,"1994), Bird (1994), and Biviano et al. ("
2002) found substructure in 31% (21/67). 40%. 38% (6/16). 44% (11/25). and 40% (9/23) of their clusters respectively.,"2002) found substructure in $\%$ (21/67), $\%$, $\%$ (6/16), $\%$ (11/25), and $\%$ (9/23) of their clusters respectively."
 In contrast. Dressler Shectman (1988) found a larger percentage of clusters with substructure: 53% (8/15).," In contrast, Dressler Shectman (1988) found a larger percentage of clusters with substructure: $\%$ (8/15)."
 The amount of substructure in the outskirts of our clusters is larger., The amount of substructure in the outskirts of our clusters is larger.
 In this case. 44% of the clusters show substructure at the 95% significancd level.," In this case, $\%$ of the clusters show substructure at the $\%$ significancd level."
 The value of A was computed taking into account the local environment of each galaxy in the clusters., The value of $\Delta$ was computed taking into account the local environment of each galaxy in the clusters.
 Nevertheless. different galaxy populations could show different substructure properties.," Nevertheless, different galaxy populations could show different substructure properties."
 Therefore. one individual cluster could show substructure —or not- depending on the galaxy population used to computed A.," Therefore, one individual cluster could show substructure –or not– depending on the galaxy population used to computed $\Delta$."
 Thus. the study of the substructure in clusters could be biased if the clusters in the sample does not have auniform absolute magnitude completeness.," Thus, the study of the substructure in clusters could be biased if the clusters in the sample does not have auniform absolute magnitude completeness."
 Our galaxy cluster sample does not show a uniform absolute magnitude completeness (see Fig., Our galaxy cluster sample does not show a uniform absolute magnitude completeness (see Fig.
 5 in ASMO?)., 5 in ASM07).
" All the clusters have data for the galaxy population brighter than M,=-20.. but fainter galaxies are lost as the redshift increases."," All the clusters have data for the galaxy population brighter than $M_{r}=-20.0$, but fainter galaxies are lost as the redshift increases."
 Therefore. different clusters trace different galaxy populations.," Therefore, different clusters trace different galaxy populations."
 In order to analyse the influence of this on the study of the substructure we ran the DS test on two galaxy population samples., In order to analyse the influence of this on the study of the substructure we ran the DS test on two galaxy population samples.
" The first consisted of those galaxies brighter than M,=—20.0 located in clusters at z«0.1.", The first consisted of those galaxies brighter than $M_{r}=-20.0$ located in clusters at $z<0.1$.
" The second galaxy population is formed by those galaxies brighter than M,=-19.0 located in the clusters at z«0.07.", The second galaxy population is formed by those galaxies brighter than $M_{r}=-19.0$ located in the clusters at $z<0.07$.
 In accordance with fig., In accordance with fig.
 5 of ASMOT. these restrictions allow us to have two families of clusters with uniform galaxy populations.," 5 of ASM07, these restrictions allow us to have two families of clusters with uniform galaxy populations."
 Table | shows the percentage of clusters with substructure in their inner and outer regions. taking into account the previous restrictions on redshift and galaxy absolute magnitudes.," Table 1 shows the percentage of clusters with substructure in their inner and outer regions, taking into account the previous restrictions on redshift and galaxy absolute magnitudes."
 We can see that. independently of the galaxy population. the percentage of clusters with substructure is higher when the galaxies in their outskirts are considered.," We can see that, independently of the galaxy population, the percentage of clusters with substructure is higher when the galaxies in their outskirts are considered."
" In the inner cluster regions (r< roo) few clusters (11%) show substructure if we consider galaxies brighter than M,= —20.0.", In the inner cluster regions $r<r_{200}$ ) few clusters $11\%$ ) show substructure if we consider galaxies brighter than $M_{r}=-20.0$ .
 That percentage increases to 33% when a fainter galaxy population is considered., That percentage increases to $\%$ when a fainter galaxy population is considered.
 This indicates that the detected fraction of clusters with substructure in the inner regions strongly depends on the limiting magnitude of the surveys., This indicates that the detected fraction of clusters with substructure in the inner regions strongly depends on the limiting magnitude of the surveys.
 Table 1| also shows that the percentage of clusters with substructure does not depend strongly on thegalaxy population in the outer cluster regions., Table 1 also shows that the percentage of clusters with substructure does not depend strongly on thegalaxy population in the outer cluster regions.
 We have analysed some global properties of the clusters with and without substructure. such as the fraction of blue galaxies (fh). cluster velocity dispersion (co) and the luminosity difference between the 2 brightest cluster galaxies (Aun).," We have analysed some global properties of the clusters with and without substructure, such as the fraction of blue galaxies $f_{b}$ ), cluster velocity dispersion $\sigma_{c}$ ) and the luminosity difference between the 2 brightest cluster galaxies $\Delta m_{12}$ )."
 Por this comparison we have considered galaxies within an aperture ¢<foo., For this comparison we have considered galaxies within an aperture $r<r_{200}$.
 In the previous subsection. we have seen that mapping different galaxy populations in clusters could affect the percentage of clusters with substructure.," In the previous subsection, we have seen that mapping different galaxy populations in clusters could affect the percentage of clusters with substructure."
 We should therefore take this into account and select a cluster sample with a galaxy population free of this bias., We should therefore take this into account and select a cluster sample with a galaxy population free of this bias.
 We have also selected clusters with more than 30 galaxies., We have also selected clusters with more than 30 galaxies.
" This makes a final number of 28 and 32 clusters when we consider galaxies with and M,« -19. respectively."," This makes a final number of 28 and 32 clusters when we consider galaxies with $_{r}<-20$ and $_{r}<-19$ , respectively."
 Table 2 shows the mean values of c. fp and Aunjs for clusters with and without substructure.," Table 2 shows the mean values of $\sigma_{c}$ , $f_{b}$ and $\Delta m_{12}$ for clusters with and without substructure."
 These values were, These values were
GIGO)).,(0)).
 Expressed as associated Legeudre (uuctious equation (2)) becomes 75qo0 right)) ) p right)) |]., Expressed as associated Legendre functions equation \ref{DlP}) ) becomes ;z)= ) ) - ) ) ].
 Iu this expression the associated Legendre ftictious take ou their their analyticaly continued values the arguments are on the real axis auk > 1)., In this expression the associated Legendre functions take on their their analytically continued values the arguments are on the real axis and $> 1$ ).
 When the filliϱ parameter has values or 2. equation (27)) reduces respectively to equatious (22). (39) arid (51). of (2000)..," When the filling parameter has values $\nu=0,1,$ or $2$, equation \ref{Pans}) ) reduces respectively to equations (22), (39) and (54), of \cite{KKT}."
 Because t15 assoclatec Legeudre equation is a special type oftie hypergeometric equation it is always possible to write associatecdl Legeudre [uuctions in terms o .h“'Dergeolinetr€ [unctions., Because the associated Legendre equation is a special type of the hypergeometric equation it is always possible to write associated Legendre functions in terms of hypergeometric functions.
 Aud because hype'eeometric fnetious are the mo'e universally available. t1ese results :ive thle nore uxelul [or most parameter vales.," And because hypergeometric functions are the more universally available, these results are the more useful for most parameter values."
 That the hypergeouietricresult. exised las lndepeldeutly been seen by lxantowskietal.(20()0) aud Damiauskietal.(2000)., That the hypergeometricresult existed has independently been seen by \cite{KKT} and \cite{DM}.
. That t learea equatio1 rectuces to the associated Leeὑπ equatiou for another special case (A= 0) µας bee1 known for some time. see Ixantowskietal.(1995) αιd Seitz&Schueider(199 L).," That the area equation reduces to the associated Legendre equation for another special case $\Lambda=0$ ) has been known for some time, see \cite{KVB} and \cite{SS}. ."
. The approoriae change o: variables is, The appropriate change of variables is
warp in the disk.,warp in the disk.
" For a disk illuniuated at au angle ty to the normal direction. the incideut flux on the cisk in fomv)/(laR?). where Lyzmbs10! eres + for NGC ""M1258 (Makishiima ct al."," For a disk illuminated at an angle $^{-1} \mu$ to the normal direction, the incident flux on the disk is $f \approx (\mu L_X)/(4 \pi R^2)$ , where $L_X
\approx 4 \times 10^{40}$ ergs $^{-1}$ for NGC 4258 (Makishima et al."
 1991) and µ may be as large as X (NAME Uerrustein 1997)., 1994) and $\mu$ may be as large as $\approx 0.2$ (NM; Herrnstein 1997).
" The volume jouizatiou rate due to the incident N-rayv flux is £mtypical(1.τ)ΕΠΕ) an? sto where E;m37 eV electron(Classeold. derethNajita. Igea 1997). 7=p1X/X,. is the shiclding optical of the disk. and X.zzle ? is the colin density correspoudiug to order uuitv optical depth for hard N-ravs 210 keV N-vays)."," The volume ionization rate due to the incident X-ray flux is $\xi \approx {\rm min}(1,\tau) f /(H
E_i)$ $^{-3}$ $^{-1}$, where $E_i \approx 37$ eV (Glassgold, Najita, Igea 1997), $\tau = \mu^{-1} \Sigma/\Sigma_c$ is the shielding optical depth of the disk, and $\Sigma_c \approx 1$ g $^{-2}$ is the column density corresponding to order unity optical depth for hard X-rays $\gsim 10$ keV )."
" NM find à,2:3:«10* ? iu the masing region aud so Xz0. recombinationg 7."," NM find $n_n \approx 3
\times 10^7$ $^{-3}$ in the masing region and so $\Sigma \approx
0.1$ g $^{-2}$ ."
" Balancing N-vrav ionization ""HDagainst ssociative at a rate &.7\101/2 7 1 yields nyzm300 3 and thus scm107."," Balancing X-ray ionization against dissociative recombination at a rate $8.7 \times 10^{-6} n^2_e T^{-1/2}$ $^{-3}$ $^{-1}$ yields $n_e \approx 300$ $^{-3}$ and thus $x_e \approx
10^{-5}$."
 From equations (1)) aud (2)). this corresponds to Πο~108 and Rey~107.," From equations \ref{rem}) ) and \ref{rea}) ), this corresponds to $Re_M \sim 10^{11}$ and $Re_A \sim 10^3$."
 .... counterimtuitivelv the disk m NGC 1258 may be both masneg and MIID-turbuleut!," Somewhat counterintuitively, the disk in NGC 4258 may be both masing and MHD-turbulent!"
 Observational support for this conclusion is provided by the work of Wallin. Watson. Wrild (1998. 1999): they showed that the spectral line features observed in NGC 1258 can be reproduced reasonably well by iucludiug a turbulent velocity field ina thin Kepleriau disk model.," Observational support for this conclusion is provided by the work of Wallin, Watson, Wyld (1998, 1999); they showed that the spectral line features observed in NGC 4258 can be reproduced reasonably well by including a turbulent velocity field in a thin Keplerian disk model."
" Iu order to account for the absence of masing at radi S01 pe. NM propose that N-rav inradiatiou ""shuts off inside z0.1 pc (because the warp decreases with radius. BOO» 0)."," In order to account for the absence of masing at radii $\lsim 0.1$ pc, NM propose that X-ray irradiation “shuts off” inside $\approx 0.1$ pc (because the warp decreases with radius, $\mu \rightarrow 0$ )."
 Te correct. ATID turbulence probably ceases to be a viable angular momentum transport mnechauisui ⋅ ⋅⋅⋅ ⋖↸⊳∪↴∖↴⊔↕↸⊳≓↥⋅⋜↧⋅↖↽↕∪⋯∑⋜↧↑↕∪∐⋜↧↕∪↕∐∖⋅↖↽↕↸∖↕≼↧↴∖↴∫↿⋟↙↼∖∣∿∐∣⋚⊥⊤∙↴⋝∏↑ ∙ ↽−⊥−≻ teraction↽⊥⊐ ∫↿∿∪∙⊥≦⊥⊤⋅↖↖⇁∐↸∖↥⋅↸∖≦∶↓∩↽Woe s lds⋅ the cosniic-ray⋅ 1 rate per hydrogen This illustrates a more general worry: the role of ronthermal heating and ionization 1s quite uncertain. epeudiug ou. e.g. the geometry of the disk (varps. daring. ete).," If correct, MHD turbulence probably ceases to be a viable angular momentum transport mechanism (cosmic-ray ionization alone yields $Re_M
\sim 10^7 \xi_{17}^{1/2}$, but $Re_A \sim 0.1 \xi_{17}^{1/2}$, where $\xi = 10^{-17} \xi_{17}$ $^{-1}$ is the cosmic-ray interaction rate per hydrogen This illustrates a more general worry; the role of nonthermal heating and ionization is quite uncertain, depending on, e.g., the geometry of the disk (warps, flaring, etc.),"
 the presence of X-ray scatterers. aud the οκτν of an anomalously laree cosmic-ray flux due o a nearby jet.," the presence of X-ray scatterers, and the possibility of an anomalously large cosmic-ray flux due to a nearby jet."
 It is possible that many parsec scale isks in ACN iuenof magnetically well coupled., It is possible that many parsec scale disks in AGN are magnetically well coupled.
 In this case eravitational mstabilitv is the most promising augular uonientun transport mechanism., In this case gravitational instability is the most promising angular momentum transport mechanism.
 Thin disks arelocally evavitationally unstable for Qx1. where Qc.OfCEGN).," Thin disks are gravitationally unstable for $Q \lsim 1$, where $Q = c_s \Omega/(\pi G \Sigma)$."
 The nonlinear outcome of local eravitational instability depends on the ratio of the cooling time to the rotational period of the disk (Shlosiman Beechuan 1989: Shlosiman et al., The nonlinear outcome of local gravitational instability depends on the ratio of the cooling time to the rotational period of the disk (Shlosman Begelman 1989; Shlosman et al.
 1990: Camunie 2000)., 1990; Gammie 2000).
" For loug cooling times. the disk reaches a steady state with efficient angular momentum transport produced bv ""eravito-turbuleuce (Shlosiunau et al."," For long cooling times, the disk reaches a steady state with efficient angular momentum transport produced by “gravito-turbulence” (Shlosman et al."
 1990: Ciunnunie 2000)., 1990; Gammie 2000).
" For parsec-scale disks in ACN. however. the cooling time is generally uch shorter than the rotational period of the disk: iu this case the disk fragments. aud probably ""undergoes efficicut star formation (Shlosiman Beechuau 1989: Game 2000)."," For parsec-scale disks in AGN, however, the cooling time is generally much shorter than the rotational period of the disk; in this case the disk fragments, and probably undergoes efficient star formation (Shlosman Begelman 1989; Gammie 2000)."
" For Maijz243XR7""iguificantle.UusM. however. the disk isglobally eravitationally unustal"," For $M_{\rm disk} \approx 2 \pi \Sigma R^2 \gsim M$, however, the disk is gravitationally unstable."
" AT—?xXR[rotationalE ~-- where es is the (Ixeplerian) velocity. this condition can be rewritten as (Shilosiman Beechuau 1950) AL Tywhere T=107735 K aud e,=100645 lau"," Using $\dot M = 2 \pi
\Sigma R |v_r|$ and $|v_r| \approx \alpha c^2_s/v_\phi$ , where $v_\phi$ is the (Keplerian) rotational velocity, this condition can be rewritten as (Shlosman Begelman 1989) M, where $T = 10^3 T_{3}$ K and $v_{\phi} = 100 v_{100}$ km $^{-1}$."
 If nouthermal heating aud ionization are msuffücieut to maintain MIID coupling. disks will become MIID stable if T5x1.," If nonthermal heating and ionization are insufficient to maintain MHD coupling, disks will become MHD stable if $T_3 \lsim 1$."
" For hunuinous ACN with Ar>lo7AY,Vrl however. the disk is eloballv eravitationally unstable n this region (eq. [fj "," For luminous AGN with $\dot M \gsim 10^{-2} \mpy$, however, the disk is globally gravitationally unstable in this region (eq. \ref{global}] ])."
It is therefore likely that bar formation iu the gaseous disk leads to siguificaut angular iuoiaentuni fransport and thus accretion on a dynamical timescale (Shlosiman et al., It is therefore likely that bar formation in the gaseous disk leads to significant angular momentum transport – and thus accretion -- on a dynamical timescale (Shlosman et al.
 1990)., 1990).
" At sunaller radi. where 7,21. the disk is both MIID and eravitationally unstable: the dynamics iu this regine has been poorly explored but may be accessible with munerical simulations."," At smaller radii, where $T_3 \gsim 1$, the disk is both MHD and gravitationally unstable; the dynamics in this regime has been poorly explored but may be accessible with numerical simulations."
 More eenerallv. in luminous ACN the accretion disk probably evolves from eravitationally uustable aud MIID stable at large radii to gravitationally uustable. MIID unstable. aud finally to eravitationallv stable. MHTD unstable at the smallest radii.," More generally, in luminous AGN the accretion disk probably evolves from gravitationally unstable and MHD stable at large radii to gravitationally unstable, MHD unstable, and finally to gravitationally stable, MHD unstable at the smallest radii."
" Iu low-huninosity AGN with A/<10?Aw! equation 1)) shows that the disk is globally exavitationallv stable where it is MITD stable: for AL<10.7AL,vr> the disk has Q21 aud is locally stable as well: this raises he interesting possibility of au MITID aud. eravitationally stable ""dead zoue in which accretion may proceed very incffidieutlv (or perlaps not at Mass will build up in lis region uutil MaizM. until the disk warp evolves so as to provide siguificaut X-ray ionization. or until a elobal bydrodvuaiiic instability sets iu (analogous to GMsS xoposal for DN)."," In low-luminosity AGN with $\dot M \lsim 10^{-2} \mpy$ equation \ref{global}) ) shows that the disk is globally gravitationally stable where it is MHD stable; for $\dot M \lsim 10^{-3} \mpy$ the disk has $Q \gsim 1$ and is locally stable as well; this raises the interesting possibility of an MHD and gravitationally stable “dead zone” in which accretion may proceed very inefficiently (or perhaps not at Mass will build up in this region until $M_{\rm disk} \gsim M$, until the disk warp evolves so as to provide significant X-ray ionization, or until a global hydrodynamic instability sets in (analogous to GM's proposal for DN)."
 It is possible that such piling up of nass is presently occurring in nianu nearby salaxies., It is possible that such piling up of mass is presently occurring in many nearby galaxies.
" Du articular. returning again to NGC 1258. NMs imasing uodel eives AFzm10ag4Myr| and thus a very eravitationally stabledisk: AM~LOOMS. and Q~10029T (see Camunic, Naravau. Blandford 1999 for alteruate AL estimates),"," In particular, returning again to NGC 4258, NM's masing model gives $\dot M \approx 10^{-5} \alpha_{0.1}
\mpy$ and thus a very gravitationally stabledisk: $M_{\rm disk} \sim
100 M_\odot \ll M$ and $Q \approx 100 \gg 1$ (see Gammie, Narayan, Blandford 1999 for alternate $\dot M$ estimates)."
 If N-rayv radiation aud ΑΠΟ turbulence iudeed shut off for Rz. pe. it is unlikely that sienificaut accretion occurs at these rac.," If X-ray irradiation and MHD turbulence indeed shut off for $R \lsim 0.1$ pc, it is unlikely that significant accretion occurs at these radii."
 It is then also uulikely that NAUs accretion rate estimate is relevant for the cucrev-producing portions ofthe accretion flow at simiall raclii., It is then also unlikely that NM's accretion rate estimate is relevant for the energy-producing portions ofthe accretion flow at small radii.
V84: the period. used by 865 fits well also to our data.,: the period used by S65 fits well also to our data.
 The scatter is quite small ancl the light curves are well defined with no indication of variations.V8'T:, The scatter is quite small and the light curves are well defined with no indication of variations.:
 double-mode pulsator., double-mode pulsator.
 Lhe period. derived. by NC€SO fits well also to our data.V88:, The period derived by NC89 fits well also to our data.:
 this star was reanalvsed by NCS9. who derived a period 0.298985 based on old photometric data.," this star was reanalysed by NC89, who derived a period 0.298985 based on old photometric data."
 The period that best fits to our data is somewhat longer. ic. 0.2080033. compatible with the sinusoidal shape of the O-C curve (865).," The period that best fits to our data is somewhat longer, i.e. 0.2989933, compatible with the sinusoidal shape of the O-C curve (S65)."
 The L data have a very large scatter. and the average 1 magnitudes and amplitude are therefore very. uncertain.V100:," The I data have a very large scatter, and the average I magnitudes and amplitude are therefore very uncertain.:"
 the period. used. ον S65 fits very well also to our data., the period used by S65 fits very well also to our data.
 The scatter is small and the curves are very. well defined.V101:, The scatter is small and the curves are very well defined.:
 the period used by 865 fits very well also to our data., the period used by S65 fits very well also to our data.
 The scatter on the descending branch is somewhat larger than normal and may indicate light curve variations.109:, The scatter on the descending branch is somewhat larger than normal and may indicate light curve variations.:
 our best period is slightly shorter than the period used. by 865. ancl is compatible with the oscillating O-C Curve.V110:," our best period is slightly shorter than the period used by S65, and is compatible with the oscillating O-C curve.:"
 our best period is significantly longer than the period given by 865. indicating that the trend of the O-C curve has reversed.," our best period is significantly longer than the period given by S65, indicating that the trend of the O-C curve has reversed."
 The light. curves are well defined. and there is no significant indication of variations. however the minimum light has been missed by our observations.V11I:," The light curves are well defined and there is no significant indication of variations, however the minimum light has been missed by our observations.:"
 This star was studied by 573. who found strong variations in the light curve and a significantly negative O-C.," This star was studied by S73, who found strong variations in the light curve and a significantly negative O-C."
 In agreement with that. our best. period is shorter than the value listed by 873 and SLITS: we also find indication of Blazhko elfect.V121:," In agreement with that, our best period is shorter than the value listed by S73 and SH73; we also find indication of Blazhko effect.:"
 our best period. ds slightly. longer than the period used by S65. in agreement. with the oscillating C curve.," our best period is slightly longer than the period used by S65, in agreement with the oscillating O-C curve."
 The exact time of maximum light is missing in our observations.V128:, The exact time of maximum light is missing in our observations.:
 This star was studied by S73 who found a period P=0.292271 days. and was later analysed by NCSO9. who found a period 0.292042 days.," This star was studied by S73 who found a period P=0.292271 days, and was later analysed by NC89 who found a period 0.292042 days."
 This latter period fits to our cata as well.V129:, This latter period fits to our data as well.:
 This star is not among those studied: by S65 and S73. but was analysed by NCSO who derived a period 0.305474.," This star is not among those studied by S65 and S73, but was analysed by NC89 who derived a period 0.305474."
 Thev noted. however. that 7... the available photometry only. weakly constrains the period ... “Phe Larink and Cireenstein's data cannot distinguish. between 0.300 or O.43d.," They noted, however, that “... the available photometry only weakly constrains the period ... The ... Larink and Greenstein's data cannot distinguish between 0.30d or 0.43d.”"
. With our data we can clearly rule out a period. around. 0.30d: the period that best. fits to our observations is 0.43112903.V130:, With our data we can clearly rule out a period around 0.30d; the period that best fits to our observations is 0.4112903.:
" This star was studied by 873. who derived a period. P-0.5688172 avs. noting however that P=0.569665 seems almost just as good""."," This star was studied by S73, who derived a period P=0.5688172 days, noting however that “... P=0.569665 seems almost just as good”."
 The O-C was significantly. negative., The O-C was significantly negative.
 Our best. period. P=0.5692737 seems to indicate that the alternative (longer) period found by 873 was probably the correct one., Our best period P=0.5692737 seems to indicate that the alternative (longer) period found by S73 was probably the correct one.
 The indication that the star may show the Blazhko elfect. is confirmed. although only marginallv. by our data.V131:," The indication that the star may show the Blazhko effect is confirmed, although only marginally, by our data.:"
 This star has been studied in detail both by S65 and NCSO. who suggest the period 0.2976919.," This star has been studied in detail both by S65 and NC89, who suggest the period 0.2976919."
 Although onlv mareinally different. the period that best fits to our data is 0.2076886.V132:," Although only marginally different, the period that best fits to our data is 0.2976886.:"
 This star was not included. in the studies by S65 and 873. but was reanalvsed by NCSO who derived the period 0.339825 days.," This star was not included in the studies by S65 and S73, but was reanalysed by NC89 who derived the period 0.339825 days."
 However. our data provide a somewhat better fit using the older period listed by SLITS. namely 0.3398479 cavs.V133:," However, our data provide a somewhat better fit using the older period listed by SH73, namely 0.3398479 days.:"
 This star was not included in the studies by S65 and S73., This star was not included in the studies by S65 and S73.
 The period listed by SLUTS provides a good [fit to our data as well. however our photometry does not put much constraint on the determination of a new period.V134:," The period listed by SH73 provides a good fit to our data as well, however our photometry does not put much constraint on the determination of a new period.:"
 This star was not included in the studies by S65 and S73., This star was not included in the studies by S65 and S73.
 The period could be slightly improved with respect to the period listed by SLUTS., The period could be slightly improved with respect to the period listed by SH73.
 The scatter in the data may suggest light curve variations.V135:, The scatter in the data may suggest light curve variations.:
 This star was not included. in the studies by S65 and 873., This star was not included in the studies by S65 and S73.
 Our data suggest a period. certainly. shorter than the period listed by SLITS., Our data suggest a period certainly shorter than the period listed by SH73.
 A rather large scatter in the photometry may suggest light curve variations.V136:, A rather large scatter in the photometry may suggest light curve variations.:
 This star had no previous period determination as it lies very close to the cluster center.V140:, This star had no previous period determination as it lies very close to the cluster center.:
 The star was analysed both by S65 and NCS. and their best. period also fits well to our data.," The star was analysed both by S65 and NC89, and their best period also fits well to our data."
 NC'S9 commented that 7... there seem to be some real irregularities in the light curves., NC89 commented that “... there seem to be some real irregularities in the light curves.
 For example. there is a phase shift tween ..27 different sets of observations.," For example, there is a phase shift between ...” different sets of observations."
 The photomoetric scatter of our data does not allow us to confirm or reject his suggestion.V142:, The photometric scatter of our data does not allow us to confirm or reject this suggestion.:
 The period used by S65 provides à good fit to our cata as well., The period used by S65 provides a good fit to our data as well.
 Phe scatter on the descending branch seems o indicate variations in the shape of the light curves.V143:, The scatter on the descending branch seems to indicate variations in the shape of the light curves.:
 This star was not included in the studies by S65 and 873., This star was not included in the studies by S65 and S73.
 Our best. period. is significantly. longer than the period Histed by στὸ., Our best period is significantly longer than the period listed by SH73.
 The star is quite close to the center. some of the large scatter around minimum light may be due o photometric errors.V146:," The star is quite close to the center, some of the large scatter around minimum light may be due to photometric errors.:"
 This star was not included in the studies by S65 and 873., This star was not included in the studies by S65 and S73.
 The period listed by SIIT3 (0.596740 days) fits to our data as well. however our photometry for this star has a time baseline of 8S clays only. therefore does not constrain any new period determination.," The period listed by SH73 (0.596740 days) fits to our data as well, however our photometry for this star has a time baseline of 8 days only, therefore does not constrain any new period determination."
 This star was later analysed by Ixholopoy (1977). however his updated period (0.502193 cays) does not fit to our data.V149:," This star was later analysed by Kholopov (1977), however his updated period (0.502193 days) does not fit to our data.:"
 This star was not included in the studies by S65 and S73., This star was not included in the studies by S65 and S73.
 Our best period (0.5406744. days) is significantly shorter than the period listed by SLITS (0.54985 davs)., Our best period (0.5496744 days) is significantly shorter than the period listed by SH73 (0.54985 days).
 The scatter on the descending branch is rather large. especially in the I-band.V150:," The scatter on the descending branch is rather large, especially in the I-band.:"
 This star was not included in the studies by S65 and 873., This star was not included in the studies by S65 and S73.
 Our best period (0.5239411 days) is somewhat shorter than the period listed by SLITS (0.52397. clays).V155:, Our best period (0.5239411 days) is somewhat shorter than the period listed by SH73 (0.52397 days).:
 This star had no previous period determination.V167:, This star had no previous period determination.:
 This star was included in the study by S73., This star was included in the study by S73.
 The period that best fits to our data is slightly longer than the period listed by S73 and SLITS., The period that best fits to our data is slightly longer than the period listed by S73 and SH73.
 There is significant scatter along the descending branch.V168:, There is significant scatter along the descending branch.:
 This star was not included in the studies by S65, This star was not included in the studies by S65
"absorption. so the imner disk actually radiates approximately as a ""diluted"" blackbody with the peak effective temperature lower than that derived from fitting the spectra ος,","absorption, so the inner disk actually radiates approximately as a “diluted” blackbody with the peak effective temperature lower than that derived from fitting the spectrum \cite{ehs84}."
" Unfortunately, this ""color correction factor"" is still poorly determined. although it appears to depend only weakly ou the properties of the black hole. mass accretion rate. or the location on thedisk’."," Unfortunately, this “color correction factor” is still poorly determined, although it appears to depend only weakly on the properties of the black hole, mass accretion rate, or the location on thedisk \cite{st95}."
 Taking iuto account these factors. we found that for several BIBCs the interred radius of the immer disk edee is cousistent with that of the last stable orbit around uon-rotatiug black holes!’..," Taking into account these factors, we found that for several BHBCs the inferred radius of the inner disk edge is consistent with that of the last stable orbit around non-rotating black holes \cite{zcc97}."
 When we applied the same model to the spectriun of GRO J1655-10 duriug an outburst. however. we found that the inner edee of the disk is only about 1.2 Sclawarzschild radii away from the black bole?) which is. of course. impossible if the black hole docs uot rotate.," When we applied the same model to the spectrum of GRO J1655-40 during an outburst, however, we found that the inner edge of the disk is only about 1.2 Schwarzschild radii away from the black hole \cite{zcc97}, which is, of course, impossible if the black hole does not rotate."
 Therefore. we were forced to conclude that GRO J1655-10 contains arapidly spinning black hole.," Therefore, we were forced to conclude that GRO J1655-40 contains a spinning black hole."
 The spin of the black hole was deteriuined to be ~9: maximal rotation for this source., The spin of the black hole was determined to be $\sim$ maximal rotation for this source.
" The ""ordiuuv nature of GRO J1655-10 as a BUBC (in terms of its spectral properties) is strouglv supported by recent observations with theExplorer (RXTE).", The “ordinary” nature of GRO J1655-40 as a BHBC (in terms of its spectral properties) is strongly supported by recent observations with the (RXTE).
 The source was mouitored by RNTE extensively throughout its recent (19961997) N-vav outburst., The source was monitored by RXTE extensively throughout its recent (1996–1997) X-ray outburst.
 From these observatious. Sobezak et al.," From these observations, Sobczak et al."
°? found that the observed N-ray spectrum eau be well characterized by the canonical spectral shape of DIIBCs (soft nulti-color blackbody plus hard power law) throughout the cutive period. which coufixiis the previous findiugs . (although the actual values of the parameters differ slightly).," \cite{sob98} found that the observed X-ray spectrum can be well characterized by the canonical spectral shape of BHBCs (soft multi-color blackbody plus hard power law) throughout the entire period, which confirms the previous findings \cite{zh97} (although the actual values of the parameters differ slightly)."
 Iu addition. they found that the interred radius of the inner disk edee remained roughly constant (vith occasional low points) as the N-rav flix varied by a factor of 3.L. similar to normal BUBCs??.," In addition, they found that the inferred radius of the inner disk edge remained roughly constant (with occasional low points) as the X-ray flux varied by a factor of 3–4, similar to normal BHBCs \cite{tl95}."
", Towever. these authors mistakenly concluded that the correctious for relativistic effects are ueeligible for this source (actually they mis-quoted Zhaug et al."," However, these authors mistakenly concluded that the corrections for relativistic effects are negligible for this source (actually they mis-quoted Zhang et al."
 on this issuc)., \cite{zcc97} on this issue).
" As a matter of fact. the generalo relativistic effects are very significant in this case ο, Tu."," As a matter of fact, the general relativistic effects are very significant in this case \cite{zcc97}."
" particular. the iuner boundary condition (i... torque free at the last stable orbit) can drastically change the temperature profile of the immer portion of the accretion disk under Newtonian gravity?στον,"," In particular, the inner boundary condition (i.e., torque free at the last stable orbit) can drastically change the temperature profile of the inner portion of the accretion disk under Newtonian gravity \cite{pt74,ha89}."
 For GRO J1655-10. the correction amounts to a factor of ~2. after taking iuto account all the effects.," For GRO J1655-40, the correction amounts to a factor of $\sim$ 2, after taking into account all the effects."
 Consequently. the radius of the inner disk edge iu Sobezalk. ct al.," Consequently, the radius of the inner disk edge in Sobczak et al."
 was over-estimated by the same amoun 32, was over-estimated by the same amount \cite{sob98}.
 Our interpretation of the same data would. therefore. put the last stable orbit roughly at 1.5 Sclowarzschild radi. which confrus the ueed for the presence ofa rapidly rotating black hole in this svstem (although tle spin of the black hole is ~78% maximal rotation in this case).," Our interpretation of the same data would, therefore, put the last stable orbit roughly at 1.5 Schwarzschild radii, which confirms the need for the presence of a rapidly rotating black hole in this system (although the spin of the black hole is $\sim$ maximal rotation in this case)."
 We take note of occasional low values of the iferred radius when the measured N-ray Iuniuositv is relatively high °°.., We take note of occasional low values of the inferred radius when the measured X-ray luminosity is relatively high \cite{sob98}. .
 We interpret them as the times when the adopted spectral model, We interpret them as the times when the adopted spectral model
goals. and it is more readily achieved with MSPs because of their short spin periods ancl highly stable average pulse shapes.,"goals, and it is more readily achieved with MSPs because of their short spin periods and highly stable average pulse shapes."
 Currently. several MSPs have already been timed at precisions down to a few hundred nanoseconds over time spans of a decade or more (?)..," Currently, several MSPs have already been timed at precisions down to a few hundred nanoseconds over time spans of a decade or more \citep{vbc+09}."
 Although the integrated. profiles of ALSPs appear stable over time scales of vears. there are a variety. of cllects that can allect the shape of an integrated. profile on short time scales: multi-path propagation in the turbulent ISAL. pulse jitter. data processing artefacts and. improper calibration. for exemple.," Although the integrated profiles of MSPs appear stable over time scales of years, there are a variety of effects that can affect the shape of an integrated profile on short time scales: multi-path propagation in the turbulent ISM, pulse jitter, data processing artefacts and improper calibration, for example."
 Profile variations from these effects may only change the pulse shape at. low levels. but. will cause the subsequent POA calculation to be less accurate and precise than what is expected if only radiometer noise were contributing to the uncertainty.," Profile variations from these effects may only change the pulse shape at low levels, but will cause the subsequent TOA calculation to be less accurate and precise than what is expected if only radiometer noise were contributing to the uncertainty."
 This will complicate timing with the next generation of radio telescopes since in these cases the timing will be limited by factors other than merely telescope sensitivity., This will complicate timing with the next generation of radio telescopes since in these cases the timing will be limited by factors other than merely telescope sensitivity.
 In order to investigate the level at which short-term instabilities in pulse shape may allect pulsar timing with this new generation of telescopes. we present an analysis on PSR 4715.," In order to investigate the level at which short-term instabilities in pulse shape may affect pulsar timing with this new generation of telescopes, we present an analysis on PSR $-$ 4715."
 This pulsar was discovered by ? and is the nearest and. brightest MISP known. resulting in outstanding timing precision that has already. led to a varicty of interesting results (22)...," This pulsar was discovered by \cite{jlh+93} and is the nearest and brightest MSP known, resulting in outstanding timing precision that has already led to a variety of interesting results \citep{vbb+01,vbv+08}."
 Furthermore. the TOA precision of PSR. 4715 obtained. by current instruments (seee.g.7) is already comparable to. the precision future telescopes may expect to obtain on other less bright AISPs (see Section 5)). making it a perfect target for investigations of the pulsar timing potential of future tclescopes.," Furthermore, the TOA precision of PSR $-$ 4715 obtained by current instruments \citep[see e.g.][]{vbb+10} is already comparable to the precision future telescopes may expect to obtain on other less bright MSPs (see Section \ref{sec:Conclusions}) ), making it a perfect target for investigations of the pulsar timing potential of future telescopes."
 The structure of this paper is as follows., The structure of this paper is as follows.
 First we describe the observations and data preprocessing in Section ?7.., First we describe the observations and data preprocessing in Section \ref{sec:Obs}. .
 Some statistical tools are introduced in Section ??.., Some statistical tools are introduced in Section \ref{sec:Tool}.
 Next we review the possible elfects involved in profile distortion and present the results of data reduction in Section ??.., Next we review the possible effects involved in profile distortion and present the results of data reduction in Section \ref{sec:Issues}.
 We conclude with an overview of our main findings. prospects for the precision timing with the next generation of radio telescopes. and a brief. discussion. of future research in Section 5..," We conclude with an overview of our main findings, prospects for the precision timing with the next generation of radio telescopes, and a brief discussion of future research in Section \ref{sec:Conclusions}."
 The data used. in this paper consist of [ive long observations of PSIUJ0437. 4715. taken between June 2005 and March 2008 at the Parkes radio telescope.," The data used in this paper consist of five long observations of PSR $-$ 4715, taken between June 2005 and March 2008 at the Parkes radio telescope."
 Observations were taken with the Caltech-Parkes-Swinburne Iecorder 2 (CPSB2:?).., Observations were taken with the Caltech-Parkes-Swinburne Recorder 2 \citep[CPSR2;][]{hbo06}.
 Phe CPSB2 is a 2-bit baseband recorder that »erforms on-line coherent. dedispersion and records two 64-MlIz wide observing bands simultaneouslv., The CPSR2 is a 2-bit baseband recorder that performs on-line coherent dedispersion and records two 64-MHz wide observing bands simultaneously.
 For the data used in this paper. these bands are centred. at. observing requencies of 1341 and MMIEIz.," For the data used in this paper, these bands are centred at observing frequencies of 1341 and MHz."
 Lt also. effectively removes REL online by monitoring the total power on pes iniescales and does not record any data whenever the power evels deviate significantly from a. Gaussian., It also effectively removes RFI online by monitoring the total power on $\mu$ s timescales and does not record any data whenever the power levels deviate significantly from a Gaussian.
 On two of the ive days the cata were taken with the LI-OLL receiver. on he remaining three davs the central beam of the 20ccm multibeam (MD) receiver (C2). was used. as listed in Table 1..," On two of the five days the data were taken with the H-OH receiver, on the remaining three days the central beam of the cm multibeam (MB) receiver \citep{swb+96} was used, as listed in Table \ref{tab:Data}."
 During each dav of observations the data were folded. in near-real time to ss for the carly data and to 67.1ss for the later data (see Table 1))., During each day of observations the data were folded in near-real time to s for the early data and to s for the later data (see Table \ref{tab:Data}) ).
 Oll-source observations of a pulsed noise probe at 45° to the linear feed probes but with otherwise identical set-up. were taken at regular intervals to allow for polarimetric calibration.," Off-source observations of a pulsed noise probe at $^{\circ}$ to the linear feed probes but with otherwise identical set-up, were taken at regular intervals to allow for polarimetric calibration."
 For the data processing we used the software package (?).., For the data processing we used the software package \citep{hvm04}.
 We removed. bandpass to avoid. possible effects of aliasing ancl spectral leakage., We removed bandpass to avoid possible effects of aliasing and spectral leakage.
 “Pwo models named “single axis” ancl “full reception. respectively. were used for calibration purposes ancl details will be presented in Section ??..," Two models named “single axis” and “full reception”, respectively, were used for calibration purposes and details will be presented in Section \ref{ssec:Calib}."
 Unless otherwise specilieled in the text. we combined the polarisations into total power (Stokes 1) and the power across the remaining 96 frequency channels.," Unless otherwise specificied in the text, we combined the polarisations into total power (Stokes I) and the power across the remaining 96 frequency channels."
 “Phrough the following analvsis. TOAS and their uncertainties were determined. through the standard cross-correlation approach (2).. with the fully integrated 2005-07-24 profiles (one for each observing band). unless otherwise stated.," Through the following analysis, TOAs and their uncertainties were determined through the standard cross-correlation approach \citep{tay92}, with the fully integrated 2005-07-24 profiles (one for each observing band), unless otherwise stated."
 Where needed. we used the timing model derived by 2? without fitting for any parameters.," Where needed, we used the timing model derived by \citet{vbv+08} without fitting for any parameters."
 In order to evaluate any effects on profile shape. we first introduce the concepts of elective pulse number ancl pulse sharpness below and then brielly illustrate their behaviour with pulse S/N and POA measurement uncertainty.," In order to evaluate any effects on profile shape, we first introduce the concepts of effective pulse number and pulse sharpness below and then briefly illustrate their behaviour with pulse S/N and TOA measurement uncertainty."
 As pulsars are weak racio sources and individual pulses are often not. detectable. the signal needs to be. folded ab the rotation period. in order to obtain profiles with sulliciently high S/N to derive. precise TOXs.," As pulsars are weak radio sources and individual pulses are often not detectable, the signal needs to be folded at the rotation period in order to obtain profiles with sufficiently high S/N to derive precise TOAs."
 Le is useful to check whether this procedure is as ellective as expected., It is useful to check whether this procedure is as effective as expected.
 Theoretically. the signal is expected to inerease linearly with integration length. while the root-mean-square (MS) of the noise increases according to a square-root law.," Theoretically, the signal is expected to increase linearly with integration length, while the root-mean-square (RMS) of the noise increases according to a square-root law."
 Consequently. the corresponding improvement in S/N is expected. to be proportional to the square-root. of the number of pulses.," Consequently, the corresponding improvement in S/N is expected to be proportional to the square-root of the number of pulses."
 Given IN profiles with peak amplitudes of ly and noise λος olay (£= 1....N). the single pulse S/N is: and the S/N of a folded. profile is:," Given $N$ profiles with peak amplitudes of $A_{\rm i}$ and noise RMSs of$\sigma_{\rm i}$ $i=1,\ldots N$ ), the single pulse S/N is: and the S/N of a folded profile is:"
Our numerical study confirms the focusing effect and the above analvtical scaling relationships (Cerntli 2011. in preparation).,"Our numerical study confirms the focusing effect and the above analytical scaling relationships (Cerutti 2011, in preparation)."
 Figure G shows an electron's orbit in the (yz)-plane with no guide field ancl (the evolution of its Lorentz factor and its midplaue-crossing angle along the z-direction., Figure \ref{fig-2} shows an electron's orbit in the $(yz)$ -plane with no guide field and the evolution of its Lorentz factor and its midplane-crossing angle along the $z$ -direction.
" A non-zero guide field adds a circular motion to the particle's orbit in the Cry)-plane (see Figure 7)). but (he overall evolution of 5 and 0, is almost unchanged even for D.=By."," A non-zero guide field adds a circular motion to the particle's orbit in the $(xy)$ -plane (see Figure \ref{fig-3}) ), but the overall evolution of $\gamma$ and $\theta_0$ is almost unchanged even for $B_z=B_0$."
" Figure 8. gives the characteristic energy. 64, Of svnchrotron photons radiated by the electrons leaving the laver after four davs of acceleration. as a function of the inital parameters 5j; aud Fy; in à 5 mG magnetic field."," Figure \ref{fig-4} gives the characteristic energy $\epsilon_{\rm sync}$ of synchrotron photons radiated by the electrons leaving the layer after four days of acceleration, as a function of the inital parameters $\gamma_{\rm inj}$ and $\theta_{\rm inj}$ in a 5 mG magnetic field."
 We find that >100 MeV photons can be emitted for ijS10* regardless of the initial angle θµ., We find that $>100$ MeV photons can be emitted for $\gamma_{\rm inj}\lesssim 10^7$ regardless of the initial angle $\theta_{\rm inj}$.
 The particles are confined within a light cone of semi-aperture angle of only a few degrees., The particles are confined within a tight cone of semi-aperture angle of only a few degrees.
 In order to explain the short flare (nmescales (7j<1 day. see Balboetal.2011)). the flaring region must be compact (/<LO! em). suggesting that the flares originate just outside the pulsar wind termination shock.," In order to explain the short flare timescales $\tau_{\rm fl} < 1$ day, see \citealt{Balbo_etal-2011}) ), the flaring region must be compact $l < 10^{16}$ cm), suggesting that the flares originate just outside the pulsar wind termination shock."
 There are (wo places where reconnection current sheets may form in the inner Crab Nebula., There are two places where reconnection current sheets may form in the inner Crab Nebula.
 First. the equatorial plane contains a reversing toroidal field (Degelman1999:Ixonissarov&Lyubarsky2004).," First, the equatorial plane contains a reversing toroidal field \citep{Begelman-1999,Komissarov_Lyubarsky-2004}."
. Second. we expect a cvlindrical z-pinch along the rotational axis. which is unstable to kink-like MIID instabilities the nonlinear development of which may lead to episodes of reconnection-driven dissipation (similar to quasi-periodic sawtooth crashes in tokamaks). perhaps powering X-ray. enission in (he axial jet (Degelnan1998:Mizunoetal.2011).," Second, we expect a cylindrical z-pinch along the rotational axis, which is unstable to kink-like MHD instabilities the nonlinear development of which may lead to episodes of reconnection-driven dissipation (similar to quasi-periodic sawtooth crashes in tokamaks), perhaps powering X-ray emission in the axial jet \citep{Begelman-1998,Mizuno_etal-2011}."
. Since the PeV particles are focused. along the current sheet. we can see (he flare only when the reconnection electric [field points toward us.," Since the PeV particles are focused along the current sheet, we can see the flare only when the reconnection electric field points toward us."
 While neither (he equatorial plane nor the rotational axis lie close to our line of sight. instabilities may swing (the current sheets through wide angles. allowing us to observe the radiation intermittently.," While neither the equatorial plane nor the rotational axis lie close to our line of sight, instabilities may swing the current sheets through wide angles, allowing us to observe the radiation intermittently."
 Given (he compact scale of (he flaring region. the voltage drop Hof required to explain the energies of radiaiing electrons implies By> several mG. A similar estimate is obtained by requiring τῃ lo exceed the svnchrotron cooling time for >100 MeV-emitting particles (svnehrotron cooling can indeed be shown to dominate over acliabatic cooling). vielding nsτις73. where 7.5=79/10?s.," Given the compact scale of the flaring region, the voltage drop $E_0 l$ required to explain the energies of radiating electrons implies $B_0 > $ several mG. A similar estimate is obtained by requiring $\tau_{\rm fl}$ to exceed the synchrotron cooling time for $>100\,\MeV$ -emitting particles (synchrotron cooling can indeed be shown to dominate over adiabatic cooling), yielding $B_{0,-3}^{3/2}\, \tau_{\rm fl,5} > 3$, where $\tau_{\rm fl,5} \equiv \tau_{\rm fl}/10^5\, {\rm s}$."
 These values are substantially higher than the typical fields in the inner Crab Nebula usually inferred [rom cdvnamical arguments (Rees&GunnIxennel&Coronili 1984)..," These values are substantially higher than the typical fields in the inner Crab Nebula usually inferred from dynamical arguments \citep{Rees_Gunn-1974,Kennel_Coroniti-1984a}."
 Bul Chis discrepancy need not be problematic., But this discrepancy need not be problematic.
 First. if the axial z-pinch is responsible for the flares. then the field might be amplified by the pinch effect.," First, if the axial z-pinch is responsible for the flares, then the field might be amplified by the pinch effect."
 Furthermore. (he traditional estimates for the field strength in (he nebula may be incorrect.," Furthermore, the traditional estimates for the field strength in the nebula may be incorrect."
version 8.2.,version 8.2.
) The light curves are given in s~!.," The light curves are given in $\,$ $^{-1}$ ."
 The keV count rates can be converted into other units with the relation |Crab=117countss!9x107?eresem-7s7!.," The 22--50 keV count rates can be converted into other units with the relation $1\,\mathrm{Crab}=117\,\mathrm{counts}\,\mathrm{s}^{-1}=9\times10^{-9}\ \ecms$."
 The time unit IJD corresponds to MJD=IJD+51544., The time unit IJD corresponds to $\mathrm{MJD}=\mathrm{IJD}+51544$.
 The main scientific instrument onboard the X-ray Multi-Mirror Mission (XMM-Newton)) satellite is the EPIC camera composed of two MOS (?) and one pn (?) CCD cameras., The main scientific instrument onboard the X-ray Multi-Mirror Mission ) satellite is the EPIC camera composed of two MOS \citep{Turneral01} and one pn \citep{Struderal01} CCD cameras.
 It has imaging. timing. and spectral capabilities in the 0.2—12 keV energy range with a 30’ FOV.," It has imaging, timing, and spectral capabilities in the 0.2--12 keV energy range with a $\arcmin$ FOV."
 The EPIC cameras were operating in Imaging science mode with full window for MOS]. large window for MOS2 and pn. and with medium filters for each camera.," The EPIC cameras were operating in imaging science mode with full window for MOS1, large window for MOS2 and pn, and with medium filters for each camera."
 wwas observed with oon March 31. 2007. from 08:03:37 to 11:27:40 UTC (MJD 54190.337-54190.478) for a total exposure of 12.2 ks.," was observed with on March 31, 2007, from 08:03:37 to 11:27:40 UTC (MJD 54190.337–54190.478) for a total exposure of 12.2 ks."
 There was no simultaneous observation withINTEGRAL., There was no simultaneous observation with.
.. Event lists for each MOS and pn camera were generated with the Science Analysis Software (SAS?)) version 7.0.0 using the and tools. respectively.," Event lists for each MOS and pn camera were generated with the Science Analysis Software ) version 7.0.0 using the and tools, respectively."
 The event lists were corrected for enhanced background features observed at energies higher than 10 keV. disregarding time lapses when count rates exceeded 0.52 ffor pn and 0.2 ffor both MOS.," The event lists were corrected for enhanced background features observed at energies higher than 10 keV, disregarding time lapses when count rates exceeded 0.52 for pn and 0.2 for both MOS."
 Therefore. the net exposure is 5.6 out of 10 ks exposure for pn. 10.8 out of 12 ks for MOSI. and 11.1 out of 12 ks for MOS2.," Therefore, the net exposure is 5.6 out of 10 ks exposure for pn, 10.8 out of 12 ks for MOS1, and 11.1 out of 12 ks for MOS2."
 Images for MOS[12] and pn were generated with 2” and 4 resolution. respectively. using good events until the quadruple level in the 0.8—10 keV energy range and disregarding bad pixels.," Images for MOS[12] and pn were generated with $\arcsec$ and $\arcsec$ resolution, respectively, using good events until the quadruple level in the 0.8–10 keV energy range and disregarding bad pixels."
 An accurate X-ray position determined with EPIC was calculated with the SAS taskchain., An accurate X-ray position determined with EPIC was calculated with the SAS task.
 Four images with energy ranges 0.5—2. 2—4.5. 4.5-7.5. and 7.5-—.12 keV for each MOS and pn camera were extracted.," Four images with energy ranges 0.5–2, 2–4.5, 4.5–7.5, and 7.5--12 keV for each MOS and pn camera were extracted."
 Then. the best position for each individual EPIC camera was determined.," Then, the best position for each individual EPIC camera was determined."
 Finally. the best source position was calculated as the mean of the positions given by the three cameras.," Finally, the best source position was calculated as the mean of the positions given by the three cameras."
 The source location precision is limited by the astrometry of the S/C. that is of 2”°.. the statistical error of 0.1 being insignificant in comparison.," The source location precision is limited by the astrometry of the S/C, that is of $\arcsec$, the statistical error of $0.1\arcsec$ being insignificant in comparison."
 In the EPIC/pn image. one bright source was detected 11 the CCD#I1 near the read-out node.," In the EPIC/pn image, one bright source was detected in the 1 near the read-out node."
 The event list of the source- background was extracted from a region of 35” radius centred on the source., The event list of the $+$ background was extracted from a region of $\arcsec$ radius centred on the source.
 À background event list was extracted in the same CCD at same distance of the read-out node from a region of similar size not affected by the bright source., A background event list was extracted in the same CCD at same distance of the read-out node from a region of similar size not affected by the bright source.
 Spectra were extracted by selecting single+double events but disregarding bad pixels., Spectra were extracted by selecting $+$ double events but disregarding bad pixels.
 Specific RMF and ancillary response files (ARF) were generated with the SAS tasks andarfgen. respectively.," Specific RMF and ancillary response files (ARF) were generated with the SAS tasks and, respectively."
 The version 11.3.2t package was used to plot and fit the resulting spectra corrected from background., The version 11.3.2t package was used to plot and fit the resulting spectra corrected from background.
 For light curves. single and double events were also selected within the same regions defined in the spectral step.," For light curves, single and double events were also selected within the same regions defined in the spectral step."
 The source light curves were corrected from the background using the SAS taskLecorr. and we applied the barycentric correction with the SAS taskbarycen.," The source light curves were corrected from the background using the SAS task, and we applied the barycentric correction with the SAS task."
 Multiwavelength observations were undertaken soon after the accurate X-ray position was given by ? and ?.., Multiwavelength observations were undertaken soon after the accurate X-ray position was given by \citet{Romanoal07a} and \citet{Kong07}.
 The observations were achieved with the 3.5 m ESO/NTT telescope in two domains: in the near IR (NIR) domain (1—2.4ym) with the spectro-imager SOFI and in the optical domain with the imager SUSI-2 (350—900 nm)., The observations were achieved with the 3.5 m ESO/NTT telescope in two domains: in the near IR (NIR) domain $1-2.4\ \mum$ ) with the spectro-imager SOFI and in the optical domain with the imager SUSI-2 $350-900$ nm).
 The observations were carried. out as part of the ToO programme 079.D-0432(A) (PL: S. Chaty). through service mode.," The observations were carried out as part of the ToO programme 079.D-0432(A) (PI: S. Chaty), through service mode."
 Astrometry. photometry. and spectroscopy were achieved during those observations.," Astrometry, photometry, and spectroscopy were achieved during those observations."
 The spectroscopy was performed on the bright counterpart proposed by ? (2MASS source #11)., The spectroscopy was performed on the bright counterpart proposed by \citet{Romanoal07a} (2MASS source 1).
 The NIR photometry in the bands J. H. and Ks was performed on April 3. 2007. with the spectro-imager SOFI installed on a Nasmyth focus of the NTT.," The NIR photometry in the bands $J$, $H$, and $K_{\mathrm{S}}$ was performed on April 3, 2007, with the spectro-imager SOFI installed on a Nasmyth focus of the NTT."
 The observations were centred on the known X-ray position ofJ1749., The observations were centred on the known X-ray position of.
"1—2733.. The large imaging mode was used during those observations. and 1t gives an image pixel scale of 0.288"" and an FOV of 4.92’x4.92’,"," The large imaging mode was used during those observations, and it gives an image pixel scale of $0.288\arcsec$ and an FOV of $4.92\arcmin\times 4.92\arcmin$."
 Nine images were taken for each band with integration times of 60 s for J and 47.3 s for H andΚ., Nine images were taken for each band with integration times of 60 s for $J$ and 47.3 s for $H$ and.
.. For each band. four of the nine observations were taken with a slight offset of ~30” that allowed us to build the NIR sky to subtract it from the images.," For each band, four of the nine observations were taken with a slight offset of $\sim30\arcsec$ that allowed us to build the NIR sky to subtract it from the images."
 Six standard stars chosen from the faint NIR standard star catalogue (?) were also observed: S262-E. S495-E. S708-D. $264-D. P565-C. and $875-C. Five observations per band were performed on each standard star.," Six standard stars chosen from the faint NIR standard star catalogue \citep{Perssonal98} were also observed: S262-E, S495-E, S708-D, S264-D, P565-C, and S875-C. Five observations per band were performed on each standard star."
" The first observation was centred on the target and then. the next four images were taken with an offset of ~45"" compared to the first one."," The first observation was centred on the target and then, the next four images were taken with an offset of $\sim45\arcsec$ compared to the first one."
 The optical observations were carried out on April 6. 2007. between UTC O8h40 and OSh4O0 with the imager SUSI-2 also installed on the same Nasmyth focus of the NTT as SOFI.," The optical observations were carried out on April 6, 2007, between UTC 08h40 and 08h40 with the imager SUSI-2 also installed on the same Nasmyth focus of the NTT as SOFI."
 Optical photometry in U. B. V. R. J. and Z bands was obtained.," Optical photometry in $U$, $B$, $V$, $R$, $I$, and $Z$ bands was obtained."
 The FOV was 5.5’x with a binning of factor 2 that gives a pixel scale of 0.161” per pixel., The FOV was $5.5\arcmin\times 5.5\arcmin$ with a binning of factor 2 that gives a pixel scale of $0.161\arcsec$ per pixel.
 The exposure time is 60 s for each filter., The exposure time is 60 s for each filter.
 Nine photometric standards (selectedintheoptical were also observed in the fields PG 1657+078 and PG1633+099., Nine photometric standards \citep[selected in the optical standard star catalogue of][]{Landolt92} were also observed in the fields PG 1657+078 and PG1633+099.
 The integration times in each filter varied between 10—100 s., The integration times in each filter varied between 10–100 s.
"Arp 220 is a 114 Jy (14x1074 erg 7? ') source at 100 on. which translates to Q,—3xLO| pad? for Ty=59 IX (see Table 1)).","Arp 220 is a 114 Jy $1.14 \times 10^{-21}$ erg $^{-2}$ $^{-1}$ ) source at 100 $\mu$ m, which translates to $\Omega_d = 3 \times 10^{-11}$ $rad^2$ for $T_d=59$ K (see Table \ref{tab:23gals}) )."
" This corresponds to a circular area with 1.2"" (390 pe) indiameter?.. which agrees well with the size of the molecular gas complex fneling the nuclear starburst traced in CO1999)."," This corresponds to a circular area with $''$ (390 pc) in, which agrees well with the size of the molecular gas complex fueling the nuclear starburst traced in CO."
. The best fit dust SED model is then selected by examining the parameter space for 7;; and 2. between 25-85 Ix ancl 1.0-2.0. respectively.," The best fit dust SED model is then selected by examining the parameter space for $T_d$ and $\beta$, between 25-85 K and 1.0-2.0, respectively."
 Thermal Bremsstrahlung or [ree-lree [lux densities can be derived from Eq., Thermal Bremsstrahlung or free-free flux densities can be derived from Eq.
 7 bv determining the frequency. where D[ree-Iree opacity τε becomes unitv and estimating the size of the emitting region., \ref{eq:frfr2} by determining the frequency where free-free opacity $\tau_{ff}$ becomes unity and estimating the size of the emitting region.
 Alternatively. one can also compute the [ree-f[ree τιν density from the inferred SER. as it is proportional to the production rate of Lyman continuum photons.," Alternatively, one can also compute the free-free flux density from the inferred SFR as it is proportional to the production rate of Lyman continuum photons."
 Using the IIo. normalization of for a Salpeter IME ancl assuming of Lyman continuum photons are quenched by dust absorption. Eq.," Using the $\alpha$ normalization of for a Salpeter IMF and assuming of Lyman continuum photons are quenched by dust absorption, Eq."
" 23 of can be re-written as ↴∏∐↲↓≯↕⋅≼↲≼↲−∐⋅≼↲≼↲∐∏⇀↸≼⇂≼↲∐⊳∖⇁∐⋡∖↽↓⋟∪↕⋅≀↧↴≸↽↔↴≀↧↴↥≀↧↴⇀↸∡∖↽∖∖⊽↕⊔↥≀↧↴≸≟↕∖↽≼↲∐⇪∐⋩≼⇂≼↲∏∏↲≼⇂⋝∖⊽↥≀↧↴↕⋅↓⋟∪↕⋅∐↓≀↧↴∐∪∐↕⋅≀⋯↲↕⊳∖⇁↥∐↲∐ The Iree-Iree flux density Si, determined this way is nearly identical to the value derived using Eq.", 23 of can be re-written as The free-free flux density for a galaxy with a given FIR derived star formation rate is then The free-free flux density $S_{ff}$ determined this way is nearly identical to the value derived using Eq.
" 7 assvuning Trpe αἱ p—1 GlIz and 0,5;=Qu."," \ref{eq:frfr2}
 assuming $\tau_{ff}\sim 1$ at $\nu=1$ GHz and $\Omega_{ff}= \Omega_d$."
 Non-(hermal svnchrotvou [Iux clensity ὦμ can also be parameterized as a function of SER since psyxSFR., Non-thermal synchrotron flux density $S_{nth}$ can also be parameterized as a function of SFR since $\nu_{SN} \propto SFR$.
 Adjusting Eq., Adjusting Eq.
 20 of for the Salpeter IAIF. Eq.," 20 of for the Salpeter IMF, Eq."
 10 can be re-wrillen as. The svncehrotron spectral index a is known to lie within a narrow range around 0.7-0.8. and we simply adopt a=0.75 to minimize the number of free parameters in our model.," \ref{eq:nth1} can be re-written as, The synchrotron spectral index $\alpha$ is known to lie within a narrow range around 0.7-0.8, and we simply adopt $\alpha=0.75$ to minimize the number of free parameters in our model."
 Condon's original derivation arbitrarily emploved a Galactic normalization as noted earlier., Condon's original derivation arbitrarily employed a Galactic normalization as noted earlier.
" We thus add a scaling actor far, (ol order unity) here in order to determine the normalization more suitable [or starburst galaxies.", We thus add a scaling factor $f_{nth}$ (of order unity) here in order to determine the normalization more suitable for starburst galaxies.
The ultraprecise phoometry by theKepler space telescope opens up the possibility o' discovering new phenomena and shedding new light on long-sanding astrophysical problems (Gillilandetal. 2010).,The ultraprecise photometry by the space telescope opens up the possibility of discovering new phenomena and shedding new light on long-standing astrophysical problems \citep{Gil10}.
". One oft19 most interesting unsolved problems is the physical origin of the Blazhko(1907). effect. an amplitude and/or phase modulation o ""RRLLyrae stars."," One of the most interesting unsolved problems is the physical origin of the \citet{Bla07} effect, an amplitude and/or phase modulation of Lyrae stars."
 The leading explanations are: (1) an. oblique rotator model that invokes a magnetic field (Shibahashi2000): (2) a model with resonant coupling between radial and non-radia modets) (Dziembowski&Mizerski2004):: and (3) a mechanism invoking a cyclic variation of the turbulent convection caused by a transient magnetic field (Stothers20060., The leading explanations are: (1) an oblique rotator model that invokes a magnetic field \citep{Shi00}; (2) a model with resonant coupling between radial and non-radial mode(s) \citep{DzM04}; and (3) a mechanism invoking a cyclic variation of the turbulent convection caused by a transient magnetic field \citep{Sto06}.
 At present none of these models explains all the observed properties of stars showing the Blazhko effect., At present none of these models explains all the observed properties of stars showing the Blazhko effect.
 It is not even clear whether a modification of the above ideas or new astrophysical processes are needed to solve the problem., It is not even clear whether a modification of the above ideas or new astrophysical processes are needed to solve the problem.
 Comprehensive discussions of the observational and theoretical properties of Blazhko LLyrae stars are given by Szeidl(1988) and Κονάος(2009)., Comprehensive discussions of the observational and theoretical properties of Blazhko Lyrae stars are given by \cite{Sze88} and \citet{Kov09}.
. This paper paper describes new properties of LLyrae stars revealed by early data from theKepler photometer., This paper paper describes new properties of Lyrae stars revealed by early data from the photometer.
 Here we concentrate on the results based mostly on Fourier analyses., Here we concentrate on the results based mostly on Fourier analyses.
" A detailed study of all observed stars is beyond the scope of the present paper,", A detailed study of all observed stars is beyond the scope of the present paper.
 A detailed technical description of the can be found in Kochetal.(2010). and Jenkinsetal.(@010a.b)..," A detailed technical description of the can be found in \cite{Koch10} and \cite{Jen10a, Jen10b}."
 At the time of this writing three long cadence (29.4-min integration time) photometric data sets have been released to the KASC (Kepler, At the time of this writing three long cadence (29.4-min integration time) photometric data sets have been released to the KASC (Kepler
The first suberoup of experiucuts demonstrates hat a cvlindrically sviuuietiic inaguetie ecannot drive the aercury when its maguctic axis is he same as the axis of rotation.,The first subgroup of experiments demonstrates that a cylindrically symmetric magnetic cannot drive the mercury when its magnetic axis is the same as the axis of rotation.
 When the uaguetic axis is unaligned with the spin axis or the distribution of the maeuetic field is nof cevliudicallvy sviumetric. however. the mercury can © driven.," When the magnetic axis is unaligned with the spin axis or the distribution of the magnetic field is not cylindrically symmetric, however, the mercury can be driven."
 Iu the second subgroup of experiments. we ascertain the conditions under which rotating nereurv can © slowed down by a stationary nagnet.," In the second subgroup of experiments, we ascertain the conditions under which rotating mercury can be slowed down by a stationary magnet."
 To do so. we spun the mercury trough ↥⋅⋜↧↑∐↸∖↥⋅↑∐⋜⋯↑↕∐∖↸⊳↸∖∐⊓⋅⋜↧↕⋯⋜↧∶↴⋁∐↸∖↑∏∐↑∐↑∐↸∖⋯↸∖↥⋅↸⊳↿∐⋅⋅↖⇁⋅↴∖↴ revolution reached a steady state.," To do so, we spun the mercury trough rather than the central magnet until the mercury's revolution reached a steady state."
" In cach experiment one ∙ ↕↓↓≼∖↥⋅∏∏⋅⋮↖⇁⋮⋯≼↧↾↕↓≼∖⋯⋮↕⋮↴⋁⋯∖↾⋮∏⋅≼∖↕≼∐∖↓↑↕↖⊳⋮↕↕∙↽↙∏∏↴∖↴ ∙ cvlindrieally svunuetric"" magnet-- whose .magnetic canseresult was the same as the axis of rotating niercury.", In each experiment our basis of comparison was again an: a cylindrically symmetric magnet whose magnetic axis was the same as the axis of rotating mercury.
 pocemse the aligned iiagnuoet. the mercury eventually revolved at the same rate as the trough.," With the aligned magnet, the mercury eventually revolved at the same rate as the trough."
 Iu the other three cases. braking forces lanited the rate. mercury fo a slower ," In the other three cases, braking forces limited the mercury to a slower rate."
We used the siue magnets in every pair of exporiuents seen iu Braking Experiments A. D aud C. These experiments deimonustrate hat a coaxial. voutube.com/watch?v=SBAzUBzc2s\I[.-evlindvicallyDE svuuuetric magneticto feld has no braking effect on the mercury.," We used the same magnets in every pair of experiments seen in Braking Experiments A, B and C. These experiments demonstrate that a coaxial, cylindrically symmetric magnetic field has no braking effect on the mercury."
 Iun other words. under some special conditions the mercury cau cross the magnetic field lines without expericucing a braking force.," In other words, under some special conditions the mercury can cross the magnetic field lines without experiencing a braking force."
 The magnet cau exert a braking effect on the mercury only when its magnetic axis is unaligned with the axis of mercury rotation or when the maeuetic field is not cevliudricallv svuunetrical., The magnet can exert a braking effect on the mercury only when its magnetic axis is unaligned with the axis of mercury rotation or when the magnetic field is not cylindrically symmetrical.
 The experimental. results reveal two pheuomeua worthy of special attention: Iu summary. no exchangeof angular momenta will occur between the magnet aud the mercury under conditions where the magnetic field aud the voutube.com/wateh?v2C7DxTtoVdtxwiiereury share cvlindrical syuunetry.," The experimental results reveal two phenomena worthy of special attention: In summary, no exchange of angular momentum will occur between the magnet and the mercury under conditions where the magnetic field and the mercury share cylindrical symmetry."
 The degrees of axial aliguancut and svunuetry thus control the exchange of: the angular momentum., The degrees of axial alignment and symmetry thus control the exchange of the angular momentum.
 OfAp course. a change of magnetic flix through cach fluid clement is a necessary condition for the exchange of angular moment.," Of course, a change of magnetic flux through each fluid element is a necessary condition for the exchange of angular momentum."
 The υ sirronudiug a pulsar covers. the cutive spherical surface., The plasma surrounding a pulsar covers the entire spherical surface.
 In our experiments. the iierenuvy circulates within a region near he equatorial: plane.," In our experiments, the mercury circulates within a region near the equatorial plane."
 Therefore.: the results of: our study are ouly directly comparable to the behavior of plasma near the equatorial plane.," Therefore, the results of our study are only directly comparable to the behavior of plasma near the equatorial plane."
Observatory and the Department of Astronomy of the University of Texas at Austin.,Observatory and the Department of Astronomy of the University of Texas at Austin.
 WPG acknowledges financial support for this work from the Chilean Center lor Astrophysics FONDAP 15010003., WPG acknowledges financial support for this work from the Chilean Center for Astrophysics FONDAP 15010003.
The next generation of sky surveys will provide reasonably accurate photometric redshift estimates. so there is considerable interest in the development of techniques which can use these noisy distance estimates to provide unbiased estimates of galaxy scaling relations.,"The next generation of sky surveys will provide reasonably accurate photometric redshift estimates, so there is considerable interest in the development of techniques which can use these noisy distance estimates to provide unbiased estimates of galaxy scaling relations."
 While there exist a number of methods for estimating photometric redshifts (Budavari 2009 ancl references. therein). there are. fewer —or using these to estimate accurate redshift distributions (Padmanabhan ct al.," While there exist a number of methods for estimating photometric redshifts (Budavari 2009 and references therein), there are fewer for using these to estimate accurate redshift distributions (Padmanabhan et al."
 2005: Sheth 2007: Lima et al., 2005; Sheth 2007; Lima et al.
 2008: A'unha et al., 2008; Cunha et al.
 2009). the luminosity function (Sheth 2007). or the joint Iuminosityv-s1ze. color-magnitudo. etc.," 2009), the luminosity function (Sheth 2007), or the joint luminosity-size, color-magnitude, etc."
 relations (Rossi Sheth 2008: Christlein ct al., relations (Rossi Sheth 2008; Christlein et al.
 2009: Rossi et al., 2009; Rossi et al.
 10)., 2010).
 Ideally. the output. from. a photometric redshift estimator is a normalized likelihood function which gives the probability that the true redshift is 2 given the observed colors (i.c. Bolzonella et al.," Ideally, the output from a photometric redshift estimator is a normalized likelihood function which gives the probability that the true redshift is $z$ given the observed colors (i.e. Bolzonella et al."
 2000: Collister Lahay 2004: Cunha et al., 2000; Collister Lahav 2004; Cunha et al.
 2009)., 2009).
 Let Z(z[|e) denote this quantity: it may be skewed. bimodal. or more generally it may assume any arbitrary shape.," Let ${\cal L}(z|{\bm c})$ denote this quantity; it may be skewed, bimodal, or more generally it may assume any arbitrary shape."
 Let & denote the mean or the most. probable value of this distribution (it does not matter which. although some of the logic which follows is more transparent if ¢ denotes the mean).," Let $\zeta$ denote the mean or the most probable value of this distribution (it does not matter which, although some of the logic which follows is more transparent if $\zeta$ denotes the mean)."
 Often. & (sometimes with an estimate of the uncertainty on its value) is the only quantity which is available.," Often, $\zeta$ (sometimes with an estimate of the uncertainty on its value) is the only quantity which is available."
 Therefore. in Section 2.1 we first) consider how ὁ compares with the true redshift z. ancl contras 1ο convolution and cleconvolution methods for estimating Nickle while in Section 2.2 we describe how to reconstruc vw redshift’ distribution directly from colors.," Therefore, in Section \ref{dndz} we first consider how $\zeta$ compares with the true redshift $z$, and contrast the convolution and deconvolution methods for estimating ${\rm d}N/{\rm d}z$ – while in Section \ref{cfc} we describe how to reconstruct the redshift distribution directly from colors."
 Section shows what this implies if one wishes to use the ful istribution Z(z|e)., Section \ref{pdf} shows what this implies if one wishes to use the full distribution ${\cal L}(z|{\bm c})$.
 Section ?? shows how to exten 1e logic to the luminosity function. and Section ον to gacaling relations. again by contrasting the convolution anc econvolution methods. and showing what eeneralization of C(z|e) is required from the photometric redshift codes if one wishes to do this.," Section \ref{phil} shows how to extend the logic to the luminosity function, and Section \ref{phix} to scaling relations, again by contrasting the convolution and deconvolution methods, and showing what generalization of ${\cal L}(z|{\bm c})$ is required from the photometric redshift codes if one wishes to do this."
 A final section summarizes our results., A final section summarizes our results.
" Where necessary. we write the Llubble constant as Hy=1005kms+Alpe* anel we assume a spatially Dat cosmological moclel with (Q4,;.Q,.4)=(0.3.0.7.0.7). where O4, and O4 are the present-cay densities of matter. and cosmological constant scaled to the critical density."," Where necessary, we write the Hubble constant as $H_0 = 100h~{\rm km~s}^{-1}~{\rm Mpc}^{-1}$, and we assume a spatially flat cosmological model with $(\Omega_M,\Omega_{\Lambda}, h)=(0.3, 0.7, 0.7)$, where $\Omega_M$ and $\Omega_{\Lambda}$ are the present-day densities of matter and cosmological constant scaled to the critical density."
 In what follows. we will use spectroscopic and. photometric redshifts from the SDSS to illustrate some of our arguments.," In what follows, we will use spectroscopic and photometric redshifts from the SDSS to illustrate some of our arguments."
 Details of how the earlv-type galaxy. sample was selected are in Rossi et al. (, Details of how the early-type galaxy sample was selected are in Rossi et al. (
2010): the photo-zs for this sample are from Csabai et al. (,2010); the $z$ s for this sample are from Csabai et al. (
2003).,2003).
bv that amount (here.,by that amount there.
" The exceptions are Malfeis 1 2. for which we used values of extinction. eiven in ο, as well as Circinus with E(D—V)=0.677 (For 2011. in preparation)."," The exceptions are Maffeis 1 2, for which we used values of extinction, given in \cite{Maffei2}, as well as Circinus with $E(B-V)=0.677$ (For 2011, in preparation)."
 Note however (hat apart Irom those three galaxies. which have extinction-corrected. magnitudes below AK—5 mag. all the remaining ones added [rom LGA are much fainter. at least by 2 mag. and possible nmisestimation of their extinction does not largely influence our analysis.," Note however that apart from those three galaxies, which have extinction-corrected magnitudes below $K=5$ mag, all the remaining ones added from LGA are much fainter, at least by 2 mag, and possible misestimation of their extinction does not largely influence our analysis."
 In this section we will use the data prepared as described in Section ?? to calculate the clustering dipole of the galaxies [rom the 2\IASS NSC! and analvze its growth., In this section we will use the data prepared as described in Section \ref{Sec:Data} to calculate the clustering dipole of the galaxies from the 2MASS XSC and analyze its growth.
 For that purpose we change units of d into. km/s. defining the as where we have used (he Formula (12)) for (he flux dipole of the survey.," For that purpose we change units of $\bmd$ into $\kms$, defining the as where we have used the Formula \ref{eq:lim flux dipole}) ) for the flux dipole of the survey."
 The flux of each galaxy is ealeulated [rom its magnitude mj as where Sp is the flux lor a 0-magnitude object., The flux of each galaxy is calculated from its magnitude $m_i$ as where $S_0$ is the flux for a 0-magnitude object.
 As was already stated. we consider magnitudes in the band. which was the main Ctarget) band of the 2\IASS survey (for simplicity of notation. we sometimes skip Cie s subscripti).," As was already stated, we consider magnitudes in the band, which was the main (`target') band of the 2MASS survey (for simplicity of notation, we sometimes skip the $s$ ' subscript)."
 Then ((13)) takes on (he form: where and the zero point offset ZPO=0.01720.005 (?).., Then \ref{eq:g_v}) ) takes on the form: where and the zero point offset $\mathrm{ZPO}=0.017\pm0.005$ \citep{CWM}.
 The A; magnitudes in ((15)) include also a negative offset of A=—0.2 mag added following ? due to the underestimation of total [Inxes by the isophotal magnitudes in the 2\IASS ASC., The $K_i$ magnitudes in \ref{eq:g_v_Ks}) ) include also a negative offset of $\Delta=-0.2$ mag added following \cite{Kochanek} due to the underestimation of total fluxes by the isophotal magnitudes in the 2MASS XSC.
 The quantity jy is the Iuminosity density in (he A band., The quantity $j_K$ is the luminosity density in the $K$ band.
 It is obtained for example Irom the integral (10)) using the huninosity function in (liis band., It is obtained for example from the integral \ref{eq:lum.dens}) ) using the luminosity function in this band.
 The value of /y has been estimated by many authors in, The value of $j_K$ has been estimated by many authors in
Type la supernovae (SNe Ia) are of major astrophysical importance.,Type Ia supernovae (SNe Ia) are of major astrophysical importance.
 They have acquired particular cosmological significance since they have been used to measure the expansion history of the Universe (Riess et 11998; Perlmutter et 11999; Riess et 22004)., They have acquired particular cosmological significance since they have been used to measure the expansion history of the Universe (Riess et 1998; Perlmutter et 1999; Riess et 2004).
 Understanding their nature is also of importance for understanding the metallicity evolution and star-formation history of galaxies (e.g. Canal. Ruiz-Lapuente Burkert 1996; Matteucci Recchi 2001).," Understanding their nature is also of importance for understanding the metallicity evolution and star-formation history of galaxies (e.g. Canal, Ruiz-Lapuente Burkert 1996; Matteucci Recchi 2001)."
 Despite their importance. there is still no agreement on the nature of their progenitors.," Despite their importance, there is still no agreement on the nature of their progenitors."
 There is broad agreement that the destruction of a white dwarf (WD) in a thermonuclear explosion constitutes. the supernova event itself. but there are two main classes of competing models for the events which lead to the explosion.," There is broad agreement that the destruction of a white dwarf (WD) in a thermonuclear explosion constitutes the supernova event itself, but there are two main classes of competing models for the events which lead to the explosion."
 In the single-degenerate scenario. the doomed WD accretes matter from a non-degenerate companion (Whelan [ben 1973; Nomoto 1952: Han Podsiadlowski 2004).," In the single-degenerate scenario, the doomed WD accretes matter from a non-degenerate companion (Whelan Iben 1973; Nomoto 1982; Han Podsiadlowski 2004)."
 In the double-degenerate scenario. the mass donor is a second WD: the most commonly considered scenario involves the merger of two CO WDs (Iben Tutukov 1984; Webbink 1984: also see Martin. Tout Lesaffre 2006 for a variant of this scenario).," In the double-degenerate scenario, the mass donor is a second WD; the most commonly considered scenario involves the merger of two CO WDs (Iben Tutukov 1984; Webbink 1984; also see Martin, Tout Lesaffre 2006 for a variant of this scenario)."
 An explosion following the merger of two WDs would leave no remnant. whilst the companion star in the single-degenerate scenario would survive and be potentially identifiable (Ruiz-Lapuente 1997; Podsiadlowski 2003; Ruiz-Lapuente et 22004).," An explosion following the merger of two WDs would leave no remnant, whilst the companion star in the single-degenerate scenario would survive and be potentially identifiable (Ruiz-Lapuente 1997; Podsiadlowski 2003; Ruiz-Lapuente et 2004)."
 There has been no conclusive. proof to date that any individual object is the surviving non-degenerate donor from a SN Ia explosion., There has been no conclusive proof to date that any individual object is the surviving non-degenerate donor from a SN Ia explosion.
 If Chandrasekhar mass WD-WD mergers do lead to SNe la. they are expected to leave a remnant neutron star via acretion-induced collapse (AIC. see Nomoto Iben 1985: Nomoto Kondo 1991; but see also Yoon. Podsiadlowski Rosswog 2007).," If Chandrasekhar mass WD-WD mergers do lead to SNe Ia, they are expected to leave a remnant neutron star via acretion-induced collapse (AIC, see Nomoto Iben 1985; Nomoto Kondo 1991; but see also Yoon, Podsiadlowski Rosswog 2007)."
 At present we do not know whethera// WD-WD mergers leave remnants — in which case the double degenerate scenario could not be responsible for SNe la — and it seems unlikely that that this will become clear in the near future (but see. e.g.. Levan et 22006).," At present we do not know whether WD–WD mergers leave remnants – in which case the double degenerate scenario could not be responsible for SNe Ia – and it seems unlikely that that this will become clear in the near future (but see, e.g., Levan et 2006)."
 Hansen (2003) first noticed that observed high-velocity WDs (Oppenheimer et 22001) could have been produced through SNe Ia; such WDs would be the descendants of non-degenerate mass donors in the pre-supernova binaries., Hansen (2003) first noticed that observed high-velocity WDs (Oppenheimer et 2001) could have been produced through SNe Ia; such WDs would be the descendants of non-degenerate mass donors in the pre-supernova binaries.
 Hansen's idea seems to be consistent with more detailed work on the ages of the WDs in the Oppenheimer et ssample by Bergeron et ((2005) and deserves further attention. but by itself itis nota clinching argument for the single-degenerate channel.," Hansen's idea seems to be consistent with more detailed work on the ages of the WDs in the Oppenheimer et sample by Bergeron et (2005) and deserves further attention, but by itself it is not a clinching argument for the single-degenerate channel."
 Nor has the evidence that the SN Ia rate is different for different stellar populations (Mannueci et 22005) led to firm conclusions., Nor has the evidence that the SN Ia rate is different for different stellar populations (Mannucci et 2005) led to firm conclusions.
 The strongest direct evidence that non-degenerate donor stars can lead to normal type la supernovae has been provided by Patat et ((2007). who observed circumstellar material around SN 2006X which seems extremely hard to reconcile with a double-degenerate progenitor.," The strongest direct evidence that non-degenerate donor stars can lead to normal type Ia supernovae has been provided by Patat et (2007), who observed circumstellar material around SN 2006X which seems extremely hard to reconcile with a double-degenerate progenitor."
 Here we suggest that the observed. apparently single. low-mass white dwarfs (LMWDs) provide evidence that at least some SN la explosions have occurred with non-degenerate donor stars.," Here we suggest that the observed, apparently single, low-mass white dwarfs (LMWDs) provide evidence that at least some SN Ia explosions have occurred with non-degenerate donor stars."
 We define LMWDs as WDs which are too low in mass to have been produced by single-star evolution as we currently understand it., We define LMWDs as WDs which are too low in mass to have been produced by single-star evolution as we currently understand it.
 A population of single LMWDs has been implied by. e.g.. the work of Maxted. Marsh Moran We also investigate the apparently single ultra-cool white dwarfs (UCWDs) as potentially containing a useful subset of the LMWD population and indicate how further observations of the kinematies of this and other populations could lead to constraints on the progenitors of SNe Ia. In sections 2 and 3. we argue that the existence of single LMWDs is most naturally explained by the single-degenerate model for SNe la. In section 4. we introduce UCWDs. discuss to what extent the observed single UCWDs might be a useful sample of LMWDs. and consider in what way the observed single UCWD population is consistent with a SN Ia origin.," A population of single LMWDs has been implied by, e.g., the work of Maxted, Marsh Moran We also investigate the apparently single ultra-cool white dwarfs (UCWDs) as potentially containing a useful subset of the LMWD population and indicate how further observations of the kinematics of this and other populations could lead to constraints on the progenitors of SNe Ia. In sections \ref{sec:LMWDchannels} and \ref{sec:SNIaPops} we argue that the existence of single LMWDs is most naturally explained by the single-degenerate model for SNe Ia. In section \ref{sec:UCWDs} we introduce UCWDs, discuss to what extent the observed single UCWDs might be a useful sample of LMWDs, and consider in what way the observed single UCWD population is consistent with a SN Ia origin."
 Current evidence suggests that |M.« zero-age main-sequence (ZAMS) stars. left to evolve in isolation. produce white dwarfs 20.55M. (e.g. Han. Podsiadlowski Eggleton 1994:," Current evidence suggests that $\rm 1 ~M_{\odot}$ zero-age main-sequence (ZAMS) stars, left to evolve in isolation, produce white dwarfs $\rm\ga 0.55 ~M_{\odot}$ (e.g. Han, Podsiadlowski Eggleton 1994;"
The Be/X-ray and supergiant binary svstems comprise the class of massive X-ray binaries.,The Be/X-ray and supergiant binary systems comprise the class of massive X-ray binaries.
 A survey of the literature reveals that of the 96 proposed massive X-ray binary pulsar systems. of the identified svstems fall within the Berav group of binaries.," A survey of the literature reveals that of the 96 proposed massive X-ray binary pulsar systems, of the identified systems fall within the Be/X-ray group of binaries."
 The orbit of the Be star ancl the compact object. a neutron star. is generally wide and eccentric.," The orbit of the Be star and the compact object, a neutron star, is generally wide and eccentric."
 “Phe optical star exhibits Ho. line emission. aud continuum frec-free emission (revealed as excess Hux in the 119) from a disk of circumstellar gas., The optical star exhibits $\alpha$ line emission and continuum free-free emission (revealed as excess flux in the IR) from a disk of circumstellar gas.
 Most of the De/X-ray sources are also very transient in the emission of X-rays., Most of the Be/X-ray sources are also very transient in the emission of X-rays.
" The source ISAX 0544.1.710 was detected by BeppoS.AN in October 1996 (Cusumano et al. 1998) at a [lux corresponding to a luminosity of 9 x 10°"" erg/s. Their observations revealed an X-ray pulse. period. of 96s."," The source 1SAX J0544.1–710 was detected by BeppoSAX in October 1996 (Cusumano et al, 1998) at a flux corresponding to a luminosity of 9 x $10^{35}$ erg/s. Their observations revealed an X-ray pulse period of 96s."
 The transient. variable nature of the source was reported. by Laberl ct al (1998) when they linked the BeppoSAX source with a ROSAT source. RA JO544.17100. (LIaberl Pietsch 1999).," The transient, variable nature of the source was reported by Haberl et al (1998) when they linked the BeppoSAX source with a ROSAT source, RX J0544.1–7100 (Haberl Pietsch 1999)."
 Llaberl ct al. also reported a possible optical counterpart Iving within the 8 aresec ROSAT error circle., Haberl et al also reported a possible optical counterpart lying within the 8 arcsec ROSAT error circle.
 Subsequently. Haberl Pietsch (1999) reported more etails of the ROSAT source and refined the error circle to just. 3.32 arcesec radius which includes one obvious optical counterpart.," Subsequently, Haberl Pietsch (1999) reported more details of the ROSAT source and refined the error circle to just 3.3 arcsec radius which includes one obvious optical counterpart."
 “Lhe PSPC spectrum. indicated: that ib was the hardest. source. in their sample of 27 LAC objects jev studied., The PSPC spectrum indicated that it was the hardest source in their sample of 27 LMC objects they studied.
 The totality of the X-ray behaviour strongly sugeests that the object is a member of the Be/X-ray binary Class., The totality of the X-ray behaviour strongly suggests that the object is a member of the Be/X-ray binary class.
 Reported here are optical. infra-red ancl X-ray measurements of the system.," Reported here are optical, infra-red and X-ray measurements of the system."
 Phe data confirm the proposed ientity of the counterpart to TUN. JO544.17100. and. the counterpart is shown to be most consistent. with à main sequence BOV star.," The data confirm the proposed identity of the counterpart to RX J0544.1–7100, and the counterpart is shown to be most consistent with a main sequence B0V star."
 The source RN 0520.5.6982 was discovered. by IROSAT (Schmidtke ct al. 1994) at a luminosity of 5 x 10% erg/s and identified with a V14 magnitude star.," The source RX J0520.5–6932 was discovered by ROSAT (Schmidtke et al, 1994) at a luminosity of 5 x $10^{34}$ erg/s and identified with a $\sim$ 14 magnitude star."
 Optical spectral observations carried out by. Schimictke et. αἱ indicated a OSe type star with radial velocity measurements consistent with LAIC membership., Optical spectral observations carried out by Schmidtke et al indicated a O8e type star with radial velocity measurements consistent with LMC membership.
 Since the source was not detected. by. Einstein i0 is. probably exhibiting, Since the source was not detected by Einstein it is probably exhibiting
 Our knowledge of the first stages of the evolution of powerful radio sources is based on the study of the population of high frequency peaking radio sources., Our knowledge of the first stages of the evolution of powerful radio sources is based on the study of the population of high frequency peaking radio sources.
 In the framework of models explaining. the evolution. of. individual racio sources. the spectral peak of voung radio sources occurs at high frequencies.," In the framework of models explaining the evolution of individual radio sources, the spectral peak of young radio sources occurs at high frequencies."
 Given their small size. in these sources the svnchrotron. self-absorption (SSA) is à very effective mechanism.," Given their small size, in these sources the synchrotron self-absorption (SSA) is a very effective mechanism."
 As the source grows. the peak frequency is expected to shift towards lower frequencies as a consequence of adiabatic expansion.," As the source grows, the peak frequency is expected to shift towards lower frequencies as a consequence of adiabatic expansion."
 An alternative explanation suggests that the spectral peak is due to frec-free absorption from a ionized medium. enshrouding the radio emission. (Bickneletal. 1997)., An alternative explanation suggests that the spectral peak is due to free-free absorption from a ionized medium enshrouding the radio emission \citep{bicknell97}.
. Both scenarios are supported by the empirica anti-correlation found by O'Dea&Baum(1997). [rom the study of samples of compact. steep spectrum. (CSS) ane gigahertz-peakecl spectrum (GPS) radio sources., Both scenarios are supported by the empirical anti-correlation found by \citet{odea97} from the study of samples of compact steep spectrum (CSS) and gigahertz-peaked spectrum (GPS) radio sources.
 The former have peak frequencies around a few hundred: MlIIZT. typica sizes of a few kpe and ages of LO” - 107 vears. whereas the latter have spectra peaking around 1 Cillz. typical sizes of about 1 kpe or less and ages of 10% - 104 vears.," The former have peak frequencies around a few hundred MHz, typical sizes of a few kpc and ages of $^{5}$ - $^{6}$ years, whereas the latter have spectra peaking around 1 GHz, typical sizes of about 1 kpc or less and ages of $^{3}$ - $^{4}$ years."
 However. it is worth noting that the consistency between the source size and the spectral peak often found in the most compact sources strongly support. the synchrotron self-absorption scenario (Orienti&Dallacasa2008a:TingaydeKool2003).," However, it is worth noting that the consistency between the source size and the spectral peak often found in the most compact sources strongly support the synchrotron self-absorption scenario \citep{momo,
 tingay03}."
". Ligh frequency peakers (LED:Dallacasactal.2000).. with a spectral peak occurring at [frequencies above a few Gllz. are thus the best candidates to be newly born racio sources. with ages between 107 - 107 The radio properties of HET's have been. derived: by the analysis of the ""bright LEP sample (Dallacasaetal.&Dallacasa| 2008b)."," High frequency peakers \citep[HFP;][]{dd00}, with a spectral peak occurring at frequencies above a few GHz, are thus the best candidates to be newly born radio sources, with ages between $^{2}$ - $^{3}$ The radio properties of HFPs have been derived by the analysis of the “bright” HFP sample \citep{dd00,tinti05,mo06a,mo07,mo08a}."
. In. particular. from the multi-epoch analvsis of their radio spectra it has been found that the sample is composed of two different populations.," In particular, from the multi-epoch analysis of their radio spectra it has been found that the sample is composed of two different populations."
 One population consists of radio sources that maintain the convex spectrum. without showing variability. whereas the other comprises radio sources that change their. spectral shape. becoming also Dlat-spectrum objects. and. possessing substantial Hux density variability.," One population consists of radio sources that maintain the convex spectrum without showing variability, whereas the other comprises radio sources that change their spectral shape, becoming also flat-spectrum objects, and possessing substantial flux density variability."
 “Phe dillerent. spectral properties shown by the two populations suggest that the former represent voung radio sources still in an carly stage, The different spectral properties shown by the two populations suggest that the former represent young radio sources still in an early stage
analysis a described in Equ.,analysis a described in Equ.
 7 we obtain a value ofR=0.02.0.32 (R=0.010.32 without noise)., \ref{equ:rcoeff} we obtain a value of $R=0.02\pm0.32$ $R=-0.01\pm0.32$ without noise).
 The dust emissivity at GGHz relative to the IRIS 100 tm data is tabulated in Table 3.., The dust emissivity at GHz relative to the IRIS $\mu$ m data is tabulated in Table \ref{tab:emissivity}.
 We also list the predicted specitic intensities for these objects for a relative emissivity of 10 uU K«MIy//sr)| for reference., We also list the predicted specific intensities for these objects for a relative emissivity of 10 $\mu$ $^{-1}$ for reference.
 The relative emissivity of our two strongest detections is similar to that found for 11622 (Casassus et al., The relative emissivity of our two strongest detections is similar to that found for 1622 (Casassus et al.
 2006) and G159.618.5 (Watson et al., 2006) and G159.618.5 (Watson et al.
 2005)., 2005).
 This suggests that the non-detections in our sample are not an effect of our sensitivity limits., This suggests that the non-detections in our sample are not an effect of our sensitivity limits.
 If the emissivity of anomalous microwave emission relative to that seen at 100 tm was at a similar level in all dark clouds. for example 2»Iu («MJy/sr)./. then we would have detected emission from every cloud in our sample at >36g.," If the emissivity of anomalous microwave emission relative to that seen at $\mu$ m was at a similar level in all dark clouds, for example $>10\,\mu$ $^{-1}$, then we would have detected emission from every cloud in our sample at $>3\,\sigma_{\rm{rms}}$."
 The weighted average dust emissivity relative to the 100 tim. maps. for our sample is 6.6. 4K !.., The weighted average dust emissivity relative to the $\mu$ m maps for our sample is $\pm$ $\mu$ $^{-1}$.
 This value agrees with the all-sky WMAP value for cool dust clouds at high galactic latitudes (Davies et al., This value agrees with the all-sky WMAP value for cool dust clouds at high galactic latitudes (Davies et al.
 2006). given as JJy at GGHz per Ty at 100 tm. Of our five possibly anomalous objects two are known to be Class 0 objects: L944 and L1246.," 2006), given as Jy at GHz per Jy at $\mu$ m. Of our five possibly anomalous objects two are known to be Class 0 objects: L944 and L1246."
 High sensitivity maps in CO owards our two most anomalous objects do not vet exist and hev are assumed starless., High sensitivity maps in CO towards our two most anomalous objects do not yet exist and they are assumed starless.
 However the starless/protostellar divide 145 come under scrutiny recently following the discovery of Very Low Luminosity Objects (VeLLOs) withSpiüzer., However the starless/protostellar divide has come under scrutiny recently following the discovery of Very Low Luminosity Objects (VeLLOs) with.
. VeLLOs are faint infrared point sources with protostellar colours towards objects oeviously classified as starless., VeLLOs are faint infrared point sources with protostellar colours towards objects previously classified as starless.
 Young et (2004) discovered a VeLLO in LIOI4 (LIOI4-IRS). part of the Visser et ssample. coincident with the peak of dust continuum emission that had been oreviously classified as starless by Parker (1988).," Young et (2004) discovered a VeLLO in L1014 (L1014-IRS), part of the Visser et sample, coincident with the peak of dust continuum emission that had been previously classified as starless by Parker (1988)."
 Although here no anomalous microwave emission is seen towards LIOLA it is suggestive that the peak of the anomalous emission towards L944 is more coincident with the centre of the red-shifted CO 2.>| outflow lobe. mapped by Visser et al..," Although here no anomalous microwave emission is seen towards L1014 it is suggestive that the peak of the anomalous emission towards L944 is more coincident with the centre of the red-shifted CO $2\to 1$ outflow lobe, mapped by Visser et al.,"
 and not the compact SCUBA emission from the Class 0 protostar., and not the compact SCUBA emission from the Class 0 protostar.
 This spatial correspondence immediately raises the question of whether the outflow itself or xossibly the cloud turbulence could be energising the spinning dust emission., This spatial correspondence immediately raises the question of whether the outflow itself or possibly the cloud turbulence could be energising the spinning dust emission.
 Regardless of this possible connection we also point out hat the misidentification of radio emission from protostars is a xotential source of confusion when searching for emission from spinning dust., Regardless of this possible connection we also point out that the misidentification of radio emission from protostars is a potential source of confusion when searching for emission from spinning dust.
 There seems to be no obvious correlation between the AMI Hux densities and the IRAS or SCUBA flux densities. however he number of data points is low.," There seems to be no obvious correlation between the AMI flux densities and the IRAS or SCUBA flux densities, however the number of data points is low."
 It is also true that there is no correlation between the SCUBA flux densities at um and those of IRAS at um. This is perhaps not particularly surprising in light of the mismatch in measured angular scales. and would suggest that the morphology of these objects is larger at 850 tm han the SCUBA chop allows for.," It is also true that there is no correlation between the SCUBA flux densities at $\mu$ m and those of IRAS at $\mu$ m. This is perhaps not particularly surprising in light of the mismatch in measured angular scales, and would suggest that the morphology of these objects is larger at $\mu$ m than the SCUBA chop allows for."
 Obviously this is not a problem when investigating compact cores as in Visser et al. (, Obviously this is not a problem when investigating compact cores as in Visser et al. (
2001: 2002). Jowever it provides little assistance when looking at the correlation between em-wave amd mm-wave emission.,"2001; 2002), however it provides little assistance when looking at the correlation between cm-wave amd mm-wave emission."
 In conclusion. we have observed a sample of fourteen compact Lynds dark nebulae.," In conclusion, we have observed a sample of fourteen compact Lynds dark nebulae."
 We have found a significant excess towards wo of the fourteen and an indication of anomalous behaviour in hree further clouds., We have found a significant excess towards two of the fourteen and an indication of anomalous behaviour in three further clouds.
 We suggest that the excess we see is due to rotational emission from very small grains and that this emission may be correlated with a high level of background emission at ower radio frequencies., We suggest that the excess we see is due to rotational emission from very small grains and that this emission may be correlated with a high level of background emission at lower radio frequencies.
 We thank the staff of the Lord’s Bridge observatory for their invaluable assistance in the commissioning and operation of the Areminute Microkelvin Imager., We thank the staff of the Lord's Bridge observatory for their invaluable assistance in the commissioning and operation of the Arcminute Microkelvin Imager.
 We thank John Richer for useful discussions., We thank John Richer for useful discussions.
 We thank the anonymous referee. whose comments have significantly improved this paper.," We thank the anonymous referee, whose comments have significantly improved this paper."
 The AMI is supported by Cambridge University and the STFC., The AMI is supported by Cambridge University and the STFC.
 NHW. MLD. TF. CRG and TS acknowledge the support of PPARC/STFC studentships.," NHW, MLD, TF, CRG and TS acknowledge the support of PPARC/STFC studentships."
Following ignition. a convective region develops in the white dwar! that eventually grows {ο encompass most of its mass.,"Following ignition, a convective region develops in the white dwarf that eventually grows to encompass most of its mass."
 Leal is (ransported outwards. but both radiative losses aud neutrino losses are negligible.," Heat is transported outwards, but both radiative losses and neutrino losses are negligible."
 Instead. the energy mostly goes into heating the convective portion of the star. and. to a lesser extent. expansion.," Instead, the energy mostly goes into heating the convective portion of the star, and, to a lesser extent, expansion."
 The heat capacity is given by (Woosley et al., The heat capacity is given by (Woosley et al.
 2004). where e is the specific internal energy. 7;= T/10* and A0? 7.," 2004), where $e$ is the specific internal energy, $T_8
=$ $10^8\,$ K and $\rho_9 =\rho$ $10^9\,$ $\,$ $^{-3}$ ."
 For the relevant temperature and density range. Ty = 2 to 7. po=1 to 3. the ionic term dominates with a minor contribution from the electrons.," For the relevant temperature and density range, $T_8$ = 2 to 7, $\rho_9 = 1$ to 3, the ionic term dominates with a minor contribution from the electrons."
" To a factor-of-two accuracy, ep&10P erg (105 1, "," To a factor-of-two accuracy, $\cp \approx 10^{15}$ erg $^{-1}$ $^8\,$ $^{-1}$."
"The total thermal energy is The correct definition lor pure ""thermal energv should be expressed in terms of ey rather (han ep. since ep also contains an expansion term dV."," The total thermal energy is The correct definition for pure “thermal energy” should be expressed in terms of $\cv$ rather than $\cp$, since $\cp$ also contains an expansion term $PdV$."
 However. because of strong degeneracy in the interior of the white dwarl. ey22ee and Eq. (," However, because of strong degeneracy in the interior of the white dwarf, $\cv \approx \cp$ and Eq. ("
2) provides a good estimate of the thermal heat content.,2) provides a good estimate of the thermal heat content.
 Moreover. for our purpose below. to estimate the gravothermal heat content. (his is the appropriate quantity to use.," Moreover, for our purpose below, to estimate the gravothermal heat content, this is the appropriate quantity to use."
" If the mass-averaged temperature is about half the central value and the convection zone. about one solar mass. where the index ve"" stands for central quantities of the star."," If the mass-averaged temperature is about half the central value and the convection zone, about one solar mass, where the index “c” stands for central quantities of the star."
 Actually. from computer models discussed in the next section we know that the convective core grows from 0.2 (to 1.15 aas the central temperature rises from 3x105 IN to 7x10* I(see Table 1)).," Actually, from computer models discussed in the next section we know that the convective core grows from 0.2 to 1.15 as the central temperature rises from $3 \times 10^8$ K to $7 \times 10^8$ K(see Table \ref{tab1}) )."
 A better estimate of the heat in the convective region is, A better estimate of the heat in the convective region is
event.,event.
 Blended. events may be chromatic so mutItiband photometry can help estimate this ellect (2:?)..," Blended events may be chromatic so multiband photometry can help estimate this effect \cite{Wozniak97,Vermaak00}."
 We performed a combined X7 minimization Lit o both our dataset and the OGLE publicly available. data by optimizing 6 parameters: the time of maximum ampliication fy. event timescale fo. maximum amplification zl. |raseline magnitude for the OGLE data Ze‘Lp Ue magnituce ollset οjsp between the two datasets and. the blend fraction by=fiffs.," We performed a combined $\chi^2$ minimization fit to both our dataset and the OGLE publicly available data by optimizing 6 parameters: the time of maximum amplification $t_{0}$ , event timescale $t_{\mbox{E}}$, maximum amplification $A_{0}$, baseline magnitude for the OGLE data $I_{\mbox{OGLE}}$, the magnitude offset $\Delta I = I_{\mbox{OGLE}}-I_{\mbox{JKT}}$ between the two datasets and the blend fraction $b_0 = f_b/f_s$."
 fi is the blend Hux of unixsolved light sources and fs the Hux of the unlensed source., $f_b$ is the blend flux of unresolved light sources and $f_s$ the flux of the unlensed source.
 Tion the total observed Dux at time/ becomes fio0)=feoMU)|fa. where AG)=(G0)|2)(uff)Zu0)4).," Then the total observed flux at time $t$ becomes $f_{\mbox{tot}}(t) = f_s \times A(t) + f_b$, where $A(t) = (u^2(t) + 2) / ( u(t) \sqrt{u^2(t) + 4} )$."
 Phe observed maenification in this case is Our 6 parameter fits to the lighteurves of the events give A7/CN.—6) values that are generally higher than their expected value. 1. ~(2/(N6))7., The observed magnification in this case is Our 6 parameter fits to the lightcurves of the events give $\chi^{2}/(N-6)$ values that are generally higher than their expected value 1 $\pm (2/(N-6))^{1/2}$.
 To remedy. this. we rofitthe combined dataset.by introducing two additional parameters that adjust. the error. bars. f ancl ay.," To remedy this, we refitthe combined datasetby introducing two additional parameters that adjust the error bars, $f$ and $\sigma_{0}$ ."
 f , $f$ 
in bursts).,in bursts).
 Η our interpretation is correct this should occur when the accretion rate is £zο Apa. and this is indeed what is observed. (see Figure 16 of Callowayetal.(2007))).," If our interpretation is correct this should occur when the accretion rate is $\approx 3-5$ $\dot{M}_\mathrm{Edd}$, and this is indeed what is observed (see Figure 16 of \citet{GMCPH}) )."
 This picture might also explain some unusual features of the PUES bursts for this source., This picture might also explain some unusual features of the PRE bursts for this source.
 Gallowayetal.(2006). found hat while most of the PRE bursts reached the Eddington imit for pure He. two had lower peak Iluxes. requiring some 1I in the mix.," \citet{GPMC} found that while most of the PRE bursts reached the Eddington limit for pure He, two had lower peak fluxes, requiring some H in the mix."
 These two exceptional PRE bursts occur. as discussed in Section 2.. at the highest accretion rates.," These two exceptional PRE bursts occur, as discussed in Section \ref{obs}, at the highest accretion rates."
 At hese rates pure He bursts are no longer likely ancl bursts should have some mixed L/LIe character again. reducing the »eak Lux reached by the PRE bursts.," At these rates pure He bursts are no longer likely and bursts should have some mixed H/He character again, reducing the peak flux reached by the PRE bursts."
 As shown by Galloway&Cumming (2006).. there can be a substantial percentage of H1 in the mix before the Edcington limit starts to fall low that expected for pure Le.," As shown by \citet{GC}, there can be a substantial percentage of H in the mix before the Eddington limit starts to fall below that expected for pure He."
 Phe values of convexity that we measured for the bursts of 4U 1636-536 ranged from -20 for the Group | bursts up o [20 for the Group 3 bursts., The values of convexity that we measured for the bursts of 4U 1636-536 ranged from -20 for the Group 1 bursts up to +20 for the Group 3 bursts.
 Although our simulations &enerated bursts with negative convexities in the right range. convexities &LO were harder to generate (Figure 8)).," Although our simulations generated bursts with negative convexities in the right range, convexities $> 10$ were harder to generate (Figure \ref{latmany}) )."
 One reason for this is that our simulations did not take into account PRE (which all of the Group 3 bursts show)., One reason for this is that our simulations did not take into account PRE (which all of the Group 3 bursts show).
 PRE ends to fatten the top of the lighteurve: when we include his in our simulations it results in an increase in convexity of sullicient magnitude to explain the discrepancy., PRE tends to flatten the top of the lightcurve: when we include this in our simulations it results in an increase in convexity of sufficient magnitude to explain the discrepancy.
 Changing he parameters fromthe baseline scenario can also increase convexity (compare Figures Sand 9))., Changing the parameters fromthe baseline scenario can also increase convexity (compare Figures \ref{latmany} and \ref{devallcon}) ).
 A rise in peak emperature. for example (as might be expected for Le-rich »ursts) increases convexity.," A rise in peak temperature, for example (as might be expected for He-rich bursts) increases convexity."
" )v comparing the observed values of convexity and rise ime with those generated by the simulations. we can infer he range of fy and. e, required to explain the observations (comparing Figures 4-5. and Figure 8))."," By comparing the observed values of convexity and rise time with those generated by the simulations, we can infer the range of $t_\mathrm{lr}$ and $v_p$ required to explain the observations (comparing Figures \ref{f1}- \ref{f2} and Figure \ref{latmany}) )."
 For the Group 32 »ursts. lor example. we need fy0.5 s independent of ey. while for the Group 2 (and hence also the Group 1) bursts we require fyκ)0.1 s. We can therefore ask whether the values that we infer are in line with the values predicted for the suggested burning regimes.," For the Group 3 bursts, for example, we need $t_\mathrm{lr} \lesssim 0.5$ s independent of $v_p$, while for the Group 2 (and hence also the Group 1) bursts we require $t_\mathrm{lr} \gtrsim 0.1$ s. We can therefore ask whether the values that we infer are in line with the values predicted for the suggested burning regimes."
 The single point lightcurve models of Weinberg.Bildsten&Schatz(2006)— preclict a temperature rise timescale of ~0.01 s for Le bursts. rising to ~0.1 s as HH fraction increases.," The single point lightcurve models of \citet{WBS} predict a temperature rise timescale of $\sim 0.01$ s for He bursts, rising to $\sim 0.1$ s as H fraction increases."
 The timescales derived by Woosleyetal.(2004) using multizone moclels are slightly longer., The timescales derived by \citet{W} using multizone models are slightly longer.
 Ehe limits that we derive are therefore broadly compatible with these models., The limits that we derive are therefore broadly compatible with these models.
 What is harder to check is the validity of the inferred. values of ον., What is harder to check is the validity of the inferred values of $v_p$.
 Spreading speed. (equation 3)) depends on the nuclear timescale. the scale height of the burnt atmosphere ancl the strength of frictional coupling in the burning lavers.," Spreading speed (equation \ref{spreadspeed}) ) depends on the nuclear timescale, the scale height of the burnt atmosphere and the strength of frictional coupling in the burning layers."
 Naively one would expect the nuclear timescale to be related to the temperature rise timescale (although. the degree to which convection develops could. skew this relationship)., Naively one would expect the nuclear timescale to be related to the temperature rise timescale (although the degree to which convection develops could skew this relationship).
 The dependence of the frictional coupling on the burning regime. however. is very poorly understood.," The dependence of the frictional coupling on the burning regime, however, is very poorly understood."
" Without a better understanding of the burning and spreading process. it is cillicult to sav whether the values of 0, suggested by our simulations accord with the values expected for the dillerent burning regimes."," Without a better understanding of the burning and spreading process, it is difficult to say whether the values of $v_p$ suggested by our simulations accord with the values expected for the different burning regimes."
 One issue that we have not considered in our mocelling is the role of the accretion disk., One issue that we have not considered in our modelling is the role of the accretion disk.
 An optically thick accretion disk extending down to the stellar surface could obscure the southern hemisphere of the star., An optically thick accretion disk extending down to the stellar surface could obscure the southern hemisphere of the star.
 At the lowest aceretion rates. the disk is likely to be truncated sullicientlv far from the star for our unobscured: models to be valid (Done&Caüerluiski2003).," At the lowest accretion rates, the disk is likely to be truncated sufficiently far from the star for our unobscured models to be valid \citep{DG}."
. As accretion rate increases. however. the inner disk is expected to move in towards the stellar surface. obscuring the southern hemisphere.," As accretion rate increases, however, the inner disk is expected to move in towards the stellar surface, obscuring the southern hemisphere."
 ltadiation pressure from a bright burst may be able to »ush the disk back. revealing the southern hemisphere once more (Shaposhnikov.Titarchuk&Llaberl2003).," Radiation pressure from a bright burst may be able to push the disk back, revealing the southern hemisphere once more \citep{STH}."
. Even if the southern hemisphere were obscured. however. there would » little impact on our results.," Even if the southern hemisphere were obscured, however, there would be little impact on our results."
 Bursts ignited in the northern 1emisphere would still have negative convexities. and bursts ienited at the equator would still be positive. although peak countrates would be lower and apparent rise times shorter han in our simulations.," Bursts ignited in the northern hemisphere would still have negative convexities, and bursts ignited at the equator would still be positive, although peak countrates would be lower and apparent rise times shorter than in our simulations."
 The largest impact would be on rusts ignited in the southern hemisphere: these would only e visible to us once the burning front traversed the equator. so would all have positive convexities.," The largest impact would be on bursts ignited in the southern hemisphere: these would only be visible to us once the burning front traversed the equator, so would all have positive convexities."
 In Table 1 we summarized the detectability. of burst oscillations. as reported by Callowayetal.(2007).. for the rising phase of bursts from 4U. 1636-536.," In Table \ref{bprops} we summarized the detectability of burst oscillations, as reported by \citet{GMCPH}, for the rising phase of bursts from 4U 1636-536."
 The detectability criteria used. were based on power exceeding a certain threshold in short time bins (0.253)., The detectability criteria used were based on power exceeding a certain threshold in short time bins (0.25s).
 Oscillations were most likely to be detected in Group 3 and then in Group 2., Oscillations were most likely to be detected in Group 3 and then in Group 2.
 Group 1 bursts were far less likely to show oscillations., Group 1 bursts were far less likely to show oscillations.
 Can this be explained by the pattern of Hamme spreading if the bursts in Groups 1 and 2 result from polar ignition. while those in Group 3 result. from. equatorial ignition?," Can this be explained by the pattern of flame spreading if the bursts in Groups 1 and 2 result from polar ignition, while those in Group 3 result from equatorial ignition?"
 Detectability will depend: on relative amplitude of the asymmetry. the length of time for which it persists. and the overall countrate.," Detectability will depend on relative amplitude of the asymmetry, the length of time for which it persists, and the overall countrate."
 A lone-lived lower amplitude asvmametry. may. be more detectable than a short-lived high amplitude asvmametrey if the time window used for the power spectral analysis is long., A long-lived lower amplitude asymmetry may be more detectable than a short-lived high amplitude asymmetry if the time window used for the power spectral analysis is long.
 We carried out a number of simulations to test whether our model is compatible with the observations., We carried out a number of simulations to test whether our model is compatible with the observations.
 In. Figure 12. we show dynamical power spectra from simulated bursts ignitec at cülferent [atitudes., In Figure \ref{latampev} we show dynamical power spectra from simulated bursts ignited at different latitudes.
 To mimic the dillerences between the cilferent groups we assumed. a higher peak countrate for the equatorial ignition. burst., To mimic the differences between the different groups we assumed a higher peak countrate for the equatorial ignition burst.
 We find. that oscillations are most detectable in the bright equatorial ignition bursts (our model for the Croup 3 bursts)., We find that oscillations are most detectable in the bright equatorial ignition bursts (our model for the Group 3 bursts).
 lor the bursts with lower peak countrates. oscillations are more detectable for bursts that ignite in the southern hemisphere.," For the bursts with lower peak countrates, oscillations are more detectable for bursts that ignite in the southern hemisphere."
 This fits with our interpretation in which Croup 2 bursts are ignited near the south pole and Group 1 bursts near the north pole., This fits with our interpretation in which Group 2 bursts are ignited near the south pole and Group 1 bursts near the north pole.
 4U 1636-536. like many other neutron stars. shows both multi-peakecl bursts and bursts with kinks (at least two points of inllection) in the rise.," 4U 1636-536, like many other neutron stars, shows both multi-peaked bursts and bursts with kinks (at least two points of inflection) in the rise."
 This group includes those that we exeluded from our analysis in Section 2 as well as bursts with weaker kinks such as Burst 19 (see Figure 5)) and the two bursts with negative convexities in Group:Lx (ligure 4))., This group includes those that we excluded from our analysis in Section \ref{obs} as well as bursts with weaker kinks such as Burst 19 (see Figure \ref{f2}) ) and the two bursts with negative convexities in Group 3 (Figure \ref{f1}) ).
 The simulations described in Section 3.. which involved single point ignition and subsequent smooth spread. produced no simulated light curves with more than one point of inflection.," The simulations described in Section \ref{sims}, , which involved single point ignition and subsequent smooth spread, produced no simulated light curves with more than one point of inflection."
and the mass-to-Iniinositv ratio. My/Lig.~1respectively...,"and the mass-to-luminosity ratio, $M_{\mathrm{host}}/L_{K_S} \sim 1$."
 The mass ratio of the black hole to the stellar component in thie host galaxy is 1.3«105m aud 5«10.7 for LEDA 81271 aud IRAS 01250|2832., The mass ratio of the black hole to the stellar component in the host galaxy is $1.3 \times 10^{-3}$ and $5 \times 10 ^{-3}$ for LEDA 84274 and IRAS 01250+2832.
" The results are consistent with the local relation between the mass of the ceutra black hole aud the stellar mass of the surrounding spleroid or the buleeo in nearbyAES galaxies. My,//Mpjgly=l.l10?2001)."," The results are consistent with the local relation between the mass of the central black hole and the stellar mass of the surrounding spheroid or the bulge in nearby galaxies, $M_{bh}/M_{bulge}=1.4 \times 10^{-3}$."
". The mass of both host galaxies is relatively QW. ie. G«\10?AL, and Lx10°AE... for LEDA 8127 Land IRAS 01250|2832, respectivelv."," The mass of both host galaxies is relatively low, i.e., $6\times 10^9\ \mathrm{M}_{\odot}$ and $4
\times 10^{9}\ \mathrm{M}_{\odot}$, for LEDA 84274 and IRAS 01250+2832, respectively."
 Large samples of ACUNS from the Sloan Digital Sky Survey have host galaxy niasses odog η=9.5.12 with DC1000)1.22.22003).," Large samples of AGNs from the Sloan Digital Sky Survey have host galaxy masses of $\log M_{gal}=9.5-12$ with $D_\mathrm{n}(4000)=
1.2-2.2$."
". Our sample wihA. =b6«10?M. aud D,(1000)=1.11.6 seems to le| the least massive popuation that may harbor au"," Our sample with $M_{\mathrm{host}}=4-6 \times 10^9\
\mathrm{M}_{\odot}$ and $D_n(4000) = 1.1 - 1.6$ seems to be the least massive population that may harbor an AGN."
expenssive and are difficult to integrate with simulations.,sive and are difficult to integrate withgas-phase simulations.
Secondly Bekki Chiba (2007) have shown that about of the gas within the SAIC! can pass (rough the LMC about 0.2 Gyr ago.,Secondly Bekki Chiba (2007) have shown that about of the gas within the SMC can pass through the LMC about 0.2 Gyr ago.
 If the SMC's initial gas mass belore gas stripping is ~LOM... then a significant amount of gas (as much as e107M. ) can be accreted onto the LAIC.," If the SMC's initial gas mass before gas stripping is $\sim 10^9 {\rm M}_{\odot}$, then a significant amount of gas (as much as $\sim 10^8 {\rm M}_{\odot}$ ) can be accreted onto the LMC."
 This is much larger than the total amount of IIVCS that can be accreted onto the LMC for the last ~101 vr. as shown in the previous sections.," This is much larger than the total amount of HVCs that can be accreted onto the LMC for the last $\sim 10^7$ yr, as shown in the previous sections."
 Furthermore. the accretion event of a large amount of gas [rom the SAIC can occur when the SAIC approaches the LMC. very closely so that the accreted gas cansimultaneoushy (rigger star formation in the LMC: most HII region can show systematically low [N/II].," Furthermore, the accretion event of a large amount of gas from the SMC can occur when the SMC approaches the LMC very closely so that the accreted gas can trigger star formation in the LMC: most HII region can show systematically low [N/H]."
 Possibly sporadic accretion ol HIVC's would be unlikely to cause such svnchronizecl star formation in the LAIC., Possibly sporadic accretion of HVCs would be unlikely to cause such synchronized star formation in the LMC.
 Thirdly. Bekki Chiba (2007) have already. shown that the gas-transfer between the LMC and (he SAIC is possible For the last 200 Myrs using the results of numerical simulations.," Thirdly, Bekki Chiba (2007) have already shown that the gas-transfer between the LMC and the SMC is possible for the last 200 Myrs using the results of numerical simulations."
 llowever. no one has demonstrated that (he massive IIVC's like Complex C with plivsical sizes of LO kpe x 10 kpe (e.g.. Wakker et al.," However, no one has demonstrated that the massive HVCs like Complex C with physical sizes of 10 kpc $\times$ 10 kpc (e.g., Wakker et al."
 1999) can be really aceretecl onto the LMC owing to hvedrodynanmical interaction between the LMCs gas disk aud (he IIVCs in spite of the large relative velocities (~160 km !) between them., 1999) can be really accreted onto the LMC owing to hydrodynamical interaction between the LMC's gas disk and the HVCs in spite of the large relative velocities $\sim 160$ km $^{-1}$ ) between them.
 If only some minor [fractions (e.g... 10%)) of the IIVC masses can be accreted onto the LAIC curing IVC-LAIC collisions. then the required number of the Galactic ILVCs for explaining the observed [N/II] in the LAIC can be unrealistically large.," If only some minor fractions (e.g., ) of the HVC masses can be accreted onto the LMC during HVC-LMC collisions, then the required number of the Galactic HVCs for explaining the observed [N/H] in the LMC can be unrealistically large."
 Thus. if the ISM of the SMC has rather low [N/IH] and if the stripped gas can be mixed into the ISM of the LAIC and then converted into new stars. the newly formed stars can show low [N/I].," Thus, if the ISM of the SMC has rather low [N/H] and if the stripped gas can be mixed into the ISM of the LMC and then converted into new stars, the newly formed stars can show low [N/H]."
 Indeed the ΠΠ regions and voung stellar populations of the SAIC are observed to have [N/IH] by a factor of &I8 lower than the solar value (e.g.. Pilvugin et al.," Indeed the HII regions and young stellar populations of the SMC are observed to have [N/H] by a factor of $\sim 18$ lower than the solar value (e.g., Pilyugin et al."
 2003: Rolleston οἱ al., 2003; Rolleston et al.
 2003: Lill 2004). which implies that the ISM of the SMLC could possibly have low [N/1I] (though the low [N/II] could be only for the voung stellar populations. not for the entire ISM).," 2003; Hill 2004), which implies that the ISM of the SMC could possibly have low [N/H] (though the low [N/H] could be only for the young stellar populations, not for the entire ISM)."
" The required gas corresponding to this [N/II| is ~10""—10*M. (see Fig.l).", The required gas corresponding to this [N/H] is $\sim 10^6 -10^7 {\rm M}_{\odot}$ (see Fig.1).
 Thus. the predicted amount of gas transferred from the SAIC to the LMC of ~10M. (Bekki Chiba 2007) is sullicient to dilute the N abundance in the LMC as observed.," Thus, the predicted amount of gas transferred from the SMC to the LMC of $\sim 10^8 {\rm M}_{\odot}$ (Bekki Chiba 2007) is sufficient to dilute the N abundance in the LMC as observed."
 llowever. (he SAIC-(ransler scenario has some disadvantages in explaining clearly (he observed low [N/E both in the LMC and the SAIC.," However, the SMC-transfer scenario has some disadvantages in explaining clearly the observed low [N/H] both in the LMC and the SMC."
 For example. if the origin of the unusually low [N/II] in the LMC' is due to the gas transfer between the Clouds. then the next question is as to why the SMC has ISM with such low [N/IH]: this point is vet to be answered by ihe SMC-transfer scenario.," For example, if the origin of the unusually low [N/H] in the LMC is due to the gas transfer between the Clouds, then the next question is as to why the SMC has ISM with such low [N/H]: this point is yet to be answered by the SMC-transfer scenario."
 Previous chemical evolution models did not clearly show that the present-day dwarf galaxies like the SIC can have very low [N/IHI] (e.g.. Henry et al.," Previous chemical evolution models did not clearly show that the present-day dwarf galaxies like the SMC can have very low [N/H] (e.g., Henry et al."
 2000: Mollá οἱ al., 2000; Mollá et al.
 2006): the Appendix also implies that canonical chemical evolution models can hardly show very low [N/IH] in the present stellar populations for Magellanic-tvpe dwarl galaxies., 2006): the Appendix also implies that canonical chemical evolution models can hardly show very low [N/H] in the present stellar populations for Magellanic-type dwarf galaxies.
 We need to discuss why the ISM of the SMC can have low [N/II] in our future, We need to discuss why the ISM of the SMC can have low [N/H] in our future
The media is supposed to be uniform. therefore the equilibrium is satisfied automatically.,"The medium is supposed to be uniform, therefore the equilibrium is satisfied automatically."
 It ust be anentioned. however. that real astrophysical situation is auch more complicated.," It must be mentioned, however, that real astrophysical situation is much more complicated."
 In the stellar interior the eyavity aud the pressure eracdicut necessarily leack to f1C. noli uniforui spaial distribution of unperturbe physical quautities (density. temperature and maeetic. fic1d).," In the stellar interior the gravity and the pressure gradient necessarily lead to the non uniform spatial distribution of unperturbed physical quantities (density, temperature and magnetic field)."
 But iu order to understand the plysics of he wave coupling we cji0086 the simples uniforn imodel (Fig.1). which cojsiders zu uulfonu naenetic ονider with an uuiforui deusiv.," But in order to understand the physics of the wave coupling we choose the simplest uniform model (Fig.1), which considers an uniform magnetic cylinder with an uniform density."
 Thus. eyavityv is neglected in the moment CQuation {rote that almost all dvuamo models also igiore the eyavity).," Thus, gravity is neglected in the momentum equation (note that almost all dynamo models also ignore the gravity)."
 Ouce the physical erouuds of he coulius are clear. future modes Inav include| a Iuore realistic spatial distribution of the ]oivsieal variables.," Once the physical grounds of the coupling are clear, future models may include a more realistic spatial distribution of the physical variables."
 For the study of the coupine between differeut oscillations we use he perturbative method ie. all variables are perturbed around their equilibria values aud their consequent evolution is studied., For the study of the coupling between different oscillations we use the perturbative method i.e. all variables are perturbed around their equilibrium values and their consequent evolution is studied.
 We first briefly describe the linear evolution of the perturbations in form of linear waves aud then study the weakly uon-Iinear interaction between the waves. which leads to the coupling of our interest.," We first briefly describe the linear evolution of the perturbations in form of linear waves and then study the weakly non-linear interaction between the waves, which leads to the coupling of our interest."
 All physical variables are presented as a sun of unperturbed aud perturbed parts ©=£9|£i., All physical variables are presented as a sum of unperturbed and perturbed parts $\xi = \xi_0 + \xi_1$.
 Tn the linear approximation ouly the first order ternis are retained., In the linear approximation only the first order terms are retained.
 This allows us to consider the evolution of differeut waves separately., This allows us to consider the evolution of different waves separately.
 The svstei (1)-(1) includes Ανάν aud magnuetoacoustic Waves., The system (1)-(4) includes Alfvénn and magnetoacoustic waves.
 Iu cvliudrical coordinates the pure Alfvéónu waves are the torsional waves. which have azimuthal velocity and maguetie feld. compoucuts and represent the purely clectromaguetic part of oscillations.," In cylindrical coordinates the pure Alfvénn waves are the torsional waves, which have azimuthal velocity and magnetic field components and represent the purely electromagnetic part of oscillations."
" They are described by equatious where V5. 5h, are the velocity and maguetic feld perturbations."," They are described by equations where $V_{\phi}$, $b_{\phi}$ are the velocity and magnetic field perturbations."
 As we already mentioned. the unperturbed density ids considered to be homogeneous.," As we already mentioned, the unperturbed density is considered to be homogeneous."
 The restoring force for the torsional waves is the tension of maenetic field lines ouly., The restoring force for the torsional waves is the tension of magnetic field lines only.
 The waves propagate along the maguetic field lines with the Alfvénn speed Consequently the dispersion relation of the Waves Is where wa ds the frequency and &4 is the wave muuber., The waves propagate along the magnetic field lines with the Alfvénn speed Consequently the dispersion relation of the waves is where $\omega_A$ is the frequency and $k_A$ is the wave number.
 The waves are strictly transversal and they do not cause a density perturbation iu the linear regne., The waves are strictly transversal and they do not cause a density perturbation in the linear regime.
 We consider the adiabatic process. then the relmaiing linearized equations are Vg. Ve. bg. bz. py and py are the perturbations of velocity. magnetic field. deusitv and pressure respectively: e;=∖⋃⋃\/rpy/py is the adiabatie sound speed.," We consider the adiabatic process, then the remaining linearized equations are where $V_R$, $V_Z$, $b_R$, $b_Z$, $\rho_1$ and $p_1$ are the perturbations of velocity, magnetic field, density and pressure respectively; $c_s=\sqrt{\gamma p_0/\rho_0}$ is the adiabatic sound speed."
criterion: both the Abell and APAL samples have been selected using an upper Πιτ for the estimated redshift. thm.,"criterion: both the Abell and APM samples have been selected using an upper limit for the estimated redshift, $z_{lim}$."
 Estimated redshifts are subject to random errors. with approximately loe-normal distribution of dispersion 1.9 in log: (see Figure 2).," Estimated redshifts are subject to random errors, with approximately log-normal distribution of dispersion 1.3 in $\log z$ (see Figure 2)."
 This effect causes a deficit of clusters near the lait :uis., This effect causes a deficit of clusters near the limit $z \leq z_{lim}$.
" Ou the other haud. some clusters within the limit +);,, have true redshifts exceeding the estimated one. thus the density distribution has a large tail of clusters with τω29tian but text<trim."," On the other hand, some clusters within the limit $z_{lim}$ have true redshifts exceeding the estimated one, thus the density distribution has a large tail of clusters with $z_{meas} >
z_{lim}$ but $z_{est} < z_{lim}$."
 Lo decrease this distance selection effect we apply for the Abell saluple an upper linut for the estimated redshift. ;=0.15. which exceeds by Az=0.02 the redshift limit of the sample used for our structure analysis. τε=0.13.," To decrease this distance selection effect we apply for the Abell sample an upper limit for the estimated redshift, $z=0.15$, which exceeds by $\Delta z=0.02$ the redshift limit of the sample used for our structure analysis, $z_{lim}=0.13$."
 Figure 3 shows that a rapid decrease of the spatial density of clusters near the limit of the sample can be avoided by this procedure., Figure 3 shows that a rapid decrease of the spatial density of clusters near the limit of the sample can be avoided by this procedure.
" A similar cut would limit the APM sample to z;,,=0.10.", A similar cut would limit the APM sample to $z_{lim}=0.10$.
 Tustead we applied an identical cut for both cluster samples. Min=350Ape. at the cost of introducing this selection effect in the APAI sample.," Instead we applied an identical cut for both cluster samples, $r_{lim} = 350$, at the cost of introducing this selection effect in the APM sample."
 The rapid decrease of the deusity of APM clusters bevond 300 lis due to the sharp cutoff of the estimated redshift at >= 0dlsorr-325]h ({sce Figure 2)., The rapid decrease of the density of APM clusters beyond 300 is due to the sharp cutoff of the estimated redshift at $z=0.118$ or $r=325$ (see Figure 2).
 The third distance-depeudent selection effect is due to difficulty to detect a very nearby cluster spamming a large area on the skv (D97)., The third distance-dependent selection effect is due to difficulty to detect a very nearby cluster spanning a large area on the sky (D97).
 This effect is practically absent iu the Abell catalog: oulv the Virgo cluster was excluded from the Abell catalog for this reasou., This effect is practically absent in the Abell catalog; only the Virgo cluster was excluded from the Abell catalog for this reason.
" For APM clusters this effect is cuhauced by the absence in the APM. sample galaxies brighter than 5;=17 (which are overexposed aud cannot be measured automatically, see Maddox. Efstathiou Sutherland 1990)."," For APM clusters this effect is enhanced by the absence in the APM sample galaxies brighter than $b_j = 17$ (which are overexposed and cannot be measured automatically, see Maddox, Efstathiou Sutherland 1990)."
 Due to this selection effect the APM cluster sample is very sparse at simall distances of ro<100 ffrom us: this explaius also the absence of nearby rich superclusters in the APM sample. (see Figure 3).," Due to this selection effect the APM cluster sample is very sparse at small distances of $r < 100$ from us; this explains also the absence of nearby rich superclusters in the APM sample, (see Figure 3)."
 So far we have discussed selection effects in samples of all clusters., So far we have discussed selection effects in samples of all clusters.
 As not alb clusters have a measured redshift. another cistauce-dependent selection effect occurs ii saimples of clusters with only measured redshifts.," As not all clusters have a measured redshift, another distance-dependent selection effect occurs in samples of clusters with only measured redshifts."
 The overall distance-dependent selection probability was calculated by Efstathiou (1992) and Croft (1997) by snoothiug the observed redshift distribution., The overall distance-dependent selection probability was calculated by Efstathiou (1992) and Croft (1997) by smoothing the observed redshift distribution.
 We use a different approach here. and caleulate the conibined effect of all distaucce-depeudoeut selection effects for Abell clusters by eq. (6)).," We use a different approach here, and calculate the combined effect of all distance-dependent selection effects for Abell clusters by eq. \ref{eq6}) )."
 For the APM cluster samples the combined effect of distance-dependent selections cau be approxinated by the following Luv: here we assune that at a distance αν clusters are detected with a probability fy., For the APM cluster samples the combined effect of distance-dependent selections can be approximated by the following law: here we assume that at a distance $r_{max}$ clusters are detected with a probability $f_0$.
 This probability function was used to caleulate the comparison Poisson sample for the APM clusters., This probability function was used to calculate the comparison Poisson sample for the APM clusters.
 Values of the parameters tin. Vinca and fy are given in Table 1.," Values of the parameters $r_{min}$, $r_{max}$, and $f_0$ are given in Table 1."
 We stummarize the discussion of selection effects in Abell and APAL cluster cataloes as follows., We summarize the discussion of selection effects in Abell and APM cluster catalogs as follows.
 Both cluster catalogs are subject to simular sclection effects in Galactic latitude., Both cluster catalogs are subject to similar selection effects in Galactic latitude.
 The error due to overlapping of clusters iu superclusters is preseut only in the Abell catalog., The error due to overlapping of clusters in superclusters is present only in the Abell catalog.
 This error may distort the structure of individual superclusters (and the cluster correlation function on small separations)., This error may distort the structure of individual superclusters (and the cluster correlation function on small separations).
 Towever. it is of less nuportance for the study of the structure of the supercluster-void network. since it does uot decrease systematically the nmuuber of clusters iu superclusters.," However, it is of less importance for the study of the structure of the supercluster-void network, since it does not decrease systematically the number of clusters in superclusters."
 Distance-depeudent selection effects are rather stall in the Abell cluster sample. but verv huge in the APM. sample.," Distance-dependent selection effects are rather small in the Abell cluster sample, but very large in the APM sample."
 We shall discuss the influence of these sclection effects ou the study of the supercluster-void network iu section 5.5 below., We shall discuss the influence of these selection effects on the study of the supercluster-void network in section 5.5 below.
 Iu order to calculate the spatial density of Abell aud APAI clusters of galaxies we generate Poisson samples with selection function parameters as eiven in Table 1., In order to calculate the spatial density of Abell and APM clusters of galaxies we generate Poisson samples with selection function parameters as given in Table 1.
 We count the total uuuber of particles. aud the nuuber of particles left after the selection functions have been applied.," We count the total number of particles, and the number of particles left after the selection functions have been applied."
 We obtain p—27.6«10.98? P for the ACO.AL sample and p283«10557. 7. for APALAL.," We obtain $\rho = 27.6 \times
10^{-6}~h^3$ $^{-3}$ for the ACO.A1 sample and $\rho = 83 \times
10^{-6}~h^3$ $^{-3}$, for APM.A1."
 Our value for Abell clusters coufiruis earlicr deusitv estimate by E97d. bu is about twice the value fouud by DBalicall Ceu (1993).," Our value for Abell clusters confirms earlier density estimate by E97d, but is about twice the value found by Bahcall Cen (1993)."
 The reason for this discrepancy is our more detailed account of he selection fuuctiou (see eq. (7)))., The reason for this discrepancy is our more detailed account of the selection function (see eq. \ref{eq7}) )).
 The surface of the sky covered by. the sample of Abel clusters. cau be estimated. when we fix the effective Galactic atitude limit of the survey.," The surface of the sky covered by the sample of Abell clusters, can be estimated, when we fix the effective Galactic latitude limit of the survey."
 The large-scale distribution of üiegl-deusitv regious can be investigated if superclusters of richuess Αι29 [are included iu the sample (E970)., The large-scale distribution of high-density regions can be investigated if superclusters of richness $N_{cl} \ge 4$ are included in the sample (E97d).
 Figure shows that the density of clusters in rici superclusters drops o zero at sindzc0.30., Figure 4 shows that the density of clusters in rich superclusters drops to zero at $\sin b \approx 0.30$.
 Thus we find that the Abell cluster survey covers BG steradiaus (sr) ou the sky., Thus we find that the Abell cluster survey covers 8.8 steradians (sr) on the sky.
 The APN survev js linuted by 0.302sind=0.95 in declination and ARA=130° in right asceusion. corresponding to an area of L.17 sv.," The APM survey is limited by $-0.30 \ge \sin\delta \ge -0.95$ in declination and $\Delta RA = 130^{\circ}$ in right ascension, corresponding to an area of 1.47 sr."
 The volume occupied by the Abell sample ACO.AI is 126«1095.? Mpc?., The volume occupied by the Abell sample ACO.A1 is $126 \times 10^6~h^{-3}$ $^3$.
 The depth of the APM sample is from 50h Πο 350AIpe.. correspouding to a volue of the APM survey 21&10957 AIpe?.," The depth of the APM sample is from 50 to 350, corresponding to a volume of the APM survey $21 \times 10^6~h^{-3}$ $^3$."
 Here we are speaking ou the volume of the of Abell or APM. clusters. not the volume occupied by. Abell or APM clusters themselves.," Here we are speaking on the volume of the of Abell or APM clusters, not the volume occupied by Abell or APM clusters themselves."
 We can also fud the effective volume of both samples. defined by the uunmber of clusters in the sample divided by the mean deusitv (we mean the true mean density which is calculated after the correction for all selection effects).," We can also find the effective volume of both samples, defined by the number of clusters in the sample divided by the mean density (we mean the true mean density which is calculated after the correction for all selection effects)."
 We eet GOS10°2.7 Mpc? aud 11&10°bo? AIpe?. for the ACO.AL and APALAL samples.," We get $60 \times 10^6~h^{-3}$ $^3$ and $11
\times 10^6~h^{-3}$ $^3$, for the ACO.A1 and APM.A1 samples."
 The effective volumes of suuples ACO.RI aud APALRI are even less. 10«&109fh? Ape? and 5«1095.3 Mpc?. respectively.," The effective volumes of samples ACO.R1 and APM.R1 are even less, $40
\times 10^6~h^{-3}$ $^3$ and $5 \times 10^6~h^{-3}$ $^3$, respectively."
 We see that the selection effects reduce the effective volue with respect to the actual volume of samples., We see that the selection effects reduce the effective volume with respect to the actual volume of samples.
 Volume estimates show that the APM sample of all clusters occupies a volume about 1/6 of the volume of the correspoucding Abell sample ACO.AL., Volume estimates show that the APM sample of all clusters occupies a volume about 1/6 of the volume of the corresponding Abell sample ACO.A1.
 The volune estimate given by T98 is larger thaw found in the present paper. since T9585 also included regions where the sample is very sparse.," The volume estimate given by T98 is larger than found in the present paper, since T98 also included regions where the sample is very sparse."
 The cluster correlation function has been a subject of intensive studies starting from the pioneering work bv klvpiu Ἱνορνί]ον (1983) and Dalicall Soncira (1983)., The cluster correlation function has been a subject of intensive studies starting from the pioneering work by Klypin Kopylov (1983) and Bahcall Soneira (1983).
The NICAIOS images. however. suffered. [rom inirapixel sensitivity effects.,"The NICMOS images, however, suffered from intrapixel sensitivity effects."
 Camera 3 is poorly sampled at ~07.2 per pixel. and can produce as much as a flix variation depending if the peak of a PSF is centered on a given pixel. or is offset. towards the edges of the pixel (Storrsetal.1999:LauerTook&Fruchter2000)..," Camera 3 is poorly sampled at $\sim 0''.2$ per pixel, and can produce as much as a flux variation depending if the peak of a PSF is centered on a given pixel, or is offset towards the edges of the pixel \citep{storrs1999,1999PASP..111.1434L,2000adass...9..521H}."
 This flux variation in the pixel response function (PREF) is not removed in the flat-field correction. aud imposes an inherent limitation in (hese images.," This flux variation in the pixel response function (PRF) is not removed in the flat-field correction, and imposes an inherent limitation in these images."
 With many dithered exposures of the same field. it is possible to map the PIRE (Storrsetal.1999:Lauer1999).. and determine a correction to PSF photometry.," With many dithered exposures of the same field, it is possible to map the PRF \citep{storrs1999,1999PASP..111.1434L}, and determine a correction to PSF photometry."
 Unfortunately. there are no easy means (o deconvolve the PRE from the PSF.," Unfortunately, there are no easy means to deconvolve the PRF from the PSF."
 Therelore. clilferencing the (wo image stacks of the IRUDE necessarily resulted in a “checkerboard” pattern of under aud over subtractions (measured al about. £15—20%).," Therefore, differencing the two image stacks of the IRUDF necessarily resulted in a “checkerboard” pattern of under and over subtractions (measured at about $\pm 15 - 20\%$ )."
 Faint and diffuse objects were generally cleanly subtracted., Faint and diffuse objects were generally cleanly subtracted.
 In Tables 1 and 2. we list the epoch stacks created for (he UDF. UDFP. and IRUDE searches. with the mean date of the image stack. (he total number of orbits. and the total exposure (ime of each stack.," In Tables \ref{tab:tab3} and \ref{tab:tab4} we list the epoch stacks created for the UDF, UDFP, and IRUDF searches, with the mean date of the image stack, the total number of orbits, and the total exposure time of each stack."
 To asses the sensilivily aud completeness of (ae UDF. UDET. and IRUDF searches. we performed monte carlo tests with planted PSFs meant to represent false SNe.," To asses the sensitivity and completeness of the UDF, UDFP, and IRUDF searches, we performed monte carlo tests with planted PSFs meant to represent false SNe."
 In the case of the IRUDF. a DSF was generated from a lew stars in (he images. and scaled {ο one count per second using zero points and aperture corrections provided by the NICMOS eroup al Space Telescope Science Institute.," In the case of the IRUDF, a PSF was generated from a few stars in the images, and scaled to one count per second using zero points and aperture corrections provided by the NICMOS group at Space Telescope Science Institute."
 The measured aperture photometry was then corrected for intrapixel sensitivity. variations lollowing a prescription detailed in (1999)., The measured aperture photometry was then corrected for intrapixel sensitivity variations following a prescription detailed in \citet{storrs1999}.
. We placed one false SN of a given magnitude on the centers of a randomly selected set of 50 detected objects (to > 5o). subtracted (he images. and then attempted (o recover the false SNe bv visual inspection (without prior knowledge of the locations of each planted false SN).," We placed one false SN of a given magnitude on the centers of a randomly selected set of 50 detected objects (to $>5\sigma$ ), subtracted the images, and then attempted to recover the false SNe by visual inspection (without prior knowledge of the locations of each planted false SN)."
 This method was iterated (ο successively fainter magnitudes (in steps of 0.2 mag) until none ol the planted SNe were recovered., This method was iterated to successively fainter magnitudes (in steps of 0.2 mag) until none of the planted SNe were recovered.
 The resulüing histograms of percent recovered per magnitude bin is shown in Figure 1.., The resulting histograms of percent recovered per magnitude bin is shown in Figure \ref{fig:fig1}.
 The sensitivity in each epoch of the IRUDE was determined from the difference magnitude. Am. determined from the [ιν difference of objects in the residual frame. which is given by: where Fy and £5 are the flix of the false SN in first ancl second image stacks. n» ancl ms are," The sensitivity in each epoch of the IRUDF was determined from the difference magnitude, $\Delta m$, determined from the flux difference of objects in the residual frame, which is given by: where $F_1$ and $F_2$ are the flux of the false SN in first and second image stacks, $m_1$ and $m_2$ are"
mass and Likely have high spins. they will escape the cluster upon merger.,"mass and likely have high spins, they will escape the cluster upon merger."
 This leaves the cluster without a seed unless a third runswav of sufficient mass occurs., This leaves the cluster without a seed unless a third runaway of sufficient mass occurs.
 The problem is that the third rmaway is often much less massive aud therefore difficult to retain. as we have shown.," The problem is that the third runaway is often much less massive and therefore difficult to retain, as we have shown."
 Iu fact. since lower mass IMDIIS κο casily escape elobular clusters. if globular cluster observations fud that they arenof rare. it may be possible to constraiu the IMDII τοσο history. as well.," In fact, since lower mass IMBHs so easily escape globular clusters, if globular cluster observations find that they are rare, it may be possible to constrain the IMBH merger history, as well."
 For example. if niu low mass IMDBIIs exist within clusters. we may rule out low mass ratio merecrs — this would imply that there is no high mass tail iu the BIT IME.," For example, if many low mass IMBHs exist within clusters, we may rule out low mass ratio mergers – this would imply that there is no high mass tail in the BH IMF."
 Alternatively. the lower the spin. the better the retention as figure 5 shows: if low mass IMDIIS are found in large uuubers within clusters. and if DIIs are found with >2OAL.. we may have to explore wavs in which the black holes spin down aud align within a gas-poor globular.," Alternatively, the lower the spin, the better the retention as figure \ref{fig:retain} shows; if low mass IMBHs are found in large numbers within clusters, and if BHs are found with $>20 M_\odot$, we may have to explore ways in which the black holes spin down and align within a gas-poor globular."
 Makine some very simple asstuuptions for the primordial elobular cluster cuviromment. such as the BIT IME aud ceutral density structure. we have estimated that less than 5 elobular clusters retain thei IMDITS within the Milkv Wav even if every oue hosted an iitial IMDIT seed.," Making some very simple assumptions for the primordial globular cluster environment, such as the BH IMF and central density structure, we have estimated that less than $5$ globular clusters retain their IMBHs within the Milky Way – even if every one hosted an initial IMBH seed."
 Naturally. there are many uncertainties folded. iuto this estimate. such as the shape of the primordial elobular cluster IME. the degree of mass OSS in low iuetallicity svstenis and its effect on the DIT IME. and the detailed role that few-body/BU interactions plax in shaping carly globular cluster structure.," Naturally, there are many uncertainties folded into this estimate, such as the shape of the primordial globular cluster IMF, the degree of mass loss in low metallicity systems and its effect on the BH IMF, and the detailed role that few-body/BH interactions play in shaping early globular cluster structure."
 As more work 15is done on these areas; we can revise our estimates usiug more generic results.," As more work is done on these areas, we can revise our estimates using more generic results."
 For exiuuple. if the DIT IME. were instead narrowly peaked around 1037. (7) aud if the seed black hole were a massive superuova remuaut.| our caleulatious indicate that about 25% of the lilly Way elobular clusters could retain black holes as siall as ~ LOOMS...," For example, if the BH IMF were instead narrowly peaked around $10 M_\odot$ \citep{2001ApJ...554..548F} and if the seed black hole were a massive supernova remnant, our calculations indicate that about $25\%$ of the Milky Way globular clusters could retain black holes as small as $\sim 400 M_\odot$ ."
 Aun IMBIT of a few huudred. AL. may not cave an clectromaeguetically observable impact ou the strounding elobular cluster. as the dvuamiical effects on he surrounding stars may also be produced by a high ynary fraction (?)..," An IMBH of a few hundred $M_\odot$ may not leave an electromagnetically observable impact on the surrounding globular cluster, as the dynamical effects on the surrounding stars may also be produced by a high binary fraction \citep{Trenti:07imbh}."
 Towever. when stellar mass compact objects merge with these smaller πας» ΤΑΠΟΤΕ. they will xoduce a stroug eravitational wave signals that should e detectable with Advanced LIGO (?)..," However, when stellar mass compact objects merge with these smaller mass IMBHs, they will produce a strong gravitational wave signals that should be detectable with Advanced LIGO \citep{mandel:07imri}."
 With so τα small black holes having been ejected roni their host globular clusters. we speculate that ~100 black holes are swarming about iu the Milky Wav halo with masses from —1060100037... and with volocities mostly ou the order of a few hiuudred kims," With so many small black holes having been ejected from their host globular clusters, we speculate that $\sim 100$ black holes are swarming about in the Milky Way halo with masses from $\sim 100 - 1000 M_\odot$, and with velocities mostly on the order of a few hundred $\KMS$."
 The mmmber of rogues could be in the thousands if. as has been sugeested. the current globular cluster population is asinall fraction of the total uuuber originally created (2).," The number of rogues could be in the thousands if, as has been suggested, the current globular cluster population is a small fraction of the total number originally created \citep{Aguilar:88gc}."
 Although we have focused ou IAIBUs in the Galactic elobular cluster population. the same processes lay occur in other galaxies.," Although we have focused on IMBHs in the Galactic globular cluster population, the same processes may occur in other galaxies."
 Extragalactie ULNs. which may ο powered by ~10?AL. IMBUs. ave frequently: found jear. but not in young stellar clusters (o...?7)..," Extragalactic ULXs, which may be powered by $\sim 10^{2}~M_\odot$ IMBHs, are frequently found near, but not in young stellar clusters \citep[e.g.,][]{fabbianoetal01,2005ApJS..157...59L}."
 Note. hough. that the stellar clusters associated with ULXs are not always the dense stellar svstenis required by he IMDBII formation models considered here (7).," Note, though, that the stellar clusters associated with ULXs are not always the dense stellar systems required by the IMBH formation models considered here \citep{liuetal07}."
. Tf such IMDIIs did forma within the nearby clusters. they nay be ejected frou gravitational wave kicks coming roni mnergers with stellaranass black holes. especially as they would meree with tje most mnassive black holes first.," If such IMBHs did form within the nearby clusters, they may be ejected from gravitational wave kicks coming from mergers with stellar-mass black holes, especially as they would merge with the most massive black holes first."
 While this would ex]aun their separation frou the cluster center. it woul uot explain the fact that T“LNs are accreting sources dt is nof clear how au IMDII would pick up a coupanion on its wav out of the cluster aud is unlikely te) retain a stellar companion lose enough to overfill its Roche lobe.," While this would explain their separation from the cluster center, it would not explain the fact that ULXs are accreting sources; it is not clear how an IMBH would pick up a companion on its way out of the cluster and is unlikely to retain a stellar companion close enough to overfill its Roche lobe."
 Au IMDBII with a stellar conpauion. lOWOCVOY. nay be ejected from the host cluster through few-body Newtonian dynamical kicks iat harden the binary uutil it begins accreting (7777).," An IMBH with a stellar companion, however, may be ejected from the host cluster through few-body Newtonian dynamical kicks that harden the binary until it begins accreting \citep{Gultekin:2004gi,Oleary:2005bm,Gultekin:2006tb,Blecha:06imbhulx}."
 Even if the ejected INIDIIis not accreting gas ax a ULX. clectromaguctic observations may still detect rogue lack holes.," Even if the ejected IMBH is not accreting gas as a ULX, electromagnetic observations may still detect rogue black holes."
 For iustauce. if the INMDITI were to carry a few nlassive stars alougo as it is ejected. our results indicate a kinematically fas subpoptuation of massive stars near eelobular clusters.," For instance, if the IMBH were to carry a few massive stars along as it is ejected, our results indicate a kinematically fast subpopulation of massive stars near globular clusters."
 The ejected black holes may leave a cluporary imprint ou the elobular cluster as well., The ejected black holes may leave a temporary imprint on the globular cluster as well.
 Smce hey are ejected frou the svstem inapulsively. it is likely hat the elobular cluster corποπ] temporarily expaud.," Since they are ejected from the system impulsively, it is likely that the globular cluster core would temporarily expand."
 Direct simulations remain te| be done to determine how he globular cluster respouds to the ejection of an IMDII., Direct simulations remain to be done to determine how the globular cluster responds to the ejection of an IMBH.
 The consequences of these large recoil velocities ay also affect SMDII asscuubly., The consequences of these large recoil velocities may also affect SMBH assembly.
 The most likely candidates or SMDBII seeds are ~1033f. Pop III stellar remuauts at τους]τς 2212020 (7?," The most likely candidates for SMBH seeds are $\sim 10^3
M_\odot$ Pop III stellar remnants at redshifts $z \gtsim 12-20$ \citep{Heger:03sn,Volonteri:03smbh,Islam02,Wise:05snpop3,Micic:2007sb}."
" These relic seeds are predicted to form at the centers of low mass dark natter halos (~ΕνΠΟΛΗ, ", These relic seeds are predicted to form at the centers of low mass dark matter halos $\sim 4 \times 10^6 M_\odot$ ).
As dark matter halos: Herarchically merece to assemble the galaxy. the seed dack holes sink to the ceuter through dvnamical fiction and eventually mcrec.," As dark matter halos hierarchically merge to assemble the galaxy, the seed black holes sink to the center through dynamical friction and eventually merge."
 With kick velocities in the rauge of ~10?quΊανsloc. df may also be difficultDp to retain: seed SAIBUs iu high redshift low mass dark matter lalos.," With kick velocities in the range of $\sim 10^{2}-10^{3} \KMS$, it may also be difficult to retain seed SMBHs in high redshift low mass dark matter halos."
" We plan to explore black hole retention aud possible Nick suppression niechiauisuis at thelow mass eud of the alo πο ""uction using Ligh resolution cosmological N-body sinulations im our next pa]xY.", We plan to explore black hole retention and possible kick suppression mechanisms at thelow mass end of the halo mass function using high resolution cosmological N-body simulations in our next paper.
ffor Mgb. 0.1 ffor FeS270. iux O2A ffor Fe5335.,"for Mgb, 0.1 for Fe5270, and 0.2 for Fe5335."
 By combining the indices of different chemical eleimieuts aud by comparing them with models. we are able to reach sole conclusions about the stellaz population properties at various distances from the ceuter of2," By combining the indices of different chemical elements and by comparing them with models, we are able to reach some conclusions about the stellar population properties at various distances from the center of."
"1, By using the five cross-sections of obtained by us at the nun telescope of SAO RAS. we have calculated index profiles for I1. Mgb. Ee5270. and Fe5335 up to ffrom the center with a step ofLI7."," By using the five cross-sections of obtained by us at the m telescope of SAO RAS, we have calculated index profiles for $H\beta$, Mgb, Fe5270, and Fe5335 up to from the center with a step of."
. Two iron indices. Fo5270 aud Fe5335. WCTC merged into <Fe»—(Feh270| Fe5355)/2.," Two iron indices, Fe5270 and Fe5335, were merged into $<\mbox{Fe}> \equiv (\mbox{Fe5270+Fe5355})/2$ ."
 The two halves of cach profile. sviunietric around the uucleus. were averaged.," The two halves of each profile, symmetric around the nucleus, were averaged."
 The results are preseuted in Fig. 2..," The results are presented in Fig. \ref{prof1m},"
 the error bars being estimated by »oiut-to-poiut scatter under binuing of I6., the error bars being estimated by point-to-point scatter under binning of $4\farcs6$.
 lu accordance with nunerous results of carlicr investigations. the ceuter of is remarkable by the iegher equivalent widtls of magnesiwim aud wou lines.," In accordance with numerous results of earlier investigations, the center of is remarkable by the higher equivalent widths of magnesium and iron lines."
" The uicasurements at ré=9"" iav be affected by secius (let us renünd that the seciug during our observations was not etter than 17)).", The measurements at $r=9\arcsec$ may be affected by seeing (let us remind that the seeing during our observations was not better than ).
" At laveer distauces frou the ceuter. in the radius rause ofορ, radial muidex exadieuts if they exist are negligible with respect to the iudex changes )etyeen the nucleus aud the bulec."," At larger distances from the center, in the radius range of, radial index gradients if they exist are negligible with respect to the index changes between the nucleus and the bulge."
 The mean index values oe ithe bulge averaged over all the five cross-sectious in the radius range aare Meb(bulge)21.2520.02 aud <Fe>(bulge)=2.564 0.01., The mean index values in the bulge averaged over all the five cross-sections in the radius range are $4.25\pm 0.02$ and $<\mbox{Fe}>(\mbox{bulge})=2.56 \pm 0.01$ .
 If we approximate the radial index depeudeucies by near laws and extrapolate them to r=ο. we would obtain ceutral bulee index values 1.37+0.06 and <Fe>(bulge)=2.68+0.02.," If we approximate the radial index dependencies by linear laws and extrapolate them to $r=0$, we would obtain central bulge index values $4.37\pm 0.06$ and $<\mbox{Fe}>(\mbox{bulge})=2.68\pm 0.03$."
 For the nucleus we have measured Meb(uuc)-5.11+0.06 and <Fe> £0.05., For the nucleus we have measured $5.11\pm 0.06$ and $<\mbox{Fe}>(\mbox{nuc})=3.21\pm 0.05$ .
 Therefore. the differeuces. between the uucleus and the bulee are AMgb=0.86£0.10 and A<Fe>=0.65£0.06 (or AMgb=(L7140.12 and A<Fe>=0.53+0.08. if we use linear index radial dependencies for the bulee).," Therefore, the differences between the nucleus and the bulge are $\Delta \mbox{Mgb}=0.86\pm 0.10$ and $\Delta <\mbox{Fe}>=0.65\pm 0.06$ (or $\Delta \mbox{Mgb}=0.74\pm 0.12$ and $\Delta <\mbox{Fe}>=0.53\pm 0.08$, if we use linear index radial dependencies for the bulge)."
 Let us note that due to stronely iucreased stellar velocity dispersion iu the nucleus of the absorption lines there may be broadened out of the iudex measuringo ranges: so the nuclear indices wav be underestimated. aud the real index cüffereuces between the nucleus aud the bulge may be even larger.," Let us note that due to strongly increased stellar velocity dispersion in the nucleus of the absorption lines there may be broadened out of the index measuring ranges; so the nuclear indices may be underestimated, and the real index differences between the nucleus and the bulge may be even larger."
 Application, Application
"Note that Fy,/=0 since the inteeralo ouly involves odd",Note that $F_{\mu \sigma} = 0$ since the integral only involves odd powersof $x-\mu$ .
We have one run (among many others obtained over past veers) of OY Car in quiescence (S6488) which shows a coherent signal.,We have one run (among many others obtained over past years) of OY Car in quiescence (S6488) which shows a coherent signal.
 Phe light curve is given in Fig., The light curve is given in Fig.
 17. and shows a period of 47.9 s. This unusual period is perhaps an evolution from the DNOs seen during outbursts., \ref{lc6488} and shows a period of 47.9 s. This unusual period is perhaps an evolution from the DNOs seen during outbursts.
 In addition to the QPOs and. DNOs described in Sect., In addition to the QPOs and DNOs described in Sect.
 3.7 we observe IpDNOs in AQ Eri., 3.7 we observe lpDNOs in AQ Eri.
 In Pig., In Fig.
 6 there are two spikes near 100 s which are at 75.7 (40.3) s and 106.3 (0.5) s with mean amplitudes of 2.5 and 2.6 mmag. respectively (derived from non-linear least-squares fits).," \ref{ft6510} there are two spikes near 100 s which are at 75.7 $\pm$ 0.3) s and 106.3 $\pm$ 0.5) s with mean amplitudes of 2.5 and 2.6 mmag, respectively (derived from non-linear least-squares fits)."
 Phe frequency. dillerence between these corresponds to a QPO. period. of ~ 265 s. which is similar to the observed. period (Sect.," The frequency difference between these corresponds to a QPO period of $\sim$ 265 s, which is similar to the observed period (Sect."
 3.7)., 3.7).
 These appear to be direct and reprocessed IpDNOs as in VW Livi (Sect., These appear to be direct and reprocessed lpDNOs as in VW Hyi (Sect.
 1.1.2)., 4.1.2).
 In run S6516 a single strong IpDNO at 73.6 (40.1) s and mean amplitude of 2.0 mmag is present., In run S6516 a single strong lpDNO at 73.6 $\pm$ 0.1) s and mean amplitude of 2.0 mmag is present.
 The amplituce/phase plot for this IpDNO is shown in Fig. I8..," The amplitude/phase plot for this lpDNO is shown in Fig. \ref{oc6516b},"
 which may be compared. with that for the DNO that. is present simultaneously. (Fig. 7))., which may be compared with that for the DNO that is present simultaneously (Fig. \ref{oc6516}) ).
 Phe IpDNO has greater coherence than the DNO., The lpDNO has greater coherence than the DNO.
 The next night. despite the absence of DNOs or QPOs. there is a prominent IpDNO in the last half of the light curve. being most prominent in the final section as shown in Fig. 19..," The next night, despite the absence of DNOs or QPOs, there is a prominent lpDNO in the last half of the light curve, being most prominent in the final section as shown in Fig. \ref{lc6520}."
 The period is 108.6 (40.8) s and the mean amplitude is 5.2 numag. and corresponds to the reprocessed IpDNO that appears in Fig.," The period is 108.6 $\pm$ 0.8) s and the mean amplitude is 5.2 mmag, and corresponds to the reprocessed lpDNO that appears in Fig."
 6. as discussed above., \ref{ft6510} as discussed above.
 Our quiescent light curve (86159). shows Large. scale Hlickering but there is a possible IpDNO of high coherence at ST.O (40.2) s and mean amplitude 7.7 mmag., Our quiescent light curve (S6159) shows large scale flickering but there is a possible lpDNO of high coherence at 87.0 $\pm$ 0.2) s and mean amplitude 7.7 mmag.
 The soft. X-Ray observations by Cordova. Mason. et. aL.," The soft X-Ray observations by Cordova, Mason et al.,"
 referred. to. in Section. 2.13 above. revealed a suite. of modulations.," referred to in Section 2.13 above, revealed a suite of modulations."
 In addition to the 21 8 DNO and 585 s QPO there were observed periodicities at  121 s aud ~ 135 s in quiescence and. possibly ~ 152 s in outburst., In addition to the 21 s DNO and 585 s QPO there were observed periodicities at $\sim$ 121 s and $\sim$ 135 s in quiescence and possibly $\sim$ 152 s in outburst.
 Robinson Nather (1979) observed low coherence optical mocdulations near 146 s and its first harmonic during an outburst., Robinson Nather (1979) observed low coherence optical modulations near 146 s and its first harmonic during an outburst.
 These oscillations appear to have the properties of IpDNOs. in which case U Cem is the first €V to show all three tvpes of oscillation in the X-Ray region.," These oscillations appear to have the properties of lpDNOs, in which case U Gem is the first CV to show all three types of oscillation in the X-Ray region."
 Sion et al. (, Sion et al. (
1998) find esing~100 km for the primary and a mass of 1.1 M... which with / = 67 give Dua0215 s; and we again find that two pole accretion onto the primary will provide the observed IpDNO periods.,"1998) find $v \sin{i} \sim 100$ km $^{-1}$ for the primary and a mass of 1.1 $_{\odot}$, which with $i$ = $^{\circ}$ give $P_{rot} \sim 275$ s, and we again find that two pole accretion onto the primary will provide the observed lpDNO periods."
 1n the FP of the last half of the run SGOGG (see Fig. 20)).," In the FT of the last half of the run S6066 (see Fig. \ref{ft6066}) ),"
 a coherent signal is present at 112.4 (40.6) s. with a mean amplitude 6.2 mmag.," a coherent signal is present at 112.4 $\pm$ 0.6) s, with a mean amplitude 6.2 mmag."
 No DNOs or QPOs are seen during this run., No DNOs or QPOs are seen during this run.
 Given the suite of DNO and QUO frequencies already identified in Sect., Given the suite of DNO and QPO frequencies already identified in Sect.
 3.1. we associate the coherent 112.4-s signal with an IpDNO.," 3.1, we associate the coherent 112.4-s signal with an lpDNO."
method of derivation can be used for wormbholes.,method of derivation can be used for wormholes.
 The magnification of the brightness 2b is where ly and ο are magnification of the outer and inner images. 64 and £5 correspond lo outer and inner images. respectively.," The magnification of the brightness $A$ is where $A_1$ and $A_2$ are magnification of the outer and inner images, $\hat{\theta}_1$ and $\hat{\theta}_2$ correspond to outer and inner images, respectively."
 The relation between the lens and source (trajectory in the skv is shown in Figure 3.., The relation between the lens and source trajectory in the sky is shown in Figure \ref{fig3}.
 The time dependence of 2 is where 7 is (he impact parameter of the source trajectory ancl /4 is the (ime of closest approach., The time dependence of $\hat{\beta}$ is where $\hat{\beta}_0$ is the impact parameter of the source trajectory and $t_0$ is the time of closest approach.
 /j; is the Einstein radius crossing time given by where ey is the transverse velocity of the lens relative to the source and observer., $t_E$ is the Einstein radius crossing time given by where $v_T$ is the transverse velocity of the lens relative to the source and observer.
 The light curves obtained from Equations (13)) and (19)) are shown as (hick red lines in Figure 4.., The light curves obtained from Equations \ref{eqn:a}) ) and \ref{eqn:hbeta}) ) are shown as thick red lines in Figure \ref{fig4}.
 The light curves corresponding to Schwarzschild lensing are shown as thin ereen lines for comparison., The light curves corresponding to Schwarzschild lensing are shown as thin green lines for comparison.
 The magnifications by (the Ellis wormhole are generally less than those of Schwarzschild lensing., The magnifications by the Ellis wormhole are generally less than those of Schwarzschild lensing.
" The light curve of the Ellis wormhole for 3,<1.0 shows characteristic eulters on both sides of the peak immediately outside (he Einstein ring crossing times (f=!) ddp).", The light curve of the Ellis wormhole for $\hat{\beta_o} < 1.0$ shows characteristic gutters on both sides of the peak immediately outside the Einstein ring crossing times $t = t_0 \pm t_E$ ).
 The depth of the gutters is about [rom the baseline., The depth of the gutters is about from the baseline.
 Amazinely. the star becomes fainter (han normal in terms of apparent brightness in (he gutters.," Amazingly, the star becomes fainter than normal in terms of apparent brightness in the gutters."
 This means that the Ellis wormhole lensing has off-center divergence., This means that the Ellis wormhole lensing has off-center divergence.
 In conventional gravitational lensing theory (SchneiderEhlers&Falco.1992).. the convergence of light is expressed by a convolution of the surface mass density.," In conventional gravitational lensing theory \citep{sch92}, the convergence of light is expressed by a convolution of the surface mass density."
 Thus. we need to introduce negative mass," Thus, we need to introduce negative mass"
 ," \citep{bd03,keres05}. \citep[][]{bauermeister10}."
(T'~104 (Z)0.001—0.01% 2011;Faucher-Gig," $T\sim10^4$ $\langle Z \rangle \sim 0.001-0.01 Z_{\odot}$ \citep{fumagalli11,fgk11}."
"uére&Keres2011). MyaX10!*Mo 596 4096, little direct evidence for its existence."," $M_{\rm
 Halo}\lesssim10^{12} M_\odot$ \citep[or $M_\star\sim5\times10^{10}
 $5\%$ $40\%$ little direct evidence for its existence."
" QSO absorption lines can probe the circumgalactic medium of foreground galaxies, with intermediate ccolumn density systems <log 19.0) being particularly promising(15.5 tracers of N(HI)cold accretion streams (e.g.,Fumagallietal.2011;Faucher-Giguére&Keres$ 2011)."," QSO absorption lines can probe the circumgalactic medium of foreground galaxies, with intermediate column density systems $15.5 \leq
\log N(\mbox{\hi}) \leq 19.0$ ) being particularly promising tracers of cold accretion streams \citep[e.g.,][]{fumagalli11,fgk11}."
". Among these, LLSs with logN(HI)>16.5 are both readily identifiable and often allow for straightforward ccolumn density measurements due to the flux discontinuity they cause at the Lyman limit (912 iin the rest frame)."," Among these, LLSs with $\log N({\rm H\,I}) \geq 16.5$ are both readily identifiable and often allow for straightforward column density measurements due to the flux discontinuity they cause at the Lyman limit (912 in the rest frame)."
 The use of LLSs to probe infalling and outflowing matter near galaxies has the advantage that they are selected in a metallicity-independent manner., The use of LLSs to probe infalling and outflowing matter near galaxies has the advantage that they are selected in a metallicity-independent manner.
" 'Thus, unlike searches for aand other metal line-selected absorbers, LLS searches are not biased in favor of either metal-enriched winds or infalling matter in galaxy halos."," Thus, unlike searches for and other metal line-selected absorbers, LLS searches are not biased in favor of either metal-enriched winds or infalling matter in galaxy halos."
" Furthermore, when the strength of the Lyman break is not too strong (i.e., 7T $3), the ccolumn density of the system can be measured, from which the metallicity and, ultimately, the origins of the absorbing gas can be determined."," Furthermore, when the strength of the Lyman break is not too strong (i.e., $\tau \lesssim 3$ ), the column density of the system can be measured, from which the metallicity and, ultimately, the origins of the absorbing gas can be determined."
" These features circumvent some of the problems that currently cause disagreements in the interpretation of the strong -selected absorbers, for which some studies suggest the absorbers trace outflowing material while others suggest they may represent infalling material (Bouchéetal.2007;Chelouche2011;Kacprzaketal. 2011)."," These features circumvent some of the problems that currently cause disagreements in the interpretation of the strong -selected absorbers, for which some studies suggest the absorbers trace outflowing material while others suggest they may represent infalling material \citep{bouche07,mc09,chen10,bc11,kacprzak11}. ."
". Recent surveys of LLSs have examined the statistical nature of the absorber population, delineating the redshift evolution of these absorbers (Prochaskaetal. "," Recent surveys of LLSs have examined the statistical nature of the absorber population, delineating the redshift evolution of these absorbers \citep{prochaska10,sc10,ribaudo11}. ."
"The literature contains only a few LLSs for which the 2011)..physical properties of the gas (metallicity, ionizationstructure,"," The literature contains only a few LLSs for which the physical properties of the gas (metallicity, ionizationstructure,"
"kT,,=Mpo?1979),, witho=FWHM/w81n2 in cms!.","$kT_{\rm s,\,p} = m_{\rm p} \sigma^2$, with$\sigma = \rm{FWHM}/\sqrt{8\ln{2}}$ in ${\rm cm~s}^{-1}$."
" However, as cross sections for charge exchange decline for high velocities2007), Τον>mpo? for higher temperatures and shock velocities."," However, as cross sections for charge exchange decline for high velocities, $kT_{\rm s,\, p} > m_{\rm p}\sigma^2$ for higher temperatures and shock velocities."
" Recent studies focused on determining the FWHM as function of v, for non-accelerating shocksAdelsberg.", Recent studies focused on determining the FWHM as function of $v_{\rm s}$ for non-accelerating shocks.
" Here, 2)mainBodyCitationEnd1593]Heng2007,we are interested in FWHM as function of T, for a given vs instead."," Here, we are interested in FWHM as function of $T_{\rm s,\,p}$ for a given $v_{\rm s}$ instead."
" We approximate this concave function linearly between 0,0 and the FWHM and expected for a non-accelerating shock in thermal equilibriumTs,» (Fig."," We approximate this concave function linearly between 0,0 and the FWHM and $T_{\rm s,\,p}$ expected for a non-accelerating shock in thermal equilibrium (Fig."
 2 and 3))., \ref{kosenkadel} and \ref{protont}) ).
" In this way, we overestimate and the corresponding thermal pressure, leading to 8 T5,conservativey measure of the cosmic-ray pressure behind the shock front."," In this way, we overestimate $T_{\rm s,\,p}$ and the corresponding thermal pressure, leading to a conservative measure of the cosmic-ray pressure behind the shock front."
 We note that the y-axis of Fig., We note that the y-axis of Fig.
" 5 of van is labeled incorrectly (M. van Adelsberg, 2010, private communication)."," 5 of van is labeled incorrectly (M. van Adelsberg, 2010, private communication)."
" Instead of showing the ‘broad Ha FWHM’, this figure plots the ‘broad neutral velocity distribution FWHM’, which is independent of the emission line considered."," Instead of showing the `broad $\alpha$ FWHM', this figure plots the `broad neutral velocity distribution FWHM', which is independent of the emission line considered."
" To model a specific emission line such as Ha, one has to convolve the broad neutral velocity distribution with the relevant atomic cross sections."," To model a specific emission line such as $\alpha$, one has to convolve the broad neutral velocity distribution with the relevant atomic cross sections."
" The FWHM-v, relations we use in this study, obtained in electronic form from M. van Adelsberg and K. Heng, are plotted in Fig."," The $v_{\rm s}$ relations we use in this study, obtained in electronic form from M. van Adelsberg and K. Heng, are plotted in Fig."
 2 and are based upon the same relations used to generate Figure 13 and Table 1 of(2008)., \ref{kosenkadel} and are based upon the same relations used to generate Figure 13 and Table 1 of.
". Following and we interpret and v, (2008a)in terms of cosmic-ray (2009),,pressure behind the T,shock front and cosmic-ray energy flux leaving the system (respectively won=Por/Ptot in which Prot is the total pressure behind the shock front (x-axis in Figure 4)) and e&c=Fese/Ftot in which Fio is the energy flux entering the shock; ipismv® (y-axis of Figure 4)))."," Following and, we interpret $T_{\rm s,\,p}$ and $v_s$ in terms of cosmic-ray pressure behind the shock front and cosmic-ray energy flux leaving the system (respectively $w_{\rm CR} = P_{\rm CR}/P_{\rm tot}$ in which $P_{\rm tot}$ is the total pressure behind the shock front (x-axis in Figure \ref{energy}) ) and $\epsilon_{\rm esc} = F_{\rm esc}/F_{\rm tot}$ in which $F_{\rm tot}$ is the energy flux entering the shock; $\frac{1}{2}\rho_{\rm ISM}v_{\rm s}^3$ (y-axis of Figure \ref{energy}) ))."
" To conservatively estimate the post-shock cosmic-ray pressure, we assume the electrons and ions to be in thermal equilibrium."," To conservatively estimate the post-shock cosmic-ray pressure, we assume the electrons and ions to be in thermal equilibrium."
" We add wer and ees. to the equations of conservation of mass, momentum and energy over the shock front, which leads to: Formally, u is the number averaged mean particle weight, (~ 0.54 for a fully equilibrated and fully ionized plasma with LMC abundances), when considering KT;y, we can treat as well as a measure for the temperature equilibration µbehind the shock front, where wp=1 indicates no temperature equilibration, and 44=0.54 indicates a fully equilibrated plasma."," We add $w_{\rm CR}$ and $\epsilon_{\rm esc}$ to the equations of conservation of mass, momentum and energy over the shock front, which leads to: Formally, $\mu$ is the number averaged mean particle weight, $\sim$ 0.54 for a fully equilibrated and fully ionized plasma with LMC abundances), when considering $kT_{\rm s,\,p}$, we can treat $\mu$ as well as a measure for the temperature equilibration behind the shock front, where $\mu = 1$ indicates no temperature equilibration, and $\mu = 0.54$ indicates a fully equilibrated plasma."
" In addition, y is the total shock compression ratio."," In addition, $\chi$ is the total shock compression ratio."
" For a non-accelerating, adiabatic shock, x=4 and hence kT,»=4umpv2."," For a non-accelerating, adiabatic shock, $\chi = 4$ and hence $kT_{\rm s,\,p}=\frac{3}{16}\mu m_{\rm p}v_{\rm s}^2$."
" We define 8=KT,accelerations/Sumv2, to characterize the influence of cosmic-ray on "," We define $\beta \equiv kT_{\rm s,\,p}/\frac{3}{16}\mu m_{\rm p}v_{\rm s}^2$, to characterize the influence of cosmic-ray acceleration on $T_{\rm s,\,p}$."
"Figure 4 shows B in the (wor, The "," Figure \ref{energy} shows $\beta$ in the $w_{\rm CR}$, $\epsilon_{\rm esc}$ )-frame."
Typ.‘max’-line indicates the ratio of the cosmic-ray €esc)-frame.pressure and escaping cosmic-ray energy for the most efficiently accelerating shock according to theory2009)., The `max'-line indicates the ratio of the cosmic-ray pressure and escaping cosmic-ray energy for the most efficiently accelerating shock according to theory.
". Hence, the hashed region is excluded."," Hence, the hashed region is excluded."
" For vs= 5000kms~!,, we expect to measure at least a FWHM for the broad component of 3600 kms-!, corresponding to a T;ρ of 28.7 keV (Fig 2))."," For $v_{\rm s} =$ 5000, we expect to measure at least a FWHM for the broad component of 3600 , corresponding to a $T_{\rm s,\,p}$ of 28.7 keV (Fig \ref{kosenkadel}) )."
 This differs significantly from the measured 2680+70kms-!.., This differs significantly from the measured $2680 \pm 70$.
" We derive a Ty, of 15.9-Ε0.9 keV, leading to a 8<0.58, which gives a cosmic-ray pressure behind the shock front of at least (Fig. 4))."," We derive a $T_{\rm s,\,p}$ of $15.9\pm 0.9$ keV, leading to a $\beta < 0.58$ which gives a cosmic-ray pressure behind the shock front of at least (Fig. \ref{energy}) )."
" For the NE, the measured FWHM indicates a vs= 6000kms"", for 0.2«<1.0 (Fig. 2))."," For the NE, the measured FWHM indicates a $v_{\rm s}=$ 6000, for $<T_{\rm s,\,e}/T_{\rm s,\, p}<1.0$ (Fig. \ref{kosenkadel}) )."
" This leads to two possibilities:Ty,e/Ts,p 1) The shock does not efficiently accelerate cosmic rays and has a T;,c/T;, »0.2, breaking with the earlier reported trend of T;¢/Ts,pος1/v2 for v,>400citepGhavamian2007b,, as this would give T./T,«0.01 for v,=6000 2) The shock is far out of thermal equilibrium, as we might expect for a fast shock, and is accelerating particles."," This leads to two possibilities: 1) The shock does not efficiently accelerate cosmic rays and has a $T_{\rm s,\,e}/T_{\rm s,\, p}>0.2$ , breaking with the earlier reported trend of $T_{\rm s,\,e}/T_{\rm s,\,p}\propto 1/v_{\rm s}^2$ for $v_{\rm s}>400$, as this would give $T_{\rm e}/T_{\rm p} < 0.01$ for $v_{\rm s} = 6000$ 2) The shock is far out of thermal equilibrium, as we might expect for a fast shock, and is accelerating particles."
" If we assume Ts,e/p«0.1, we expect a FWHM of 25100 s7!,, whereas we measure 3900--800s-1."," If we assume $T_{\rm s,\,e}/T_{\rm s,\,p} < 0.1$, we expect a FWHM of $>$ 5100 , whereas we measure $3900 \pm 800$."
". Using the approach from section ?? and Fig. 4,,"," Using the approach from section \ref{interpretation} and Fig. \ref{energy}, ,"
 we obtain 6«0.85 and hence a cosmic-ray pressure behind the shock front of »796 of the total pressure., we obtain $\beta < 0.85$ and hence a cosmic-ray pressure behind the shock front of $>7 \%$ of the total pressure.
" Note that this is a very conservative lower limit: for both T, and vs we used conservative approximations."," Note that this is a very conservative lower limit: for both $T_{s,\,p}$ and $v_{\rm s}$ we used conservative approximations."
" Also, at this, high shock velocity, the squared line width of the broad component does not increase linearly with Typ, but flattens off."," Also, at this high shock velocity, the squared line width of the broad component does not increase linearly with $T_{\rm s,\,p}$, but flattens off."
" This makes the difference in line width lower for a given AT;5, which makes that the line width is a less sensitive temperature indicator at high shock velocities."," This makes the difference in line width lower for a given $\Delta T_{\rm s,\, p}$, which makes that the line width is a less sensitive temperature indicator at high shock velocities."
" Future progress can be made with better shock velocity estimates of the NE region itself, a higher signal-over-noise spectrum of the NE region and with models for non-radiative Balmer dominated shocks that include the effects of cosmic-ray acceleration."," Future progress can be made with better shock velocity estimates of the NE region itself, a higher signal-over-noise spectrum of the NE region and with models for non-radiative Balmer dominated shocks that include the effects of cosmic-ray acceleration."
 A remaining question is whether the magnetic field pressure makes a contribution to the post-shock pressure., A remaining question is whether the magnetic field pressure makes a contribution to the post-shock pressure.
" As SNR 0509-67.5 is at a distance of 50 kpc, we can not resolve filaments of X-ray synchrotron emission, which are often used for determining post-shock magnetic field strengths 2003)."," As SNR 0509-67.5 is at a distance of 50 kpc, we can not resolve filaments of X-ray synchrotron emission, which are often used for determining post-shock magnetic field strengths ."
". However, showed that a typical value for the magnetic field pressure(2005) is around of the total post-shock pressure."," However, showed that a typical value for the magnetic field pressure is around of the total post-shock pressure."
" Moreover, according to Bell’s theory the magnetic field energy density scales as B?/8~ /6, with U. the cosmic ray energy density."," Moreover, according to Bell's theory the magnetic field energy density scales as $B^2/8\pi \sim \frac{1}{2} v_{\rm s}U_{\rm c} /c $ , with $U_{\rm c}$ the cosmic ray energy density."
 This meansioU. that the magnetic field energy density is expected to be about of the cosmic-ray energy density., This means that the magnetic field energy density is expected to be about of the cosmic-ray energy density.
" We investigated the cosmic-ray acceleration efficiency of the 0509-67.5 SNR in the LMC, bycomparing Ty y,determined from the Ha-line widths of the SW and NEshockswith shock velocities ofrespectively 5000 aand 6000 ffor the SW and NE, based onX-ray observations."," We investigated the cosmic-ray acceleration efficiency of the 0509-67.5 SNR in the LMC, bycomparing $T_{\rm s,\,p}$ ,determined from the $\alpha$ -line widths of the SW and NEshockswith shock velocities ofrespectively 5000 and 6000 for the SW and NE, based onX-ray observations."
 Our study gives the following results:, Our study gives the following results:
A lower bound of the total apparent magnitude for these galaxies can be calculated.,A lower bound of the total apparent magnitude for these galaxies can be calculated.
 For that purpose. we consider a hwvpothetical ealaxy with a constant star density equivaleut to the survev's mean/ surface brightuess limit of μη=25 πας ? out to a cutoff radius. r4. at which point the stellar deusity drops to zero.," For that purpose, we consider a hypothetical galaxy with a constant star density equivalent to the survey's mean surface brightness limit of $\langle\mu_{0,lim}\rangle=25$ mag ${}^{-2}$ out to a cutoff radius, $r_{cut}$, at which point the stellar density drops to zero."
 We set the cutoff radius. reg. to be aarcsec which is equivaleut to the size of the largest ealaxies in our saiuple.," We set the cutoff radius, $r_{cut}$, to be arcsec which is equivalent to the size of the largest galaxies in our sample."
 This vields the brightest apparent magnitude an undetected galaxy could possibly have: This lower bound is applicable to AMOTIT-571. IXIX2000-01.. IKIS2000-06. and NOGC2781 DWI but uot II2000-03 which has a foregrouud star located directly in front of the ealaxy (see discussion below). nor HIZOAJI616-55 aud SJIX98 J1616-55 which have serious foreground coutamination.," This yields the brightest apparent magnitude an undetected galaxy could possibly have: This lower bound is applicable to AM0717-571, KK2000-04, KK2000-06 and NGC2784 DW1 but not KK2000-03 which has a foreground star located directly in front of the galaxy (see discussion below), nor HIZOAJ1616-55 and SJK98 J1616-55 which have serious foreground contamination."
 A lower bound on the, A lower bound on the
disk began to form. therefore its chemical evolution must have been relatively quick.,"disk began to form, therefore its chemical evolution must have been relatively quick."
" C05 find that Ba. which is thought to be produced predominantly in ACB stars (although a simaller r-process conrpouent lav be produced frou, Type TSN (Pagel&TautvaisicucL997))). is also cuhanced in Cr 261."," C05 find that Ba, which is thought to be produced predominantly in AGB stars (although a smaller r-process component may be produced from Type II SN \citep{pagel}) ), is also enhanced in Cr 261."
 The nuuuber of studies on the heavier n-capture clemenuts is few for old open clusters., The number of studies on the heavier n-capture elements is few for old open clusters.
 Work on other n-capture elements would be helpful in exploring the eurichment history of these elements., Work on other n-capture elements would be helpful in exploring the enrichment history of these elements.
" 005 find the star-to-star scatter to be low (a)~ 0.08. dex. which is within their estimated abundance ""uncertainties."," C05 find the star-to-star scatter to be low $\langle\sigma\rangle \sim$ 0.08 dex, which is within their estimated abundance uncertainties."
 The iudicatiou of chemical homogencity iu Cy 261 is important for testing the viability of chemical tageing as proposed by Freeman&DBlaud-ILwethoru (2002).. however the difference in the estunated ietallicities between 05 and FO3 indicated the need for an iudependenut abundance analysis.," The indication of chemical homogeneity in Cr 261 is important for testing the viability of chemical tagging as proposed by \citet{fbh02}, however the difference in the estimated metallicities between C05 and F03 indicated the need for an independent abundance analysis."
 Further. both studies were based on a πια. sample of stars.," Further, both studies were based on a small sample of stars."
 Iu our analysis of Cr 261 we have doubled their sample size in order to establish a firmer level of homogencity., In our analysis of Cr 261 we have doubled their sample size in order to establish a firmer level of homogeneity.
 If chemical homoecneity within the 0.05 dex level can be firmly established for Cr 261. this would imply that the chemical signature laid down at birth has been preserved over the time evolution of the cluster and is iudeed a true tracer of star formation history in the disk.," If chemical homogeneity within the 0.05 dex level can be firmly established for Cr 261, this would imply that the chemical signature laid down at birth has been preserved over the time evolution of the cluster and is indeed a true tracer of star formation history in the disk."
 With the aim of testing these ideas we proceed with our study ou Cr Because Cr 261 is relatively distant. we chose to observe giants in this cluster.," With the aim of testing these ideas we proceed with our study on Cr Because Cr 261 is relatively distant, we chose to observe giants in this cluster."
 A total of 15 giant stars of Cr 261 were submitted for service mode observations in May. 2001 on the Sia VLT. making use of the UVES Red arm with the FLAMES fibre array which allows up to G stars to be observed simultaucously.," A total of 18 giant stars of Cr 261 were submitted for service mode observations in May 2004 on the 8m VLT, making use of the UVES Red arm with the FLAMES fibre array which allows up to 6 stars to be observed simultaneously."
 The UVES Red arm staudard setting provides a spectral resolution of 17.000 and complete spectra from ttoG200A.," The UVES Red arm standard setting provides a spectral resolution of 47,000 and complete spectra from to."
. The imethod of observing was such that for one telescope pointing. three different fibre combinations were executed. with six stars in cach fibre combination.," The method of observing was such that for one telescope pointing, three different fibre combinations were executed, with six stars in each fibre combination."
 This is possible because the open cluster members of interest are located within the instrument field of view., This is possible because the open cluster members of interest are located within the instrument field of view.
 Each fibre configuration was observed for a total of 5 hours to obtain the required signal to noise., Each fibre configuration was observed for a total of 5 hours to obtain the required signal to noise.
 Ta practice the 5 hours were broken iuto several one hour observing blocks to facilitate the service observiug queue., In practice the 5 hours were broken into several one hour observing blocks to facilitate the service observing queue.
 Our restrictions on the observing conditions was that the secing be better than 1.2 arcsec and airmass no more than 1.2., Our restrictions on the observing conditions was that the seeing be better than 1.2 arcsec and airmass no more than 1.2.
 The final data set reduced with the UVES ESO-AIDAS pipeline consists of high quality spectra for 12 stars. with the 6 other stars having τον little signal.," The final data set reduced with the UVES ESO-MIDAS pipeline consists of high quality spectra for 12 stars, with the 6 other stars having very little signal."
 Since the maeuitudes of all stars were comparable. we assume that musaligument of a few fibres was the cause.," Since the magnitudes of all stars were comparable, we assume that misalignment of a few fibres was the cause."
 The spectra of the 12 stars have a S/N between SNO - 100. sufficient for our abundance analysis.," The spectra of the 12 stars have a S/N between 80 - 100, sufficient for our abundance analysis."
 Table 1 presents a sumunary of the stars we have The abundance analysis makes use of the MOOC code (SuedenL973) for LTE EW analvsis aud spectral svutheses., Table \ref{cr261sample} presents a summary of the stars we have The abundance analysis makes use of the MOOG code \citep{sneden73} for LTE EW analysis and spectral syntheses.
 Initial analysis was undertaken witli interpolated I&urucz model atinospheres based on the ATLAÀSO9 code (Castellietal.1997) with uo convective overshoot., Initial analysis was undertaken with interpolated Kurucz model atmospheres based on the ATLAS9 code \citep{cas97} with no convective overshoot.
 Later. our abundances were re-evaluated using MARCS inodels (Asplundetal.1997)... primavily to check the accuracy of the Iurucz models for the cooler stars. as well as to check for cousisteucv du our abundance analysis for the eutire sample.," Later, our abundances were re-evaluated using MARCS models \citep{asplund97}, primarily to check the accuracy of the Kurucz models for the cooler stars, as well as to check for consistency in our abundance analysis for the entire sample."
 Abundances for a range of clements covering cach of the a. Fe-peak aud u-capture groups were attempted.," Abundances for a range of elements covering each of the $\alpha$, Fe-peak and n-capture groups were attempted."
 The list of lines used iu this analysis is given in Table 2.., The list of lines used in this analysis is given in Table \ref{tab:line}.
" The yf values for the detected lines of Na. Me. ΑΙ. Si. Ca, Ni, and Zr were obtained from a combination of lines from AllendePrietoetal.(2001):Youg(2005):Reddyetal.(2003). and Paulsonctal.(2003)."," The $gf$ values for the detected lines of Na, Mg, Al, Si, Ca, Ni, and Zr were obtained from a combination of lines from \citet{ap04,yong05,reddy03} and \citet{P03}."
. For Mu. the gf values were taken from Prochaska&MeWilliaan(2000). aud include the effects of hyperfine splitting.," For Mn, the $gf$ values were taken from \citet{prochaska00} and include the effects of hyperfine splitting."
 The main sources of the Fe line data is the laboratory measurements by the Oxford group (Blackwell et al.," The main sources of the Fe line data is the laboratory measurements by the Oxford group (Blackwell et al.,"
 1979a.b. 1995 aud refercuces therein).," 1979a,b, 1995 and references therein)."
 This was supplemented by additional lines frou Reddyetal.(2003)., This was supplemented by additional lines from \citet{reddy03}.
. For Fe we adopt the gf values frou Dieinoutetal.(1991):Paulson(2003) and AllendePrietoctal. (2002).," For Fe we adopt the $gf$ values from \citet{biemont91,P03} and \citet{fe2lines}."
. Ba gf values were adopted frou MeWilliaan(1998)., Ba $gf$ values were adopted from \citet{mcw98}.
.. Although abundauce determinations were attempted. most of the heavier s- aud r-process clement abundances could uot be accurately derived. especially for the cooler stars because blending of lines was too ligh to allow an accurate abundauce We derive tho stellar parameters based ou spectroscopy.," Although abundance determinations were attempted, most of the heavier s- and r-process element abundances could not be accurately derived, especially for the cooler stars because blending of lines was too high to allow an accurate abundance We derive the stellar parameters based on spectroscopy."
 Abunudiuces for all Fe and lines were computed from the measured EWs., Abundances for all Fe and lines were computed from the measured EWs.
" Thy, was derived by requiring excitation equilibrimn.", $_{eff}$ was derived by requiring excitation equilibrium.
 Alicroturbulence was derived from the condition that Fe lines show uo trend with EW., Microturbulence was derived from the condition that Fe lines show no trend with EW.
 Loe ο was derived via ionization equilibrium. ic.," Log g was derived via ionization equilibrium, ie."
 the abundances from Fe equals Fer1., the abundances from Fe equals Fe.
 The resulting stellar parameters are given in Table 3.., The resulting stellar parameters are given in Table \ref{cr261params}.
 We also compare our derived parameters with those derived in the literature for the stars we have i common., We also compare our derived parameters with those derived in the literature for the stars we have in common.
 Our piriuueters are in better agreement with C05 thaw with ΕΟΟ., Our parameters are in better agreement with C05 than with F03.
 The abundances were derived by EW measurements or spectral svuthesis depending ou the streneth and level of bleudius., The abundances were derived by EW measurements or spectral synthesis depending on the strength and level of blending.
 All a. Fe-peak. and Zr abundances were estimated by EW measurements as their transitions lines were sutficicutly strong and wnblended to accurately measure EWs.," All $\alpha$, Fe-peak, and Zr abundances were estimated by EW measurements as their transitions lines were sufficiently strong and unblended to accurately measure EWs."
 Iuital Ba abuudanuces were also obtained via EW ieasurements. not faking iuto account any hyperfine structures (IFS).," Inital Ba abundances were also obtained via EW measurements, not taking into account any hyperfine structures (HFS)."
 Later we carried out spectral svuthesis of the Ba lines. incorporating the TFS eiven by MeWilliiun(1998). asstunine a solar isotopic ratio.," Later we carried out spectral synthesis of the Ba lines, incorporating the HFS given by \citet{mcw98} assuming a solar isotopic ratio."
 By taking iuto account IFS. we find the Ba abundance," By taking into account HFS, we find the Ba abundance"
The detection of giant planets in moderately close binary systems has raised many questions regarding the formation of these objects.,The detection of giant planets in moderately close binary systems has raised many questions regarding the formation of these objects.
 For many years simulations of the dynamical evolution of circumstellar disks suggested that planets may not form around the stars of a binary as the perturbation of the secondary star may (i) truncate the disk and remove the material that may be used in the formation of planets. (1) increase the relative velocities of planetesimals. which may cause their collisions to result in breakage and fragmentation. and (it) destabilize the regions where the building blocks of these objects may exist.," For many years simulations of the dynamical evolution of circumstellar disks suggested that planets may not form around the stars of a binary as the perturbation of the secondary star may (i) truncate the disk and remove the material that may be used in the formation of planets, (ii) increase the relative velocities of planetesimals, which may cause their collisions to result in breakage and fragmentation, and (iii) destabilize the regions where the building blocks of these objects may exist."
" However. the discovery of planets around the primaries of the binaries , Cephei (Hatzes et al."," However, the discovery of planets around the primaries of the binaries $\gamma$ Cephei (Hatzes et al."
 2003. Neuhuser et al.," 2003, Neuhuser et al."
 2007). GL 86 (Els et al.," 2007), GL 86 (Els et al."
 2001. Lagrange et al.," 2001, Lagrange et al."
 2006). HD 41004 (Zucker et al.," 2006), HD 41004 (Zucker et al."
 2004: Raghavan et al., 2004; Raghavan et al.
 2006). and HD 196885 (Correia et al.," 2006), and HD 196885 (Correia et al."
 2008). where the stellar separation is smaller than 20 AU. suggest that planet formation in such systems may be as efficient as around single stars.," 2008), where the stellar separation is smaller than 20 AU, suggest that planet formation in such systems may be as efficient as around single stars."
 According to the core-accretion model (e.g. Safronov 1969. Goldreich and Ward 1973. Pollack et al.," According to the core-accretion model (e.g. Safronov 1969, Goldreich and Ward 1973, Pollack et al."
 1996. Kokubo and Ida 1998. Alibert et al.," 1996, Kokubo and Ida 1998, Alibert et al."
 2004. 2005). planetary cores are the results of accretional collisions between solid planetesimals immersed in the nebular gas disk.," 2004, 2005), planetary cores are the results of accretional collisions between solid planetesimals immersed in the nebular gas disk."
 If this process is sufficiently fast to reach a few Earth-masses before the gas removal. gaseous envelops can collapse onto the embryos and result in giant planets.," If this process is sufficiently fast to reach a few Earth-masses before the gas removal, gaseous envelops can collapse onto the embryos and result in giant planets."
 If growth is slower and/or if the bodies are located inside the ice line. the volatile component cannot participate in the accretion process. leading to the formation of small rocky terrestrial-type planets.," If growth is slower and/or if the bodies are located inside the ice line, the volatile component cannot participate in the accretion process, leading to the formation of small rocky terrestrial-type planets."
 Accretional collisions require low impact velocities in order to avoid disruption., Accretional collisions require low impact velocities in order to avoid disruption.
 In single star systems. relative. velocities are usually low. particularly during the early stages of planetary formation. and aecretion appears as a natural outcome of most impacts.," In single star systems, relative velocities are usually low, particularly during the early stages of planetary formation, and accretion appears as a natural outcome of most impacts."
 In binary stellar systems. however. collisions are more complicated. especially if the pericentric distance between stellar components is lower than ~20 AU.," In binary stellar systems, however, collisions are more complicated, especially if the pericentric distance between stellar components is lower than $\sim 20$ AU."
 For instance. as the simulations show. it is possible to form terrestrial-class bodies from large ~1000 Km-sized protoplanets around a star of close binaries (e.g. Quintana et al.," For instance, as the simulations show, it is possible to form terrestrial-class bodies from large $\sim 1000$ km-sized protoplanets around a star of close binaries (e.g. Quintana et al."
 2002. Haghighipour and Raymond 2007).," 2002, Haghighipour and Raymond 2007)."
 However. simulations of the collision and accretion of planetesimals have not been able to explain how these embryos," However, simulations of the collision and accretion of planetesimals have not been able to explain how these embryos"
"will be observable with Gaia, which will be key issues in determining the applicability of any stream searching method.","will be observable with Gaia, which will be key issues in determining the applicability of any stream searching method."
" We restricted the catalogue to stars with |b|>10°, in order to avoid the Galactic Plane."," We restricted the catalogue to stars with $|b|>10^\circ$, in order to avoid the Galactic Plane."
" The tolerance usedin (1)) was 60—5? which corresponds to the half-width of each great circle cell and the GC3 pole counts were computed on a 72x cell grid, uniformly spaced on the surface of the celestial sphere."," The tolerance usedin \ref{rcriterion}) ) was $\delta\theta=5^\circ$ which corresponds to the half-width of each great circle cell and the GC3 pole counts were computed on a $72 \times 72$ cell grid, uniformly spaced on the surface of the celestial sphere."
 We chose the tolerance to be slightly less than the 60=6° half-width which Ibataetal.(2002) find to maximize the signal to noise ratio of the Sgr tidal stream feature in their 2MASS M-giant pole count maps.," We chose the tolerance to be slightly less than the $\delta\theta=6^\circ$ half-width which \citet{iba02}
 find to maximize the signal to noise ratio of the Sgr tidal stream feature in their 2MASS M-giant pole count maps."
" We computed the pole counts for the error-free mock Gaia catalogue, using the GC3 method's position criterion expressed in (1)) in a Galactocentric reference frame, i.e. position vectors and pole coordinates are Galactocentric, the latter corresponding to normal vectors of planes that go through the Galactic center."," We computed the pole counts for the error-free mock Gaia catalogue, using the GC3 method's position criterion expressed in \ref{rcriterion}) ) in a Galactocentric reference frame, i.e. position vectors and pole coordinates are Galactocentric, the latter corresponding to normal vectors of planes that go through the Galactic center."
 The resulting pole count map is shown in Fig. 2.., The resulting pole count map is shown in Fig. \ref{fig:gc3_gal_true}.
" In this reference frame we name the longitude and latitudeangles ¢ and 0 respectively, with the Galactic Plane at 0—0?, the North Galactic Pole at 0=+90° and ¢=0? in the direction away from the Sun."," In this reference frame we name the longitude and latitudeangles $\phi$ and $\theta$ respectively, with the Galactic Plane at $\theta=0^\circ$, the North Galactic Pole at $\theta=+90^\circ$ and $\phi=0^\circ$ in the direction away from the Sun."
" In this reference frame the pole count map would be expected to be uniform in ¢ and with a positive gradient in 0 (minimum at the equator), because of the axial symmetry of the Galaxy about the Galactic center and the latitude dependence in star density."," In this reference frame the pole count map would be expected to be uniform in $\phi$ and with a positive gradient in $\theta$ (minimum at the equator), because of the axial symmetry of the Galaxy about the Galactic center and the latitude dependence in star density."
" However, the pole count map shown in Fig."," However, the pole count map shown in Fig."
 2 clearly does not follow this pattern in ¢., \ref{fig:gc3_gal_true} clearly does not follow this pattern in $\phi$.
 This is due to both the exclusion criterion in Galactic latitude ([b|> 10°) and the fact we are considering only stars which will be by Gaia; both criteria being inherently heliocentric., This is due to both the exclusion criterion in Galactic latitude $|b|>10^\circ$ ) and the fact we are considering only stars which will be by Gaia; both criteria being inherently heliocentric.
" First, the exclusion criterion imposed on the heliocentric Galactic latitude does not filter stars in the Galactic Plane near the Sun at high latitudes, these stars contribute to pole counts for poles in the redish circle in Fig. 2,,"," First, the exclusion criterion imposed on the heliocentric Galactic latitude does not filter stars in the Galactic Plane near the Sun at high latitudes, these stars contribute to pole counts for poles in the redish circle in Fig. \ref{fig:gc3_gal_true}, ,"
 with their maximum contribution being for dpote~90? and φροιε~ 270°., with their maximum contribution being for $\phi_{pole}\sim90^\circ$ and $\phi_{pole}\sim270^\circ$ .
" In addition, planes with Φροιε=0°,180° "," In addition, planes with $\phi_{pole}=0^\circ,180^\circ$ "
5truciu BStrueiu Cnr Cnr Cnr Cnr σα1) clussilü ον CLUSSS ciusshbxlO 1102 ciutir clurd cutis clures 12pt- = ]2pt,"5truein 8truein cmr8 cmr8 cmr8 cmr8 cmr10 cmssi10 cmss10 cmss8 cmssbx10 2 cmti7 cmr6 cmti8 cmr8 \def\ref{\par\noindent\hangindent 15pt}
 = 12pt = 12pt"
harmonic kink oscillations of the loop.,harmonic kink oscillations of the loop.
 However. other viable explanations are also possible.," However, other viable explanations are also possible."
 For our discussion. we first recall the results of Ballaietal.(2008).," For our discussion, we first recall the results of \cite{ballai2008}."
. Using a simple coronal loop model. these authors investigated the interaction between an EIT wave and a coronal loop assuming an equilibrium of forces.," Using a simple coronal loop model, these authors investigated the interaction between an EIT wave and a coronal loop assuming an equilibrium of forces."
 Their results show that the periods recovered in a coronal loop are always a combination of the period of the driver (here EIT waves) and the natural period of the loop., Their results show that the periods recovered in a coronal loop are always a combination of the period of the driver (here EIT waves) and the natural period of the loop.
 The same authors showed that the displacement of à coronal loop (here denoted by Q(z. r)) under the influence of a driver. F(z.f). is given by where. as before. ey 1s the kink speed (propagation speed of disturbances in the loop) and ως is the cut-off frequency of kink-mode oscillations.," The same authors showed that the displacement of a coronal loop (here denoted by $Q(z,t)$ ) under the influence of a driver, $F(z,t)$, is given by where, as before, $c_K$ is the kink speed (propagation speed of disturbances in the loop) and $\omega_c$ is the cut-off frequency of kink-mode oscillations."
 These quantities aresimply given by where v4; and v4; are the Alfvénn speeds inside and outside the loop., These quantities aresimply given by where $v_{Ai}$ and $v_{Ae}$ are the Alfvénn speeds inside and outside the loop.
 Equation. 4 is an inhomogeneous Klein-Gordon equation that was solved assuming that the foot-points of the loop are fixed (ine-tying condition) and initially at rest., Equation \ref{eq:3.1} is an inhomogeneous Klein-Gordon equation that was solved assuming that the foot-points of the loop are fixed (line-tying condition) and initially at rest.
 The event occurring on 13 June 1998 was also studied in detail by Wills-Davey&Thompson(1990). who showed that the blast wave intersects the loop of interest nearly perpendicularly. meaning we can model the EIT wave as a harmonic. driver whose temporal and spatial dependence is given by Ballaietal.(2008) to be where 6(z) is the Dirac-delta function. and the constant Α΄ depends on the density of the plasma and energy of the EIT wave. both considered to be constant.," The event occurring on 13 June 1998 was also studied in detail by \cite{wills-davey1999}, who showed that the blast wave intersects the loop of interest nearly perpendicularly, meaning we can model the EIT wave as a harmonic driver whose temporal and spatial dependence is given by \cite{ballai2008} to be where $\delta(z)$ is the Dirac-delta function, and the constant $K$ depends on the density of the plasma and energy of the EIT wave, both considered to be constant."
 In Equation 5.. wer is the frequency of the EIT wave. which is assumed to be a harmonie signal.," In Equation \ref{eq:3.2}, $\omega_{EIT}$ is the frequency of the EIT wave, which is assumed to be a harmonic signal."
 In this study. we are concerned with temporal changes only. which is why the exact form of the driver is not explicitly given.," In this study, we are concerned with temporal changes only, which is why the exact form of the driver is not explicitly given."
 The form of the driver given by Equation 5 reveals that the interaction between the loop and the EIT wave occurs in two points (at z=zo andz=L— zo) simultaneously. and is placed symmetrically with respect to the end-points of the loop at z=0 and z=£L.," The form of the driver given by Equation \ref{eq:3.2} reveals that the interaction between the loop and the EIT wave occurs in two points (at $z=z_0$ and$z=L-z_0$ ) simultaneously, and is placed symmetrically with respect to the end-points of the loop at $z=0$ and $z=L$."
 Equation 4.. where F(z.£) 1s defined by Equation 5... was solved by Ballaietal.(2008).. with the temporal dependence of the displacement. Q(z.4). found to be where c=ωςαπο (n2 d) are the natural frequencies of the loop.," Equation \ref{eq:3.1}, where $F(z,t)$ is defined by Equation \ref{eq:3.2}, was solved by \cite{ballai2008}, with the temporal dependence of the displacement, $Q(z,t)$, found to be where $\omega_n^2=\omega_c^2+n^2\pi^2c_K^2/L^2$ $n\ge 1$ ) are the natural frequencies of the loop."
 According to the results of Ballaietal.(2008) (their Figure 3). the dominant (and strongest) signal in the loop is produced by the driver.," According to the results of \cite{ballai2008} (their Figure 3), the dominant (and strongest) signal in the loop is produced by the driver."
 Bearing in mind the previously presented model. we identify the two measured periods as the two temporal dependencies of the solution given by Equation 6..," Bearing in mind the previously presented model, we identify the two measured periods as the two temporal dependencies of the solution given by Equation \ref{eq:3.3}."
" Since it is visually obvious that the loop oscillates at its fundamental frequency. w, 1n Equation 6.. it is replaced by c corresponding to the frequency of the fundamental mode."," Since it is visually obvious that the loop oscillates at its fundamental frequency, $\omega_n$ in Equation \ref{eq:3.3}, it is replaced by $\omega_1$ corresponding to the frequency of the fundamental mode."
" That means that we need to solve the system where 7,=501 s and T»=274Τι s. It is easy to show that the period of the fundamental mode is 177.1+3.5 s and the period of the driving EIT wave ts 604.7+26.8 s. much higher than the period derived by Ballaietal.(2005)."," That means that we need to solve the system where $T_1=501$ s and $T_2=274$ s. It is easy to show that the period of the fundamental mode is $177.1\pm 3.5$ s and the period of the driving EIT wave is $604.7\pm 26.8$ s, much higher than the period derived by \cite{ballai2005}."
. However. we should keep in mind that the result derived by Ballaietal.(2005) refers to an average period derived from within a large field-of-view.," However, we should keep in mind that the result derived by \cite{ballai2005} refers to an average period derived from within a large field-of-view."
 Once the period of the fundamental mode is derived. it is straightforward to estimate the magnetic field strength mside the loop.," Once the period of the fundamental mode is derived, it is straightforward to estimate the magnetic field strength inside the loop."
 We. again. need to use the mathematical finding of Ballaietal.(2008) to derive the magnetic field.," We, again, need to use the mathematical finding of \cite{ballai2008} to derive the magnetic field."
 According to their analysis. the frequency of the fundamental mode is given Using the previously determined values for densities and length of the loop. together with the derived frequency of the fundamental mode. we obtain the fundamental kink speed of the loop to be 823+15 ss.," According to their analysis, the frequency of the fundamental mode is given by Using the previously determined values for densities and length of the loop, together with the derived frequency of the fundamental mode, we obtain the fundamental kink speed of the loop to be $823\pm 15$ $^{-1}$."
 Using the standard definition of the kink speed. and assuming the same magnetic field strength inside and outside the loop. we can obtain the magnetic field in the loop to be The values of the magnetic field strength determined using two different scenarios are rather different. meaning that the determination of this fundamental quantity depends on the applied theoretical model used to explain the observed periods.," Using the standard definition of the kink speed, and assuming the same magnetic field strength inside and outside the loop, we can obtain the magnetic field in the loop to be The values of the magnetic field strength determined using two different scenarios are rather different, meaning that the determination of this fundamental quantity depends on the applied theoretical model used to explain the observed periods."
 As we specified earlier the interpretation of two periods observed in a loop ts not unique because different scenarios can occur., As we specified earlier the interpretation of two periods observed in a loop is not unique because different scenarios can occur.
 Unfortunately. given the present spatial resolution constraints. it is impossible to distinguish between these models. meaning that all findings derived from the observations of loop oscillations should be treated with care.," Unfortunately, given the present spatial resolution constraints, it is impossible to distinguish between these models, meaning that all findings derived from the observations of loop oscillations should be treated with care."
 Another possible explanation of the two observed periods is connected to the limits of the spatial resolution of the TRACE instrument., Another possible explanation of the two observed periods is connected to the limits of the spatial resolution of the TRACE instrument.
 The two observed periods could belong to two neighboring thin loops that cannot be resolved by our observations moving in phase., The two observed periods could belong to two neighboring thin loops that cannot be resolved by our observations moving in phase.
 This possibility was studied using numerical simulations by Lunaetal.(2005)... and using theoretical models by VanDoorsselaereetal.(2008).. Robertsonetal. (2010).. and Robertson&Ruderman(2011).," This possibility was studied using numerical simulations by \cite{luna2008}, and using theoretical models by \cite{vandoors08}, \cite{robertson10}, and \cite{robertson11}."
. Assuming that the loops are identical. we can easily find that the ratio of d/R. where d is the distance between the longitudinal axes of the two loops and Α is their radius. is 2.00x0.11.," Assuming that the loops are identical, we can easily find that the ratio of $d/R$, where $d$ is the distance between the longitudinal axes of the two loops and $R$ is their radius, is $2.00\pm0.11$."
 Thus. the physical distance between the two loops. in units of their radius. is 0.031+ 0.001.," Thus, the physical distance between the two loops, in units of their radius, is $0.031\pm
0.001$ ."
 Furthermore. using the results of VanDoorsselaereetal. (2008).. we can estimate the magnetic field inside the loop to be 2.6+0.4 G. a value remarkably consistent with that obtained when interpreting the two periods as belonging to the fundamental and first harmonic kink mode of a single coronal loop.," Furthermore, using the results of \cite{vandoors08}, , we can estimate the magnetic field inside the loop to be $2.6\pm0.4$ G, a value remarkably consistent with that obtained when interpreting the two periods as belonging to the fundamental and first harmonic kink mode of a single coronal loop."
filters.,filters.
 DR? is a mark of the completion of the original goals of the SDSS and the end of the phase known as SDSS-II., DR7 is a mark of the completion of the original goals of the SDSS and the end of the phase known as SDSS-II.
 It includes a total imaging area of 11663 square degrees with 357 million unique objects identified., It includes a total imaging area of 11663 square degrees with 357 million unique objects identified.
" This work focuses on the Legacy Survey area of SDSS DR7, which covers more than 7,500 square degrees of the North Galactic Cap, and three stripes in the South Galactic Cap totaling 740 square degrees (?)."," This work focuses on the Legacy Survey area of SDSS DR7, which covers more than 7,500 square degrees of the North Galactic Cap, and three stripes in the South Galactic Cap totaling 740 square degrees \citep{abazajian08}."
 The galaxies are selected from the PhotoPrimary view of the SDSS Catalog Archive Server with object type tag set to 3 (galaxy) and i-band magnitude less than 21.0., The galaxies are selected from the PhotoPrimary view of the SDSS Catalog Archive Server with object type tag set to 3 (galaxy) and $i$ -band magnitude less than 21.0.
" Moreover, we require that the galaxies did not trigger the following error flags: SATURATED, SATUR.CCENTER, BRIGHT, MENT.MMAXITER, AMOMENT.SSHIFT and MENT.FFAINT."," Moreover, we require that the galaxies did not trigger the following error flags: SATURATED, CENTER, BRIGHT, MAXITER, SHIFT and FAINT."
" In addition to the above selection criteria, we also reject those galaxies with photometric errors in r and i band greater than 10 percent."," In addition to the above selection criteria, we also reject those galaxies with photometric errors in $r$ and $i$ band greater than 10 percent."
" Additionally, we require the of each galaxy in the r-band and i-band to beless than 0.8 in order to remove edge-on galaxies whose colors are not well measured."," Additionally, we require the of each galaxy in the $r$ -band and $i$ -band to be less than 0.8 in order to remove edge-on galaxies whose colors are not well measured."
" By doing this, we will retain about of the total galaxies."," By doing this, we will retain about of the total galaxies."
 All the magnitudes used in this paper are dust extinction corrected model magnitudes (?).., All the magnitudes used in this paper are dust extinction corrected model magnitudes \citep{abazajian08}.
" In order to measure the two types of alignments, we need to have a galaxy cluster catalog with well determined member galaxies."," In order to measure the two types of alignments, we need to have a galaxy cluster catalog with well determined member galaxies."
 The GMBCG cluster catalog for SDSS DR7 is a large catalog of optically selected clusters from SDSS DR7 using the GMBCG algorithm., The GMBCG cluster catalog for SDSS DR7 is a large catalog of optically selected clusters from SDSS DR7 using the GMBCG algorithm.
 The catalog is constructed by detecting the BCG plus red sequence feature that exists among most clusters., The catalog is constructed by detecting the BCG plus red sequence feature that exists among most clusters.
 The cluster satellite galaxies are within 20 of the red sequence mean color detected using a Gaussian, The cluster satellite galaxies are within $\sigma$ of the red sequence mean color detected using a Gaussian
iditious. μιεἰ the mass alxwe which au iron core dus and undergoes eravitatiowlcollapse. Mg.(5 ,"conditions, $M_{\rm He-f}$; the mass above which an iron core forms and undergoes gravitationalcollapse, $M_{\rm Fe-CC}$; etc."
VASnunuuvofsuch limits for massive star evolution hau cluphasis on core-collaoe superuova theory. ]s preseated by Hegeretal.(2003): and the fate of nuüsslve ACB stars and the poteitial for O-Ne-Me core apse are discussed. by Siess{2007) and Poelucenudsetal. (2008).," A summary of such limits for massive star evolution, with an emphasis on core-collapse supernova theory, is presented by \citet{heger2003}; and the fate of massive AGB stars and the potential for O-Ne-Mg core collapse are discussed by \citet{siess2007} and \citet{poelarends2008}."
. Dv comparing the mass lims fouud from a finely enough suupled eril of models axl observationa ar data. the theoretical niolel cau be tested.," By comparing the mass limits found from a finely enough sampled grid of models and observational stellar data, the theoretical model can be tested."
 The lancianark paper by Maeder&Nerniod(1981) Us approach to exinumne the consistency between ar cluster data and them evolijon model. alu icluded that acditional mixing cau bring observational inferred and theoretically calculated πο linüts iuto better agreement. and sunujzed this iu terius of an overshoot” parameter o4=(0.2. a quautitative vaue which remains preferred amoug stellar population modelers for stars having masses larecr than a few times ar (e.g.Girareretal.2000:Pietrinfermict2001).," The landmark paper by \citet{maeder1981} used this approach to examine the consistency between stellar cluster data and their evolution model, and concluded that additional mixing can bring observationally inferred and theoretically calculated mass limits into better agreement, and summarized this in terms of an ""overshoot"" parameter $\alpha_{\rm ov} \approx 0.2$, a quantitative value which remains preferred among stellar population modelers for stars having masses larger than a few times solar \citep[e.g.][]{girardi2000, pietrinferni2004}."
. Iu addition to the overshoot parameter. which is a iueasure of how ach materjal müxes bevoud the μιατς of a formally defined wast.ible region. the mixing processes mentioned in refsec:framework— also shift nass limits.," In addition to the overshoot parameter, which is a measure of how much material mixes beyond the limits of a formally defined unstable region, the mixing processes mentioned in \\ref{sec:framework} also shift mass limits."
" The double diffusive instability arising in thermally unstable regions which are stabilized by composa.ion eracdienuts. dubbed ""Csenmniconvection (Moerrvfek1995).. i* particularly iuportant iu massive star evolution."," The double diffusive instability arising in thermally unstable regions which are stabilized by composition gradients, dubbed ""semiconvection"" \citep{merryfield1995}, is particularly important in massive star evolution."
 This process cau change the mass of the He core &lowing main sequeuce evolution. 20111115. the parameer nost 1idicative of how a niassive star will eud its lie. by a factor o HOM Or nore (Woosley&WeaverLOSS:Staritsin2004)).," This process can change the mass of the He core following main sequence evolution, perhaps the parameter most indicative of how a massive star will end its life, by a factor of $\sim$ or more \citep{woosley1988,staritsin2009}."
. When to iichide this müxiug process or iot. and its streneths when inclided. rema1i open questions (e.g.Bicllo 2001).," When to include this mixing process or not, and its strengths when included, remain open questions \citep[e.g.][]{biello2001}."
 Fortunaolv. interesting coustraints can 6 placed ou stelar evolution theory by observational data wren the observational uncertainties are less than a few percent.," Fortunately, interesting constraints can be placed on stellar evolution theory by observational data when the observational uncertainties are less than a few percent."
" Both asteroseiuic and wide eclipsing binary data. which we discuss next. are beginning to mec these PCCurements,"," Both asteroseismic and wide eclipsing binary data, which we discuss next, are beginning to meet these requirements."
 Obscrvationally determined effective. temperatures (Ti. T5). laminosities (Ly. L5). radi (Ry. Ro). and masses (Mq. MS) ave known for mauv of these systems to better than a few percent (Torresetal.2010).," Observationally determined effective temperatures $T_1, T_2$ ), luminosities $L_1,L_2$ ), radii $R_1, R_2$ ), and masses $M_1,M_2$ ) are known for many of these systems to better than a few percent \citep{torres2010}."
. Iu some cases precision surface rotational velocities (|esin/]1.[esm /|2) aud composition lfW;=i» ave also available.," In some cases precision surface rotational velocities $[v\sin i]_1, [v\sin i]_2$ ) and compositions $X_{i,1} = X_{i,2}$ are also available."
 A stellar evolution model can be tested against this data by comparing. e.g.àY the model radi aud temperatures (Ry.Ro:Ty.1ο).=calAL.AM».XsTay oz). Where the lat syubol indicates model data.," A stellar evolution model can be tested against this data by comparing, e.g., the model radii and temperatures $(\hat{R}_1, \hat{R}_2; \hat{T}_1, \hat{T}_2) = f(M_1, M_2,X_i; t_{\rm age}, \alpha_j)$ , where the hat symbol indicates model data."
 Tere the stellar masses aux conipositions are also known obscrvationally to high xecisiou., Here the stellar masses and compositions are also known observationally to high precision.
 The age of the binary system £44.18 a fitting parameter. and the theoretical model is represeuted by he function f and the parameer set ag.," The age of the binary system $t_{\rm age}$ is a fitting parameter, and the theoretical model is represented by the function $f$ and the parameter set $\alpha_j$."
 Ribasctal.(2000) aud Claret(2007) wave studied the depeidence of the convective overshoot parameter o4 0n fje stellar mass using this type oprocedure., \citet{ribas2000} and \citet{claret2007} have studied the dependence of the convective overshoot parameter $\alpha_{\rm ov}$ on the stellar mass using this type of procedure.
" The set of normal mode oscillation yequencies [n] found by time monitoring stellar uniinuositv. toectjer with spectroscopic logy aud Tig) and photometric information (e.eο, parallax x ancl mnuimositv £). xovides another important test of stellar evolution theory."," The set of normal mode oscillations frequencies $\{\nu_k\}$ found by time monitoring stellar luminosity, together with spectroscopic $\log g$ and $T_{\rm eff}$ ) and photometric information (e.g., parallax $\pi$ and luminosity $L$ ), provides another important test of stellar evolution theory."
 Iu his case. the inodel daa vesDaglogy.Ly=FOAL.Ny.taseraj) is compared ) ιο Observed data to find a TES fit stellar mass... age. and model parameters aj; (scec.g.Vau- 2008).," In this case, the model data $\{\hat{\nu}_k,\hat{T}_{\rm eff},\log \hat{g}, \hat{L}\} = f(M,X_i,t_{\rm age};\alpha_j)$ is compared to the observed data to find a best fit stellar mass, age, and model parameters $\alpha_j$ \citep[see e.g.][]{vauclair2008}."
". The streneth o this method Les iu the aree number of observable Le1010105, cach having a uique spatial dependence ou iaernal structure (Unuo(al. 19589)."," The strength of this method lies in the large number of observable frequencies, each having a unique spatial dependence on internal structure \citep{unno1989}."
". As nuuiavoftheovershootlE paramcter aud its dependence o1 stellar mass. inferred from) wide eclipsing binary ando asteroseisnolosical data. is presented im Fie. Ἐν,"," A summary of the overshoot parameter and its dependence on stellar mass, inferred from wide eclipsing binary and asteroseismological data, is presented in Fig. \ref{fig:ov-mass}."
 Wule the error bars are still quite large in Fig. 1.. ," While the error bars are still quite large in Fig. \ref{fig:ov-mass}, ,"
the scater iu the data may be indicating that we are missing sole essential plivysics., the scatter in the data may be indicating that we are missing some essential physics.
 A simple aud intuitive possibili vods that “overshoot” nuelt not just have a dass depeideuce but also a time dependence., A simple and intuitive possibility is that “overshoot” might not just have a mass dependence but also a time dependence.
 We are just begiuuiug to collect enouch, We are just beginning to collect enough
 We are just begiuuiug to collect enouchi, We are just beginning to collect enough
of the background-subtracted counts detected by the PCA in the same energy range.,of the background-subtracted counts detected by the PCA in the same energy range.
 Due to the soft spectrum of 4L 01424614. its contribution rises to over of the counts in the 2-4 keV range.," Due to the soft spectrum of 4U 0142+614, its contribution rises to over of the counts in the 2-4 keV range."
 Therefore we included in the fits the contribution from 4U 01424614 with spectral parameters fixed at the above values., Therefore we included in the fits the contribution from 4U 0142+614 with spectral parameters fixed at the above values.
 Even taking the contribution from 4U 01424614 into account. a single power law cannot deseribe the spectrum of.," Even taking the contribution from 4U 0142+614 into account, a single power law cannot describe the spectrum of."
. The residuals show clear evidence for an iron K emission line and for a spectral turnover at energies above ~15 keV. A better fit can be obtained by adding to the model a Gaussian emission line and an exponential cut-off (or a broken power law) to the model., The residuals show clear evidence for an iron K emission line and for a spectral turnover at energies above $\sim$ 15 keV. A better fit can be obtained by adding to the model a Gaussian emission line and an exponential cut-off (or a broken power law) to the model.
 The best fit spectrum is shown in Fig., The best fit spectrum is shown in Fig.
 | and its parameters are reported in Table I., 1 and its parameters are reported in Table 1.
" Since lies at low galactic latitude (12129"".5, bz-0"".8) it is likely that the observed iron line result from the diffuse emission from the galactic ridge (Koyama et al."," Since lies at low galactic latitude $^{\rm o}$ .5, $^{\rm o}$ .8) it is likely that the observed iron line result from the diffuse emission from the galactic ridge (Koyama et al."
 1989; Yamauchi Koyama 1993)., 1989; Yamauchi Koyama 1993).
 Based on the work by Yamauchi Koyama we derived the flux from the diffuse line emission expected within the field of view of the PCA instrument., Based on the work by Yamauchi Koyama we derived the flux from the diffuse line emission expected within the field of view of the PCA instrument.
 Though several uncertainties are involved in this estimate and the parameters of the Fe line reported in Table | are affected by the uncertainty in the PCA calibration around the Xenon L edge (at ~5.5 keV: see. e.g.. figure | in Dove et al 1998). we find that the observed Fe-line flux can be easily accounted for.," Though several uncertainties are involved in this estimate and the parameters of the Fe line reported in Table 1 are affected by the uncertainty in the PCA calibration around the Xenon L edge (at $\sim$ 5.5 keV; see, e.g., figure 1 in Dove et al 1998), we find that the observed Fe-line flux can be easily accounted for."
 This conclusion is further supported by the absence of line emission in the spectrum obtained with the ASCA imaging instruments (Haberl. Angelini Motch 1998). which allow a better subtraction of the local background.," This conclusion is further supported by the absence of line emission in the spectrum obtained with the ASCA imaging instruments (Haberl, Angelini Motch 1998), which allow a better subtraction of the local background."
 The flux of in the 2-20 keV range corresponding to the best fit parameters is 1.3«10.19 ergem ? H110 ου . corrected for the absorption).," The flux of in the 2-20 keV range corresponding to the best fit parameters is $1.3\times10^{-10}$ erg $^{-2}$ $^{-1}$ $1.4\times10^{-10}$ erg $^{-2}$ $^{-1}$, corrected for the absorption)."
 For a distance of 2.5 kpe this corresponds to a luminosity of ~10 ere 1, For a distance of 2.5 kpc this corresponds to a luminosity of $\sim$ $^{35}$ erg $^{-1}$.
 To derive the pulse period of we used a standard folding technique. obtaining a value of 1407.8 + I.ο s. The light curve. shown for three different energy ranges in Fig.," To derive the pulse period of we used a standard folding technique, obtaining a value of 1407.8 $\pm$ 1.3 s. The light curve, shown for three different energy ranges in Fig."
 2. has a single broad peak. as seen in previous observations (ASCA. ROSAT. see Haberl. Angelini Motch 1998; see Haberl et al.," 2, has a single broad peak, as seen in previous observations (ASCA, ROSAT, see Haberl, Angelini Motch 1998; see Haberl et al."
 1998)., 1998).
 Moreover. thanks to the considerably higher signal to noise ratio. some substructures are. clearly visible in. our data. as well as significant pulse to pulse variability.," Moreover, thanks to the considerably higher signal to noise ratio, some substructures are clearly visible in our data, as well as significant pulse to pulse variability."
 This is shown in Fig., This is shown in Fig.
 3 where we have plotted most of the individual pulses visible in our observation., 3 where we have plotted most of the individual pulses visible in our observation.
 Some evidence for spectral variations as a function of the spin period phase are apparent from Fig., Some evidence for spectral variations as a function of the spin period phase are apparent from Fig.
 2., 2.
 To investigate this in more detail. we extracted background subtracted spectra corresponding to the four phase intervals marked in Fig.2.," To investigate this in more detail, we extracted background subtracted spectra corresponding to the four phase intervals marked in Fig.2."
 As a first step. we fitted the total spectrum with the model of Table | and then. keeping all other parameters fixed. we renormalized the power law representing for each of the four phase intervals: the ratios of the observed spectra to these renormalized average models are shown in Fig.," As a first step, we fitted the total spectrum with the model of Table 1 and then, keeping all other parameters fixed, we renormalized the power law representing for each of the four phase intervals; the ratios of the observed spectra to these renormalized average models are shown in Fig."
 4., 4.
 Some features are clearly seen in these plots: (1) a considerable excess above 10 keV during the interval D. (2) a softening of the whole spectrum during the interval A. (3) a slight variation of the intermediate energy structure with phase.," Some features are clearly seen in these plots: (1) a considerable excess above 10 keV during the interval D, (2) a softening of the whole spectrum during the interval A, (3) a slight variation of the intermediate energy structure with phase."
measurements are seen to disagree. ancl clillerent (NEW) parametric models of the cluster with widely varving masses and concentration parameters are seen by dilferent authors to provide good fits to the data.,"measurements are seen to disagree, and different (NFW) parametric models of the cluster with widely varying masses and concentration parameters are seen by different authors to provide good fits to the data."
 For example. gravitational lensing studies of the galaxy. cluster Abell 1689. (sec. c.g. Corless et al.," For example, gravitational lensing studies of the galaxy cluster Abell 1689 (see, e.g., Corless et al."
 2009: Peng et al., 2009; Peng et al.
 2009: and references therein) have found. best-ft models that span a factor of 3.5 in mass and 3 dn best-fit NEW concentration parameter., 2009; and references therein) have found best-fit models that span a factor of 3.5 in mass and 3 in best-fit NFW concentration parameter.
 Such disagreement hinders elforts to compare cluster data with the predictions from N-bods simulations described above. and thus to constrain cosmological parameters.," Such disagreement hinders efforts to compare cluster data with the predictions from N-body simulations described above, and thus to constrain cosmological parameters."
" The technique presented. in this paper is designed. to assist. in breaking some of these degeneracies. as even within a family of models such as the NEW model. the AZ, signatures for profiles with different lens masses ancl concentration parameters are seen to be substantially dillerent. [rom one another."," The technique presented in this paper is designed to assist in breaking some of these degeneracies, as even within a family of models such as the NFW model, the $\fmap$ signatures for profiles with different lens masses and concentration parameters are seen to be substantially different from one another."
 Aleasurements of gravitational Hexion. the second order eravitational lensing elfects which give rise to skewness and arciness in galaxy images. have been shown by numerous authors to be adept at detecting ealaxy- and galaxy &roup-size haloes both in the field and within clusters of galaxies (e.g. Okura. Umetsu Futamase. 2007.2008: Leonard et al.," Measurements of gravitational flexion, the second order gravitational lensing effects which give rise to skewness and arciness in galaxy images, have been shown by numerous authors to be adept at detecting galaxy- and galaxy group-size haloes both in the field and within clusters of galaxies (e.g. Okura, Umetsu Futamase, 2007,2008; Leonard et al.,"
 2008: Leonard. Ixing Wilkins. 2009). as well as providing an alternative method by which the mass distribution within a cluster of galaxies might be constrained.," 2008; Leonard, King Wilkins, 2009), as well as providing an alternative method by which the mass distribution within a cluster of galaxies might be constrained."
 In addition. Lasky Flake (2009) have found that the first Uexion signal from an SIS profile cillers from that of an NEW substantially at moderate separation between source and lens. whilst the second Lexion signal shows strong variation when the NEW concentration parameter is varied.," In addition, Lasky Fluke (2009) have found that the first flexion signal from an SIS profile differs from that of an NFW substantially at moderate separation between source and lens, whilst the second flexion signal shows strong variation when the NFW concentration parameter is varied."
 Flexion studies. could therefore provide complementary constraints on halo profiles as well as their masses., Flexion studies could therefore provide complementary constraints on halo profiles as well as their masses.
 Recently. Leonard et al. (," Recently, Leonard et al. ("
2009: hereafter LIN09) developed an aperture mass statistic for llexion. in clirect analogv with that usec for shear. and showed that it provided a robust method. by which structures within clusters of galaxies. on a range of physical scales. can be identified to appreciable signal to noise.,"2009; hereafter LKW09) developed an aperture mass statistic for flexion, in direct analogy with that used for shear, and showed that it provided a robust method by which structures within clusters of galaxies, on a range of physical scales, can be identified to appreciable signal to noise."
 This technique is formally identical to the standard. shear aperture miss methods used in weak lensing (see. for example. Schneider 1996. Sehneicer et αἱ.," This technique is formally identical to the standard shear aperture mass methods used in weak lensing (see, for example, Schneider 1996, Schneider et al."
 1998). but uses measurements of Hexion rather than shear.," 1998), but uses measurements of flexion rather than shear."
 This technique has the advantages that the noise. properties of the aperture mass maps generated are very well understood. and. that the filter functions used can be tuned. to provide optimal noise for a given lens profile.," This technique has the advantages that the noise properties of the aperture mass maps generated are very well understood, and that the filter functions used can be tuned to provide optimal signal-to-noise for a given lens profile."
 Aloreover. the flexion aperture mass technique ollers a robust method. by which the mass. distribution. of a cluster of galaxies might be mapped out vμαithout the need for parametric modelling.," Moreover, the flexion aperture mass technique offers a robust method by which the mass distribution of a cluster of galaxies might be mapped out without the need for parametric modelling."
 Εις means that the technique does not rely on assumptions about the mass profiles of the structures responsible for the lensing signal. nor does it require knowledge of the locations of the mass Concentrations responsible for the lensing signal.," This means that the technique does not rely on assumptions about the mass profiles of the structures responsible for the lensing signal, nor does it require knowledge of the locations of the mass concentrations responsible for the lensing signal."
 lt can therefore be used to place independent. constraints on the mass distribution of clusters of galaxies. without the invocation of any assumptions regarding the shape of the mass clensity profile of the structure.," It can therefore be used to place independent constraints on the mass distribution of clusters of galaxies, without the invocation of any assumptions regarding the shape of the mass density profile of the structure."
 In addition. LIANW09 noted that the zero-signal contours expected to be found. around. mass peaks vary in radius uncer change of mass profile. lens mass. filter shape and aperture size.," In addition, LKW09 noted that the zero-signal contours expected to be found around mass peaks vary in radius under change of mass profile, lens mass, filter shape and aperture size."
 LINWOO suggest the properties of this set of contours might thus be used to. provide insights into the mass ancl profile shape of the structures identified using this method. thus olfering the potential to discriminate between competing mass models in cases where degeneracies arise.," LKW09 suggest the properties of this set of contours might thus be used to provide insights into the mass and profile shape of the structures identified using this method, thus offering the potential to discriminate between competing mass models in cases where degeneracies arise."
 In this paper. we more fully investigate this claim.," In this paper, we more fully investigate this claim."
 We focus on two properties of the Uexion aperture mass signalnamely. the peak signal associated with a given structure and its zero-signal contourand investigate their behaviour for SIS and NEW profiles under variation in viria mass. NEW concentration parameter. aperture racius anc filter shape in order to quantify the discriminating power of this technique.," We focus on two properties of the flexion aperture mass signal–namely, the peak signal associated with a given structure and its zero-signal contour–and investigate their behaviour for SIS and NFW profiles under variation in virial mass, NFW concentration parameter, aperture radius and filter shape in order to quantify the discriminating power of this technique."
 We demonstrate that the Hexion aperture miss signatures of these two mass profiles are very dilferen under changes to the aperture and filter properties., We demonstrate that the flexion aperture mass signatures of these two mass profiles are very different under changes to the aperture and filter properties.
 As a result of this divergent behaviour. aperture mass filtering of Ilexion data using a variety of aperture parameters provides a convenient and straightforward method for estimating both the mass and. profile shape of the structures detecte without the need for parametric modelling.," As a result of this divergent behaviour, aperture mass filtering of flexion data using a variety of aperture parameters provides a convenient and straightforward method for estimating both the mass and profile shape of the structures detected without the need for parametric modelling."
 Moreover. we demonstrate on simulated data that the total mass can be constrainedto within a factor of ~1.5 for both galaxy-eroup and. cluster scale haloes. ancl the input. profile shape recovered. for à signal to noise in the Hlexion aperture ass measurement as low as 1.," Moreover, we demonstrate on simulated data that the total mass can be constrainedto within a factor of $\sim 1.5$ for both galaxy-group and cluster scale haloes, and the input profile shape recovered, for a signal to noise in the flexion aperture mass measurement as low as 1."
 Finally. we demonstrate that this method significantly outperforms a Fourier transform-based direct. inversion technique (similar to that used. in Okura ot al," Finally, we demonstrate that this method significantly outperforms a Fourier transform-based direct inversion technique (similar to that used in Okura et al."
s 2008 analysis of Abell 1689). vielding both higher resolution and much better constraints on the shape of the cluster mass profilo.,"'s 2008 analysis of Abell 1689), yielding both higher resolution and much better constraints on the shape of the cluster mass profile."
 This paper is structured. as follows., This paper is structured as follows.
 In 2. we provide a brief review of the origin of the flexion. signal. an overview of the flexion. aperture mass statistic. and a description of the mass models considered.," In \ref{sec:formalism}, we provide a brief review of the origin of the flexion signal, an overview of the flexion aperture mass statistic, and a description of the mass models considered."
 In 2.42... we consider the radial profile of the aperture mass for cach of the mass models and. for a range of filters and. aperture radii. and for varving values of the lens virial mass and concentration parameter (in the case of NEW lenses).," In \ref{sec:radprof}, we consider the radial profile of the aperture mass for each of the mass models and for a range of filters and aperture radii, and for varying values of the lens virial mass and concentration parameter (in the case of NFW lenses)."
 The behaviour of the peak signal and the zero-signal contour under changes to the underlying mass model anclchanges to the aperture and filter properties is considered., The behaviour of the peak signal and the zero-signal contour under changes to the underlying mass model andchanges to the aperture and filter properties is considered.
 In 4.. we investigate the behaviour of a single mass profile uncer changes to the aperture and filter properties. and. examine whether the use of several cüllerent combinations of aperture radius and filter shape in aperture mass reconstructions enables one to discriminate between dillerent. halo masses and density profiles.," In \ref{sec:discrim}, we investigate the behaviour of a single mass profile under changes to the aperture and filter properties, and examine whether the use of several different combinations of aperture radius and filter shape in aperture mass reconstructions enables one to discriminate between different halo masses and density profiles."
 In 5.. we apply aperture mass ancl direct reconstruction techniques to Hexion data obtained by ravtracing simulations through a cluster extracted from the Alillennium simulation (see LIN09 and references therein) and compare the performance of the two methods.," In \ref{sec:nfw}, we apply aperture mass and direct reconstruction techniques to flexion data obtained by raytracing simulations through a cluster extracted from the Millennium simulation (see LKW09 and references therein) and compare the performance of the two methods."
 We conclude in 6 with a discussion of our results and their implications forfuture IHexion studies., We conclude in \ref{sec:summary} with a discussion of our results and their implications forfuture flexion studies.
" '""l'hroughout. the text. we assume a standard. (CDM cosmology with ο= 0.27. Oy,= O73. and 1005 + +."," Throughout the text, we assume a standard $\Lambda$ CDM cosmology with $\om=0.27$ , $\Omega_\Lambda=0.73$ , and $H_0=100h$ $^{-1}$ $^{-1}$ ."
 We begin by providing a very brief. introduction to the, We begin by providing a very brief introduction to the
The current. picture of Classical T Tauri stus (CTTSs). the so called class LD objects (Lada1987).. consists of a central voung star. surrounded by a geometrically thin disk.,"The current picture of Classical T Tauri stars (CTTSs), the so called class II objects \citep{lada87}, consists of a central young star, surrounded by a geometrically thin disk."
 Instead of a classical boundary laver connecting the disk directly to the star. as proposed bv Lynden-Bell&Pringle(1974).. the disk is disrupted by (the stars magnetic field al a eiven radius.," Instead of a classical boundary layer connecting the disk directly to the star, as proposed by \citet{lynden...74}, the disk is disrupted by the star's magnetic field at a given radius."
 Accretion flow for smaller radii follows the stars magnetic field lines until il impacts on the stellar surface (Ghosh&Lamb1979a.b:IxXónigl1991).," Accretion flow for smaller radii follows the star's magnetic field lines until it impacts on the stellar surface \citep{ghosh...79a,ghosh...79b,konigl91}."
. This “magnetospheric accretion model” explains observational signatures seen in some CITSs as. lor example. the excess of optical and ultraviolet continuum flix (veiling) anc redshift absorption features in the emission line profiles (inverse P Cveni profiles) (Muzerolle.Hartmann.&Calvet1993:ILartmann.IHewett.&Calvet1994.hereafter HIICS).," This “magnetospheric accretion model"" explains observational signatures seen in some CTTSs as, for example, the excess of optical and ultraviolet continuum flux (veiling) and redshift absorption features in the emission line profiles (inverse P Cygni profiles) \citep*[hereafter HHC]{muz..98,hart..94}."
. Low rotation rates. inferred from observations lor C'TTSs. are hare to explain by (he classical boundary Iaver model.," Low rotation rates, inferred from observations for CTTSs, are hard to explain by the classical boundary layer model."
 However. they can be explained in the magnetospheric accretion model.," However, they can be explained in the magnetospheric accretion model."
 Orrigeinnallly suggested by Ghosh&Lamb(1979a.b) lor (τοῦ stars. the (losppherric acccrettion. moddel was proppossed to expplain the hot sppots obsservved in DF ανα by Bertout.Dasri&Bouvier(1983).," lly suggested by \citet{ghosh...79a,ghosh...79b} for tron stars, the ric tion del was sed to plain the hot pots ved in DF ri by \citet{bertout...88}."
. Camenzincd(1990) and EKónigl(1991) applied the original Ghosh-Lamb model to CTTSs., \citet{camez90} and \citet{konigl91} applied the original Ghosh-Lamb model to CTTSs.
 It is assumed. in this model. that the star has a dipole magnetic field.," It is assumed, in this model, that the star has a dipole magnetic field."
 The basic idea behind this mechanism is that a sufficiently strong field can halt disk accretion at a given radius., The basic idea behind this mechanism is that a sufficiently strong field can halt disk accretion at a given radius.
 At this radius. the magnetic pressure needs (to be equal to the ram accretion pressure.," At this radius, the magnetic pressure needs to be equal to the ram accretion pressure."
 For protostellar accretion disks. magnetic fields on the order of 1kG at the stars surface are sufficient to disrupt the disk.," For protostellar accretion disks, magnetic fields on the order of 1kG at the star's surface are sufficient to disrupt the disk."
 Magnetic fields of this magnitude are inferred. [rom observations (Jobhns-Ixrulletal. 1999).," Magnetic fields of this magnitude are inferred from observations \citep{johns-krull...99,guenther...99}."
. In order to follow the magnetic field lines. the gas needs to be coupled to the magnetic field.," In order to follow the magnetic field lines, the gas needs to be coupled to the magnetic field."
 For C'TTss disks. this coupling is achieved if the temperatures al the (iruncation radius (2—0.1 AU) are greater than LO? IN since collisional ionization of metal atoms is then effective (Umebavashi&Nakano1988).," For CTTSs disks, this coupling is achieved if the temperatures at the truncation radius $R \leq 0.1$ AU) are greater than $10^3$ K since collisional ionization of metal atoms is then effective \citep{ume...88}."
. The truncation radius. {ρω must be smaller than the co-rotation radius. A. in order for accretion (to proceed.," The truncation radius, $R_{trun}$, must be smaller than the co-rotation radius, $R_{co}$, in order for accretion to proceed."
" Contrary (o observational evidences. for (he case A,«B4. the star should spin up."," Contrary to observational evidences, for the case $R_{trun} < R_{co}$, the star should spin up."
 Wind models that possess open magnetic field lines have been proposed to explain the observed low rotation rates., Wind models that possess open magnetic field lines have been proposed to explain the observed low rotation rates.
 Llowever. (he exact position (or region) of the truncation radius is still under debate (Coamenzind1990:Shuetal.1994:Hartinann1998).," However, the exact position (or region) of the truncation radius is still under debate \citep{camez90,shu..94, hart98}."
. These open field lines carry off mass and angular momentum., These open field lines carry off mass and angular momentum.
 Several CTTSs do. in fact. show P Cveni profiles in many lines. as well as in lorbidden-line emission. indicating the presence of outflows.," Several CTTSs do, in fact, show P Cygni profiles in many lines, as well as in forbidden-line emission, indicating the presence of outflows."
 Some CTTSs are known to have jets (e.g..DGTan.seeDacci," Some CTTSs are known to have jets \citep[e.g.,
DG Tau, see][]{bacci..00}."
ottietal.2000).. IWIC and more recently. Muzerroleetal.(1993). calculated magnetospheric accretion models. solving radiative transfer equations in the Sobolev approximation. in order to obtain," \citeauthor{hart..94} and more recently \citet{muz..98} calculated magnetospheric accretion models, solving radiative transfer equations in the Sobolev approximation, in order to obtain"
barely manages to cool below Tz:105IS when the medium Ix stationary. but iu the model with »=LO?ci” aud e—300018! a substantially ereater mass of gas cools and exists for a siguificautly longer period.,"barely manages to cool below $T \approx 10^{6} \K$ when the medium is stationary, but in the model with $n = 10^{5} \pcm3$ and $v = 3000 \kmps$ a substantially greater mass of gas cools and exists for a significantly longer period."
 The results of most observational work are reported in terms of the ionization parameter ( (Eq. 2))., The results of most observational work are reported in terms of the ionization parameter $U$ (Eq. \ref{eq:u_ip}) ).
 Since we know the relationship between C and E for the AGN spectrin adopted in our models (Eq. 3)).," Since we know the relationship between $U$ and $\Xi$ for the AGN spectrum adopted in our models (Eq. \ref{eq:u_chi}) ),"
 we can therefore casily compare our results to observations. where a large range in C is ποσα.," we can therefore easily compare our results to observations, where a large range in $U$ is seen."
 Low ionization lines (such as A2S00) typically have C~0.01. which trauslates into Zoϱ for eas at Fox200001.," Low ionization lines (such as $\lambda2800$) typically have $U \sim 0.01$, which translates into $\Xi \sim 0.3$ for gas at $T \approx 20000 \K$."
 Iu contrast. high ionization lines (such as ALS L9) are characterized by larger values of C - low values of A977/O ALO| nuply the preseuce of gas with P—1 (Laor 1991)).," In contrast, high ionization lines (such as $\lambda1549$ ) are characterized by larger values of $U$ - low values of $\lambda977$ $\lambda1034$ imply the presence of gas with $U \sim 1$ (Laor \cite{L1994}) )."
" This translates iuto Z~25 for gas existing iu the cool phase. which is clearly iu good agreement with the results presened in Fie. τν,"," This translates into $\Xi \sim 25$ for gas existing in the cool phase, which is clearly in good agreement with the results presented in Fig. \ref{fig:mass_ip_evolution}."
 The simulations shown so far were computed with au ACN flux which was ligh cnough to maintain the ambient gas in the hot phase Zz150 - see the equilibriun curve in Fie. 1))., The simulations shown so far were computed with an AGN flux which was high enough to maintain the ambient gas in the hot phase $\Xi \approx 150$ - see the equilibrium curve in Fig. \ref{fig:teq}) ).
 This resulted iu a relatively low value of = for the shocked eas aud. provided a good opportunity for the shocked eas to cool to Tz2«101 K., This resulted in a relatively low value of $\Xi$ for the shocked gas and provided a good opportunity for the shocked gas to cool to $T \approx 2 \times 10^{4} \K$ .
 However. if aront were to be inmucrsed iu aubicut gas with a hügher," However, if aremnant were to be immersed in ambient gas with a higher"
the 29 stars for which Hipparcos parallaxes with 5-parameter fits (tvpe 5) are not available (van Leeuwen 2007) tend to have parallaxes with substantially [larger error. bars.,the 29 stars for which Hipparcos parallaxes with 5-parameter fits (type 5) are not available (van Leeuwen 2007) tend to have parallaxes with substantially larger error bars.
 These 29 stars have therefore been omitted., These 29 stars have therefore been omitted.
 Of the remaining 197 stars. six were also omitted from our final good list one with the reddest J-H color (and hence possibly reddened). one with a less than optimal parallax fit in the original Llippareos reduction. wo with low metal abundances outside 1ο range of the res of the sample. one whose absolute magnitude was clearv àn outlier for its colors. ancl one with an abnormally large parallax error.," Of the remaining 197 stars, six were also omitted from our final 'good' list – one with the reddest J-H color (and hence possibly reddened), one with a less than optimal parallax fit in the original Hipparcos reduction, two with low metal abundances outside the range of the rest of the sample, one whose absolute magnitude was clearly an outlier for its colors, and one with an abnormally large parallax error."
 Including these stars would decrease 10 mean absolute magnitude in both ορίων and Weaiss by about S mamas., Including these stars would decrease the mean absolute magnitude in both $_{2MASS}$ and $_{2MASS}$ by about 8 mmag.
 The sample we actually used. in determining mean absolute magnitudes verelore includes 191 of the 226 stars observed., The sample we actually used in determining mean absolute magnitudes therefore includes 191 of the 226 stars observed.
 Among these stars. there is a slight (26) tenceney (lig.," Among these stars, there is a slight $\sigma$ ) tendency (Fig."
 2) for the stars with parallaxes lower than about 12 mas to give fainter absolute magnitudes. which is in the expected sense for a sample with a cutolf determined cither by parallax or by percentage error in parallax.," 2) for the stars with parallaxes lower than about 12 mas to give fainter absolute magnitudes, which is in the expected sense for a sample with a cutoff determined either by parallax or by percentage error in parallax."
 Note that below 12 mas the parallax error begins to increase markedly (Fig., Note that below 12 mas the parallax error begins to increase markedly (Fig.
 1)., 1).
 Lf we define [to be 1 for parallaxes less than 12 mas and ϐ for parallaxes & this value. we can write where Ix. HE and JJ are on the 24LASS system.," If we define f to be 1 for parallaxes less than 12 mas and 0 for parallaxes $\geq$ this value, we can write where K, H and J are on the 2MASS system."
 Calculation of the cllects of Lutz-Welker correction (Smith 1999) for the S6 stars with parallaxes (van Leeuwen 2007) of 12 mas or greater gives a very small mean correction. which raises the mean Ix. LE anc.) absolute magnitudes for this large parallax! subset to -1.6072:0.022. -].484-E0.022 ancl -0.9762:0.020. respectively.," Calculation of the effects of Lutz-Kelker correction (Smith 1999) for the 86 stars with parallaxes (van Leeuwen 2007) of 12 mas or greater gives a very small mean correction, which raises the mean K, H and J absolute magnitudes for this 'large parallax' subset to $\pm$ 0.022, $\pm$ 0.022 and $\pm$ 0.020, respectively."
 Since Lutz-Ixelker. bias is à selection effect. ancl we selected: stars withrevised (1.0. 2007) Llipparcos parallaxes ess than 12 mas. our calculation. of the Lutz-Ixelker corrections was likewise based on the revised. Hipparcos xwallaxes and errors.," Since Lutz-Kelker bias is a selection effect, and we selected stars with (i.e. 2007) Hipparcos parallaxes less than 12 mas, our calculation of the Lutz-Kelker corrections was likewise based on the revised Hipparcos parallaxes and errors."
 But our complete sample (191 stars) shares the eutolf in the original list of Paezvisski Stanck (1998). of which our observing list was a southern subset.," But our complete sample (191 stars) shares the cutoff in the original list of Paczyńsski Stanek (1998), of which our observing list was a southern subset."
 This cutoll was based on theος (1997). Llipparcos results. ancl our calculation of the Lutz-Ixelker corrections or our sample of 191 stars must. likewise be based on the original Llipparcos parallaxes and errors.," This cutoff was based on the (1997) Hipparcos results, and our calculation of the Lutz-Kelker corrections for our sample of 191 stars must likewise be based on the original Hipparcos parallaxes and errors."
 Such a calculation elves, Such a calculation gives
In recent vears the black hole accretion disk model for GRBs has received much attention (Frver. Woosley Hartmann 1999: Popham. Wooslev Fiver 1999: Mésszárros 2000. 2002: Naravan. Piran Ixiumar 2001).,"In recent years the black hole accretion disk model for GRBs has received much attention (Fryer, Woosley Hartmann 1999; Popham, Woosley Fryer 1999; Mésszárros 2000, 2002; Narayan, Piran Kumar 2001)."
 Progenitors likely to lead to this accretion svstem include binary mergers aud collapsars: double neutron stars (DNS). black hole - neutron star black hole - white dwar! (DII-WD). black hole - helium star (BII-IHe). and fast-rotating massive stellar collapses.," Progenitors likely to lead to this accretion system include binary mergers and collapsars: double neutron stars (DNS), black hole - neutron star (BH-NS), black hole - white dwarf (BH-WD), black hole - helium star (BH-He), and fast-rotating massive stellar collapses."
 If the viscosity parameter of (he disks has a standard: value of o—0.1. DNS and DII-NS mergers can explain short GRBs with durations under a second. but thev are unlikely to produce long GRBs with durations of tens or hundred of seconds.," If the viscosity parameter of the disks has a standard value of $\alpha=0.1$, DNS and BH-NS mergers can explain short GRBs with durations under a second, but they are unlikely to produce long GRBs with durations of tens or hundred of seconds."
 On (he other hand. DII-WD and DII - He mergers and collapsars might produce long GRBs.," On the other hand, BH-WD and BH - He mergers and collapsars might produce long GRBs."
 Recently Frver et al. (, Recently Fryer et al. (
1999b) and Belezvnski. Dulik Ruedak (2002) have estimated the formation rate of these progenitors by using population svnthesis methods.,"1999b) and Belczynski, Bulik Rudak (2002) have estimated the formation rate of these progenitors by using population synthesis methods."
 The results of Fiver et al. (, The results of Fryer et al. (
1999b) are stunmarizecl in Table 1. where the standard values of the formation rates and the uncertainty ranges are listed.,"1999b) are summarized in Table 1, where the standard values of the formation rates and the uncertainty ranges are listed."
" Assuming the galaxy density ny,=0.02 3, we can estimate the distance inside which an event is expected to happen within in a vear from the formation rates A."," Assuming the galaxy density $n_{glx}=0.02$ $^{-3}$, we can estimate the distance inside which an event is expected to happen within in a year from the formation rates $R$."
 The estimates on the formation rates by Belezvnski et al. (, The estimates on the formation rates by Belczynski et al. (
20020) are consistent with the results of Frver οἱ al. (,2002a) are consistent with the results of Fryer et al. (
1999b) and within the uncertaintv range in table 1 in most of their models.,1999b) and within the uncertainty range in table 1 in most of their models.
 Though some of their models predict higher formation rates by a [actor of a few than the upper limits in table 1. (he uncertzintv range of (he distances are similar because the distances are rather insensitive to the rate dx RY.," Though some of their models predict higher formation rates by a factor of a few than the upper limits in table 1, the uncertainty range of the distances are similar because the distances are rather insensitive to the rate $d\propto R^{-1/3}$ ."
At relativistic shock waves the bulk flow velocities are comparable to particle velocities.,At relativistic shock waves the bulk flow velocities are comparable to particle velocities.
 This leads to. highlv anisotropic particle distributions al the shock., This leads to highly anisotropic particle distributions at the shock.
" Unlike the case of nonrelativistic shocks. acceleration processes are very sensitive to (he background conditions. in particular to the structure of the perturbed (""turbulent) magnetic field and the details of parlicle-wave interactions."," Unlike the case of nonrelativistic shocks, acceleration processes are very sensitive to the background conditions, in particular to the structure of the perturbed (“turbulent”) magnetic field and the details of particle-wave interactions."
 These are. however. poorly known and modeling of the particle acceleration must rely on simplifving assumptions regarding particle scattering and transport.," These are, however, poorly known and modeling of the particle acceleration must rely on simplifying assumptions regarding particle scattering and transport."
 llere we consider (he first-order Fermi acceleration processes. involving only the hieh-enerey parücles with evroraclii much ereater than (he thickness of the shock.," Here we consider the first-order Fermi acceleration processes, involving only the high-energy particles with gyroradii much greater than the thickness of the shock."
 The first consistent semianalvtic method to study (he acceleration process al parallel relativistic shock was proposed bv irk&Sehneider(1987). ancl it was further extended {ο {real more general conditions at the shock by IHeavens&Drury(1983)., The first consistent semianalytic method to study the acceleration process at parallel relativistic shock was proposed by \citet{kir87a} and it was further extended to treat more general conditions at the shock by \citet{hea88}.
. The method uses the stationary. Fokker-Planck pitch-anele dilfusion equation describing anisotropic particle distributions near the shock., The method uses the stationary Fokker-Planck pitch-angle diffusion equation describing anisotropic particle distributions near the shock.
 Matching (he upstream and downstream solutions of the diffusion equation at the shock vields both the power-law index of (he resulting spectrum and the form of anisotropic particle angular distribution., Matching the upstream and downstream solutions of the diffusion equation at the shock yields both the power-law index of the resulting spectrum and the form of anisotropic particle angular distribution.
" The spectral indices lor the phase space distribution function. a. derived with this method for parallel relativistic shocks are clilferent from the value of ayy,=4 (or the equivalent.energy spectral index 2) obtained lor strong nonrelativistic shocks (e.g.. Drury. 19382) and depend on the wave power spectrum of the magnetic field perturbations (= the form of the pitch-angle diffusion coellicient)."," The spectral indices for the phase space distribution function, $\alpha$, derived with this method for parallel relativistic shocks are different from the value of $\alpha_{\rm NR} = 4$ (or the equivalent spectral index $\sigma_{\rm NR} =\alpha_{\rm NR}-2= 2$ ) obtained for strong nonrelativistic shocks (e.g., Drury 1983) and depend on the wave power spectrum of the magnetic field perturbations $\equiv$ the form of the pitch-angle diffusion coefficient)."
 The same approach. augmented by the assumption of magnetic moment conservation for particles interactinge with the shock. was used to study acceleration processes in oblique," The same approach, augmented by the assumption of magnetic moment conservation for particles interacting with the shock, was used to study acceleration processes in oblique"
"occurred on EV Lac on UT 2009 October 27 and UT 2010 November 27, and on YZ CMi on UT 2011 February 14, each showed infrared emission lines.","occurred on EV Lac on UT 2009 October 27 and UT 2010 November 27, and on YZ CMi on UT 2011 February 14, each showed infrared emission lines."
 These flares are discussed in detail in Section 4.1.., These flares are discussed in detail in Section \ref{sec:flare}.
" We were observing with all four instruments during the most energetic event, a Au — magnitude flare on EV Lac on UT 27 October 2009."," We were observing with all four instruments during the most energetic event, a $\Delta u$ = magnitude flare on EV Lac on UT 27 October 2009."
 The light curves for our observations are shown in Figure 3.., The light curves for our observations are shown in Figure \ref{fig:evoct}.
" The photometry (in U-, u-, and g-band) exhibits a typical flare light curve with a fast rise and exponential decay."," The photometry (in $U$ -, $u$ -, and $g$ -band) exhibits a typical flare light curve with a fast rise and exponential decay."
 The u-band flare emission lasted 1.68 hours and released a total energy of 3.9 x10?? ergs., The $u$ -band flare emission lasted 1.68 hours and released a total energy of 3.9 $\times$ $^{32}$ ergs.
" The combination of optical (DAO) and infrared (TripleSpec) spectroscopy allows us to examine a total of nine emission lines - Hy, Hd, He I \4471A,, and Ca II K in the UV/blue part of the spectrum, and P, P», Pó, Bry, and He I A10830À in the infrared."," The combination of optical (DAO) and infrared (TripleSpec) spectroscopy allows us to examine a total of nine emission lines - $\gamma$, $\delta$, He I $\lambda$, and Ca II K in the UV/blue part of the spectrum, and $\beta$, $\gamma$, $\delta$, $\gamma$, and He I $\lambda$ in the infrared."
" Figure 4 shows the lightcurve of each emission line normalized to its value at t — 4.97 hours (the peak of u-band emission), and the ratio of each line to Hy for comparison of their evolution during the flare."," Figure \ref{fig:linec} shows the lightcurve of each emission line normalized to its value at t = 4.97 hours (the peak of $u$ -band emission), and the ratio of each line to $\gamma$ for comparison of their evolution during the flare."
" The light curves for Hd, and He I \4471A have a fast-rise exponential-decayHy, shape similar to the photometry."," The light curves for $\gamma$, $\delta$, and He I $\lambda$ have a fast-rise exponential-decay shape similar to the photometry."
" Py and Pó show a similar fast rise, but their decay is slower than the Balmer series lines."," $\gamma$ and $\delta$ show a similar fast rise, but their decay is slower than the Balmer series lines."
" The P8 and Ca II K emission both peak after the other Paschen and Balmer series lines, and exhibit an even slower decay after their late peaks."," The $\beta$ and Ca II K emission both peak after the other Paschen and Balmer series lines, and exhibit an even slower decay after their late peaks."
" Bry is similar to P8 and Ca II K in its late peak, but seems to decay faster than any other line."," $\gamma$ is similar to $\beta$ and Ca II K in its late peak, but seems to decay faster than any other line."
" This may be an observational effect, as it is by far the weakest line detected."," This may be an observational effect, as it is by far the weakest line detected."
" Without a stronger detection, we assume that its ratio to the Paschen lines is constant throughout the flare."," Without a stronger detection, we assume that its ratio to the Paschen lines is constant throughout the flare."
" The He I \10830A emission shows a shape distinct from the rest of the lines — it remains nearly at itspeak flux for 0.8 hours, approximately half of the duration of the flare in u-band."," The He I $\lambda$ emission shows a shape distinct from the rest of the lines – it remains nearly at itspeak flux for 0.8 hours, approximately half of the duration of the flare in $u$ -band."
" The slow decay during the gradual phase is a well-known property of Ca II K (e.g.Bopp&Moffett1973;Hawley&Pettersen1991;Fuhrmeisteretal. 2008),, but in this flare, He I \10830A emission traces a region that remains heated for an even longer portion of the gradual phase than Ca II K. This could be due to the Neupert effect, where the line responds to the total cumulative flare heating for which the time integral of the U-band (white light emission) is often used as a proxy (Hawleyetal.1995;Osten 2005)."," The slow decay during the gradual phase is a well-known property of Ca II K \citep[e.g.\ ][]{Bopp1973,Hawley1991,Fuhrmeister2008}, but in this flare, He I $\lambda$ emission traces a region that remains heated for an even longer portion of the gradual phase than Ca II K. This could be due to the Neupert effect, where the line responds to the total cumulative flare heating for which the time integral of the $U$ -band (white light emission) is often used as a proxy \citep{Hawley1995,Osten2005}."
. Section 5 describes our efforts to model the emission lines from this flare., Section \ref{sec:mod} describes our efforts to model the emission lines from this flare.
 We observed another flare with infrared line emission on EV Lac on UT 2010 November 27., We observed another flare with infrared line emission on EV Lac on UT 2010 November 27.
" The flare peaked at Au — 1.68, and over the course of t — 1.30 hours it emitted 5.5 x10?! ergsin the u-band."," The flare peaked at $\Delta u$ = 1.68, and over the course of t = 1.30 hours it emitted 5.5 $\times$ $^{31}$ ergsin the $u$ -band."
" We observed with both ARCSAT and TripleSpec during the flare, and have photometry in g and r-band in addition to the u-band data."," We observed with both ARCSAT and TripleSpec during the flare, and have photometry in $g$ and $r$ -band in addition to the $u$ -band data."
" The photometry and the line flux lightcurves for PG, Py, and He I \10830A are shown in Figure 5.."," The photometry and the line flux lightcurves for $\beta$, $\gamma$, and He I $\lambda$ are shown in Figure \ref{fig:evnov}."
 There was no discernible emission in Pó and Bry., There was no discernible emission in $\delta$ and $\gamma$.
 This peculiarly-shaped flare contains three separate peaks in the u-band photometry., This peculiarly-shaped flare contains three separate peaks in the $u$ -band photometry.
" After the first and third peak, the fluxseems to decay exponentially, but after the middle peak there is a gentle rise in the u-band flux."," After the first and third peak, the fluxseems to decay exponentially, but after the middle peak there is a gentle rise in the $u$ -band flux."
" TripleSpec was taking observations of a standard star during the first peak of the flare,so it is unknown if the emission lines showed the same fast-rise exponential-decay as the first photometric peak."," TripleSpec was taking observations of a standard star during the first peak of the flare,so it is unknown if the emission lines showed the same fast-rise exponential-decay as the first photometric peak."
 The rise in P5 and Py line emission before and after the standard star gap suggests that those lines showed some emission between the first and second peaks of the flare., The rise in $\beta$ and $\gamma$ line emission before and after the standard star gap suggests that those lines showed some emission between the first and second peaks of the flare.
" An observed increase in infrared line emission occurred ~0.2 hours after the second peak in the u-band photometry, tracing a gentle rise and decay."," An observed increase in infrared line emission occurred $\sim$ 0.2 hours after the second peak in the $u$ -band photometry, tracing a gentle rise and decay."
" The shape of this flare is very different than that of the UT 2009 October 27 flare on EV Lac, and the relative line strengths are also different."," The shape of this flare is very different than that of the UT 2009 October 27 flare on EV Lac, and the relative line strengths are also different."
" In the previous flare, P, Py and He I \10830A emitted nearly the same peak flux."," In the previous flare, $\beta$, $\gamma$ and He I $\lambda$ emitted nearly the same peak flux."
" In this flare, He I \10830A peaked at twice the strength of the P5 and P« lines, indicating a different pattern of atmospheric heating during the two flares."," In this flare, He I $\lambda$ peaked at twice the strength of the $\beta$ and $\gamma$ lines, indicating a different pattern of atmospheric heating during the two flares."
" On UT 2011 February 14, we observed a AU = 1.38 flare on YZ CMi with the NMSU 1-m, ARCSAT, and TripleSpec."," On UT 2011 February 14, we observed a $\Delta U$ = 1.38 flare on YZ CMi with the NMSU 1-m, ARCSAT, and TripleSpec."
 The flare lasted for t = 0.5 hours and released a total U-band energy of 4.4 x10?! ergs., The flare lasted for t = 0.5 hours and released a total $U$ -band energy of 4.4 $\times$ $^{31}$ ergs.
" Figure 6 shows the U, g, and r-band light curves (i-band was also observed but showed no change during the flare) and line fluxes from PZ, Py and He I \10803A.."," Figure \ref{fig:yzfeb} shows the $U$ , $g$ and $r$ -band light curves $i$ -band was also observed but showed no change during the flare) and line fluxes from $\beta$ , $\gamma$ and He I $\lambda$ ."
 This is the, This is the
observations of Mrk421 in different activity states.,observations of Mrk421 in different activity states.
 A complete account of the observations on Mrk421 will be reported in a dedicated paper., A complete account of the observations on Mrk421 will be reported in a dedicated paper.
 As mentioned in the Introduction. two different flares have been observed from Mrk421 in June 2008. the first one peaking m X-rays on June 4-6 and the second one on June 11-13.," As mentioned in the Introduction, two different flares have been observed from Mrk421 in June 2008, the first one peaking in X-rays on June 4-6 and the second one on June 11-13."
 Concerning VHE gamma rays. Cherenkov telescopes data are available only for the first flare.," Concerning VHE gamma rays, Cherenkov telescopes data are available only for the first flare."
 An energy spectrum for E 400 GeV has been provided by VERITAS for June 6., An energy spectrum for E $\geq$ 400 GeV has been provided by VERITAS for June 6.
 Since the ARGO-YBJ sensitivity does not allow. the observation of a flux a few times larger than the Crab one in only one day (re. during one transit of the source m the detector field of view). we integrated the measurement over 3 days.," Since the ARGO-YBJ sensitivity does not allow the observation of a flux a few times larger than the Crab one in only one day (i.e. during one transit of the source in the detector field of view), we integrated the measurement over 3 days."
" Fig.1 shows the rate of events with Nj,= 100 observed by ARGO-YBJ from June 3 to June 15. averaged over 3 days. compared with the X-ray flux measured by in the 2-10 keV energy range."," Fig.1 shows the rate of events with $_{pad} \ge$ 100 observed by ARGO-YBJ from June 3 to June 15, averaged over 3 days, compared with the X-ray flux measured by in the 2-10 keV energy range."
 A correlation between the gamma ray and X-ray light curves is clearly visible., A correlation between the gamma ray and X-ray light curves is clearly visible.
 During the days June 11-13. when the maximum of the second flare occurred. the excess of events from Mrk421 reached a statistical significance of 3.8 standard deviations.," During the days June 11-13, when the maximum of the second flare occurred, the excess of events from Mrk421 reached a statistical significance of 3.8 standard deviations."
 Beside the statistical error. this measurement could be affected by a systematic uncertainty due to. the background evaluation. that is the most delicate step of the analysis.," Beside the statistical error, this measurement could be affected by a systematic uncertainty due to the background evaluation, that is the most delicate step of the analysis."
 In order to estimate this effect. a completely different procedure for the background calculation has been implemented. using the so-called method (Amenomorietal.2005).," In order to estimate this effect, a completely different procedure for the background calculation has been implemented, using the so-called method \cite{Ame05}."
. In this method the events collected in 10 off-source windows of the same size of the on-source window. and aligned on both sides of the same zenith angle belt. are used to obtain the background.," In this method the events collected in 10 off-source windows of the same size of the on-source window, and aligned on both sides of the same zenith angle belt, are used to obtain the background."
 A detailed study of the two methods in the same sky region has shown that on average they give significances of the excesses consistent within 0.7 standard deviations. corresponding to about 20% uncertainty on the flux estimate of the observed signal.," A detailed study of the two methods in the same sky region has shown that on average they give significances of the excesses consistent within 0.7 standard deviations, corresponding to about $\%$ uncertainty on the flux estimate of the observed signal."
 The event rate as a function of the minimum pad multiplicity. obtained integrating the data during June 4-6 for the first flare (17.9 hours) and during June 11-13 for the second one (18.2 hours). is shown in Fig.2.," The event rate as a function of the minimum pad multiplicity, obtained integrating the data during June 4-6 for the first flare (17.9 hours) and during June 11-13 for the second one (18.2 hours), is shown in Fig.2."
 On the same plot. the two solid lines represent the expected rates according to the Donnarumma et al. (," On the same plot, the two solid lines represent the expected rates according to the Donnarumma et al. ("
2009) model. obtanined by a simulation procedure.,"2009) model, obtanined by a simulation procedure."
 The SED proposed by this model has been corrected for the EBL absorption using the parameters given by Raue & Mazin (2008) in order to have the flux at Earth., The SED proposed by this model has been corrected for the EBL absorption using the parameters given by Raue $\&$ Mazin (2008) in order to have the flux at Earth.
 Then. using the absorbed spectrum. we simulated a source moving along the Mrk421 path on the sky. and evaluated the number of events expected in the detector. for different thresholds.," Then, using the absorbed spectrum, we simulated a source moving along the Mrk421 path on the sky, and evaluated the number of events expected in the detector, for different $_{pad}$ thresholds."
" The complete simulation procedure (which includesN,,, the gamma ray showers propagation in the atmosphere. and the detector response) has been tested evaluating the Crab Nebula flux. as shown in the previous section."," The complete simulation procedure (which includes the gamma ray showers propagation in the atmosphere, and the detector response) has been tested evaluating the Crab Nebula flux, as shown in the previous section."
 In the limit of the statistical accuracy of this measurement. our data suggest for both flares a gamma ray flux higher than that expected by the model. indicating in particular a possible hardening of the spectrum during the second flare.," In the limit of the statistical accuracy of this measurement, our data suggest for both flares a gamma ray flux higher than that expected by the model, indicating in particular a possible hardening of the spectrum during the second flare."
 Considering the first flare. the integral flux measured by ARGO-YBJ above | TeV is about 1.5 times higher than the model based on the VERITAS measurement. but still marginally consistent with it.," Considering the first flare, the integral flux measured by ARGO-YBJ above 1 TeV is about 1.5 times higher than the model based on the VERITAS measurement, but still marginally consistent with it."
 The apparent disagreement between ARGO-YBJ and VERITAS can be likely attributed to the non-coincidence of the data taking periods of the two detectors and to the well known small variability time scale of the source., The apparent disagreement between ARGO-YBJ and VERITAS can be likely attributed to the non-coincidence of the data taking periods of the two detectors and to the well known small variability time scale of the source.
 The VERITAS data refer to June 6. while the ARGO-YBJ data are integrated over 3 days. from June 4 to 6.," The VERITAS data refer to June 6, while the ARGO-YBJ data are integrated over 3 days, from June 4 to 6."
 Furthermore. given the difference in longitude of the two detectors (— 160) and the fact that they observe the source during few hours around the culmination time. they can never observe simultaneously the same object.," Furthermore, given the difference in longitude of the two detectors $\sim$ $^{\circ}$ ) and the fact that they observe the source during few hours around the culmination time, they can never observe simultaneously the same object."
 The disagreement of our data with the model is more significant. for the second flare., The disagreement of our data with the model is more significant for the second flare.
 In. order to evaluate the spectral behaviour in this period. we assume again à power law spectrum multiplied by the EBL absorption factor e.," In order to evaluate the spectral behaviour in this period, we assume again a power law spectrum multiplied by the EBL absorption factor $^{-\tau(E)}$ ."
 From our fitting procedure we obtain: dN/dE = (3.2+1.0) « 107! (E/2.5 jy?55 e? photons em? s! Τον)., From our fitting procedure we obtain: dN/dE = $\pm1.0$ ) $\times$ $^{-11}$ (E/2.5 $^{-2.1^{+0.7}_{-0.5}}$ $^{-\tau(E)}$ photons $^{-2}$ $^{-1}$ $^{-1}$.
 This spectrum is shown in Fig.3 as a solid line., This spectrum is shown in Fig.3 as a solid line.
 The shaded band in the figure represents the | o statistical error., The shaded band in the figure represents the 1 $\sigma$ statistical error.
 The systematic errors are mainly related to the background evaluation. às discussed previously. and to the uncertainty in the absolute energy scale.," The systematic errors are mainly related to the background evaluation, as discussed previously, and to the uncertainty in the absolute energy scale."
 According to our estimate. they globally affect the quoted fluxes for = 30%.," According to our estimate, they globally affect the quoted fluxes for $\lesssim$ $\%$."
 Due to the low statistics. our data cannot constrain the shape of the spectrum above —8 TeV. Nevertheless the obtained flux appears. for energies 72 TeV. significantly larger than predicted by Donnarumma et al. (," Due to the low statistics, our data cannot constrain the shape of the spectrum above $\sim$ 8 TeV. Nevertheless the obtained flux appears, for energies $>$ 2 TeV, significantly larger than predicted by Donnarumma et al. ("
2009). while the spectrum slope is consistent with that measured by the Whipple Cherenkov telescope during the 2000/2001 observing season for a flare of comparable intensity (~ 7 times the Crab Nebula flux). also shown in Fig.3 (dataset ILL Krennrich et al. (,"2009), while the spectrum slope is consistent with that measured by the Whipple Cherenkov telescope during the 2000/2001 observing season for a flare of comparable intensity $\sim$ 7 times the Crab Nebula flux), also shown in Fig.3 (dataset III, Krennrich et al. ("
2002)).,2002)).
 The integral flux measured above | TeV during June 11-13 is ~6 times larger than the Crab one. making this flare one of the most powerful ever observed from Mrk421.," The integral flux measured above 1 TeV during June 11-13 is $\sim$ 6 times larger than the Crab one, making this flare one of the most powerful ever observed from Mrk421."
 Mrk421 has been continuously monitored by ARGO-YBJ since December 2007. showing an average VHE flux about twice the Crab Nebula one from February to June 2008. and decreasing afterwards.," Mrk421 has been continuously monitored by ARGO-YBJ since December 2007, showing an average VHE flux about twice the Crab Nebula one from February to June 2008, and decreasing afterwards."
 Two strong flares in June 2008 have been observed in a multiwavelength campaign from optical to TeV energies., Two strong flares in June 2008 have been observed in a multiwavelength campaign from optical to TeV energies.
 ARGO-YBJ measured the spectra of Mrk421 above 0.3 TeV during the second flare. completing the multifrequency observations.," ARGO-YBJ measured the spectra of Mrk421 above 0.3 TeV during the second flare, completing the multifrequency observations."
 A clear correlation between the gamma ray intensity measured by ARGO-YBJ and the X-ray flux measured by RXTE/ASM ts found., A clear correlation between the gamma ray intensity measured by ARGO-YBJ and the X-ray flux measured by RXTE/ASM is found.
 The ARGO-YBJ data. although averaged over 3 days. appear to support in both episodes a gamma ray flux higher than that predicted in the analysis of Donnarumma et al. (," The ARGO-YBJ data, although averaged over 3 days, appear to support in both episodes a gamma ray flux higher than that predicted in the analysis of Donnarumma et al. ("
2009).,2009).
 However. considering the short time scale variability of Mrk421. it has to be noticed that our observation time Is not fully coincident with the period referred to by the theoretical curves (June 6 for the first flare and June 12-13 for the second one).," However, considering the short time scale variability of Mrk421, it has to be noticed that our observation time is not fully coincident with the period referred to by the theoretical curves (June 6 for the first flare and June 12-13 for the second one)."
 The intensity of the second flare allows us to assess its spectral shape., The intensity of the second flare allows us to assess its spectral shape.
 The deabsorbed spectrum can be fitted by a power law & E7los extending up to several TeV. This spectrum appears definitively harder than that predicted on the basis of June 12-13 data collected up to GeV energies., The deabsorbed spectrum can be fitted by a power law $\propto$ $^{-2.1^{+0.7}_{-0.5}}$ extending up to several TeV. This spectrum appears definitively harder than that predicted on the basis of June 12-13 data collected up to GeV energies.
 On the contrary. our data follow the behaviour of the energy spectra measured during different activity statesby the Whipple Cherenkov telescope.," On the contrary, our data follow the behaviour of the energy spectra measured during different activity statesby the Whipple Cherenkov telescope."
 In particular. the ARGO-YBJ data fully satisfy the relation between thespectral index," In particular, the ARGO-YBJ data fully satisfy the relation between thespectral index"
(he very inner protoplanetary disk.,the very inner protoplanetary disk.
 We thank the NASA AISRP for providing financial assistance for the development of the PINTofALE package., We thank the NASA AISRP for providing financial assistance for the development of the PINTofALE package.
 JJD was supported by NASA contract NASS-39073 to theCenter during the course of (his research., JJD was supported by NASA contract NAS8-39073 to the during the course of this research.
 PT was supported by Chandra award number G03-4005A issued by CAC. and SAO contract SV3-73016 to MIT. for support of CAC. which is operated by SAO for ancl on behalf of NASA under contracts NÀS3-39073. and NAÀS8-03060.," PT was supported by Chandra award number G03-4005A issued by CXC, and SAO contract SV3-73016 to MIT for support of CXC, which is operated by SAO for and on behalf of NASA under contracts NAS8-39073 and NAS8-03060."
16 of Peterson et al. (,"16 of Peterson et al., ("
2004) shows that a reduction by a factor 3 of SAIBLT masses estimated in this way would put most of the sample of 35 reverberationmapped AGN close to their Eclelineton luminosities.,2004) shows that a reduction by a factor $\sim 3$ of SMBH masses estimated in this way would put most of the sample of 35 reverberation–mapped AGN close to their Eddington luminosities.
 In addition to this. estimating whether an AGN is near Leaq requires us to know not only its SMDLII mass. but also its true bolometric luminosity Li. both to high accuracy.," In addition to this, estimating whether an AGN is near $\le$ requires us to know not only its SMBH mass, but also its true bolometric luminosity $L_{\rm bol}$, both to high accuracy."
 The latter problem is unlikely to be easier than the former., The latter problem is unlikely to be easier than the former.
 This paper has argued that the black hole mass is a factor ofa few below the AL60 mass in active galaxies. and that a large [fraction of AGN are fed mass at a superExldington rate. acereting just the Lelelington value and expelling the COXCOSS.," This paper has argued that the black hole mass is a factor of a few below the $M - \sigma$ mass in active galaxies, and that a large fraction of AGN are fed mass at a super–Eddington rate, accreting just the Eddington value and expelling the excess."
 The first point follows from noting that SAIBLL growth towards the momentumdriven limit (2)) 1s inevitable given à sullicient mass supply., The first point follows from noting that SMBH growth towards the momentum–driven limit \ref{msigmom}) ) is inevitable given a sufficient mass supply.
 In. particular. energy.driven outflows are RayleighVavlor unstable. so the mass is not constrained by the energydriven limit. (3)).," In particular, energy–driven outflows are Rayleigh–Taylor unstable, so the mass is not constrained by the energy–driven limit \ref{msigen}) )."
" Growth only slows when momentumdriven outllows become Rayleigh'""avlor stable. ie. when the black hole is a factor of a few below the AZ.a value."," Growth only slows when momentum–driven outflows become Rayleigh--Taylor stable, i.e. when the black hole is a factor of a few below the $M - \sigma$ value."
 So ΛΙΠΗ masses in AGN are likely to be below. but fairly close to. this critical value.," So SMBH masses in AGN are likely to be below, but fairly close to, this critical value."
 This agrees with the suggestion by Bateheldor (2010) that the AL6 relation is an upper limit to SALBLL masses., This agrees with the suggestion by Batcheldor (2010) that the $M - \sigma$ relation is an upper limit to SMBH masses.
 The idea that AGN regularly reach Ley follows naturally from noting tha SMDILI have to grow rapiclly o reach the masses specified. by the Soltan relation., The idea that AGN regularly reach $\le$ follows naturally from noting that SMBH have to grow rapidly to reach the masses specified by the Soltan relation.
 [t is Consistent with the first proposition above (low SALBLI masses): Exldington ratios for observed AGN must be higher han previously estimated if their black holes lie below the AMPc relation rather than on it. as is sometimes assumed.," It is consistent with the first proposition above (low SMBH masses): Eddington ratios for observed AGN must be higher than previously estimated if their black holes lie below the $M -
\sigma$ relation rather than on it, as is sometimes assumed."
 The strongest evidence for Ecldington accretion comes rom the papers by Tomboesi et al. (, The strongest evidence for Eddington accretion comes from the papers by Tombesi et al. (
"2010a. b). which show hat a large fraction of nearby AGN have outllow with velocities Ole and ionization parameters £~10h10"". as expected.","2010a, b), which show that a large fraction of nearby AGN have outflow with velocities $\sim 0.1c$ and ionization parameters $\xi \sim 10^4 - 10^5$, as expected."
 At face value this suggests that a large fraction of local AGN are fed at superExldington rates. and | have argued that it is dillieult to avoid this conclusion.," At face value this suggests that a large fraction of local AGN are fed at super–Eddington rates, and I have argued that it is difficult to avoid this conclusion."
 ] thank Brad Peterson. Wen Pounds. James Reeves. and Alarianne Vestergaard for illuminating ciscussions. and the referee for à very thorough reading of the paper.," I thank Brad Peterson, Ken Pounds, James Reeves, and Marianne Vestergaard for illuminating discussions, and the referee for a very thorough reading of the paper."
 Pheoretical astrophysics research at Leicester is supported by an STEC rolling grant., Theoretical astrophysics research at Leicester is supported by an STFC rolling grant.
eenerally zero. nor is it necessarily close to zero.,"generally zero, nor is it necessarily close to zero."
" Although many satellites in the Solar system are in state L with vanishinely small obliquity. (he Moon is in state 2 with 0=675."" Hlealiziug the planet as au oblate rigid body ou a circular ancl watlormly precessing orbit of inclination /=cos.!(kn). the Cassini obliquities 0; obey Here we have defined €=—9g/o. where g is the nodal precession frequency. and à is the spin precessional constant for a fixed orbit."," Although many satellites in the Solar system are in state 1 with vanishingly small obliquity, the Moon is in state 2 with $\theta=6\fdg5$ Idealizing the planet as an oblate rigid body on a circular and uniformly precessing orbit of inclination $I = \cos^{-1}(\hat{\mathbf
k}\cdot\hat{\mathbf n})$, the Cassini obliquities $\theta_i$ obey Here we have defined $\epsilon = -g / \alpha$, where $g$ is the nodal precession frequency and $\alpha$ is the spin precessional constant for a fixed orbit."
 The latter cau be written where C>B= Aare the planets principal moments of inertia. and w is its spin [requeucy.," The latter can be written where $C>B=A$ are the planet's principal moments of inertia, and $\omega$ is its spin frequency."
 During svuchronization. αἱ4n.," During synchronization, $\omega\rightarrow n$."
" When e<eqq=(sin£+cos’?E)""7. Eq. (3))"," When $\epsilon < \epsilon_{\rm crit} \equiv
(\sin^{2/3} I + \cos^{2/3} I)^{-3/2}$, Eq. \ref{eq:cassini-obliquity}) )"
 bas [| roots. corresponcdiug to the two stable states. 1 aud 2. ancl two uustable states. 3 aud {.," has 4 roots, corresponding to the two stable states, 1 and 2, and two unstable states, 3 and 4."
 For €>eoi. there are only. 2 roots. corresponding to states 2 aud 3.," For $\epsilon > \epsilon_{\rm crit}$, there are only 2 roots, corresponding to states 2 and 3."
 Eq. (3)), Eq. \ref{eq:cassini-obliquity}) )
 cau be derived from the governiug Hamiltonian wader the assumption of principal-axis rotation (see. e.g.. Ward 1975). where Hy is the s--incdepencdent portion.," can be derived from the governing Hamiltonian under the assumption of principal-axis rotation (see, e.g., Ward 1975), where ${\mathcal H}_0$ is the -independent portion."
 Fig., Fig.
 2 shows contours of H(s)) for au illustrative case., 2 shows contours of ${\mathcal H}$ ) for an illustrative case.
magnetohverodsnamies in similar two-dimensional collapse calculations and in one model. with a large initial magnetic ield. produced a jet with enough energv to power a *- burst but still with too much material in the jet to be accelerated to the required. velocity.,"magnetohydrodynamics in similar two-dimensional collapse calculations and in one model, with a large initial magnetic field, produced a jet with enough energy to power a $\gamma$ -ray burst but still with too much material in the jet to be accelerated to the required velocity."
 This is often called the xwvon loading problem., This is often called the baryon loading problem.
 Other numerical simulations. even hose that examine accretion on to black holes such as those w Porth&Fendt(2010).. have similar problems However jet xoduction and collimation is still far from fully understood (Lyubarsky2010:Ixomissarov.Vlahakis&Ixónigl.2010) and so we regard these models as promising rather than as creating an insurmountable problem with this scenario.," Other numerical simulations, even those that examine accretion on to black holes such as those by \citet{porth2010}, have similar problems However jet production and collimation is still far from fully understood \citep{lyubarsky2010,komissarov2010} and so we regard these models as promising rather than as creating an insurmountable problem with this scenario."
 To estimate the rate at which such systems would. give rise to LGRBs we have carried. out binary population synthesis with the code developed by Hurley.Pout&Pols (2002)., To estimate the rate at which such systems would give rise to LGRBs we have carried out binary population synthesis with the code developed by \citet{hurley2002}.
. Their standard. prescription for common envelope evolution is included., Their standard prescription for common envelope evolution is included.
 Their ace parameter. the efficiency of transferring orbital energy to the envelope during common envelope evolution. is set to 1.," Their $\alpha_{\rm CE}$ parameter, the efficiency of transferring orbital energy to the envelope during common envelope evolution, is set to 1."
 Though this parameter is very uncertain. we do not investigate its ellects in detail because the observed οταν burst rate is even more uncertain.," Though this parameter is very uncertain, we do not investigate its effects in detail because the observed $\gamma$ -ray burst rate is even more uncertain."
 At solar metallicity. Z=0.02. the range of possible initial separations that lead to the described systems. is narrow.," At solar metallicity, $Z = 0.02$, the range of possible initial separations that lead to the described systems is narrow."
 Their initial separations are mostly around 1000X 25]t..," Their initial separations are mostly around $1000\pm 25\,\rm R_\odot$ ."
 The precise range depends on the component masses of the system., The precise range depends on the component masses of the system.
 Ifthe svstem is too wide then either the third common envelope phase or the merging event is avoided., If the system is too wide then either the third common envelope phase or the merging event is avoided.
 Lf the system is too close the ONe white dwarl accretes enough material to collapse to a neutron star before the common envelope forms., If the system is too close the ONe white dwarf accretes enough material to collapse to a neutron star before the common envelope forms.
 The actual distribution of initial periods of binary stars is not well known., The actual distribution of initial periods of binary stars is not well known.
 A common practice is to assume the separation is uniform in logarithmic space (I5egeleton.Fitehett&Tout.1989)., A common practice is to assume the separation is uniform in logarithmic space \citep{eggleton1989}.
". With this assumption. only about ο610""7 of systems have suitable initial separations."," With this assumption, only about $5-6\times10^{-3}$ of systems have suitable initial separations."
 A second requirement is that one component must be massive enough to develop an ONe core., A second requirement is that one component must be massive enough to develop an ONe core.
 To do so its core must ignite carbon gently before reaching the Chandrasekhar limit anc become a super-asvmptotic giant branch (SAGB) star., To do so its core must ignite carbon gently before reaching the Chandrasekhar limit and become a super-asymptotic giant branch (SAGB) star.
 The mass boundaries for SAGB stars are not clear cut ancl depend. on different assumptions for convective overshooting (Poelarendsctal.2008)., The mass boundaries for SAGB stars are not clear cut and depend on different assumptions for convective overshooting \citep{poelarends2008}.
. The models used to construct the formulae used by Hurley.Pout&Pols(2002). include overshooting and hence give SAGD stars from initial masses 6.4.S.LM...," The models used to construct the formulae used by \citet{hurley2002} include overshooting and hence give SAGB stars from initial masses $6.4-8.1\,\rm M_\odot$."
 Phe fraction of SAGB stars is then around. 10.7. for a Ixroupa.Tout.&Gilmore(1993) initial mass function., The fraction of SAGB stars is then around $10^{-2}$ for a \citet{kroupa1993} initial mass function.
 The secondary must. then be within a suitable mass range for merging to take place., The secondary must then be within a suitable mass range for merging to take place.
 This range is less restricted. than that for the separations., This range is less restricted than that for the separations.
 For most of the svstems that lead to à z-rav burst. the mass ratio q ds between 0.6 anc 0.85.," For most of the systems that lead to a $\gamma$ -ray burst, the mass ratio $q$ is between 0.6 and 0.85."
 For a Hat. distribution of mass ratio about pper cent of the binary. svstems fall within this range., For a flat distribution of mass ratio about per cent of the binary systems fall within this range.
 Phere are also suitable systems with lower q but the range of suitable separations for these is much narrower., There are also suitable systems with lower $q$ but the range of suitable separations for these is much narrower.
 Our binary population svnthesis shows that the fraction of binary svstemis with at least one component of initial mass above (SAL. that evolve to give a 5-rav burst is of the order of 10.7.," Our binary population synthesis shows that the fraction of binary systems with at least one component of initial mass above $0.8\,\rm M_\odot$ that evolve to give a $\gamma$ -ray burst is of the order of $10^{-5}$."
 Typically one such binary system is formed in our own galaxy cach vear so this agrees well with the observed rarity of gamma-ray bursts., Typically one such binary system is formed in our own galaxy each year so this agrees well with the observed rarity of gamma-ray bursts.
 ‘Table 1 [ists the fractional rates for cülferent metallicity populations of binary stars., Table \ref{table1} lists the fractional rates for different metallicity populations of binary stars.
 As metallicity. decreases. our estimated rate cloes not. vary very much., As metallicity decreases our estimated rate does not vary very much.
 At a metallicity of Z=10* the frequency remains about the same for the same star-formation rate and initial mass function., At a metallicity of $Z=10^{-4}$ the frequency remains about the same for the same star-formation rate and initial mass function.
 The suitable initial primary mass shifts to 5.1<Alp/M.6.8 for an SAGBstar in this lower metallicity. environment. so the frequency of suitable initial primary mass increases even if the IME is unchanged.," The suitable initial primary mass shifts to $5.1 < M_1/\rm M_\odot <6.8$ for an SAGBstar in this lower metallicity environment, so the frequency of suitable initial primary mass increases even if the IMF is unchanged."
 Lowever. some of the low-q systems can no longer produce +-ray bursts because the total mass of the system when it merges is too low to trigger the accretion induced. collapse.," However, some of the $q$ systems can no longer produce $\gamma$ -ray bursts because the total mass of the system when it merges is too low to trigger the accretion induced collapse."
 Almost all the suitable systems have q greater than 0.6., Almost all the suitable systems have $q$ greater than 0.6.
 These two clleets at lower metallicity balance cach other out and hence the the fraction of binary systems that lead to bursts remains ofthe order of 10.7., These two effects at lower metallicity balance each other out and hence the the fraction of binary systems that lead to bursts remains of the order of $10^{-5}$.
 A different q clistribution which favoured the high q systems or a shift in the EME towards intermecdiate-mass stars would cause the frequeney of 5-ray bursts. to increase at low metallicity., A different $q$ distribution which favoured the high $q$ systems or a shift in the IMF towards intermediate-mass stars would cause the frequency of $\gamma$ -ray bursts to increase at low metallicity.
 Otherwise. our scenario shows that the 5-rav ourst rate does not have a high dependence of metallicity.," Otherwise, our scenario shows that the $\gamma$ -ray burst rate does not have a high dependence of metallicity."
 This would explain the observational deduction of Savaglio(2010) that the burst rate is proportional to the star ormation rate alone., This would explain the observational deduction of \citet{savaglio2010} that the burst rate is proportional to the star formation rate alone.
 Eryveretal.(1999) raised concerns about the amount of neutron-rich ejecta from accretion induced collapse events xluting the Galaxy., \citet{fryer1999} raised concerns about the amount of neutron-rich ejecta from accretion induced collapse events polluting the Galaxy.
 Observed abundances of r-process isotopes place a rather low limit on the rate of the events hey model., Observed abundances of $r$ -process isotopes place a rather low limit on the rate of the events they model.
" Dessartctal.(2007) agree ancl place a imiting rate of about 10.""[Evr ‘on their particular highly magnetic collapses. rising to 510νι for their. less magnetic cases."," \citet{dessart2007} agree and place a limiting rate of about $10^{-6}\rm\, yr^{-1}$ on their particular highly magnetic collapses, rising to $5\times 10^{-5}\,\rm yr^{-1}$ for their less magnetic cases."
 Given the uncertainties in the mocdels this is consistent with our GRB rate., Given the uncertainties in the models this is consistent with our GRB rate.
 Llowever we note that the accretion induced. collapse events considered. here. because hey take place within a hvdrogen-free. common envelope. are a rather special subset. of all such. events.," However we note that the accretion induced collapse events considered here, because they take place within a hydrogen-free common envelope, are a rather special subset of all such events."
 Indeed. the otal rate. predicted. in. population svnthesis. caleulations w LHurlev.“Vout&Pols (2002)... of at least. 10tye+ sugeests that the amount of neutron-rich material ejected by accretion induced. collapse of white dwarfs in general must xf somewhat smaller than found by Erveretal.(1999). and Dessartοἱal.(2007 )..," Indeed the total rate predicted in population synthesis calculations by \citet{hurley2002}, , of at least $10^{-4}\,\rm yr^{-1}$ suggests that the amount of neutron-rich material ejected by accretion induced collapse of white dwarfs in general must be somewhat smaller than found by \citet{fryer1999} and \citet{dessart2007}. ."
sky density is converted to an elfective change in a using an empirical relation which was chosen to ensure that the number density of galaxies is uniform when averaged over many UWS plates.,sky density is converted to an effective change in $\alpha$ using an empirical relation which was chosen to ensure that the number density of galaxies is uniform when averaged over many UKS plates.
 This correction will be generally applicable for other SB measurements. except for the mean isophotal surface brightness. fas.," This correction will be generally applicable for other SB measurements, except for the mean isophotal surface brightness, $\mu_{\rm iso}$."
 Since the threshold £/ is fixed in terms of observed APM density. the actual threshold isophote varies over cach field and a more complex correction would be required to ensure that fa. is uniform.," Since the threshold $t$ is fixed in terms of observed APM density, the actual threshold isophote varies over each field and a more complex correction would be required to ensure that $\mu_{\rm
iso}$ is uniform."
 Alost survey galaxies are located: within the central 3° radius of a UINST plate. and so the correction is very small. typically <0.1 magnitude.," Most survey galaxies are located within the central $3^\circ$ radius of a UKST plate, and so the correction is very small, typically $\leq 0.1$ magnitude."
 For galaxies outside this region the correction can increases up to 0.4 mag., For galaxies outside this region the correction can increases up to 0.4 mag.
 See figure 4 [or the pattern of averaged Zn of field correction.," See figure \ref{fig
vigmap} for the pattern of averaged $\triangle \mu_{1}$ of field correction."
 See the Ligures of Maddox et., See the figures of Maddox et.
 al (1990b) for further details., al (1990b) for further details.
 Figures 5((a) to (b) show that the field. correction slightly reduces. the cillerence between the SB measurements for those galaxies imaged on two independent, Figures \ref{fig_us409471}( (a) to (b) show that the field correction slightly reduces the difference between the SB measurements for those galaxies imaged on two independent
The last case we consider is magnetohydrodynamic instabilities. for which we apply the Tayler-Spruit dynamo (Spruit2002).,"The last case we consider is magnetohydrodynamic instabilities, for which we apply the Tayler-Spruit dynamo \citep{spr02}."
. In this picture. shearing stretches any small component of poloidal magnetic field into a strong toroidal field.," In this picture, shearing stretches any small component of poloidal magnetic field into a strong toroidal field."
 Once sufficiently large. the toroidal field initiates Tayler instabilities (non-axisymmetric.pinch-likeinstabili-tiesincludingstratification.Tayler1973:Spruit 1999).. which turbulently create poloidal field components that once again shear to be toroidal.," Once sufficiently large, the toroidal field initiates Tayler instabilities \citep[non-axisymmetric, pinch-like instabilities
including stratification,][]{tay73,spr99}, which turbulently create poloidal field components that once again shear to be toroidal."
 This cyele continues and results in a steady-state field that transmits angular momentum via Maxwell stresses., This cycle continues and results in a steady-state field that transmits angular momentum via Maxwell stresses.
 In the limit when the magnetic diffusivity. i. is much less than the thermal diffusivity. A. the minimum shear needed for this process to activate is (Spruit2002). =," In the limit when the magnetic diffusivity, $\eta$, is much less than the thermal diffusivity, $K$, the minimum shear needed for this process to activate is \citep{spr02}, =."
 When 0>dys ci. the effective viscosity due to the state magnetic fields is1/244)/2.," When $\sigma>\sigma_{\rm TS,crit}$ , the effective viscosity due to the steady-state magnetic fields is."
(45) We wait until the following section to present the shear associated with this process., We wait until the following section to present the shear associated with this process.
 We now calculate isothermal WD profiles and the shear profiles for the mechanisms described above., We now calculate isothermal WD profiles and the shear profiles for the mechanisms described above.
 Such models allow us to argue that is the most likely result., Such models allow us to argue that is the most likely result.
 The WD models are computed by solving for hydrostatic balance with the effects of spin ignored since we generally consider spins of the order of 0.1Oy.We solve for p using the analytic equation of state from Paezynski(1983)., The WD models are computed by solving for hydrostatic balance with the effects of spin ignored since we generally consider spins of the order of $0.1\Omega_{\rm K}$.We solve for $\rho$ using the analytic equation of state from \citet{pac83}.
. The importance of Coulomb interactions is measured by the parameter =1/3.(49) where A is the mass per ion and e is the 10n separation.," The importance of Coulomb interactions is measured by the parameter 		=, where $A$ is the mass per ion and $a$ is the ion separation."
 For the liquid phase. when |<Px: 173. we include the ionic free energy of Chabrier&Potekhin(1998).," For the liquid phase, when $1\le\Gamma\le173$ , we include the ionic free energy of \citet{cp98}."
". The composition is set to το, 'O. and Ne by mass."," The composition is set to $^{12}$ C, $^{16}$ O, and $^{22}$ Ne by mass."
 In Figure | we compare the shear rates found by calculating the effects of each viscous mechanism individually., In Figure \ref{fig:comparison} we compare the shear rates found by calculating the effects of each viscous mechanism individually.
" In addition. we plot the critical shear required for the Tayler-Spruit dynamo to be activated. s44, (eq. [41]."," In addition, we plot the critical shear required for the Tayler-Spruit dynamo to be activated, $\sigma_{\rm TS,crit}$ (eq. \ref{eq:sigmatscrit}] ])."
 All models use an isothermal temperature of 7;=105K and a WD mass of 1.37M.. (e.. near the eritical mass forcarbon ignition).," All models use an isothermal temperature of $T_i=10^8\ {\rm K}$ and a WD mass of $1.37\ M_\odot$ (i.e., near the critical mass forcarbon ignition)."
 We calculate oy using the approximation σκη~2N., We calculate $\sigma_{\rm KH}$ using the approximation $\sigma_{\rm KH}\approx2N$.
 Both ogc and σις are calculated by substituting their associated viscosities into equation (11)) and solving for the shear using Q-20.10&20.67 sand M2107M. yr., Both $\sigma_{\rm BC}$ and $\sigma_{\rm TS}$ are calculated by substituting their associated viscosities into equation \ref{eq:angularmomentum}) ) and solving for the shear using $\Omega=0.1\wk=0.67\ {\rm s^{-1}}$ and $\dot{M}=10^{-7}\ M_\odot\ {\rm yr^{-1}}$ .
 Though the structure of an accreting WD is not exactly isothermal due to the competition of compression and cooling (forexample.Nomoto1982).. we can still make many conclusions using our simple model.," Though the structure of an accreting WD is not exactly isothermal due to the competition of compression and cooling \citep[for example,][]{nom82}, we can still make many conclusions using our simple model."
 Both oxy and opc are consistent with what we estimated analytically., Both $\sigma_{\rm KH}$ and $\sigma_{\rm BC}$ are consistent with what we estimated analytically.
 In fact. oy has a value within a factor of a few of what Yoon&Langer(2004) found for detailed accreting models (see their Fig.7).," In fact, $\sigma_{\rm KH}$ has a value within a factor of a few of what \citet{yl04} found for detailed accreting models (see their Fig.7)."
 Our calculations demonstrate that the baroclinic instability does not allow the shear to grow sufficiently for the Kelvin-Helmholtz instability to ever be important., Our calculations demonstrate that the baroclinic instability does not allow the shear to grow sufficiently for the Kelvin-Helmholtz instability to ever be important.
 Since opc«Q. the WD should exhibit nearly solid body rotation.," Since $\sigma_{\rm BC}\ll\Omega$, the WD should exhibit nearly solid body rotation."
 Also. note that this is for ο20.1O&.," Also, note that this is for $\Omega=0.1\wk$."
 Larger spins result in even smaller shear since oyexO77 (eq. [37]])., Larger spins result in even smaller shear since $\sigma_{\rm BC}\propto\Omega^{-3/4}$ (eq. \ref{eq:sigmabc}] ]).
 This is because at higher © the relative amount of specific angular momentum in the disk versus the WD surface is smaller., This is because at higher $\Omega$ the relative amount of specific angular momentum in the disk versus the WD surface is smaller.
 We also consider the Tayler-Spruit dynamo mFigure .., We also consider the Tayler-Spruit dynamo inFigure \ref{fig:comparison}.
" The thermal diffusivity is given by K=l6os57?(3eign). where osx is the Stefan-Boltzmann constant. c, is the specific heat capacity at constant pressure. and # 1s theopacity."," The thermal diffusivity is given by $K =16\sigma_{\rm SB}T^3/(3c_p\kappa\rho^2)$, where $\sigma_{\rm SB}$ is the Stefan-Boltzmann constant, $c_p$ is the specific heat capacity at constant pressure, and $\kappa$ is theopacity."
 For the opacity we include electron-scattering (Paczynski 1983). free-free. and conductivecontributions (Schatzetal. 1999).," For the opacity we include electron-scattering \citep{pac83}, , free-free, and conductivecontributions \citep{sch99}."
. The magnetic diffusivity is set as 5=whiTc(1207 Ko). where KA. is the conductivity from Schatzetal. (1999).," The magnetic diffusivity is set as $\eta=\pi k_{\rm B}^2Tc^2/(12 e^2 K_c)$ , where $K_c$ is the conductivity from \citet{sch99}."
. The prescriptions given by Spruit(2002) imply aneven smaller shear rate than the baroclinic instability., The prescriptions given by \citet{spr02} imply aneven smaller shear rate than the baroclinic instability.
 Associated, Associated
 we use a model to simulate the observed Extreme Ultra Violet (EUW) emitted radiation [rom STEREO and SDO which has been applied successfully to the UV radiance fluctuation in (he «quiet Sun (Paululn Solanki 2007) and later to SUMMER observations of the corona in an active region (Dazarghan et al., we use a model to simulate the observed Extreme Ultra Violet (EUV) emitted radiation from STEREO and SDO which has been applied successfully to the UV radiance fluctuation in the quiet Sun (Pauluhn Solanki 2007) and later to SUMER observations of the corona in an active region (Bazarghan et al.
 2008)., 2008).
 This paper is organized as follow: STEREO/EUVI and SDO/ALA data analvsis are described in Section ??.., This paper is organized as follow: STEREO/EUVI and SDO/AIA data analysis are described in Section \ref{data}.
 The nanoflare model is treated in Section ??.., The nanoflare model is treated in Section \ref{model}.
 A kind of Artificial Neural Networks (Probabilistie Neural Network) is briefly discussed in Section +., A kind of Artificial Neural Networks (Probabilistic Neural Network) is briefly discussed in Section 4.
 In sections TT and ?? the method and results are presented., In sections \ref{method} and \ref{result} the method and results are presented.
 The conclusions are given in Section ??.., The conclusions are given in Section \ref{conc}.
 STEREO (Solar TErrestrial RElation Observatory) is the mission in NASA‘s Solar Terrestrial Probes program (STP) which has been launched on October 2006 probes solar active phenomena and dynamics., STEREO (Solar TErrestrial RElation Observatory) is the mission in NASA`s Solar Terrestrial Probes program (STP) which has been launched on October 2006 probes solar active phenomena and dynamics.
 It contains two identical observatories. one ahead (A) and the other behind (DB) of the orbit of the Earth.," It contains two identical observatories, one ahead (A) and the other behind (B) of the orbit of the Earth."
 Imaging the same events from two different locations enables us to have (liree dimensional images /))., Imaging the same events from two different locations enables us to have three dimensional images ).
 The Extreme Ultra Violet Bmager (EUVI) telescope is a part of SECCIIL instrument suite which is sensitive al 171À.. 195Α.. 284Α.. and 304A.," The Extreme Ultra Violet Imager (EUVI) telescope is a part of SECCHI instrument suite which is sensitive at 171, 195, 284, and 304."
. In the present work we restrict ourselves to 171. images with time cadence of 2.5 minutes (Wiieelser οἱ al., In the present work we restrict ourselves to 171 images with time cadence of 2.5 minutes (Wüeelser et al.
 2004)., 2004).
 The spatial pixel size of both A and D image is 1.6 are second., The spatial pixel size of both A and B image is 1.6 arc second.
 The SDO (Solar Dynamics Observatory) is designed to simultaneously. study the solar atmosphere al small scales of space and (ime and in many wavelengths, The SDO (Solar Dynamics Observatory) is designed to simultaneously study the solar atmosphere at small scales of space and time and in many wavelengths
distribution fuuction with mean given by the measured 1lagiucle aid siema by the magnitude error.,distribution function with mean given by the measured magnitude and sigma by the magnitude error.
 The actual photometric redshift error was calculated rol |LOO cliffereit realizations using tli algorithin., The actual photometric redshift error was calculated from 100 different realizations using this algorithm.
 For each different realization. a photometric redshift was calculated for every galaxy 1 he photometric redshift catalog.," For each different realization, a photometric redshift was calculated for every galaxy in the photometric redshift catalog."
 The acual error was oj»tinialy determiued to be giveu by tl 101inalized difference between the Liftl ald second quauties of he estimaecd redshift distributio or each individual galaxy (Bruunere/«al.1909a)., The actual error was optimally determined to be given by the normalized difference between the fifth and second quantiles of the estimated redshift distribution for each individual galaxy \citep{brunner99}.
. As expected the average estimated e‘ror is th argest at the up)per atd lower recdshil liniis where the iicomipleteness i he calibrating sample is most evident., As expected the average estimated error is the largest at the upper and lower redshift limits where the incompleteness in the calibrating sample is most evident.
" The majority of the res of the objects with extremely. E:‘oe redshift errors are plericecd in oue or riore uds. wlich causes these objects to be isolated from tie hieh deusity surface delineated by the majority of ga""maxles jn he four flux space£."," The majority of the rest of the objects with extremely large redshift errors are blended in one or more bands, which causes these objects to be isolated from the high density surface delineated by the majority of galaxies in the four flux space."
. The ellect these objects inipart Ollaiy subseqtent aualvsis. however. is miulinized yw the inclusiot of their photometric error. which causes tlie ntoberou-Iocalized in recsüt space.," The effect these objects impart on any subsequent analysis, however, is minimized by the inclusion of their photometric error, which causes them to be non-localized in redshift space."
 As a result. tjese objects provide a niuinal con‘ibution to talM7 “redshift bins” ratler thau st‘onlely biasing ouly a ew bins.," As a result, these objects provide a minimal contribution to many “redshift bins” rather than strongly biasing only a few bins."
 A subtle. ancl often overloosed. effect in auy plotometric redshift atalysis is the requirement or reliable potometry in all program filters.," A subtle, and often overlooked, effect in any photometric redshift analysis is the requirement for reliable photometry in all program filters."
 Ideally we woi obtain aceurate recsift estimates for all galaxies: Owever. sluce we ieed accurate. multi-od »l lometry iu order to reliably estimate 'ecshlifts. we uust place restricious ou the plotomeric Calaog used iu je analysis.," Ideally we would obtain accurate redshift estimates for all galaxies; however, since we need accurate, multi-band photometry in order to reliably estimate redshifts, we must place restrictions on the photometric catalog used in the analysis."
 In particular. we restrict 1e full sample of «etected sources to tlOse οjects which |ave both fay<2L0 aud ueasured maguitude errors «0.25 inΠ.," In particular, we restrict the full sample of detected sources to those objects which have both $I_{AB} < 24.0$ and measured magnitude errors $< 0.25$ in."
. This iminimizes any selectiou bias 10 ouly Laitul early-type galaxies at high. recshifts. or very high recdshi[t drop-out ojects (see for more discussion). nelther of which siguilicautly affect the rest of our analysis.," This minimizes any selection bias to only faint early-type galaxies at high redshifts, or very high redshift drop-out objects (see \citealt{brunner99} for more discussion), neither of which significantly affect the rest of our analysis."
 Due to the lower precision o ‘photometric redshift determination as compared to spectroscopic redshifts (roughv a [actor of 20). we have developed a new. statistica approach to quantifying the evolution of galaxies (Brinler1997:Connollyefal.1995:Brunnereb1999a).," Due to the lower precision of photometric redshift determination as compared to spectroscopic redshifts (roughly a factor of 20), we have developed a new, statistical approach to quantifying the evolution of galaxies \citep{myThesis,connolly98,brunner99}."
. This approach capitaizes on our ability to reliably generate not only a redsuli estimate [or a galaxy using broadbaink photometry. bt also a reliable redshift error estimate.," This approach capitalizes on our ability to reliably generate not only a redshift estimate for a galaxy using broadband photometry, but also a reliable redshift error estimate."
 Asa result. we celine the probability density function. P(z). for an individual galaxys redshift to je a Gaussian probability distribution fui‘don with mea (Hu) given by the estimated photometdc redshift aud staudard deviation (o) deiued by the estiuated error in the photometric redshift.," As a result, we define the probability density function, $P(z)$, for an individual galaxy's redshift to be a Gaussian probability distribution function with mean $\mu$ ) given by the estimated photometric redshift and standard deviation $\sigma$ ) defined by the estimated error in the photometric redshift."
 In order to 1ueasure an interestingOm Cosmologicale quantity. we egenerate multiple ensembles (or realizations) of the relevant. properties of the galaxy distribution using the statistical redshift aud," In order to measure an interesting cosmological quantity, we generate multiple ensembles (or realizations) of the relevant properties of the galaxy distribution using the statistical redshift and"
The light from the point source is spread over an area having a Pull Width Wall Maximum (EWLIIM) given by: The value is in eresec.,The light from the point source is spread over an area having a Full Width Half Maximum (FWHM) given by: The value is in $arcsec$.
 The amplitude of this elfect is independent of the pupil diameter., The amplitude of this effect is independent of the pupil diameter.
 The motion of the image. as a functionof A. telescope chameter (D) and ry. is given by: This motion is in aresee. and can be expressed in linear units (miclers) by means of the formulae: The latter effect is very important for the fluctuation of delay times.," The motion of the image, as a functionof $\lambda$, telescope diameter (D) and $r_{0}$, is given by: This motion is in $arcsec$, and can be expressed in linear units $meters$ ) by means of the formulae: The latter effect is very important for the fluctuation of delay times."
 One can calculate a new optical path as a function of this image motion. and then a new delay time (See Figure 2)).," One can calculate a new optical path as a function of this image motion, and then a new delay time (See Figure \ref{mot}) )."
" Figure 2. shows the optical path length in vacuum and the graphical representation (not to scale) of its We define OPL,—nj-OPL and OPLs=nOPL. where n, is calculated using the AMarini-\lurray model (sce Formula 3)) and. OPL through the Formula 4..."," Figure \ref{mot} shows the optical path length in vacuum and the graphical representation (not to scale) of its We define $OPL_{1}=n_{1}\cdot OPL$ and $OPL_{2}=n_{2}\cdot OPL$, where $n_{1}$ is calculated using the Marini-Murray model (see Formula \ref{index}) ) and $OPL$ through the Formula \ref{opl}."
 Phe dillerence between the previously calculated time ane this new one gives the Duetuation., The difference between the previously calculated time and this new one gives the fluctuation.
 Phe total motion is given by the formula: ‘This motion is <<OL. then we can calculate the new OPL through the formula: where: 1n this Section we calculate the celay time Fluctuation.," The total motion is given by the formula: This motion is $<<OPL$, then we can calculate the new OPL through the formula: where: In this Section we calculate the delay time fluctuation."
 Lt is due to two contributions: one correction is due to the change in photon path (gcometric). and the other (physical) is due to the faet that the photon is traveling in à medium where the refractive index is changed.," It is due to two contributions: one correction is due to the change in photon path (geometric), and the other (physical) is due to the fact that the photon is traveling in a medium where the refractive index is changed."
" The delay time (οο(ο. 2)) due only to the geometric variation of the OPL is given by: ‘Through this new time we get the geometric [Ductuation of the delay time ολους.D): ‘Taking into account that: we obtain the following Formula: In this Section. we calculate the clelay time (f2,p(ro. D2)) due to the physical variation of the atmosphere."," The delay time $t_{2,G}(r_{0},D)$ ) due only to the geometric variation of the OPL is given by: Through this new time we get the geometric fluctuation of the delay time $\Delta t_{G}(r_{0},D)$: Taking into account that: we obtain the following formula: In this Section, we calculate the delay time $t_{2,P}(r_{0},D)$ ) due to the physical variation of the atmosphere."
 In the previous section we saw how the OPL changes due to the atmosphere (image motion)., In the previous section we saw how the OPL changes due to the atmosphere (image motion).
 Phe change in OPL also induces a change in the refractive index., The change in OPL also induces a change in the refractive index.
 In fact. lluctuations in optical path length must correspond to refractive angle variations.," In fact, fluctuations in optical path length must correspond to refractive angle variations."
 We can calculate the refractive angle Uuctuation assuming the atmosphere uniform clistribution: The corresponding atmospheric refractive index ne. obtained by Snell's law. is: refractive. index is a function of ry and the telescope diamoeter(D).," We can calculate the refractive angle fluctuation assuming the atmosphere uniform distribution: The corresponding atmospheric refractive index $n_{2}$ , obtained by Snell's law, is: This refractive index is a function of $r_{0}$ and the telescope $D$ )."
"data, whilst mareinally consistent with theirs. indicate no additional enhancement.","data, whilst marginally consistent with theirs, indicate no additional enhancement."
 We now explore how the two-dimensional line-streugth maps coustrain the star formation Listory of both the main body aud the core of 11365., We now explore how the two-dimensional line-strength maps constrain the star formation history of both the main body and the core of 4365.
 There is a dramatic difference in the kinematics of the two regious of the galaxy. but other properties sugeest that 1365 is anormal elliptical galaxy aud that the core aud main body hada commnon star formation history.," There is a dramatic difference in the kinematics of the two regions of the galaxy, but other properties suggest that 4365 is a normal elliptical galaxy and that the core and main body had a common star formation history."
 Furthermore. the Ἱν-baud surface brightness fluctuations iu 11365 place it amonest the old metalrich ellipticals (Jensen.Toury.&Luppiuo 1995).," Furthermore, the K-band surface brightness fluctuations in 4365 place it amongst the old metal-rich ellipticals \citep{jtl1998}."
 The elevated. maguesmnito-dronun ratio is roughly constant across the cutive galaxy (a region of [42 kpc)., The elevated magnesium-to-iron ratio is roughly constant across the entire galaxy (a region of $\times$ 3 kpc).
 Such nou-solar abundance ratios arise in populations chviched primarily with the products of Type IT supernovac. cither in a rapid initial burst of star formation or one skewed to massive stars (Worthey1998).," Such non-solar abundance ratios arise in populations enriched primarily with the products of Type II supernovae, either in a rapid initial burst of star formation or one skewed to massive stars \citep{wor1998}."
. The uuiformity of the elevated masuesiuni-to-ron ratio also sugeests that the whole ealaxv experienced a common star formation history. involving considerable gaseous dissipation. thus generating the high central metallicity and inward inetallieitv eradicut.," The uniformity of the elevated magnesium-to-iron ratio also suggests that the whole galaxy experienced a common star formation history, involving considerable gaseous dissipation, thus generating the high central metallicity and inward metallicity gradient."
 A possible formation scenario would be the mereer of gas-rich fragments at lugh redshift., A possible formation scenario would be the merger of gas-rich fragments at high redshift.
 Such an event would be modest compared to the rates of star formation inferred for high-redshift sub-nullimeter ealaxies (e.g.Ivisonotal.2000)., Such an event would be modest compared to the rates of star formation inferred for high-redshift sub-millimeter galaxies \citep[\eg][]{ivi2000}.
. The decoupled core could originate from stars ejected into a tidal tail (ith the appropriate augular nonieutuni) as a result of a major merger that formed the bulk of the stars., The decoupled core could originate from stars ejected into a tidal tail (with the appropriate angular momentum) as a result of a major merger that formed the bulk of the stars.
 These stars fall back to produce the kinematically distinct component at the ceutroe., These stars fall back to produce the kinematically distinct component at the centre.
 If star formation was taken to completion aud the residual eas exhausted roughly 12 Gyr ago. then the decoupled Kinematic structure in [1365 αι be long-lived.," If star formation was taken to completion and the residual gas exhausted roughly 12 Gyr ago, then the decoupled kinematic structure in 4365 must be long-lived."
 The muisalieuuieut of the kinematic ancl photometric axes show that the main body of the galaxy is triaxial. with the bulk of its stars on loug-axis tubes aud the stars in the core predominantly ou short-axis tubes (Statler1991:Arnold.deZeeuw.&ITIunter199 D..," The misalignment of the kinematic and photometric axes show that the main body of the galaxy is triaxial, with the bulk of its stars on long-axis tubes and the stars in the core predominantly on short-axis tubes \citep{sta1991,azh1994}. ."
 This is simular to the structure inferred for. 11261 (Davies&Birkiushaw1986). and LLLOG (Frans.Ilusworth.&Deckman1989).," This is similar to the structure inferred for, 4261 \citep{db1986}
 and 4406 \citep*{fih1989}."
. The full two- structure and kinematics derived from the ddata. when combined with our dvuunuical models (seee.g...Crettonetal.1999)... will enable us to distinguish between a thin disk or a thick structure for the core.," The full two-dimensional structure and kinematics derived from the data, when combined with our dynamical models \citep[see \eg\/][]{cre1999}, will enable us to distinguish between a thin disk or a thick structure for the core."
 The nuiuaps preseut ai complete view of the kinematics and stellar populations of 11365., The maps present a complete view of the kinematics and stellar populations of 4365.
 They show two iudepeudeut kinematic subsystems: the ceutral 2009τοῦ pe and the main body of the ealaxy. rotating almost at right angles to each other.," They show two independent kinematic subsystems: the central $300 \times 700$ pc and the main body of the galaxy, rotating almost at right angles to each other."
 The misalignment of 827 between the photometric aud kinematic axes of the main body is unambigous evidence of txiaxialitv., The misalignment of $82^{\circ}$ between the photometric and kinematic axes of the main body is unambigous evidence of triaxiality.
 The nuuaps euable us to compare the stellar population iu the decoupled component with that in the main body of the galaxy at the sae radius., The maps enable us to compare the stellar population in the decoupled component with that in the main body of the galaxy at the same radius.
 We fined these populations to be inclistinemshable iu age. mictallicity aud abundance ratios.," We find these populations to be indistinguishable in age, metallicity and abundance ratios."
 We find an age of zLE Cyr aud a decrease in metallicity. from larger than solar iu the center to half solar at a radius of 2 kpc (2Lr).," We find an age of $\approx$ 14 Gyr and a decrease in metallicity, from larger than solar in the center to half solar at a radius of 2 kpc $\approx0.4 \, r{_e}$ )."
 We sugeest that 115365 uuderwent dissipative star formation at ligh redshift. probably through oue or more mergers.," We suggest that 4365 underwent dissipative star formation at high redshift, probably through one or more mergers."
 Later eeucrations of stars formed a more cenutrall-conceutrated. mietal-eunrched stellar population.," Later generations of stars formed a more centrally-concentrated, metal-enriched stellar population."
 Star formation was complete and the residual eas was exhausted roughly 12 Cor ago., Star formation was complete and the residual gas was exhausted roughly 12 Gyr ago.
 This also suggests that the observed kinematics aud triaxial structure is stable., This also suggests that the observed kinematics and triaxial structure is stable.
 It is a pleasure to thank Rene Rutten aud the ING staff. in particular Tom Cregory. for support on La Pahua.," It is a pleasure to thank Rene Rutten and the ING staff, in particular Tom Gregory, for support on La Palma."
 We thauk Richard MeDoeriid for assistance during the observing run., We thank Richard McDermid for assistance during the observing run.
" The project is made possible through grants 611.123.003 and 781.701.203 from ASTRON/NWO. PPARC eraut “Extragalactic Astronomy Cosmology at Dirham 1998-2002"" and financial contributions frou the LIustitut National des Sciences de PUuivers. the Université Claude Bernard Lyon L together with the universities of Durhamand Leiden."," The project is made possible through grants 614.13.003 and 781.74.203 from ASTRON/NWO, PPARC grant “Extragalactic Astronomy Cosmology at Durham 1998-2002” and financial contributions from the Institut National des Sciences de l'Univers, the Université Claude Bernard Lyon I, together with the universities of Durhamand Leiden."
 RED eratetully acknowledges the award of a Research Fellowship from the Leverluliue Trust., RLD gratefully acknowledges the award of a Research Fellowship from the Leverhulme Trust.
" Mj. Neptune"" of mass 0.08 Mj, and radius 0.42 δι on an eccentric. 4.9-day orbit around à K4 dwarf (Bakos et al."," $M_{\rm Jup}$ Neptune” of mass 0.08 $M_{\rm Jup}$ and radius 0.42 $R_{\rm Jup}$ on an eccentric, 4.9-day orbit around a K4 dwarf (Bakos et al."
 2010: B10 hereafter)., 2010; B10 hereafter).
 We observed the Rossiter-McLaughlin (RM) effect 2). and modeled it 3). finding the orbit and stellar spin to be misaligned 4).," We observed the Rossiter-McLaughlin (RM) effect 2), and modeled it 3), finding the orbit and stellar spin to be misaligned 4)."
 We obtained 132 new spectra of HAT-P-11 with the High Resolution Spectrograph (HIRES: Vogt et al., We obtained 132 new spectra of HAT-P-11 with the High Resolution Spectrograph (HIRES; Vogt et al.
 1994) on the Keck I lOm telescope., 1994) on the Keck I 10m telescope.
 Most of the new spectra were gathered on nights when transits were predicted., Most of the new spectra were gathered on nights when transits were predicted.
 On 2009 Aug 2/3 we gathered 7 spectra during a transit. although fog prevented us from observing before or after the transit.," On 2009 Aug 2/3 we gathered 7 spectra during a transit, although fog prevented us from observing before or after the transit."
 On 2010 May 26/27 we obtained 32 spectra starting at around first contact and extending for a few hours beyond the transit., On 2010 May 26/27 we obtained 32 spectra starting at around first contact and extending for a few hours beyond the transit.
 On 2010 Aug 22/23 we obtained 70 spectra spanning the entire transit and a few hours beforehand and afterward., On 2010 Aug 22/23 we obtained 70 spectra spanning the entire transit and a few hours beforehand and afterward.
 The remaining 23 spectra were obtained sporadically throughout the 2009-2010 observing season., The remaining 23 spectra were obtained sporadically throughout the 2009–2010 observing season.
 We used the instrument settings and observing procedures that are standard for the California Planet Search (Howard et al., We used the instrument settings and observing procedures that are standard for the California Planet Search (Howard et al.
 2009)., 2009).
 In particular. we used an todine gas absorption cell to track the instrumental response and wavelength scale.," In particular, we used an iodine gas absorption cell to track the instrumental response and wavelength scale."
 The radial velocity (RV) of each spectrum was measured with respect to an iodine-free template spectrum. using a descendant of the algorithm of Butler et al. (," The radial velocity (RV) of each spectrum was measured with respect to an iodine-free template spectrum, using a descendant of the algorithm of Butler et al. ("
2006).,2006).
 Measurement errors were estimated from the scatter among the fits to individual spectral segments spanning a few Angstroms., Measurement errors were estimated from the scatter among the fits to individual spectral segments spanning a few Angstroms.
 Table | gives all the Keck/HIRES RVs. including re-reductions of the 50 spectra presented by B10.," Table 1 gives all the Keck/HIRES RVs, including re-reductions of the 50 spectra presented by B10."
 Merging all the RVs into a single analysis requires some care because the host star 1s chromospherically active., Merging all the RVs into a single analysis requires some care because the host star is chromospherically active.
 BIO found a photometric signal with period 29.2. days and amplitude 3 mmag. which they attributed to starspots being," B10 found a photometric signal with period 29.2 days and amplitude 3 mmag, which they attributed to starspots being"
"against the observed column density dependence of atomic and molecular gas fractions in the Milky Way, LMC, and SMC (see Appendix).","against the observed column density dependence of atomic and molecular gas fractions in the Milky Way, LMC, and SMC (see Appendix)."
" In particular, the model reproduces the metallicity dependence of the column density of the sharp transition from the atomic to fully molecular gas observed in the MW, LMC, and SMC."," In particular, the model reproduces the metallicity dependence of the column density of the sharp transition from the atomic to fully molecular gas observed in the MW, LMC, and SMC."
" In order to investigate the environmental dependence of the star formation rate in the simulations, we perform a series of controlled test simulations."," In order to investigate the environmental dependence of the star formation rate in the simulations, we perform a series of controlled test simulations."
" For each of these tests, we fix the dust-to-gas ratio in the Hz model and normalization of the of stellar particles at 1000À to constant values and run the emissivitysimulations for a significant period of time."," For each of these tests, we fix the dust-to-gas ratio in the $\H2$ model and normalization of the emissivity of stellar particles at $1000\ \AA$ to constant values and run the simulations for a significant period of time."
 We explore a grid of values of dust-to-gas ratio Dyw from 107 to 1.0 relative to the Milky Way value., We explore a grid of values of dust-to-gas ratio $\D$ from $10^{-3}$ to $1.0$ relative to the Milky Way value.
" The variable Dyw scales the H5 on dust formation rate coefficient Rp and the absorption cross-section of dust in the Lyman-Werner band Ow to the values characteristic for the Milky Way: where Ro=3.5107!”cm?s! anda=2x10?!cm?(?2),, respectively."," The variable $\D$ scales the $_2$ on dust formation rate coefficient $R_D$ and the absorption cross-section of dust in the Lyman-Werner band $\sigma_{\rm LW}$ to the values characteristic for the Milky Way: where $R_0=3.5\times 10^{-17}\rm\ cm^3\, s^{-1}$ and $\sigma_0=2\times 10^{-21}\rm\ cm^2$, respectively."
" The normalization of interstellar FUV flux at 1000A: used throughout this paper, is also defined to be in the units of the typical Milky Way value Juw=10°photonscm""?s!ster!eV! (?2).."," The normalization of interstellar FUV flux at $1000\ \AA$: used throughout this paper, is also defined to be in the units of the typical Milky Way value $J_{\rm
MW}=10^6\dim{photons}\,\dim{cm}^{-2}\,\dim{s}^{-1}\,\dim{ster}^{-1}\,\dim{eV}^{-1}$ ."
 We explore the range of Umw from 0.1 to 100 in our test simulations., We explore the range of $\U$ from $0.1$ to $100$ in our test simulations.
 The star formation model in our simulations closely follows therecipe2 of with small numerical modifications., The star formation model in our simulations closely follows the recipe 2 of with small numerical modifications.
" Namely, the rate of star formation in each computational cell with molecular fraction fy,>0.1 is evaluated as where the time scale for star formation is defined as Tsp Tmax)."," Namely, the rate of star formation in each computational cell with molecular fraction $f_{\rm H_2}\geq 0.1$ is evaluated as where the time scale for star formation is defined as $\tau_{\rm SF} =
\min(\tau_{\rm ff},\tau_{\max})$ ."
" We follows the definition of for the gas time, (here p is the total mass density, including helium), and Tmax is the free-fall time in the gas with Πας=50cm"," We follows the definition of for the gas free-fall time, (here $\rho$ is the total mass density, including helium), and $\tau_{\max}$ is the free-fall time in the gas with $n_{\rm SF}=50\dim{cm}^{-3}$."
" We adopt ésr=0.005, which is lower than the value we 2,adopted in and is still within the range of values advocated by?."," We adopt $\epsilon_{\rm SF} = 0.005$, which is lower than the value we adopted in and is still within the range of values advocated by."
. The lower value of esr that we adopt provides a better fit the THINGS measurements of the KS relation(?)., The lower value of $\epsilon_{\rm SF}$ that we adopt provides a better fit the THINGS measurements of the KS relation.
". The τει we adopt assumes that in low density cells, in which molecular fraction fy, is below unity, star formation proceeds in unresolved molecular clouds on scales."," The $\tau_{\rm sf}$ we adopt assumes that in low density cells, in which molecular fraction $f_{\H2}$ is below unity, star formation proceeds mainly in unresolved molecular clouds on subgrid scales."
 This mainlyassumption then also motivates setting the subgridmaximum free fall time to Tmax corresponding to the number density of 50cm? typical average density of molecular clouds.," This assumption then also motivates setting the maximum free fall time to $\tau_{\rm max}$ corresponding to the number density of $50\,\,\rm
cm^{-3}$ typical average density of molecular clouds."
" The fu,«1 in these cells then can be viewed as reflecting the fraction of the total gas in such star forming molecular clouds, which themselves have fu,—1, rather than incomplete conversion of the atomic gas into the molecular form inside the clouds."," The $f_{\H2}<1$ in these cells then can be viewed as reflecting the fraction of the total gas in such star forming molecular clouds, which themselves have $f_{\H2}=1$, rather than incomplete conversion of the atomic gas into the molecular form inside the clouds."
 As we show below (see Fig., As we show below (see Fig.
[/| and discussion in H4). the KS relation in our simulations is not very sensitive to variations of esp between 0.005 and 0.01 and nsp between 10 and 50 cm.," \ref{fig:sflpars1} and discussion in \ref{sec:sfl}) ), the KS relation in our simulations is not very sensitive to variations of $\epsilon_{\rm SF}$ between $0.005$ and $0.01$ and $n_{\rm SF}$ between $10$ and $50\,\,\rm cm^{-3}$ ."
" The effect of two primary the ratio Dmw and the interstellar FUVparameters, flux Uww, ondust-to-gas the transition from atomic to molecular gas is illustrated in Figure [I] as a function of the total hydrogen density, ny=ng+Nyy2ng, (the contribution of ionized gas ng is negligible for densities shown in Figure [I))."," The effect of two primary parameters, the dust-to-gas ratio $\D$ and the interstellar FUV flux $\U$, on the transition from atomic to molecular gas is illustrated in Figure \ref{fig:fh2den} as a function of the total hydrogen density, $n_\Ht \equiv n_\HI + n_\HII + 2n_\H2$ (the contribution of ionized gas $n_\HII$ is negligible for densities shown in Figure \ref{fig:fh2den}) )."
" As can be seen from the figure, both parameters affect the atomic-to-molecular transition in a non-trivial way."," As can be seen from the figure, both parameters affect the atomic-to-molecular transition in a non-trivial way."
 This scaling can be understood approximately if we ignore all physical processes except the formation of molecular hydrogen on dust and dissociation of molecular hydrogen the UV radiation in the band., This scaling can be understood approximately if we ignore all physical processes except the formation of molecular hydrogen on dust and dissociation of molecular hydrogen by the UV radiation in the Lyman-Werner band.
" This is bynecessarily an approximation, Lyman-Werneras many other processes are indeed important for the detailed balance of molecular hydrogen (see Appendix), but the formation on dust and photo-dissociation are the dominant processes that control the atomic-to-molecular gas transition under normal ISM conditions."," This is necessarily an approximation, as many other processes are indeed important for the detailed balance of molecular hydrogen (see Appendix), but the formation on dust and photo-dissociation are the dominant processes that control the atomic-to-molecular gas transition under normal ISM conditions."
" In this approximation, the equilibrium abundance of molecular hydrogen can be determined from the balance of the formation and dissociation rates (cf."," In this approximation, the equilibrium abundance of molecular hydrogen can be determined from the balance of the formation and dissociation rates (cf."
 Appendix) where I1w=Uwwl? is the free space photo-destruction rate and Rp and ciw are given by Equation (1)., Appendix) where $\Gamma_{\rm LW}=\U\Gamma_0$ is the free space photo-destruction rate and $R_D$ and $\sigma_{\rm LW}$ are given by Equation \ref{eq:pardefs}) ).
 The atomic gas becomes molecular only due to self-shielding and shielding by dust (the last two factors on the left-hand-side of Equation , The atomic gas becomes molecular only due to self-shielding and shielding by dust (the last two factors on the left-hand-side of Equation \ref{eq:h2bal}) )).
"If the FUV flux is not too strong, the self- by (3))).molecular hydrogen dominates; in this limit dust absorption can be neglected and Equation (3)) becomes where fu,=ΠΗ,/ΠΗ and we ignore ionized gas."," If the FUV flux is not too strong, the self-shielding by molecular hydrogen dominates; in this limit dust absorption can be neglected and Equation \ref{eq:h2bal}) ) becomes where $f_\H2 \equiv n_\H2/n_\Ht$ and we ignore ionized gas."
" For our ansatz for theself-shielding factor Sy,«n3/4 (Equation (AT1))). so that Thus, the characteristic density at which molecular hydrogen fraction reaches a particular value (e.g., 50%))"," For our ansatz for theself-shielding factor $S_\H2 \propto n_\H2^{-3/4}$ (Equation \ref{eq:sh2}) )), so that Thus, the characteristic density at which molecular hydrogen fraction reaches a particular value (e.g., )"
general coincidence.,general coincidence.
 However the detailed correspondence between Εν. Wa. aud eenission is ore complicated.," However the detailed correspondence between FUV, $\alpha$, and emission is more complicated."
 To illustrate this richucss of detail. we preseut aud discuss the images in 5 fields positioned as iudicated in Fig...," To illustrate this richness of detail, we present and discuss the images in 5 fields positioned as indicated in \ref{fullgal}. ."
 In refficldouc--6.. we show for cach field first the contours of the FUV euissiou overlaid on a exev-scale represcutation of itself. then overlaid ou the Wa. aud finally ou the eenission.," In \\ref{fieldone}- \ref{fieldfive}, we show for each field first the contours of the FUV emission overlaid on a grey-scale representation of itself, then overlaid on the $\alpha$, and finally on the emission."
 Iu cach middle panel we also mark the B- baud dust filaments of Ikaufiiai. Elincercen Bash (1989b).," In each middle panel we also mark the $B$ -band dust filaments of Kaufman, Elmegreen Bash (1989b)."
 Dust in the Galaxy is unevenly distributed. aud the continui extinction at À2150 nni ds about { times that at visual waveleugths.," Dust in the Galaxy is unevenly distributed, and the continuum extinction at $\lambda \approx 150$ nm is about 4 times that at visual wavelengths."
 Therefore the FUV image ought to show significantly more small-scale structure than the ITo image., Therefore the FUV image ought to show significantly more small-scale structure than the $\alpha$ image.
" Instead. the opposite occurs: the FUY cussion is smoother and spread more widely than the Ta. as can be seen from a comparison of the “FUV-on-FUWand ""CEUV-on-He panels in reffiicldonc--6.."," Instead, the opposite occurs; the FUV emission is smoother and spread more widely than the $\alpha$ , as can be seen from a comparison of the “FUV-on-FUV”and $\alpha$ ” panels in \\ref{fieldone}- \ref{fieldfive}."
 There are two aspects to this unexpected IHa-FUV correspondence., There are two aspects to this unexpected $\alpha$ -FUV correspondence.
 First. every reliable bright peak iu the Πα has a counterpart in the FUV.," First, every reliable bright peak in the $\alpha$ has a counterpart in the FUV."
 Second. there are niauiv places with extended aud relatively intense FUV cinission which have little or no associated Ia.," Second, there are many places with extended and relatively intense FUV emission which have little or no associated $\alpha$."
 The fact that every reliable bright peak in the IIa has a counterpart in the FPUV aust mean that the effects of extinction on the morphology are simall ou the scale of 150 pe. so that either both the Wa aud the FUV appear either esscutially unobscured. or both are partly hidden in approximately the same way.," The fact that every reliable bright peak in the $\alpha$ has a counterpart in the FUV must mean that the effects of extinction on the morphology are small on the scale of 150 pc, so that either both the $\alpha$ and the FUV appear either essentially unobscured, or both are partly hidden in approximately the same way."
 The extinction may also be so high thatneither the FUYnor the Hà arevisible?., The extinction may also be so high that the FUV the $\alpha$ are.
. There are a few reeiousOo which appear to cuit relatively strong Ta but do not have a counterpart in FUV., There are a few regions which appear to emit relatively strong $\alpha$ but do not have a counterpart in FUV.
" Such regions are for mstauce located at(01021105, (in the middle of a UV void in Field 1). at095509337, (linear structure 307 lone in Field 3). or at09550367. (inall crescent-shaped object iu Field 3)."," Such regions are for instance located at, (in the middle of a UV void in Field 1), at, (linear structure $\sim 30''$ long in Field 3), or at, (small crescent-shaped object in Field 3)."
 However. none of these Ia features appear on the older Ia inage of Kaufinan et (198928) (not shown here). confirming that these features on the Devereux ct Ilo image are most probably not rregious at all. but artifacts such as (s1ioothed) cosmic ray eveuts or iproporly-subtracted foreeround," However, none of these $\alpha$ features appear on the older $\alpha$ image of Kaufman et (1989a) (not shown here), confirming that these features on the Devereux et $\alpha$ image are most probably not regions at all, but artifacts such as (smoothed) cosmic ray events or improperly-subtracted foreground."
 While every reliable bright peak ou the Πα image has a counterpart in the FUV image with the same position and general shape. there are many places with extended aud relatively iuteuse Εν cussion which have little or no associated Πα.," While every reliable bright peak on the $\alpha$ image has a counterpart in the FUV image with the same position and general shape, there are many places with extended and relatively intense FUV emission which have little or no associated $\alpha$ ."
" There are even regions of relatively bright FUV cussion. such as those at107, (Field 1). aud09251037. (Field 1). which slow hardly auy counterparts in IIo at the present levels of scusitivity."," There are even regions of relatively bright FUV emission, such as those at, (Field 1), and, (Field 4), which show hardly any counterparts in $\alpha$ at the present levels of sensitivity."
 Iu principle. some of these UV sources could be artifacts on the UIT FUV nmuage.," In principle, some of these UV sources could be artifacts on the UIT FUV image."
 There are five kinds of artifacts in the UIT data which could be iuportaut for us: 1) There are oue or two bright spots in each CIT camera: they occur within 200 pixels of the edee of the image., There are five kinds of artifacts in the UIT data which could be important for us: 1) There are one or two bright spots in each UIT camera; they occur within 200 pixels of the edge of the image.
 The M81 nuage is in the ceutral parts of the field. so we are uot concerned with these artifacts.," The M81 image is in the central parts of the field, so we are not concerned with these artifacts."
 2)Rays: These are rare on UIT images. rangiug from none to several per tage.," 2) These are rare on UIT images, ranging from none to several per image."
 They are always very bright. saturated. aud exteuded blobs which do not look like stars.," They are always very bright, saturated, and extended blobs which do not look like stars."
 The fullacsolution UCIT FUV. frame we have used does not appear to have such features., The full-resolution UIT FUV frame we have used does not appear to have such features.
 3)Stars: Typically there are one or two UV-bright Galactic foreground stars in cach CIT field at the intermediate Galactic latitudes of ADSI., 3) Typically there are one or two UV-bright Galactic foreground stars in each UIT field at the intermediate Galactic latitudes of M81.
 These are mostly V z11 mag A stars. so they are bright iu optical CC'D images.," These are mostly V $\approx 11$ mag A stars, so they are bright in optical CCD images."
 Again. there are no such stars known within the optical image of MBI.," Again, there are no such stars known within the optical image of M81."
 1)Seratehes: The CIT detector is photographic filam. and scratches ean appear on it from the handling aud developing processes.," 4) The UIT detector is photographic film, and scratches can appear on it from the handling and developing processes."
 These are visible at faint levels. but are casily recognizable as long narrow parallel lues.," These are visible at faint levels, but are easily recognizable as long narrow parallel lines."
 Smoothing will reduce their impact. aud our AISI nuage does not show the effects of scratches.," Smoothing will reduce their impact, and our M81 image does not show the effects of scratches."
 5)Specks: During deusitometry of the flight film in a clean room environment. some dustcontamination still appears.which ninmnices stars.," 5) During densitometry of the flight film in a clean room environment, some dustcontamination still appears,which mimics stars."
 Since only the larger, Since only the larger
quickly decreased {ο almost zero about 9 minutes later.,quickly decreased to almost zero about 9 minutes later.
 For the wave front. it also accelerated to the lateral velocity of 960 km | at 06:27. UT. but the lateral velocity only decreased (o ~600 kms ! in the next nine minutes.," For the wave front, it also accelerated to the lateral velocity of 960 km $^{-1}$ at $\sim$ 06:27 UT, but the lateral velocity only decreased to $\sim$ 600 km $^{-1}$ in the next nine minutes."
 Moreover. the wave traversed the nearby AR and continued to propagate at the velocity of ~G600 km ' (squares in Figure 5((a)) 2011).," Moreover, the wave traversed the nearby AR and continued to propagate at the velocity of $\sim$ 600 km $^{-1}$ (squares in Figure \ref{f4}( (a)) \citep[see also,][]{li11}."
. The apparent lateral propagation of the CME bubble and the wave at the heliocentric height of 1.05 2. is similar to (hat at 1.15. Ro., The apparent lateral propagation of the CME bubble and the wave at the heliocentric height of 1.05 $R_\odot$ is similar to that at 1.15 $R_\odot$.
 At 06:26 UT. both of them obtained the peak lateral velocity of 7880 kms |.," At $\sim$ 06:26 UT, both of them obtained the peak lateral velocity of $\sim$ 880 km $^{-1}$."
 However. alter 06:26 UT. the lateral velocity of the bubble front rapidly decreased. while (he wave front only decreased to 7600 kins HL," However, after $\sim$ 06:26 UT, the lateral velocity of the bubble front rapidly decreased, while the wave front only decreased to $\sim$ 600 km $^{-1}$."
 Similarly. the wave front at the heliocentric height of 0.95 R. accelerated [rom 150 km hat “06:18 to 8380 km | —06:25. and afterwards propagated freely with a velocity larger than 7600 km 1," Similarly, the wave front at the heliocentric height of 0.95 $R_\odot$ accelerated from 150 km $^{-1}$ at $\sim$ 06:18 to 830 km $^{-1}$ $\sim$ 06:25, and afterwards propagated freely with a velocity larger than $\sim$ 600 km $^{-1}$."
 Apparently. in the early evolution stage immediately. following the eruption onset. the wave [ront can not be cliscerned [rom the CME bubble front. indicating that the wave front is süll undergoing compression from (the expaucing bubble.," Apparently, in the early evolution stage immediately following the eruption onset, the wave front can not be discerned from the CME bubble front, indicating that the wave front is still undergoing compression from the expanding bubble."
 The standolf distance between the two [ronts is almost zero., The standoff distance between the two fronts is almost zero.
 Both of them obtain the maximum lateral velocity. at the same time., Both of them obtain the maximum lateral velocity at the same time.
 When the CAIE bubble starts to decrease the velocity. the wave front starts to separate and propagate away [rom its driver.," When the CME bubble starts to decrease the velocity, the wave front starts to separate and propagate away from its driver."
 From Figure 5.. one can notice (hat the wave front has different peak lateral velocities at different heliocentric height.," From Figure \ref{f4}, one can notice that the wave front has different peak lateral velocities at different heliocentric height."
 The wave's lateral peak velocities increase with the heliocentric heights: the corresponding peak times of the velocities also delay with respect (o the increasing height. (Table 2))., The wave's lateral peak velocities increase with the heliocentric heights; the corresponding peak times of the velocities also delay with respect to the increasing height (Table \ref{tb}) ).
 Such increase of the peak lateral velocity ancl its Gime delay. are most likely from the combination effect of the intrinsic expansion motion aud the fast rising motion of the CME bubble., Such increase of the peak lateral velocity and its time delay are most likely from the combination effect of the intrinsic expansion motion and the fast rising motion of the CME bubble.
 In this Letter. we focus on studying (he separation process of two disünct fronts associated with a solar eruption that occurred. on 2011 June 7.," In this Letter, we focus on studying the separation process of two distinct fronts associated with a solar eruption that occurred on 2011 June 7."
 Following the eruption onset. the magnetic field of the source region quickly expands and forms a circular bubble.," Following the eruption onset, the magnetic field of the source region quickly expands and forms a circular bubble."
 In the early stage of the eruption. the bubble expands strongly with an accelerating velocity.," In the early stage of the eruption, the bubble expands strongly with an accelerating velocity."
 Afterwards. the apparent expansion velocity of the bubble close to the solar surface quickly decelerates to almost zero.," Afterwards, the apparent expansion velocity of the bubble close to the solar surface quickly decelerates to almost zero."
 In the meantime. a diffuse wave front starts (o separate from (he sharp bubble front.," In the meantime, a diffuse wave front starts to separate from the sharp bubble front."
 We conclude that the wave originates from the compression of the surrounding plasma by the impulsively expanding CME bubble., We conclude that the wave originates from the compression of the surrounding plasma by the impulsively expanding CME bubble.
 Due to a small standolE distaice between (he compression front and the driver front. the (wo fronts can not be distinguished during the early stage of the evolution when the driver is still undergoing acceleration.," Due to a small standoff distance between the compression front and the driver front, the two fronts can not be distinguished during the early stage of the evolution when the driver is still undergoing acceleration."
 Through examining the radio data from CALLISTO radio spectrometer. we find that a tvpe LI radio," Through examining the radio data from CALLISTO radio spectrometer, we find that a type II radio"
progenitor stars from the zero age main sequence. including the core H and He burning phases. the thermally pulsing asymptotic giant branch phase. the born-again episode that is responsible for the H deficiency. and from time-dependent element diffusion predictions during the white-dwarf stage.,"progenitor stars from the zero age main sequence, including the core H and He burning phases, the thermally pulsing asymptotic giant branch phase, the born-again episode that is responsible for the H deficiency, and from time-dependent element diffusion predictions during the white-dwarf stage."
 By considering the mean period spacing exhibited by the star. we found that KIC 5626021 should have a stellar mass in the range 0.60xΜ.Μ.0.87. substantially larger than those derived by previous spectroscopic (4.~0.56M4: OEATI) and asteroseismic (M.~0.57M.: BK@I1) studies.," By considering the mean period spacing exhibited by the star, we found that KIC 8626021 should have a stellar mass in the range $0.60
\lesssim M_*/M_{\odot} \lesssim 0.87$, substantially larger than those derived by previous spectroscopic $M_* \sim 0.56 M_{\odot}$; EA11) and asteroseismic $M_* \sim 0.57 M_{\odot}$; 11) studies."
 We also found that period-to-period fits point to an asteroseismological model with an effective temperature of ~27300 K. in strong conflict with the spectroscopic estimate (Ty~24900 K).," We also found that period-to-period fits point to an asteroseismological model with an effective temperature of $\sim
27\,300$ K, in strong conflict with the spectroscopic estimate $T_{\rm eff} \sim 24\, 900$ K)."
 Our results are in agreement with the recent asteroseismic analysis of BKOÓIL1 on KIC 8626021. in particular regarding its effective temperature.," Our results are in agreement with the recent asteroseismic analysis of 11 on KIC 8626021, in particular regarding its effective temperature."
 In fact. these authors conclude that KIC 8626021 a hot DBV with Zr~29200 K. It would be interesting to see what a spectroscopic analysis based on higher signal-to-noise spectra will tell about the surface gravity and effective temperature of the star.," In fact, these authors conclude that KIC 8626021 a hot DBV with $T_{\rm eff} \sim 29\,200$ K. It would be interesting to see what a spectroscopic analysis based on higher signal-to-noise spectra will tell about the surface gravity and effective temperature of the star."
 If KIC 8626021 is a hot DBV. as first found by BKOI1 and confirmed now by our results. then further monitoring of KIC 8626021 with in the next years probably will allow a measurement of IL. which in turn could open the possibility to constrain the plasmon neutrino emission rate (Winget et al.," If KIC 8626021 is a hot DBV, as first found by 11 and confirmed now by our results, then further monitoring of KIC 8626021 with in the next years probably will allow a measurement of $\dot{\Pi}$, which in turn could open the possibility to constrain the plasmon neutrino emission rate (Winget et al."
 2004: BK@I1)., 2004; 11).
 This endeavour is evidently dependent on the models. which can always be improved.," This endeavour is evidently dependent on the models, which can always be improved."
 Uncertainties in the models can also be assessed (Bischoff-Kim et., Uncertainties in the models can also be assessed (Bischoff-Kim et.
 al., al.
 2008)., 2008).
Our observations were taken curing two differeut epochs. between which the instrument uucerweut substantial changes.,"Our observations were taken during two different epochs, between which the instrument underwent substantial changes."
 The first rui was during the commissioning phase of Hydra in 1999. and only concentrated on NGC 6752 giants. while the second run oceurred iu 2001. aud involvecl both clusters.," The first run was during the commissioning phase of Hydra in 1999, and only concentrated on NGC 6752 giants, while the second run occurred in 2001, and involved both clusters."
 The differeut instrument. parameters for each epoch are listed tu Table 1.., The different instrument parameters for each epoch are listed in Table \ref{tab:t01}.
 The uet effect ol the chauge between the two ruus is the higher resolution offered in 2001 by placiug slit plates iu [ront of the large fibers and using the longer focal-leneth camera., The net effect of the change between the two runs is the higher resolution offered in 2001 by placing slit plates in front of the large fibers and using the longer focal-length camera.
 The resolution was measured uxing the FWHMN. of narrow emission lines in tlie comparison lamps., The resolution was measured using the FWHM of narrow emission lines in the comparison lamps.
 Both observing ruus utilized the echelle erating., Both observing runs utilized the echelle grating.
 Compreheusive membership surveys were available for neither MSO nor NGC 6752 when stars were selected lor observation with Hydra. limiting our ability to ensure that fibers were assigned to actual cluster members aud not to field stars.," Comprehensive membership surveys were available for neither M80 nor NGC 6752 when stars were selected for observation with Hydra, limiting our ability to ensure that fibers were assigned to actual cluster members and not to field stars."
 Both clusters are located at relatively low galactic latitucle (+19 degrees for M80 aud —22 degrees for NGC 6752). aud field star contamination is likely without proper motion or radial velocity information.," Both clusters are located at relatively low galactic latitude (+19 degrees for M80 and –25 degrees for NGC 6752), and field star contamination is likely without proper motion or radial velocity information."
 For NCC 6752. we used the B.V photographie photometry of Buonaunoetal.(1986) to select likely cluster members.," For NGC 6752, we used the $B,V$ photographic photometry of \citet{ngc6752} to select likely cluster members."
 This cluster has a large tidal radius of 55./31 (Harris1996).. compared with the field of view for Hydra. eusuriug that most stars in the aperture were likely to be members.," This cluster has a large tidal radius of 34 \citep{Harris96}, compared with the field of view for Hydra, ensuring that most stars in the aperture were likely to be members."
 Since no wide-field) photometry exists for M80. we obtained 58.V. CCD photometry of nine 13x fields centered on MSO with the CTIO 0.91 telescope prior to our Hydra run.," Since no wide-field photometry exists for M80, we obtained $B,V$ CCD photometry of nine ${\times}$ fields centered on M80 with the CTIO 0.9m telescope prior to our Hydra run."
 The weather was uot photometric. but we were able to obtain reasonable estimates of colors (c 0705). aux accurate astrometry after tying the system to the USNO-A2.0 catalog (Monetetal.1998).," The weather was not photometric, but we were able to obtain reasonable estimates of colors ${\pm}$ 05), and accurate astrometry after tying the system to the USNO-A2.0 catalog \citep{USNO}."
. Asa best guess for determining actual members of both clusters prior to our runs. we combine the existing photometry with the available proper imotiou data.," As a best guess for determining actual members of both clusters prior to our runs, we combined the existing photometry with the available proper motion data."
 For both clusters. we receive accurate astrometric data from D. Dinescu (1998. 2001. private communication). which also include proper motion information.," For both clusters, we received accurate astrometric data from D. Dinescu (1998, 2001, private communication), which also included proper motion information."
" The average proper motions for 098 NCC 6722 stars in the Dinesct sample were fi, = —0.5+23.0 (1o) mas Ἐ and fs = $3.0+31.0 (la) mas Luaround the cluster center."," The average proper motions for 998 NGC 6752 stars in the Dinescu sample were ${\mu}_{\alpha}$ = $-0.5~{\pm}~23.0$ ) mas $^{-1}$, and ${\mu}_{\delta}$ = $+3.0~{\pm}~31.0$ ) mas $^{-1}$, around the cluster center."
 We selected for observation oulv stars with —1L2xpxd13.7 mas loui —OQs€ps49.9 mas | for observing.," We selected for observation only stars with $-14.2~{\le}~{\mu}_{\alpha}~{\le}~+13.7$ mas $^{-1}$, and $-9.8~{\le}~{\mu}_{\delta}~{\le}~+9.9$ mas $^{-1}$ for observing."
 Dinescu's data for MSO were for stars in an annulus [ar outside the simall cluster. aud were less useful lor selectiug probable members.," Dinescu's data for M80 were for stars in an annulus far outside the small cluster, and were less useful for selecting probable members."
 The final lists of stars that we ultimately. determined to be cluster members auc that had spectra with sufficient S/N to analyze reliably are given in Tables 2. and 3.., The final lists of stars that we ultimately determined to be cluster members and that had spectra with sufficient S/N to analyze reliably are given in Tables \ref{tab:t02} and \ref{tab:t03}.
 The staridentification in the first column in Table 2.. as well as the photometry for the NGC 6752 giants. are from Buonannoetal.(1986).. while the alternate name in columau 2 is [rom Dinescus work.," The staridentification in the first column in Table \ref{tab:t02}, as well as the photometry for the NGC 6752 giants are from \citet{ngc6752}, while the alternate name in column 2 is from Dinescu's work."
 The colors for NGC 6752 are corrected asstuning E(B— V) = 0.0L as listed by Buonannoetal. (1986)..," The colors for NGC 6752 are corrected assuming $B~-~V$ ) = 0.04, as listed by \citet{ngc6752}. ."
 The, The
Computer models of accreting white dwarls approaching criticality were constructed using the KEPLER. stellar evolution code (Weaveretal.LOTS).,Computer models of accreting white dwarfs approaching criticality were constructed using the KEPLER stellar evolution code \citep{wzw78}.
.. A composition of was assumed. though the outcome will not depend appreciably on (his assumption.," A composition of was assumed, though the outcome will not depend appreciably on this assumption."
 The initial model consisted of a swarm” white dwarf with central temperature 105 IKIN. ancl a mass of 2.6x10* ee (~1.307AML. ).," The initial model consisted of a “warm” white dwarf with central temperature $^8$ K and a mass of $2.6\times10^{33}$ g $\sim1.307\,\msol$ )."
 Test caleulations that started [rom a cooler white dwarf resulted ina higher mass al ignition. but the results of the pulsation analysis were not affected by this modification.," Test calculations that started from a cooler white dwarf resulted in a higher mass at ignition, but the results of the pulsation analysis were not affected by this modification."
" The white cwarl then accreted matter (also carbon and oxvgen in the same proportion) al LO* M, +."," The white dwarf then accreted matter (also carbon and oxygen in the same proportion) at $10^{-7}$ $\msol\,$ $^{-1}$."
 The accretion was stopped when the runaway had started. but about. 80 centuries before the final incineration. to allow the addition of the well-resolved surface lavers.," The accretion was stopped when the runaway had started, but about 80 centuries before the final incineration, to allow the addition of the well-resolved surface layers."
" At this point the star has reached. a central density of po,=3.64 and a central temperature of Ty.=2.43."," At this point the star has reached a central density of $\rho_{9,\rm c}=3.64$ and a central temperature of $T_{8,\rm
c}=2.43$."
 In the remaining lime the star would have accreted less than 10CM.. which does not affect the structure of the star or the runaway (note that the runaway occurs many times that mass before reaching the Chandrasekhar mass).," In the remaining time the star would have accreted less than $10^{-3}\,\msol$, which does not affect the structure of the star or the runaway (note that the runaway occurs many times that mass before reaching the Chandrasekhar mass)."
 The Lagrangian grid uses zone masses ranging [rom 107’ ee in the center over some 10ee in the middle of the star to a smooth gradient in zone size down to LO ee at the surface., The Lagrangian grid uses zone masses ranging from $^{29}$ g in the center over some $10^{31}$ g in the middle of the star to a smooth gradient in zone size down to $^{15}$ g at the surface.
 Convection is treated using standard mixing length theory with a mixing length Luis—Hy., Convection is treated using standard mixing length theory with a mixing length $L_{\rm mix} = H_{\rm P}$.
" During the last ~ vvr prior to explosion (he nuclear energy. generation rale. equ. rises rapidly in the center of the white clwarl,"," During the last $\sim$ yr prior to explosion the nuclear energy generation rate, $\epsilon_{\rm nuc}$, rises rapidly in the center of the white dwarf."
 This is illustrated in Fig., This is illustrated in Fig.
" 5 that displays the evolution of central temperature. densitv and nuclear energv as a function of the time remaining belore explosion (lex),=0 corresponds to the (ime of flame ignition/start of explosion)."," \ref{fig1} that displays the evolution of central temperature, density and nuclear energy as a function of the time remaining before explosion $\texpl=0$ corresponds to the time of flame ignition/start of explosion)."
 While only a small fraction of the energy released goes into expanding the star. the expansion is significant because [os4/3.," While only a small fraction of the energy released goes into expanding the star, the expansion is significant because $\Gamma \approx 4/3$."
" The svstem of equations which are linearized. are the basic hvedrocdyvnanmie equations written under (he assumption of spherical sviumetry. (οἱ,", The system of equations which are linearized are the basic hydrodynamic equations written under the assumption of spherical symmetry (cf.
 Unno et al., Unno et al.
 1989. p.89).," 1989, p.89)."
 Details of the method and pulsation code can be found in Daraffe et ((2001)., Details of the method and pulsation code can be found in Baraffe et (2001).
 The unperturbed. equilibrium state is described by hydrostatie equilibrium.," The unperturbed, equilibrium state is described by hydrostatic equilibrium."
 The nuclear energy term appearing in (he energv conservation equation includes neutrino energy loss., The nuclear energy term appearing in the energy conservation equation includes neutrino energy loss.
 An important uncertainty in the present analvsis is due to the assumption that convection is frozen in. neglecting the perturbation of the convective Πας.," An important uncertainty in the present analysis is due to the assumption that convection is frozen in, neglecting the perturbation of the convective flux."
 This simplification is based on the argument that the convective timescales in the interior of the white dwarf remain significantly larger than the, This simplification is based on the argument that the convective timescales in the interior of the white dwarf remain significantly larger than the
FG.LY. that would. produce such observable kinematics.,"$f(E,L)$, that would produce such observable kinematics."
 This method builds an estimate of the distribution function using just the data [rom the upper part of the linc-ol-sight velocity distribution where the velocities exceed the eieeular velocity., This method builds an estimate of the distribution function using just the data from the upper part of the line-of-sight velocity distribution where the velocities exceed the circular velocity.
 H£ the. correct. gravitational potential is. adopted. then the rest. of the velocity distribution. automatically matches the data: however. a mismatch.. will. occur if» the wrong potential. is. assumed.," If the correct gravitational potential is adopted, then the rest of the velocity distribution automatically matches the data; however, a mismatch will occur if the wrong potential is assumed."
 rp.Thus. this. algorithm. algorithm. returns not only an estimate for the disc distribution function. but also constrains the form of the gravitational potential.," Thus, this algorithm algorithm returns not only an estimate for the disc distribution function, but also constrains the form of the gravitational potential."
 In principle. the gravitational potential in the dise plane could take any form. but the data are not of high enough quality to allow a completely non-parametric derivation.," In principle, the gravitational potential in the disc plane could take any form, but the data are not of high enough quality to allow a completely non-parametric derivation."
 We therefore adopt the simple but sulliciently general form of a softened isothermal sphere potential of the form bL)i =— nii , We therefore adopt the simple but sufficiently general form of a softened isothermal sphere potential of the form (r) = ( 1 + ).
ForEMH this potential. the circular velocity can be written," For this potential, the circular velocity can be written (r) ="
of (focosas.dosing.) for the three orbits in 11.,"of $(I_2\cos\sigma_2,
I_2\sin\sigma_2)$ for the three orbits in 1."
" The plane is defined as σι=2107.0,70."," The plane is defined as $\sigma_1=270\degr, \dot{\sigma}_1>0$."
 To obtain these. we adopt the initial conditions of orbits from 11. and then integrate the corresponding Hamiltonian equations based on the expansion as ((2.3).," To obtain these, we adopt the initial conditions of orbits from 1, and then integrate the corresponding Hamiltonian equations based on the expansion as (2,3)."
 00ο indicates case has a chaotic orbit., 9c indicates case has a chaotic orbit.
 On the contrary. the invariant curves for cases andb θα.) imply that both these two orbits are regular.," On the contrary, the invariant curves for cases and 9a,b) imply that both these two orbits are regular."
 That is. no matter whether the apsidal corotation happens or not. the system trapped in the 3:1 MMB could be stable.," That is, no matter whether the apsidal corotation happens or not, the system trapped in the 3:1 MMR could be stable."
 From this point of view we may argue the apsidal corotation only has a limited contribution to the stability ofthe system., From this point of view we may argue the apsidal corotation only has a limited contribution to the stability of the system.
 Because the Hamiltonian is expressed explicitly in e;.6; and the integrals of motion Jauu- Jay allect the svstem as constrains. we can only define an energy surface (44= Ly) with certain pre-determined. Joun-Ja. then calculate the surface of section.," Because the Hamiltonian is expressed explicitly in $a_i,e_i$ and the integrals of motion $J_{\rm sum}$, $J_{\rm dif}$ affect the system as constrains, we can only define an energy surface $H
\equiv H_0$ ) with certain pre-determined $J_{\rm sum}, J_{\rm
dif}$, then calculate the surface of section."
 We find the structure of the phase space and the stability of the system depends sensitively not only on df but also on Jou. and Jay., We find the structure of the phase space and the stability of the system depends sensitively not only on $H$ but also on $J_{\rm sum}$ and $J_{\rm dif}$.
 Por example. with the same values of £4.Jou and Jag as the ones in lib. we calculate tens of orbits with different initial conditions.," For example, with the same values of $H, J_{\rm
sum}$ and $J_{\rm dif}$ as the ones in 1b, we calculate tens of orbits with different initial conditions."
 On the surface of section. these orbits occupy a big regular-motion region.," On the surface of section, these orbits occupy a big regular-motion region."
 This result. does not conflict with the Lact that there are only a small fraction. of stable svstems in numerical simulations. in fact. when we change 4. (or Ju. Jag) just a little. we find remarkable chaotic region on the surface of section.," This result does not conflict with the fact that there are only a small fraction of stable systems in numerical simulations, in fact, when we change $H$, (or $J_{\rm sum }$, $J_{\rm dif}$ ) just a little, we find remarkable chaotic region on the surface of section."
 The application of the surlace-of-section technique is limited by the high dimension of the svstem., The application of the surface-of-section technique is limited by the high dimension of the system.
 This will be discussed in detail in our future paper., This will be discussed in detail in our future paper.
 With hundreds. of numerical simulations of the planetary system of the 55 Caneri. we find the third. planet. has a very. weak influence on the motion of the inner two planets.," With hundreds of numerical simulations of the planetary system of the 55 Cancri, we find the third planet has a very weak influence on the motion of the inner two planets."
 We confirm the inner two could be trapped in a 3:1 mean motion resonance and three dilferent types of motion are found., We confirm the inner two could be trapped in a 3:1 mean motion resonance and three different types of motion are found.
 Judging from the Lyapunoy character indicators and the surviving time of integration. two of them (case b) are oactically stable. so that the real system could be running in one of these configurations.," Judging from the Lyapunov character indicators and the surviving time of integration, two of them (case ) are practically stable, so that the real system could be running in one of these configurations."
 Via à new Llamiltonian expansion which is suitable for ugh-cecentricitics planar three-body. problem. we study the dvnanmües of the cdillerent configurations.," Via a new Hamiltonian expansion which is suitable for high-eccentricities planar three-body problem, we study the dynamics of the different configurations."
 We discuss the variations of eccentricities and resonant angles. explain the iippenings of cdillerent evolving tvpes. and give a criterion of the occurrence of the apsidal corotation.," We discuss the variations of eccentricities and resonant angles, explain the happenings of different evolving types, and give a criterion of the occurrence of the apsidal corotation."
 The surfaces ofsection for the three tvpes of motion are calculated and they reveal the stabilities of svstems with or without the apsidal corotation., The surfaces of section for the three types of motion are calculated and they reveal the stabilities of systems with or without the apsidal corotation.
 With these results we argue that the stability of the svstem is mainly due to the 3:1 MIALR. ancl the apsidal corotation has only a limite contribution.," With these results we argue that the stability of the system is mainly due to the 3:1 MMR, and the apsidal corotation has only a limited contribution."
 We would like to mention that this methoc can also be applied to other extra-solar. planetary. systems with other mean motion resonances., We would like to mention that this method can also be applied to other extra-solar planetary systems with other mean motion resonances.
 Numerical simulations suggest at least LO percent of systems are in a 3:12 MMB. while the Hamiltonian analyses eive an upper limit of ~30%. which however will drop own after considering the stability.," Numerical simulations suggest at least $\sim10$ percent of systems are in a 3:1 MMR, while the Hamiltonian analyses give an upper limit of $\sim 30\%$, which however will drop down after considering the stability."
 We also list the initia 'onditions leading to this MMI., We also list the initial conditions leading to this MMR.
 Systems with different motion configurations have iferent energy. (Lf) levels., Systems with different motion configurations have different energy $H$ ) levels.
 The apsidal corotation happens when the Hamiltonian approaches the extreme value., The apsidal corotation happens when the Hamiltonian approaches the extreme value.
 So. if the two planets are captured into current configuration wough orbital migration caused by the action of non-conservative forces. the svstem should have an extremum of energy so that the apsical corotation happens (lev2003).," So, if the two planets are captured into current configuration through orbital migration caused by the action of non-conservative forces, the system should have an extremum of energy so that the apsidal corotation happens \cite{kle03}."
. When the future observations would reveal more accurate properties of this svstem. we may consider what signatures of the migration are still presented in this svsten.," When the future observations would reveal more accurate properties of this system, we may consider what signatures of the migration are still presented in this system."
 The masses of planets adopted in this paper are the values from the orbital solutions when assuming sin;=1., The masses of planets adopted in this paper are the values from the orbital solutions when assuming $\sin i=1$.
 As for the situations of sin?«1. our initial analvsis with the Hamiltonian get the very similar results in a wide range of sin;.," As for the situations of $\sin i<1$, our initial analysis with the Hamiltonian get the very similar results in a wide range of $\sin
i$."
 This is also consistent with the results in (Deaugéal 2003)., This is also consistent with the results in \cite{bea03a}.
 We have also analysed the possible motion configurations and their stabilities i£ the initial eccentricities dilfer from the values adopted above., We have also analysed the possible motion configurations and their stabilities if the initial eccentricities differ from the values adopted above.
 With the help of the Hamiltonian model. we find that a higher e» favors the establishment of a 3:1 MAIR.," With the help of the Hamiltonian model, we find that a higher $e_2$ favors the establishment of a 3:1 MMR."
 Anyway. wed like to leave more details of these to our future paper.," Anyway, we'd like to leave more details of these to our future paper."
 Last but not least. the general relativity οσοι may allects the secular cvnamics of the 55 Cancri system. since the Companion D and C are quite close to the central star.," Last but not least, the general relativity effect may affects the secular dynamics of the 55 Cancri system, since the Companion B and C are quite close to the central star."
 For the innermost planet. the orbital precession caused. by the eeneral relativity elect. is calculated.," For the innermost planet, the orbital precession caused by the general relativity effect, is calculated."
" Although this periastron shift. ~1.66«10"" radians per orbit. is quite small. its about three times larger than that of Mercury in our Solar systent."," Although this periastron shift, $\sim1.66\times 10^{-6}$ radians per orbit, is quite small, it's about three times larger than that of Mercury in our Solar system."
 We thank Dr. Beaugé for helpful discussions., We thank Dr. Beaugé for helpful discussions.
 Appreciations also go to Dr. Tsevi Mazeh for the constructive comments ancl suggestions., Appreciations also go to Dr. Tsevi Mazeh for the constructive comments and suggestions.
 This work is supported by Academy, This work is supported by Academy
"s/p as. where i denote the mass of hydrogen atom and /?,,, represent the s/p ratio.","s/p as, where $m$ denote the mass of hydrogen atom and $R_{sp}$ represent the s/p ratio."
 Using Eq. (, Using Eq. (
"19). we can calculate the CR path length for a given /?.,.","19), we can calculate the CR path length for a given $R_{sp}$."
" For the path length calculation within the SNRs. Ry, is given by the ratio ΑΝ taken at time /=7' (see section 2.2) and for the path length in the Galaxy. {ινn.fny from section 3.2."," For the path length calculation within the SNRs, $R_{sp}$ is given by the ratio $N_s/N_p$ taken at time $t=T$ (see section 2.2) and for the path length in the Galaxy, $R_{sp}=n_s/n_p$ from section 3.2."
 Their comparison corresponding to the B/C ratio shown in Fig. (, Their comparison corresponding to the B/C ratio shown in Fig. (
2) is plotted in Fig. (,2) is plotted in Fig. (
"3) where the dot-dashed line represents the path-length inside the SNRs .V. and the dotted line that in the Galaxy .V,.",3) where the dot-dashed line represents the path-length inside the SNRs $X_s$ and the dotted line that in the Galaxy $X_g$.
" Also shown in the figure by the solid line is the total path length CY.| .X,) traversed by the CRs during their whole lifetime in the Galaxy.", Also shown in the figure by the solid line is the total path length $X_s+X_g$ ) traversed by the CRs during their whole lifetime in the Galaxy.
" The average path length within the SNRs is found to be VY.0.09 gm 7? fori= 7 independent of energy whereas the path length in the Galaxy has a maximum value of X,zz5 gm 7 at around 1 GeV/n which then decreases with energy as V,xfo7 because of the energy dependent escape of CRs from the Galaxy.", The average path length within the SNRs is found to be $X_s\approx 0.09$ gm $^{-2}$ for $\eta^\prime=1$ $^{-3}$ independent of energy whereas the path length in the Galaxy has a maximum value of $X_g\approx 5$ gm $^{-2}$ at around $1$ GeV/n which then decreases with energy as $X_g\propto E^{-\delta}$ because of the energy dependent escape of CRs from the Galaxy.
 From Fig., From Fig.
 3. we can also see that CRs with energies greater than around 7 TeV/n traversed most of the matter within the source itself and its effect is seen in the B/C ratio in Fig. (," 3, we can also see that CRs with energies greater than around $7$ TeV/n traversed most of the matter within the source itself and its effect is seen in the B/C ratio in Fig. ("
2) already at energies around | TeV/n. We present a simple model based on the considerations of DSA theory which can explain both the observed electron spectrum and the s/p ratios for a conservative set of model parameters.,2) already at energies around $1$ TeV/n. We present a simple model based on the considerations of DSA theory which can explain both the observed electron spectrum and the s/p ratios for a conservative set of model parameters.
 In our model. we assume that CRs after acceleration by SNR shock waves. escape downstream of the shock and remain contined within the remnant for some time before they are released into the ISM.," In our model, we assume that CRs after acceleration by SNR shock waves, escape downstream of the shock and remain confined within the remnant for some time before they are released into the ISM."
 During this time. CR electrons suffer from radiative energy losses while the nuclear species undergo nuclear fragmentations.," During this time, CR electrons suffer from radiative energy losses while the nuclear species undergo nuclear fragmentations."
 For a magnetic field strength of 65/G inside the SNRs and assuming a uniform and continuous distribution of SNRs in our Galaxy. we find that a CR confinement time of 1.2.10 vr can produce the observed break in the electron spectrum at ~1 TeV. Moreover. the hardening in the available B/C data above ~100 GeV/n can also be explained if we assume the averaged matter density inside the SNRs to be —2 em —.," For a magnetic field strength of $6\mu$ G inside the SNRs and assuming a uniform and continuous distribution of SNRs in our Galaxy, we find that a CR confinement time of $1.2\times 10^5$ yr can produce the observed break in the electron spectrum at $\sim 1$ TeV. Moreover, the hardening in the available B/C data above $\sim 100$ GeV/n can also be explained if we assume the averaged matter density inside the SNRs to be $\sim 2$ cm $^{-3}$."
 Our results on the B/C ratio which are based on a simple model are very similar to those obtained in Berezhko et al., Our results on the B/C ratio which are based on a simple model are very similar to those obtained in Berezhko et al.
 2003 for the case of secondary production inside SNRs calculated for the normal ISM density of 1 em. and the CR confinement time of 10 yr., 2003 for the case of secondary production inside SNRs calculated for the normal ISM density of $1$ $^{-3}$ and the CR confinement time of $10^5$ yr.
 Their results were calculated using a detailed self consistent model of CR production inside SNRs., Their results were calculated using a detailed self consistent model of CR production inside SNRs.
 Our model. in its present form. looks similar to the the nested leaky box model proposed by Cowsik & Wilson 1973. 1975.," Our model, in its present form, looks similar to the the nested leaky box model proposed by Cowsik $\&$ Wilson 1973, 1975."
 However. there are major differences in the basic assumptions between the two models.," However, there are major differences in the basic assumptions between the two models."
 They assumed that CRs after acceleration spend some time in a cocoon-lihe region surrounding the sources where the primaries interact with the matter and produce secondaries., They assumed that CRs after acceleration spend some time in a cocoon-like region surrounding the sources where the primaries interact with the matter and produce secondaries.
 The residence time of CRs inside the cocoon was assumed to be energy and after they are released from the source region. they undergo an energy propagation in the Galaxy.," The residence time of CRs inside the cocoon was assumed to be energy and after they are released from the source region, they undergo an energy propagation in the Galaxy."
 In their model. secondary production inside the cocoon dominates at lower energies and at higher energies. it is dominated by the production in the ISM.," In their model, secondary production inside the cocoon dominates at lower energies and at higher energies, it is dominated by the production in the ISM."
 On the other hand. the basic idea of our model comes from our understanding of DSA theory inside SNRs.," On the other hand, the basic idea of our model comes from our understanding of DSA theory inside SNRs."
 In our model. the CR. confinement region as well as the confinement time are strongly related. to qe acceleration mechanism itself.," In our model, the CR confinement region as well as the confinement time are strongly related to the acceleration mechanism itself."
 Moreover. secondary production inside the remnant dominates only at higher energies while at ower energies. they are dominated mostly by those produced in ye Galaxy.," Moreover, secondary production inside the remnant dominates only at higher energies while at lower energies, they are dominated mostly by those produced in the Galaxy."
 A more proper treatment of our model would be to yerform a self consistent ealeulation of primary CR acceleration and their confinement. both of which are strongly related. to 1e. efficieney. of CR scattering around the shocks by magnetic urbulence.," A more proper treatment of our model would be to perform a self consistent calculation of primary CR acceleration and their confinement, both of which are strongly related to the efficiency of CR scattering around the shocks by magnetic turbulence."
 Also. we should include the secondaries produced during the acceleration process along with those produced during 1e confinement period and if there. also their acceleration by the P4ame shock waves which accelerate their primaries.," Also, we should include the secondaries produced during the acceleration process along with those produced during the confinement period and if there, also their acceleration by the same shock waves which accelerate their primaries."
 Such a scenario of secondary acceleration has been considered to explain the rise in 1e. positron fraction reported by the PAMELA experiment (Blasi 2009)., Such a scenario of secondary acceleration has been considered to explain the rise in the positron fraction reported by the PAMELA experiment (Blasi 2009).
 Though it is beyond the scope of this paper to discuss Us issue. if is worthwhile to mention in relation to our present model. that the relative contribution of the accelerated and the non-accelerated secondaries to their total spectrum strongly depends on de relative time their primaries spend in the acceleration region and in the downstream region (see e.g. Kachelriess et al.," Though it is beyond the scope of this paper to discuss this issue, it is worthwhile to mention in relation to our present model, that the relative contribution of the accelerated and the non-accelerated secondaries to their total spectrum strongly depends on the relative time their primaries spend in the acceleration region and in the downstream region (see e.g. Kachelriess et al."
 2010)., 2010).
 We emphasize that under our present model. both the high energy electron spectrum and the s/p ratio depend strongly on the CR confinement time inside the SNRs.," We emphasize that under our present model, both the high energy electron spectrum and the s/p ratio depend strongly on the CR confinement time inside the SNRs."
 Therefore. their data can be used to put constraints on the average continement time provided that detailed informations about the magnetic field strengths and the matter densities inside the remnants are taken into account.," Therefore, their data can be used to put constraints on the average confinement time provided that detailed informations about the magnetic field strengths and the matter densities inside the remnants are taken into account."
 Note that the value of the magnetic field strength of 6//G and also that of the matter density jj—(1.2) adopted in our present work can be different from those expected in SNRs., Note that the value of the magnetic field strength of $6 \mu$ G and also that of the matter density $\eta^\prime=(1-2)$ $^{-3}$ adopted in our present work can be different from those expected in SNRs.
 For SNRs expanding in an environment consisting of monoatomie ideal gas. their values are expected to be equal to the ISM values scaled by some constant factor which in the case of strong shocks is approximately equal to 4.," For SNRs expanding in an environment consisting of monoatomic ideal gas, their values are expected to be equal to the ISM values scaled by some constant factor which in the case of strong shocks is approximately equal to $4$."
 Moreover. these values can also be different for different SNRs and their true values can only be inferred from observations of radio or X-ray synchrotron emissions and thermal X-rays from SNRs (Bamba et al.," Moreover, these values can also be different for different SNRs and their true values can only be inferred from observations of radio or X-ray synchrotron emissions and thermal X-rays from SNRs (Bamba et al."
 2003. Uchiyama et al.," 2003, Uchiyama et al."
 2007)., 2007).
 In future. we will include such details in our calculation and also try to extend our work to other secondary species like the CR anti-protons and the xositrons.," In future, we will include such details in our calculation and also try to extend our work to other secondary species like the CR anti-protons and the positrons."
 In addition. we will also include some important aspects which we have neglected in our present study like the evolution of he remnant. the weakening of the shocks and the energy dependent escape of CRs from the SNRs.," In addition, we will also include some important aspects which we have neglected in our present study like the evolution of the remnant, the weakening of the shocks and the energy dependent escape of CRs from the SNRs."
 Adding such aspects. particularly he energy dependent escape. can strongly affect our results.," Adding such aspects, particularly the energy dependent escape, can strongly affect our results."
 For instance. assuming an escape model which follows the same energy dependence as in the Galaxy can lead to disappearance of the flattening in the s/p ratio at higher energies.," For instance, assuming an escape model which follows the same energy dependence as in the Galaxy can lead to disappearance of the flattening in the s/p ratio at higher energies."
 The authors would like to thank the anonymous referee for his/her constructive comments., The authors would like to thank the anonymous referee for his/her constructive comments.
 ST would like to thank M. Pohl for useful discussions during NAC 2010 in Nijmegen., ST would like to thank M. Pohl for useful discussions during NAC 2010 in Nijmegen.
 ST would also like to thank D. Mülller for carefully reading the first draft of this manuscript and for giving valuable Abdo. A. Α.. et al.," ST would also like to thank D. Mülller for carefully reading the first draft of this manuscript and for giving valuable Abdo, A. A., et al."
 2009. Phys.," 2009, Phys."
 Rev. Lett..," Rev. Lett.,"
 102. Aharonian. F. Α.. et al.," 102, Aharonian, F. A., et al."
 2007. AWA. 467.," 2007, $\&$ A, 467,"
GALEN JL98156.8|011745 (GALEN 1931]0117. thereafter)— is à hyelrogen-rich white dwarf. discovered bv Vennes.WKawka.&Németh(2010a) ancl characterized by an opulent heavy-element line spectrum and an infrared excess.,"GALEX J193156.8+011745 (GALEX J1931+0117, thereafter) is a hydrogen-rich white dwarf discovered by \citet{ven2010a} and characterized by an opulent heavy-element line spectrum and an infrared excess."
" The original low-resolution spectrum obtained with the New ""Technology Telescope. (NT) at. La Silla Observatory showed astrong ILAJASI doublet and weaker silicon lines.", The original low-resolution spectrum obtained with the New Technology Telescope (NTT) at La Silla Observatory showed astrong $\lambda$ 4481 doublet and weaker silicon lines.
 Follow-up echelle spectroscopy. obtained. with the Very. Large Telescope (VLP)-Kueven enabled a detailed abundance studs., Follow-up echelle spectroscopy obtained with the Very Large Telescope (VLT)-Kueyen enabled a detailed abundance study.
 “Phe near-solar. abundances of oxygen. magnesium. silicon. calcium and iron bear the signature of an external supply of material accreting onto the surface of the white dwarf.," The near-solar abundances of oxygen, magnesium, silicon, calcium and iron bear the signature of an external supply of material accreting onto the surface of the white dwarf."
 Based on available data. Vennes et al.," Based on available data, Vennes et al."
 concluded that the supply may originate from a close. sub-stellar companion or [rom a cool debris disc.," concluded that the supply may originate from a close, sub-stellar companion or from a cool debris disc."
 The presence of heavy elements in hydrogen-rich white dwarls has variously been interpreted. as intrinsic to the white chvarl or as extrinsic. i.e. supplied by the interstellar mecium (Dupuis.Fontaine.&Wesemael1993).. by a nearby companion as in post-common envelope systems. 2006:Ixawka.etal. 2008)... or by a debris clise (Zuckerman 2008).," The presence of heavy elements in hydrogen-rich white dwarfs has variously been interpreted as intrinsic to the white dwarf, or as extrinsic, i.e., supplied by the interstellar medium \citep{dup1993}, by a nearby companion as in post-common envelope systems \citep{deb2006,kaw2008}, or by a debris disc \citep{zuc2003,kil2006,far2008}."
. However. aceretion from the interstellar medium is unlikely because of supply shortages (Euihietal.2010a).," However, accretion from the interstellar medium is unlikely because of supply shortages \citep{far2010a}."
. In the extrinsic scenarios. the elements are acereted: ad dilfusecl in the atmosphere and envelope of the star. (seeFontaine&Michaud1979:Ixoester 2009).," In the extrinsic scenarios, the elements are accreted and diffused in the atmosphere and envelope of the star \citep[see][]{fon1979,koe2009}."
.. An intrinsic. or internal. reservoir of heavy. elements. is also possible. but in either scenario a self-consistent solution of the diffusion equation must explore the effect of radiative acceleration on trace elements (Chaver.Fontaine.&Wesemael1995:etal. 1995).," An intrinsic, or internal, reservoir of heavy elements is also possible, but in either scenario a self-consistent solution of the diffusion equation must explore the effect of radiative acceleration on trace elements \citep{cha1995a,cha1995b}. ."
 As a class. the polluted DA white darfs. or DAZs. are," As a class, the polluted DA white dwarfs, or DAZs, are"
barvon of(he most massive cascade chain. (ii) theincident. valence diquark tends to pick,up a spin-down sea quark (or conversely the spin-up incident valence quark tends to turn
corresponding control sample (see also Papert).,corresponding control sample (see also PaperI).
 In the small box of Fig., In the small box of Fig.
 3 we show the corresponding f* for the galaxy pair. the close pair ancl the control samples as a function of the galactrocentric distance.," \ref{brcentroran} we show the corresponding $f^\star$ for the galaxy pair, the close pair and the control samples as a function of the galactrocentric distance."
 This figure agrees with the trend. found for the mean 6. indicating that in the central regions the star formation activity is weaker for pair. close pairs ancl control galaxics.," This figure agrees with the trend found for the mean $b$, indicating that in the central regions the star formation activity is weaker for pair, close pairs and control galaxies."
" We analyse the dependence of star formation on pair relative projected. separation rj, and relative radial velocity AY estimating mean values <b2 as a function of +, and AY [or our sample of galaxy pairs in groups.", We analyse the dependence of star formation on pair relative projected separation $r_p$ and relative radial velocity $\Delta {\rm V}$ estimating mean values $<b>$ as a function of $r_{\rm p}$ and $\Delta {\rm V}$ for our sample of galaxy pairs in groups.
 The results are shown in Fig., The results are shown in Fig.
 4. and Fig. 5..," \ref{betarg}
 and Fig. \ref{betavg}."
 It. can be seen that. as it occurs in pairs in the field (Paper D. at ryc25h! kpe the star formation activity is significantly enhanced. over the control sample.," It can be seen that, as it occurs in pairs in the field (Paper I), at $r_p< 25 h^{-1} $ kpc the star formation activity is significantly enhanced over the control sample."
 Similarly. pairs with smaller relative racial velocity dillerences have larger mean b values. consistent with the results found. for field: pairs.," Similarly, pairs with smaller relative radial velocity differences have larger mean b values, consistent with the results found for field pairs."
 This behaviour indicates that the physies of star formation induced by pair interactions operates in a similar fashion in high density environments. although. with a lower general level of star formation activity.," This behaviour indicates that the physics of star formation induced by pair interactions operates in a similar fashion in high density environments, although with a lower general level of star formation activity."
 Given the reduced. star formation activity of pairs in the central regions of groups (Fig. 3)).," Given the reduced star formation activity of pairs in the central regions of groups (Fig. \ref{brcentroran}) ),"
 we have carried out a similar analysis adopting the restriction. Byfyi.<0.5., we have carried out a similar analysis adopting the restriction $R_D/R_{Vir}< 0.5$.
 The results for this subsample of centrally located pairs are shown in Fie., The results for this subsample of centrally located pairs are shown in Fig.
 4 and Fig.," \ref{betarg}
 and Fig."
 5. (dashed lines) from which it can be seen the similar behaviour of the centrally located: pairs. albeit with an overall weaker star formation activity.," \ref{betavg} (dashed lines) from which it can be seen the similar behaviour of the centrally located pairs, albeit with an overall weaker star formation activity."
 We etect a trend for the mean star formation birth rate parameter b of close galaxy. pairs to be more densely vopulated by carly twpe galaxies. with respect to the corresponding mean values (6) of the control samples from xürs in the field (<ὐbia=1.43 40.14) to pairs in he densest regions («bboss=1.09+ 0.01)., We detect a trend for the mean star formation birth rate parameter $b$ of close galaxy pairs to be more densely populated by early type galaxies with respect to the corresponding mean values $\bar{b}$ ) of the control samples from pairs in the field $ <b>/\bar{b}_{\rm field} = 1.43 \pm 0.14$ ) to pairs in the densest regions $<b>/\bar{b}_{\rm groups}= 1.09 \pm 0.01$ ).
 This rend indicates that tidal torques generated by interactions could be less ellicicnt in pair svstems (with similar orbital xwameters) in high density regions., This trend indicates that tidal torques generated by interactions could be less efficient in pair systems (with similar orbital parameters) in high density regions.
 The fact that densest regions are more populated by early type galaxies suggests wt the dillerent. response could. due to dillerences in the vnamics of the galaxies in pairs and the available gas reservoir to forni stars in these svstenis., The fact that densest regions are more populated by early type galaxies suggests that the different response could due to differences in the dynamics of the galaxies in pairs and the available gas reservoir to form stars in these systems.
 We should. also take into account the possibility. that μα»urious galaxy pairs whieh are more probable in denser regions. can contribute to diminish the signal. producing 16 observed. trend.," We should also take into account the possibility that spurious galaxy pairs which are more probable in denser regions, can contribute to diminish the signal, producing the observed trend."
 In order to assess the elfects of spurious ours. we use stricter dillerence velocity cut-olfs. similarly to 1e analysis we carried out in Paperl. As we can see from. =ig. 6..," In order to assess the effects of spurious pairs, we use stricter difference velocity cut-offs, similarly to the analysis we carried out in PaperI. As we can see from Fig. \ref{brvel},"
 as pairs with larger velocity differences are excluclect. 10 mean b values behave similar to close pairs.," as pairs with larger velocity differences are excluded, the mean b values behave similar to close pairs."
 Erom this igure. we see that spurious pairs could contaminate the results by reducing the star formation activity signal but. wir cllects are not significant enough to change the trends.," From this figure, we see that spurious pairs could contaminate the results by reducing the star formation activity signal but, their effects are not significant enough to change the trends."
 The small box in Fig.6 shows the points distribution of b xwanmeter as à funetionol projected distance for all galaxies in pairs., The small box in \ref{brvel} shows the points distribution of $b$ parameter as a functionof projected distance for all galaxies in pairs.
 (From this figure it is clear that at small projected separations there are few points with low star formations activity., >From this figure it is clear that at small projected separations there are few points with low star formations activity.
 Hence. the enhacement of the SE activity lor very," Hence, the enhacement of the SF activity for very"
statistical mechanics. the deusitv of states gil) for an enusenible is where O is the nmuuber of mücrostates and 5 is the eutropv of the eusemible.,"statistical mechanics, the density of states $g(E)$ for an ensemble is where $\Omega$ is the number of microstates and $S$ is the entropy of the ensemble."
 For a canonical eusenible iu quasi-equilibrimm. the eutropy is given by (Αίαςet2002) where T is the uuscaled kinetic temperature of a cell iu units where the Boltzmann coustaut is 1. V is the volume of a cell. N is the number of ealaxies in the cell. 0 is the mass of a galaxy and A is a normalizing factor.," For a canonical ensemble in quasi-equilibrium, the entropy is given by \citep{2002ApJ...571..576A}
 where $T$ is the unscaled kinetic temperature of a cell in units where the Boltzmann constant is 1, $V$ is the volume of a cell, $N$ is the number of galaxies in the cell, $m$ is the mass of a galaxy and $\Lambda$ is a normalizing factor."
 Since equation relates E.to T. we can write the wunber of nucrostates O(£.) for scaled enerey £. in terms of T as (c.f. L, Since equation relates $\overline{E}_*$to $\overline{T}_*$ we can write the number of microstates $\Omega(\overline{E}_*)$ for scaled energy $\overline{E}_*$ in terms of $\overline{T}_*$ as (c.f. \citealt{2004ApJ...608..636L}) )
eong&Saslaw 20013) The other quautitics iu equation are found iu Alunadctal.(2002).., Then $g(\overline{E}_*)$ is The other quantities in equation are found in \citet{2002ApJ...571..576A}.
" For the erand canonical οποίο, the fueacity and partition fiction are aud where b as iu equation is the clustering parameter for the erand canonical ensemble. Nis the average uunuber of galaxies in a cell. and Ty is the temperature of the exaud canonical euseiuble."," For the grand canonical ensemble, the fugacity and partition function are and where $b$ as in equation is the clustering parameter for the grand canonical ensemble, $\overline{N}$ is the average number of galaxies in a cell, and $T_0$ is the temperature of the grand canonical ensemble."
" Substituting equations(26).. and iuto equation(21). the tenus involving A aud a cancel aud we ect To write equation in terns of T, we solve for T/T, and £/Ty."," Substituting equations, and into equation, the terms involving $\Lambda$ and $m$ cancel and we get To write equation in terms of $\overline{T}_*$ we solve for $T/T_0$ and $E/T_0$."
 Equations aud eive Using equation we ect and from equation we ect Substituting equations aud into equation(29).. we eet which eives the differeutial conditional probability that a cell has scaled energy E. given that it has NV ealaxics.," Equations and give Using equation we get and from equation we get Substituting equations and into equation, we get which gives the differential conditional probability that a cell has scaled energy $\overline{E}_*$ given that it has $N$ galaxies."
 The probability that a cell las a scaled energy in the range Be€E.νου comes frou integrating over the relevant rauge so that which is normalized by integrating over all possible values of E Because E[T| las adouble valued regime for E 0. the inteerals iu equations aud are taken by inteerating over both the positive and negative specific heat brauches.," The probability that a cell has a scaled energy in the range $\overline{E}_\stx{1} \leq \overline{E}_* \leq \overline{E}_\stx{2}$ comes from integrating over the relevant range so that which is normalized by integrating over all possible values of $\overline{E}_*$ Because $\overline{E}_*[\overline{T}_*]$ has adouble valued regime for $\overline{E}_* < 0$ , the integrals in equations and are taken by integrating over both the positive and negative specific heat branches."
" We cau split the inteeral such that where P aud P, deuote probabilities for the negative and positive specific heat brauches of Tm| respectively,", We can split the integral such that where $P_-$ and $P_+$ denote probabilities for the negative and positive specific heat branches of $\overline{T}_*[\overline{E}_*]$ respectively.
" These ranges are also subject to the quasi-equilibiunm limits such that T.>0.1 and E,= 0.390.", These ranges are also subject to the quasi-equilibrium limits such that $\overline{T}_* > 0.1$ and $\overline{E}_* \geq -0.390$ .
 To simplify the analysis. we cau rewrite the probability in terms of T. and c.," To simplify the analysis, we can rewrite the probability in terms of $\overline{T}_*$ and $\overline{\psi}$ ."
 The chanee of variables to rewrite the probability in terms of T. is, The change of variables to rewrite the probability in terms of $\overline{T}_*$ is
"cunits)), but are nevertheless consistent with being Compton-thick within the errors.","), but are nevertheless consistent with being Compton-thick within the errors."
" However, for both sources there are only photometric redshifts available and therefore the column density estimates are uncertain."," However, for both sources there are only photometric redshifts available and therefore the column density estimates are uncertain."
 Only two 6 Sources have fluxes f2-10Kev>107?funits., Only two 6 sources have fluxes $\rm f_{2-10 keV} > 10^{-15}$.
". These sources have been also detected by,, allowing a spectral fit with both the photon-index and the column density considered as free parameters."," These sources have been also detected by, allowing a spectral fit with both the photon-index and the column density considered as free parameters."
 These are CDFS-9 and CDFS-398., These are CDFS-9 and CDFS-398.
 In Table 3 we present the spectral fit results for these two sources., In Table \ref{xmm} we present the spectral fit results for these two sources.
" 'The spectrum of CDFS-9 is highly absorbed with a column density of ~1035cunits, but certainly it is not a Compton-thick source."," The spectrum of CDFS-9 is highly absorbed with a column density of $\sim10^{23}$, but certainly it is not a Compton-thick source."
 From Table 3 we see that the spectrum of CDFS-398 is flat (T'+0.5-Ε 0.3)., From Table \ref{xmm} we see that the spectrum of CDFS-398 is flat $\Gamma\approx 0.8\pm 0.3$ ).
 Since the source is detected by, Since the source is detected by
 The proper motionofthe barveenter is notimportant nol matterhowthe observed. proper motionis,"In order to maximize the yield of HOSAs (and some SOSAs), an SQL program needs to avoid MS and BD multiples."
 divided between (he center-ofF-mmass- ancl orbital components. The 57A elploving the orbital parameters only. We," The subset of 73,000 stars \citep{ARIHIP} that show no signs of binarity is a good starting point for the target selection of an SQL survey."
 have performed extensive mmuerical simulations to test analvtical relations forthe position differences, Those systems that do not show signs of binarity in the survey are likely to have either sub-stellar companions or stellar companions with very long-periods.
 derived above (Olling., Those systems warrant further SIM observations.
 2007).. Ourmodeling of the svstemcomprises an implementationof equations (1))withan arbitrary, The SQL follow-up survey of those stars with suspected sub-stellar companions would be significantly more sensitive than the SQL survey.
 barycentric motionanda periodicsignal in both coordinates (with random phases). We use this modelto predict the position atthe HIDPPARCOS eepoch.We, Figures similar to figure \ref{fig:SQL_position_residuals} but with employing the SQL follow-up data indicate (not shown) that the ESGPs can be detected with masses as low as 0.1 $_J$ in 10 year orbits.
 (hen generate.in Monte-Carlo fashion. many random realizations of the model whichare eepo, Period estimation for 1 [10] $_J$ is extended by a factor four [two] (to 40 [160] years).
"ch tovield A,,,.We perfor", A judicial combination of
"ch tovield A,,,.We perform", A judicial combination of
"ch tovield A,,,.We perform:", A judicial combination of
 zzc6 Z108M.. 10* inactive galaxies (e.g. Heckman et al., $z\approx 6$ $\gtsimeq 10^8 M_\odot$ $10^4$ inactive galaxies (e.g. Heckman et al.
 1991: Fynbo et al., 1991; Fynbo et al.
 1999; Steidel et al., 1999; Steidel et al.
 2000: Matsuda et al., 2000; Matsuda et al.
 2004; Weidinger et al., 2004; Weidinger et al.
 2004: Christensen et al., 2004; Christensen et al.
 2006: Hennawi et al., 2006; Hennawi et al.
 2009)., 2009).
 All of the above mechanisms have been proposed to explain the eemission from these objects and it is likely that a range of mechanisms are at work., All of the above mechanisms have been proposed to explain the emission from these objects and it is likely that a range of mechanisms are at work.
 JJ232908-030158 (hereafter JJ2329-0301) is a quasar at z=6.417 discovered in the Canada-France High-z Quasar Survey (CFHQS: Willott et al., J232908-030158 (hereafter J2329-0301) is a quasar at $z=6.417$ discovered in the Canada-France High-z Quasar Survey (CFHQS; Willott et al.
 2007)., 2007).
 It is radio-quiet (Wang et al., It is radio-quiet (Wang et al.
 2008) and powered by a black hole with mass ~2«108M... (Willott et al., 2008) and powered by a black hole with mass $\approx 2 \times 10^8 M_\odot$ (Willott et al.
 2010)., 2010).
 There is some evidence for a protocluster of companion star-forming galaxies based on deep multi-color imaging (Utsumi et al., There is some evidence for a protocluster of companion star-forming galaxies based on deep multi-color imaging (Utsumi et al.
 2010)., 2010).
 However. most of these objects are visible in the / band thumbnail images and therefore likely lie at redshift lower than z26.4.," However, most of these objects are visible in the $i'$ band thumbnail images and therefore likely lie at redshift lower than $z=6.4$."
 Goto et al. (, Goto et al. (
"2009; hereafter GO9) presented deep broad-band imaging observations of this quasar and showed that it is spatially extended at z/ band and possibly also at z, band.",2009; hereafter G09) presented deep broad-band imaging observations of this quasar and showed that it is spatially extended at $z'$ band and possibly also at $z_r$ band.
 The high level of extended emission at z/ band suggests that there is a large flux due to extended eemission., The high level of extended emission at $z'$ band suggests that there is a large flux due to extended emission.
 Willott et al. (, Willott et al. (
2007) found that the broad lline in this quasar has twice the equivalent width of typical quasars.,2007) found that the broad line in this quasar has twice the equivalent width of typical quasars.
 We present a deep long-slit spectroscopic observation of JJ2329-0301 with the aim of determining how much of the extended flux of G09 is due to eemission and its spatial and kinematic. distributions., We present a deep long-slit spectroscopic observation of J2329-0301 with the aim of determining how much of the extended flux of G09 is due to emission and its spatial and kinematic distributions.
 In Section 2 we analyze the imaging data of GO9., In Section 2 we analyze the imaging data of G09.
 In Section 3 we describe the spectroscopic observations and their analysis., In Section 3 we describe the spectroscopic observations and their analysis.
 Section 4 discusses the physical nature of this galaxy., Section 4 discusses the physical nature of this galaxy.
 All optical and near-IR magnitudes in this paper are on the AB system., All optical and near-IR magnitudes in this paper are on the AB system.
" Cosmological parameters of Hy=70kms!Mpe. On,=0.28 and O420.72 (Komatsu et al."," Cosmological parameters of $H_0=70~ {\rm km~s^{-1}~Mpc^{-1}}$, $\Omega_{\mathrm M}=0.28$ and $\Omega_\Lambda=0.72$ (Komatsu et al."
 2009) are assumed throughout., 2009) are assumed throughout.
 One aresecond on the sky corresponds to a physical size of kkpe at z= 6.417., One arcsecond on the sky corresponds to a physical size of kpc at $z=6.417$ .
 GO9 presented Subaru Suprime-Cam images of JJ2329-0301 in three broad-band filters: i’.— = and z.," G09 presented Subaru Suprime-Cam images of J2329-0301 in three broad-band filters: $i'$, $z'$ and $z_r$."
 The data were obtained in excellent conditions with seeing of 0.57., The data were obtained in excellent conditions with seeing of 0.5”.
 The quasar is very faint in the /' band (/2 25.5) due to IGM absorption shortward of the eemission line., The quasar is very faint in the $i'$ band $i'=25.5$ ) due to IGM absorption shortward of the emission line.
 Therefore no extended emission inthis filter, Therefore no extended emission inthis filter
The expressions for fafa’) ave presented in Appendix B of (Murray Dermott 1999).,The expressions for $f(a/a')$ are presented in Appendix B of (Murray Dermott 1999).
 Under a series of variable trausformatious (seo Peale 1986 for derivation). this Ihuniltoniaun cau be rewritten to take a simpler fori.," Under a series of variable transformations (see Peale 1986 for derivation), this Hamiltonian can be rewritten to take a simpler form."
 Let us iutroduce the coustauts o. 2 id e: where s] ds sum of the EKKeplenan mean motion aud the secular change in mean longitudes.," Let us introduce the constants $\alpha$ , $\beta$ and $\epsilon$: where $n^*$ is sum of the Keplerian mean motion and the secular change in mean longitudes."
 It is important to note that these expressions are uot strictly constant. siuce seni-imajor axis changes.," It is important to note that these expressions are not strictly constant, since semi-major axis changes."
 However. Jis only weakly dependent on senianajor axis (Peale 1976). aud in the case of e. variations due to the cosine term dominate. so the asstuuption of constant coefficients is sound (Murray and Derinott 1999).," However, $\beta$ is only weakly dependent on semi-major axis (Peale 1976), and in the case of $\epsilon$, variations due to the cosine term dominate, so the assumption of constant coefficients is sound (Murray and Dermott 1999)."
 Relative to the original Tamiltouian. we scale the momentum as: The corresponding conjugate angle o is simply the cosine argument in equation (5). although if e>0. we also need to add x to the expression (Murray Dermott 1999).," Relative to the original Hamiltonian, we scale the momentum as: The corresponding conjugate angle $\phi$ is simply the cosine argument in equation (5), although if $\epsilon > 0$, we also need to add $\pi$ to the expression (Murray Dermott 1999)."
 That said. the trausforiied Tamiltonian takes the forma This IEuniltonian is parameterized by which is a measure of the perturbed objects proximity to exact resonance.," That said, the transformed Hamiltonian takes the form This Hamiltonian is parameterized by which is a measure of the perturbed object's proximity to exact resonance."
 Finally we note that this Wamultomian Is most casily visualized in terms of polar coordinates. so we introduce the new mixed canonical variables «=Y20coso aud y=VY2@sine (TWeurard Lamaitre 1983).," Finally we note that this Hamiltonian is most easily visualized in terms of polar coordinates, so we introduce the new mixed canonical variables $x = \sqrt{2 \Phi} \cos{\phi}$ and $y = \sqrt{2 \Phi} \sin{\phi}$ (Henrard Lamaitre 1983)."
" The Tanultomian now takes the form Upon application of Iuniltou equatious. we see that the stationary points of the aboves Ihuniltoniamn are described by the equation For resonant eucouuters aided by divergent migration. à<3 initially,"," The Hamiltonian now takes the form Upon application of Hamilton's equations, we see that the stationary points of the above Hamiltonian are described by the equation For resonant encounters aided by divergent migration, $\delta < 3$ initially."
 In this case. the existence of a separatrix is ensured. aud there are three real fixed. points. all of which lie on the x-axis.," In this case, the existence of a separatrix is ensured, and there are three real fixed points, all of which lie on the x-axis."
 Two of these poiuts are always uceative. aud the more negative oue is unstable. as it lies ou the intersection of the inner aud the outer branches of the separatrix.," Two of these points are always negative, and the more negative one is unstable, as it lies on the intersection of the inner and the outer branches of the separatrix."
 This is crucial to the estimation of eccentricity juups cing resonant eucouuters., This is crucial to the estimation of eccentricity jumps during resonant encounters.
 If migration is slow enough for à to be approximatcly constant over one period of motion. the action. defied as is an adiabatic invariant (Peale 1986).," If migration is slow enough for $\delta$ to be approximately constant over one period of motion, the action, defined as is an adiabatic invariant (Peale 1986)."
 Iun other words. it ix constant except durus separatrix crossing.," In other words, it is constant except during separatrix crossing."
 Furthermore. when the separatrix is far away. the trajectories of the circulating orbits in (Gc.4) space are circles to a good approximation.," Furthermore, when the separatrix is far away, the trajectories of the circulating orbits in $x,y$ ) space are circles to a good approximation."
 Cousequenthy. we can write J=270 (Muay Dermott 1999).," Consequently, we can write $J = 2 \pi \Phi$ (Murray Dermott 1999)."
 When two planets approach connaieusurabilitv. a wide separatiix is ποσα as shrinkiug down on the orbit of 1ο perturbed planet in (60.4) space.," When two planets approach commensurability, a wide separatrix is seen as shrinking down on the orbit of the perturbed planet in $x,y$ ) space."
 When the inner vauch of the separatrix eugulfs the planetary orbit. le process of resonance crossing ds characterized bv 16 planet switching to the separatrixs outer circulating xench.," When the inner branch of the separatrix engulfs the planetary orbit, the process of resonance crossing is characterized by the planet switching to the separatrix's outer circulating branch."
 The outer branch has a wider radius. thus 1ο inerease dn action.," The outer branch has a wider radius, thus the increase in action."
 However. during this switch. 1e perturbed planet must necessarily pass through the unstable stationary point described above.," However, during this switch, the perturbed planet must necessarily pass through the unstable stationary point described above."
" Cousequeutly. je caleulation is as follows: kuowine the action prior to ie resonant encounter. we can determine the value of >, at the transition using equation (13)."," Consequently, the calculation is as follows: knowing the action prior to the resonant encounter, we can determine the value of $\delta$ at the transition using equation (13)."
 Recall however. wat 6 also parancterizes the Wamiltonian. and therefore determines the shape of the separatrix. while the area eueulfed by the outer branch corresponds to the new action (sce supplemental material of Tsiaganis et al.," Recall however, that $\delta$ also parameterizes the Hamiltonian, and therefore determines the shape of the separatrix, while the area engulfed by the outer branch corresponds to the new action (see supplemental material of Tsiaganis et al."
 2005 ‘or an intuitive discussion)., 2005 for an intuitive discussion).
 It can be shown that the actions before and after resonance crossing are related N Thus. the new eccentricity can be easily backed out.," It can be shown that the actions before and after resonance crossing are related by Thus, the new eccentricity can be easily backed out."
 The above analysis can also be applied to external resonances., The above analysis can also be applied to external resonances.
 Iu this case. > in the cosine arguineut of the ILuuiltoniau (5) is replaced by 5. aud its factor 20A is replaced by ονAT since we are now concerned with ane’ resonance.," In this case, $\gamma$ in the cosine argument of the Hamiltonian (5) is replaced by $\gamma'$, and its factor $\sqrt{2 \Gamma / \Lambda}$ is replaced by $\sqrt{2 \Gamma' / \Lambda'}$, since we are now concerned with an $e'$ resonance."
 Accordingly. we change tle scaling factors to while 2j! remains the same.," Accordingly, we change the scaling factors to while $\beta$ remains the same."
 Note also that any indirect ternis in the expansion of the disturbing function must be accounted for in flefat)., Note also that any indirect terms in the expansion of the disturbing function must be accounted for in $f(a/a')$.
 Under these trausformatious. ILuniltonian (10) still applies. aud so docs the subsequent analysis (Murray and Dermott 1999).," Under these transformations, Hamiltonian (10) still applies, and so does the subsequent analysis (Murray and Dermott 1999)."
 The resulting estimates of eccentricity jumps for various first-order resonant encounters between Urauus Neptune and Satur Uranus are listed in Table (1)., The resulting estimates of eccentricity jumps for various first-order resonant encounters between Uranus Neptune and Saturn Uranus are listed in Table (4).
 As can be seen frou these caleulatious. all first-order resonant eucounters between Urauus aud Neptune produce rather small eccentricity jumps.," As can be seen from these calculations, all first-order resonant encounters between Uranus and Neptune produce rather small eccentricity jumps."
 Therefore. we disfavor them as good options for trigecringCoco» instability scenarios in which cucounters with Saturn take place.," Therefore, we disfavor them as good options for triggering instability scenarios in which encounters with Saturn take place."
 NAunuernical iutegrations performed iu the two previous sections are sugecstive of this as well., Numerical integrations performed in the two previous sections are suggestive of this as well.
 We therefore rule out the configurations where Saturn aud Uranus are πι a 2:1 MMR., We therefore rule out the configurations where Saturn and Uranus are in a 2:1 MMR.
" Resonaut eucouuters between Satur ando Uranus. however. are ao different storv: du adl cases, Uranus acquires an eccentricity comparable to 0.1."," Resonant encounters between Saturn and Uranus, however, are a different story: in all cases, Uranus acquires an eccentricity comparable to $0.1$."
 Suuulatious reveal that the configurations where Saturn aud Uranus are in a 3:2 MM do not resultiu strong instabilities., Simulations reveal that the configurations where Saturn and Uranus are in a 3:2 MMR do not resultin strong instabilities.
 This is because the system is eiven a chance to encounter lieh-order MMB between Uranus aud Neptune aud spread out before crossing8 the, This is because the system is given a chance to encounter high-order MMR's between Uranus and Neptune and spread out before crossing the
J0612 was observed with over two consecutive days with a total of 392216 s from PCU?2 (see Table 1)).,J0612 was observed with over two consecutive days with a total of 216 s from PCU2 (see Table \ref{observing_log}) ).
 The 2- keV raw count rate varied between 1.95.3 ct s! and the background subtracted count rate had à mean of close to 0.0 et s7!., The 2--10 keV raw count rate varied between 1.9–5.3 ct $^{-1}$ and the background subtracted count rate had a mean of close to 0.0 ct $^{-1}$.
 The background may therefore be over-subtracted. but in any case the source is at the limit of detectability in this observation.," The background may therefore be over-subtracted, but in any case the source is at the limit of detectability in this observation."
 Fig., Fig.
 5 shows the cLEANed power spectrum of the 2-10 keV background subtracted light curve., \ref{J0612_cleaned} shows the ed power spectrum of the 2–10 keV background subtracted light curve.
" Five peaks stand out in the plot. 50 cycles day! (173449 s). SO cycles day! (1083 4). 296 cycles day! (292.3+033 κ]. 592 cycles day! (146.0+0.1 s). and 626 cycles day""! nO0+0.1 s)."," Five peaks stand out in the plot, 50 cycles $^{-1}$ $1734\pm9$ s), 80 cycles $^{-1}$ $1083\pm4$ s), 296 cycles $^{-1}$ $292.3\pm0.3$ s), 592 cycles $^{-1}$ $146.0\pm0.1$ s), and 626 cycles $^{-1}$ $138.0\pm0.1$ s)."
 The 2-10 keV light curve folded at the one of these that is most typical of an IPspin period (1.9. 292.3 s) is shown in Fig. 6.., The 2–10 keV light curve folded at the one of these that is most typical of an IP spin period (i.e. 292.3 s) is shown in Fig. \ref{J0612_folded_at_292p3}.
 A coherent modulation is seen. but the error bars are large and the profile is consistent with zero modulation (and indeed zero flux).," A coherent modulation is seen, but the error bars are large and the profile is consistent with zero modulation (and indeed zero flux)."
 As with JOI53. the background subtracted spectrum 1s too faint to obtain a meaningful fit.," As with J0153, the background subtracted spectrum is too faint to obtain a meaningful fit."
 An uncategorised X-ray source Is also in the field of view. and may contribute a comparable count rate to the target.," An uncategorised X-ray source is also in the field of view, and may contribute a comparable count rate to the target."
 We also note that JO162 is not found in the all sky survey. so is likely to be a transient object.," We also note that J0162 is not found in the all sky survey, so is likely to be a transient object."
 Sadly. given its faintness in this observation. we cannot comment further on its nature.," Sadly, given its faintness in this observation, we cannot comment further on its nature."
 V436 Car (RX JO744.9-5257) was identified as a CV by ? in the all-sky survey.," V436 Car (RX $-$ 5257) was identified as a CV by \citet{motch96}
 in the all-sky survey."
 ? carried out optical and X-ray analysis of the object. concluding it was a likely IP.," \citet{ramsay98} carried out optical and X-ray analysis of the object, concluding it was a likely IP."
 They found, They found
The TW Hydrae Association (TWA) is à young. nearby association consisting of about 25 known members.,"The TW Hydrae Association (TWA) is a young, nearby association consisting of about 25 known members."
 Due to its youth and proximity. this association has been intensively studied in the last decade revealing a great variety of systems: tight astrometric binaries good to calibrate PMS models. stars and brown dwarfs harbouring circumstellar disks. planetary and brown dwarf companions. and more recently a putative massive planet embedded in its own proto-planetary disks (TW Hya: Setiawanetal. 2008)).," Due to its youth and proximity, this association has been intensively studied in the last decade revealing a great variety of systems: tight astrometric binaries good to calibrate PMS models, stars and brown dwarfs harbouring circumstellar disks, planetary and brown dwarf companions, and more recently a putative massive planet embedded in its own proto-planetary disks (TW Hya; \cite{seti08}) )."
 Surprisingly. only five members have known trigonometric parallaxes.," Surprisingly, only five members have known trigonometric parallaxes."
 De la Reza et al. (, De la Reza et al. (
2006) report a trace-back age of 8.3+0.8 Myr. independent of evolutionary models.,"2006) report a trace-back age of $8.3\pm0.8$ Myr, independent of evolutionary models."
 Relying on astrometric and spectroscopic data. the Galactic space motions of TWA members are traced backward in time until they occupy à minimum volume in space.," Relying on astrometric and spectroscopic data, the Galactic space motions of TWA members are traced backward in time until they occupy a minimum volume in space."
 This age estimation would greatly benefit from parallax neasurements of additional TWA nembers., This age estimation would greatly benefit from parallax measurements of additional TWA members.
 Scholzetal.(2005). discovered a new young sub-stellar object. SSSPMJI1102-343] (SSSPMJIIO2). a probable nember of TWA.," \cite {scho05} discovered a new young sub-stellar object, SSSPMJ1102-3431 (SSSPMJ1102), a probable member of TWA."
 Its photometric and spectroscopic characteristics suggest à young brown dwarf of spectral type 15.5., Its photometric and spectroscopic characteristics suggest a young brown dwarf of spectral type M8.5.
 Located 12 from TW Hya and sharing similar proper notions. Scholz et al. (," Located $12\arcmin$ from TW Hya and sharing similar proper motions, Scholz et al. ("
2005) suggested that SSSPMJI102 could form a binary system with TW Hya.,2005) suggested that SSSPMJ1102 could form a binary system with TW Hya.
 Assuming an age of 10 Myr (Webbetal. 1999)) and the Hipparcos distance for TW Hya they derived for SSSPMJ1102 a mass of =25M., Assuming an age of 10 Myr \cite {webb99}) ) and the Hipparcos distance for TW Hya they derived for SSSPMJ1102 a mass of $\approx 25 M_{Jup}$.
 Recently. a flat optically thick disk was discovered arounc SSSPMJI102 (Riaz&Gizis 2008)) based on a reconstructed mid-infrared spectral energy distribution using broad-band photometry (Sterziketal.2004:; Riazetal. 2006)).," Recently, a flat optically thick disk was discovered around SSSPMJ1102 \cite {riaz08}) ) based on a reconstructed mid-infrared spectral energy distribution using broad-band photometry \cite {ster04}; \cite {riaz06}) )."
 Utilizing combined NASA IRTF and Spitzer spectroscopic observations. Morrowetal.2008 argued in favor of high degrees of dust settling to the disk midplane as well as significant grain growth in the upper layers. suggesting rapid dust processing compared to disks around stars.," Utilizing combined NASA IRTF and Spitzer spectroscopic observations, \cite {morr08} argued in favor of high degrees of dust settling to the disk midplane as well as significant grain growth in the upper layers, suggesting rapid dust processing compared to disks around stars."
 Characterization of SSSPMJI102 itself and its disk properties and the question of binarity status with TW Hya make a distance determination of substantial interest., Characterization of SSSPMJ1102 itself and its disk properties and the question of binarity status with TW Hya make a distance determination of substantial interest.
 Since January 2006 we have conducted astrometric and photometric observations at the ESO NTT telescope to derive the trignometric parallax of SSSPMJ1102., Since January 2006 we have conducted astrometric and photometric observations at the ESO NTT telescope to derive the trignometric parallax of SSSPMJ1102.
 Our observations are presented in Section 2., Our observations are presented in Section 2.
 The data reduction and analysis and the result of this trigonometric parallax programme are given in Section 3., The data reduction and analysis and the result of this trigonometric parallax programme are given in Section 3.
 Finally. membership in TWA. the physical properties of SSSPMJ1102 compared to other TWA substellar objects. and the binarity status with TW Hya are discused respectively in Sections 4. 5 and 6.," Finally, membership in TWA, the physical properties of SSSPMJ1102 compared to other TWA substellar objects, and the binarity status with TW Hya are discused respectively in Sections 4, 5 and 6."
came to the same conclusion analyzing the clustering properties of barred and unbarred galaxies of similar stellar mass and finding it indistinguishable over all the scales probed ~20 kpc to 30 M,came to the same conclusion analyzing the clustering properties of barred and unbarred galaxies of similar stellar mass and finding it indistinguishable over all the scales probed (from $\sim$ 20 kpc to 30 Mpc).
"ore recently, the Coma cluster (fromwas studied by Méndez-AbreuMpc).etal. (2010):: they find that the bar fraction does not vary significantly even when going from the center to the cluster outskirts."," More recently, the Coma cluster was studied by \cite{MendezAbreu2010}: they find that the bar fraction does not vary significantly even when going from the center to the cluster outskirts."
" However, the Coma cluster is such an extreme environment that most of its apparent spiral galaxy population may be field galaxies in projection."," However, the Coma cluster is such an extreme environment that most of its apparent spiral galaxy population may be field galaxies in projection."
" In the light of these observational results and motivation from numerical simulation studies, we aim at measuring the bar fraction (as number of barred discs over the total number of discs) as a function of environment and disc morphology, at z~0 in two carefully selected samples representative of a low-density environment (the isolated galaxies from the AMIGA sample) and of a moderately dense environment (galaxies in the Virgo cluster)."," In the light of these observational results and motivation from numerical simulation studies, we aim at measuring the bar fraction (as number of barred discs over the total number of discs) as a function of environment and disc morphology, at $z\sim0$ in two carefully selected samples representative of a low-density environment (the isolated galaxies from the AMIGA sample) and of a moderately dense environment (galaxies in the Virgo cluster)."
" 'To achieve this goal it is important to use homogeneous classifications since, as we have shown in Giordano et al, ("," To achieve this goal it is important to use homogeneous classifications since, as we have shown in Giordano et al., ("
"2010) (paperl hereafter), the bar fraction is very stable against sample selection but that some (possibly spurious) differences can arise if the comparison is based on samples classified using different methods (for example visual classification versus automated profile ","2010) (paperI hereafter), the bar fraction is very stable against sample selection but that some (possibly spurious) differences can arise if the comparison is based on samples classified using different methods (for example visual classification versus automated profile fitting)."
"In particular, the way the disc population is fitting).identified and isolated plays a crucial role, since, if no detailed morphological information is available, discs can easily be miscounted (for example applying only color magnitude cuts)."," In particular, the way the disc population is identified and isolated plays a crucial role, since, if no detailed morphological information is available, discs can easily be miscounted (for example applying only color and/or magnitude cuts)."
" In and/ororder to address this, we use data from the UKIDSS Large Area Survey (Lawrenceetal.2007) and from SDSS DR7 (Abazajianetal. with the great advantage of combining opticalrgb 2009),,images with near-infrared (H-band) imaging with excellent resolution for local universe studies, that allow us to visually inspect the images to provide detailed morphological classifications."," In order to address this, we use data from the UKIDSS Large Area Survey \citep{Lawrence2007} and from SDSS DR7 \citep{Abazajian2009}, with the great advantage of combining optical images with near-infrared (H-band) imaging with excellent resolution for local universe studies, that allow us to visually inspect the images to provide detailed morphological classifications."
" The outline of the paper is the following: in section 2 we present the data that we are using, their classification and the selection of the samples based on local density estimation."," The outline of the paper is the following: in section \ref{sec.data} we present the data that we are using, their classification and the selection of the samples based on local density estimation."
 The results about the bar fraction in the different cases are presented in section and discussed in section 84.., The results about the bar fraction in the different cases are presented in section and discussed in section \ref{sec.discussion}.
 In PaperI we presented a thorough study of the barred galaxies in the Virgo Cluster from which we adopt all the classified galaxies with a measured H-band magnitude from 2MASS., In PaperI we presented a thorough study of the barred galaxies in the Virgo Cluster from which we adopt all the classified galaxies with a measured H-band magnitude from 2MASS.
" The ddisk sample is composed of moderately inclined (axis ratio larger than 0.4) members with UKIDSS near-IR imaging of Hubble type between SO and Sm, spanning a H-band magnitude (stellar mass) range of -17 to -25 mag (105 to 1013 Ma)."," The disk sample is composed of moderately inclined (axis ratio larger than 0.4) members with UKIDSS near-IR imaging of Hubble type between S0 and Sm, spanning a H-band magnitude (stellar mass) range of -17 to -25 mag $10^8$ to $10^{12}$ $_{\odot}$ )."
" In the following analysis, we use the H-band magnitudes from Paper I to compute stellar masses assuming a flat (B—H) color with a Ty,=1."," In the following analysis, we use the H-band magnitudes from Paper I to compute stellar masses assuming a flat $(B-H)$ color with a $\Upsilon_{H,*}=1$."
" 'The local galaxy density for members is determined via the ps proxy (Baldryetal.2006),, using the positions and magnitudes from the Virgo Cluster Catalog etal. 1984)."," The local galaxy density for members is determined via the $\rho_5$ proxy \citep{Baldry2006}, using the positions and magnitudes from the Virgo Cluster Catalog \citep{Binggeli1984_P1}."
" To provide a robust comparison to the ssample, we select a true ssample using the AMIGA (Analysis of the interstellar Medium of Isolated GAlaxies) project (Verdes-Montenegroetal. 2005)."," To provide a robust comparison to the sample, we select a true sample using the AMIGA (Analysis of the interstellar Medium of Isolated GAlaxies) project \citep{Verdes-Montenegro2005_A01}."
. The AMIGA catalogue is based on the KIG catalog Karachentseva of isolated galaxies (z< ," The AMIGA catalogue is based on the KIG catalog \cite{Karachentseva1973} of isolated galaxies $z \lesssim
0.1$ )."
The KIG catalog is (1973)composed of 1050 galaxies with apparent0.1). blue magnitudes brighter than 15.7 mag; these isolated galaxies are selected to have no neighbor of comparable size within twenty galactic diameters., The KIG catalog is composed of 1050 galaxies with apparent blue magnitudes brighter than 15.7 mag; these isolated galaxies are selected to have no neighbor of comparable size within twenty galactic diameters.
 The KIG catalog has been used by multiple studies to investigate the effects of under-dense environment on galaxy properties (Adamsetal.1980;Haynes&Giovanelli1980) and the AMIGA project quantified the isolation of KIG galaxies identifying their sample of 791 genuinely isolated galaxies Verleyetal. (2007a)..," The KIG catalog has been used by multiple studies to investigate the effects of under-dense environment on galaxy properties \citep{Adams1980, Haynes1980} and the AMIGA project quantified the isolation of KIG galaxies identifying their sample of 791 genuinely isolated galaxies \cite{Verley2007_A05}."
 The AMIGA project has also compiled multiwavelength coverage of this statistically significant sample of the most isolated galaxies in the local universe and the dataset includes optical photometry, The AMIGA project has also compiled multiwavelength coverage of this statistically significant sample of the most isolated galaxies in the local universe and the dataset includes optical photometry
cometary activity that appears distinct from Echeclus itself.,cometary activity that appears distinct from Echeclus itself.
White D.A.. Jones €.. Forman W.. 1997. MNILAS. 292. White S.D.M. Rees AL. 1978. MINAS. 183. Wu Ek.S. Fabian A.C... Nulsen 110... 1905. MNILAS. 301. Wu WAALS... Fabian A.C.. Nulsen 110... 2000. NMINILAS. 31S. Zamorani αι. Alienoli M.. Hasinger G.. Bure R.. Ciacconi I... Schmidt AL. Trumper J.. Ciliegi P. Ciruppioni C.. Marano D.. 1999. VA. 346. In this appendix we give descriptions of the additional candidate groups and clusters.,"White D.A., Jones C., Forman W., 1997, MNRAS, 292, White S.D.M. Rees M., 1978, MNRAS, 183, Wu K.K.S., Fabian A.C., Nulsen P.E.J., 1998, MNRAS, 301, Wu K.K.S., Fabian A.C., Nulsen P.E.J., 2000, MNRAS, 318, Zamorani G., Mignoli M., Hasinger G., Burg R., Giacconi R., Schmidt M., Trumper J., Ciliegi P., Gruppioni C., Marano B., 1999, A, 346, In this appendix we give descriptions of the additional candidate groups and clusters."
 MOS. noted that this source. is in a confused area., M98 noted that this source is in a confused area.
 The PSPC X-ray source consists of a dominant. point-like source with a fainter. possibly extended. component. to he SW.," The PSPC X-ray source consists of a dominant point-like source with a fainter, possibly extended, component to the SW."
 There are several pieces of evidence. suggesting hat the dominant source is not a cluster., There are several pieces of evidence suggesting that the dominant source is not a cluster.
 The PSPC yurdness ratio (0.37250.03) is inconsistent with the hardness ratios of the confirmed group and clusters. and. with that oedieted: for thermal X-ray spectra (see MOS).," The PSPC hardness ratio $\pm$ 0.03) is inconsistent with the hardness ratios of the confirmed group and clusters, and with that predicted for thermal X-ray spectra (see M98)."
 Phe HEU data are consistent with a point-like source. anc finally he PSPC count rates in both the hare ancl soft. bands vary significantly (ancl consistently) between the two PSPC observation epochs. separated by 2 vears.," The HRI data are consistent with a point-like source, and finally the PSPC count rates in both the hard and soft bands vary significantly (and consistently) between the two PSPC observation epochs, separated by 2 years."
 After measuring and subtracting the point-source flux within an aperture of radius 30 aresec (containing of the 1 keV flux). the remaining total extended PSPC lux is <4.9x10 1%L5. below the Bux limit considered bere.," After measuring and subtracting the point-source flux within an aperture of radius 30 arcsec (containing of the 1 keV flux), the remaining total extended PSPC flux is $\la$ $^{-15}$, below the flux limit considered here."
 As noted by M9S. this source (which we label 5b) is coincident with an excess of faint galaxies. the redshifts of which are unknown.," As noted by M98, this source (which we label 5b) is coincident with an excess of faint galaxies, the redshifts of which are unknown."
 A nearby stellar object is also a possible counterpart to source 5b., A nearby stellar object is also a possible counterpart to source 5b.
 An absorption-line galaxy at a redshilt of z=0.709 [ies only 0.6 aresec from the HAE position. which confirms the SPC counterpart.," An absorption-line galaxy at a redshift of z=0.709 lies only 0.6 arcsec from the HRI position, which confirms the PSPC counterpart."
 The optical spectrum of the galaxy is of low signal-noise., The optical spectrum of the galaxy is of low signal-noise.
 No exeess of galaxies is visible to a imit in It 223.5 mag fainter than this galaxy., No excess of galaxies is visible to a limit in R $\approx$ 3.5 mag fainter than this galaxy.
 The mere fact of detection in the LIRI suggests that the X-ray emission does not originate in an extended: intra-cluster medium. rut in à point source associated with the galaxy.," The mere fact of detection in the HRI suggests that the X-ray emission does not originate in an extended intra-cluster medium, but in a point source associated with the galaxy."
 “Phe X-rav luminosity (3x104? 13) is. however. much higher han expected for a normal galaxy. ancl this source may be similar to the sources found in deep Chandra surveys which iive optically unremarkable late-tvpe galaxy. counterparts (ος.," The X-ray luminosity $^{43}$ ) is, however, much higher than expected for a normal galaxy, and this source may be similar to the sources found in deep Chandra surveys which have optically unremarkable late-type galaxy counterparts (eg."
 Alushotzky 2000)., Mushotzky 2000).
 Lt is unlikely to originate in a cluster., It is unlikely to originate in a cluster.
 The X-ray source has at least 2 components., The X-ray source has at least 2 components.
 An LIU detection of a point source coincident with an absorption line galaxy at. z=0.257 (confirming the PSPC) position) sugeests that the tentative identification of ALOS with a narrow emission line galaxy was incorrect., An HRI detection of a point source coincident with an absorption line galaxy at z=0.257 (confirming the PSPC position) suggests that the tentative identification of M98 with a narrow emission line galaxy was incorrect.
 As noted by ALOS. the X-ray. data are Consistent with two point sources. although some contribution from an extended. intra-group mecium is possible.," As noted by M98, the X-ray data are consistent with two point sources, although some contribution from an extended intra-group medium is possible."
 Phere are several R=18-19 mae galaxies nearby. but none of the four measured redshifts falls within 1000 km of any of the others. suggesting that the excess of galaxies is partlv a projection ellect.," There are several R=18-19 mag galaxies nearby, but none of the four measured redshifts falls within 1000 km $^{-1}$ of any of the others, suggesting that the excess of galaxies is partly a projection effect."
 The HII detection (with. a [lux consistent with the PSPC Lux) sugeests that most of the X-ray emission originates in the 2=0.257 absorption line galaxy rather than in an intra-group Μποαμα., The HRI detection (with a flux consistent with the PSPC flux) suggests that most of the X-ray emission originates in the z=0.257 absorption line galaxy rather than in an intra-group medium.
" The galaxy is luminous optically (Alj=-23.5) and in X-ravs (Ly=tx10"" 13) and has LLg)z- Ls. higher than that of anv of the SI early tvpe galaxies stucied by Canizares. Fabbiano Trinchieri (1987)."," The galaxy is luminous optically $_R$ =-23.5) and in X-rays $_X$ $^{42}$ ) and has $L_X^{bol}/L_B$ $\approx$ -1.8, higher than that of any of the 81 early type galaxies studied by Canizares, Fabbiano Trinchieri (1987)."
 It may contain an AGN. like the early tvpe galaxy counterparts to sources detected in deep Chandra surveys. although no optical emission lines are observed.," It may contain an AGN, like the early type galaxy counterparts to sources detected in deep Chandra surveys, although no optical emission lines are observed."
 A luminous (M; —-22.7) galaxy at a recdshift of z=0.251 lies 9 avesce from the PSPC position and there is a small excess of fainter galaxies (1119) nearby., A luminous $_R$ =-22.7) galaxy at a redshift of z=0.251 lies 9 arcsec from the PSPC position and there is a small excess of fainter galaxies $>$ 19) nearby.
 The X-ray. source is unresolved by the PSPC. but is undetected by the LEBU. suggesting that it is either a low luminosity (Lx 107 iy. compact extended source (of extent zz 10-20 aresee or 50-100 kpe at z=0.251). or a variable point source.," The X-ray source is unresolved by the PSPC, but is undetected by the HRI, suggesting that it is either a low luminosity $L_X$ $^{42}$ ), compact extended source (of extent $\approx$ 10-20 arcsec or 50-100 kpc at z=0.251), or a variable point source."
 There are no optical objects of stellar appearance with 1124.5 in the error circle. which could. be QSOs. but. rather several [aint (R~22) galaxies.," There are no optical objects of stellar appearance with $<$ 24.5 in the error circle, which could be QSOs, but rather several faint $\sim$ 22) galaxies."
 Phe source could be à poor group dominated by the luminous galaxy (with the lowest X-rav luminosity of any system in the eroup/cluster sample). but the positional olfset of the luminous galaxy. makes this uncertain.," The source could be a poor group dominated by the luminous galaxy (with the lowest X-ray luminosity of any system in the group/cluster sample), but the positional offset of the luminous galaxy makes this uncertain."
 A very luminous elliptical galaxy of Aly 2-23.7 (3L) with an absorption line spectrum at a redshift of z=0.307 is the probable counterpart to the X-ray source., A very luminous elliptical galaxy of $M_R\approx$ -23.7 $\approx$ $^*$ ) with an absorption line spectrum at a redshift of z=0.307 is the probable counterpart to the X-ray source.
 A second. nearby. fainter galaxy has the same recdshilt.," A second, nearby, fainter galaxy has the same redshift."
 Phe lack of an obvious excess of galaxies to a limit 6 magnitudes Painter than that of the bright galaxy and the low X-ray luminosity (34x10 13) suggest that a large fraction of the X- emission may originate in an individual elliptical galaxy rather than in an intra-group medium. although the value ο Lm Lg)7z-1.9 is. higher. than that of any of⋅ the early type galaxies ofCanizares (1987).," The lack of an obvious excess of galaxies to a limit 6 magnitudes fainter than that of the bright galaxy and the low X-ray luminosity $^{42}$ ) suggest that a large fraction of the X-ray emission may originate in an individual elliptical galaxy rather than in an intra-group medium, although the value of $L_X^{bol}/L_B$ $\approx$ -1.9 is higher than that of any of the early type galaxies of Canizares (1987)."
 Phe source may be a fossil group of the twpe studied by Jones et al. (, The source may be a fossil group of the type studied by Jones et al. (
2000b).,2000b).
 The olfset between the X-ray centroid and the brightest galaxy is large (15 aresee). but this source is the furthest oll-axis in the PSPC of any in the sample.," The offset between the X-ray centroid and the brightest galaxy is large (15 arcsec), but this source is the furthest off-axis in the PSPC of any in the sample."
 At this oll-axis angle (14 arcmin) the PSPC 1 keV PSE is almost double the size of the on-axis value. so larger position errors are expected.," At this off-axis angle (14 arcmin), the PSPC 1 keV PSF is almost double the size of the on-axis value, so larger position errors are expected."
to LGRBs that are expected to be more energetic (e.g. MacFadyen Woosley 1999): [rom (hese assumptions low metallicities should produce LGRBs with a higher energv release in ihe gamma-ray regime (47. ).,to LGRBs that are expected to be more energetic (e.g. MacFadyen Woosley 1999); from these assumptions low metallicities should produce LGRBs with a higher energy release in the gamma-ray regime $E_{\gamma}$ ).
 several previous studies have investigated this possibili., Several previous studies have investigated this possibility.
 Ramirez-Raiz et ((2002) found a (tentative positive correlation between (he isotropic energv release (£7.το) and the olfset ofa GRB from the center of its host galaxy (r4).," Ramirez-Ruiz et (2002) found a tentative positive correlation between the isotropic energy release $E_{\gamma,iso}$ ) and the offset of a GRB from the center of its host galaxy $r_0$ )."
 This offset correlation was proposed be a potential arlilact of a correlation between. νοτο and low metallicity chemical abundance gradients have shown that stars at higher rj. in the outskirts of their hosts. have lower metallicities on average (e.g. Zaritskv et 11994. van Zee 1998. Henry Worthey 1999).," This offset correlation was proposed to be a potential artifact of a correlation between $E_{\gamma,iso}$ and low metallicity – chemical abundance gradients have shown that stars at higher $r_0$, in the outskirts of their hosts, have lower metallicities on average (e.g. Zaritsky et 1994, van Zee 1998, Henry Worthey 1999)."
 Since Eyο is calculated assuming a quasi-spherical GRB explosion geometry. rather than accounting for the expected effects of a potential conical geometry wilh a narrow opening angle lor the GRB jet (0 see Frail et 22001). this result suggested that low metallicity was associated with either higher E or narrower GRB jets.," Since $E_{\gamma,iso}$ is calculated assuming a quasi-spherical GRB explosion geometry, rather than accounting for the expected effects of a potential conical geometry with a narrow opening angle for the GRB jet $\theta_j$; see Frail et 2001), this result suggested that low metallicity was associated with either higher $E_{\gamma}$ or narrower GRB jets."
 A comparison between host metallicity and νοτω lor 5 nearby GRBs (z < 0.3) was performed by Stanek et ((2006).," A comparison between host metallicity and $E_{\gamma,iso}$ for 5 nearby GRBs (z $<$ 0.3) was performed by Stanek et (2006)."
 These authors found a correlation between (he two quantities., These authors found a correlation between the two quantities.
" All but one of the bursts in this sample were “sub-luninous” LGRBs. a potentially unique class of GRB with ££; that are much lower (han the general population (e.g. Soderberg et ""22004a. Soderberg MN2006)."," All but one of the bursts in this sample were “sub-luminous"" LGRBs, a potentially unique class of GRB with $E_{\gamma,iso}$ values that are much lower than the general population (e.g. Soderberg et 2004a, Soderberg 2006)."
" οStanek et ((2006) argued (hat this correlation supported the of a “threshold” for producing “cosmological GRBs with more (vpical huninosities. given (hat the burst with the highest yj. in the sample was produced in the host galaxy. with the lowest metallicity,"," Stanek et (2006) argued that this correlation supported the idea of a “threshold"" metallicity for producing “cosmological"" GRBs with more typical luminosities, given that the burst with the highest $E_{\gamma,iso}$ in the sample was produced in the host galaxy with the lowest metallicity."
 However. (μον also cautioned (hat (his conclusion was speculative due to the small size and sub-Iuminous nature of their sample.," However, they also cautioned that this conclusion was speculative due to the small size and sub-luminous nature of their sample."
" Wolf Podsiadlowski (2007) also imvestigated (he possibility of a (vend relating ££; and metallicitv. performing the same comparison described in Stanek οἱ ((2006) and including a of 13 ""cosmological (2> 0.2) LGRBs."," Wolf Podsiadlowski (2007) also investigated the possibility of a trend relating $E_{\gamma,iso}$ and metallicity, performing the same comparison described in Stanek et (2006) and including a sample of 13 “cosmological"" $z > 0.2$ ) LGRBs."
 They concluded that. while the Sianek et uM((2006) relation holds true for the nearby sub-luminous LGRBs. no relation is apparent in (he larger sample.," They concluded that, while the Stanek et (2006) relation holds true for the nearby sub-luminous LGRBs, no relation is apparent in the larger sample."
 However. the metallicies derived [or (hese “cosmological” LGRBs were extvapolated [rom the general Iuminositv-metallicitv relation for star-lormine a relation host are now known to not follow (Ixewlev οἱ . veeModjaz et Oe08. MNLevesque et NN22010).," However, the metallicies derived for these “cosmological"" LGRBs were extrapolated from the general luminosity-metallicity relation for star-forming galaxies, a relation that LGRB host galaxies are now known to not follow (Kewley et 2007, Modjaz et 2008, Levesque et 2010a)."
" To perform a robust test for a correlation between metallicity and the eamima-rav energy release. a large and uniform sample of LGRDs with known host metallicities. E;;,;. and 6; is required."," To perform a robust test for a correlation between metallicity and the gamma-ray energy release, a large and uniform sample of LGRBs with known host metallicities, $E_{\gamma,iso}$, and $\theta_j$ is required."
" Ποιο we present (he results of such a comparison. using LGRD host metallicities from Levesque et ((2010a. 2010b) and E.;,; and 9; measurements for these LGRDs drawn from the literature."," Here we present the results of such a comparison, using LGRB host metallicities from Levesque et (2010a, 2010b) and $E_{\gamma,iso}$ and $\theta_j$ measurements for these LGRBs drawn from the literature."
Lone-duration gauuna-rav bursts (LORBs). thought o be generated during the core-collapse of inassive stars (Woosley 1903). are amois the most enersetic yhenomena observed in the nuiverse.,"Long-duration gamma-ray bursts (LGRBs), thought to be generated during the core-collapse of massive stars (Woosley 1993), are among the most energetic phenomena observed in the universe."
 LGRDs are vpically associated with star-for1wine host ονολοτς and voung massive star progelitors., LGRBs are typically associated with star-forming host environments and young massive star progenitors.
" As a result. a ΠΟ of studies cite these expksive events as potential unbiased tracers of the star fornation aud metallicity ustory of the universe at high redshifts (ο,οι, Bloom et 22002. Fyubo et 22006a. Chary ct 22007. Savaglio et 22009)."," As a result, a number of studies cite these explosive events as potential unbiased tracers of the star formation and metallicity history of the universe at high redshifts (e.g., Bloom et 2002, Fynbo et 2006a, Chary et 2007, Savaglio et 2009)."
 Tlowever. several recent studies lave uncovered a connection between LORBs aud low-uectallicitv galaxies;," However, several recent studies have uncovered a connection between LGRBs and low-metallicity galaxies."
 Such a trcond could potentially challenge the use of these phenomena as tracers of star ormation iu normal ealaxies at large look-hacl. times., Such a trend could potentially challenge the use of these phenomena as tracers of star formation in normal galaxies at large look-back times.
 ADuch of the previous work on LORBs aud their uctallicities las focused on a comparison with the standard Iuniuositvauetallicitv (£-Z) relation for star-ornüue @alaxies., Much of the previous work on LGRBs and their metallicities has focused on a comparison with the standard luminosity-metallicity ) relation for star-forming galaxies.
 Stanek et ((2006) examined the tost galaxies of 5 τσ0.3 LGRDs and found that their uctallicities were lower than equally-huninous clwart nreenlar galaxies., Stanek et (2006) examined the host galaxies of 5 $z < 0.3$ LGRBs and found that their metallicities were lower than equally-luminous dwarf irregular galaxies.
 NWewley et ((2007) noted that these 2<0.3 LORBs occupied the same position on theZ diagram as low-netallicityv galaxies. falling below the eeneral relation for divarf regular galaxies.," Kewley et (2007) noted that these $z < 0.3$ LGRBs occupied the same position on the diagram as low-metallicity galaxies, falling below the general relation for dwarf irregular galaxies."
 Modjaz oet ((2008) similarly found that LGRD host ealaxies had ower lnctallicitics than the host galaxies of nearby broad-ined Type Ic supernovac., Modjaz et (2008) similarly found that LGRB host galaxies had lower metallicities than the host galaxies of nearby broad-lined Type Ic supernovae.
 Evubo ct ((2008) adopt a theoreticalL-Z yvelation for use with bigherredshitt (2~ 3) observations of LGRB hosts. sueecstinege that hese ligher-+vedshitt hosts may be good represcutative siuuples of higher-redshitt star-forming galaxies.," Fynbo et (2008) adopt a theoretical relation for use with higher-redshift $z \sim 3$ ) observations of LGRB hosts, suggesting that these higher-redshift hosts may be good representative samples of higher-redshift star-forming galaxies."
 The mnassauetallietv. 412) relation is cited as the Undennental property that drives the observed£-Z relation., The mass-metallicty ) relation is cited as the fundamental property that drives the observed relation.
 While huuinosity is often adopted as a proxy or stellar mass; a galaxys luminosity is also extremely dependent on star formation rate (SER) aud star onuation lüstoryv as well as metallicity. aud thus does not effectivelv isolate stellar mass as a parameter.," While luminosity is often adopted as a proxy for stellar mass, a galaxy's luminosity is also extremely dependent on star formation rate (SFR) and star formation history as well as metallicity, and thus does not effectively isolate stellar mass as a parameter."
 TheAÁ-Z relation for nearby galaxies may be attributable to the arecr neutral eas fractions and more effüicieut stripping of reavy elemieuts by eal:τοις winds in lowerauass galaxies (AIcCangh de Blok |997. Bell de Joug 2000. Bosclli et 22001. Garnett 2002. Tremonti et 22001). though lis iiv uot be the donuünant effect driviug theALZ relation at higher redshüfts (see Zahid ot 22010).," The relation for nearby galaxies may be attributable to the larger neutral gas fractions and more efficient stripping of heavy elements by galactic winds in lower-mass galaxies (McGaugh de Blok 1997, Bell de Jong 2000, Boselli et 2001, Garnett 2002, Tremonti et 2004), though this may not be the dominant effect driving the relation at higher redshifts (see Zahid et 2010)."
 Work ou theAZ relation dates back to Lequeux et ((1979). who found a positive correlation between mass and metallicity that agreed with model predictions for six nearby regular galaxies.," Work on the relation dates back to Lequeux et (1979), who found a positive correlation between mass and metallicity that agreed with model predictions for six nearby irregular galaxies."
 More recently. Tremouti ct ((2001) found aA-Z relation for ~53.000 ucarby (i< 0.3) star-foriung galaxies from the Sloan Digital Skv Survey.," More recently, Tremonti et (2004) found a relation for $\sim$ 53,000 nearby $z < 0.3$ ) star-forming galaxies from the Sloan Digital Sky Survey."
 Savaelio ct (2005) found that this correlation extended to higher redshifts. based on observations of ealaxies from the Cemini Deep Deep Survey (CDDS: Abraham cet 22001) at 0.1z<1.," Savaglio et (2005) found that this correlation extended to higher redshifts, based on observations of galaxies from the Gemini Deep Deep Survey (GDDS; Abraham et 2004) at $0.4 < z < 1$."
 Erb et (2006) measured a monotonicAZZ relation for galaxies at a mean redshift of +~ 2. and found that this relation was offset from the localAl-Z relation by ~0.3 dex. with ealaxies of a eiven stellar mass having lower metallicities at ligher redshifts.," Erb et (2006) measured a monotonic relation for galaxies at a mean redshift of $z \sim 2$ , and found that this relation was offset from the local relation by $\sim$ 0.3 dex, with galaxies of a given stellar mass having lower metallicities at higher redshifts."
 Determining anAZ relation for LORB host galaxies. and comparing this relation to the general galaxypopulation. is critical.," Determining an relation for LGRB host galaxies, and comparing this relation to the general galaxypopulation, is critical."
 A clearer understaudiug of the, A clearer understanding of the
" where a, should be uuderstood as the radius of clusters in units of Hubble leueth Z7.+. since in this case we cannot define a scale factor globally iu the clusters and we normalize a, asa,2:a whend >0.","] where $a_p$ should be understood as the radius of clusters in units of Hubble length $H^{-1}$, since in this case we cannot define a scale factor globally in the clusters and we normalize $a_p$ as $a_p\approx a$ when $a\rightarrow0$."
" Using relation: where Ap is the Boltzmann coustaut.in, is the mass of proton. while jin, is the average mass of particles. > ds the ratio of |inetic energv to temperature."," Using relation: where $k_B$ is the Boltzmann constant,$m_p$ is the mass of proton, while $\mu m_p$ is the average mass of particles, $\beta$ is the ratio of kinetic energy to temperature."
 The composition & has pliysical meaning of cucrex transformation cfiiciency from thermal dvuauiuec fori to x-ray form., The composition $\frac{\mu}{\beta}$ has physical meaning of energy transformation efficiency from thermal dynamic form to x-ray form.
" Substituting eq(53)) iuto eq(5 1)) we ect the followingC» mass-temperature relation: Or with and A,. given by eq(26)) and i=a?1.", Substituting \ref{vMrelation}) ) into \ref{vTrelation}) ) we get the following mass-temperature relation: or with ] and $\Delta_c$ given by \ref{DeltacDefinition2}) ) and $z=a_c^{-1}-1$.
 Just as (Wang&Steiuπαντα1998) pointec out. since the imass-tenperature relation is red-shift dependent. simply substituting eq(55)) iuto l5)) cannot give us correct nuuber density of clusters im a given temperature range today.," Just as \citep[]{WangSteinhardt1} pointed out, since the mass-temperature relation is red-shift dependent, simply substituting \ref{RTrelation}) ) into \ref{diff-M-Function2}) ) cannot give us correct number density of clusters in a given temperature range today."
 Tustead. we should fist fud out the wvirialization rate and uniltiply it by the mass-tempcrature relation then iutegrate over red-shift From eqxt56)). (55)) aud (17)) we can see that besides 5. ntT.2} will also depend ou the cosinological paranueters (c. O59. h. n. and the normalization σς of the cosimic density fluctuations.," Instead, we should first find out the virialization rate and multiply it by the mass-temperature relation then integrate over red-shift From \ref{diff-T-Function}) ), \ref{RTrelation}) ) and \ref{sigmaRz}) ) we can see that besides $\frac{\mu}{\beta}$, $n(T,z)$ will also depend on the cosmological parameters $w$, $\Omega_{m0}$, $h$, $n_s$ and the normalization $\sigma_8$ of the cosmic density fluctuations."
 Iu principle. if we can measure the nuuber density v.s. tenperatiure relation preciselv enough. bv umuerical fittings. we can deteriune all these parameters sinultaucouslv from) observations.," In principle, if we can measure the number density v.s. temperature relation precisely enough, by numerical fittings, we can determine all these parameters simultaneously from observations."
 However. in practice. because of parauueter degeneracy and measure errors; we can oulv determine some of then or their combinations partly.," However, in practice, because of parameter degeneracy and measure errors, we can only determine some of them or their combinations partly."
" Now let us return to the strange phenomenon displaved iu FIC.2 aud 3.. Ίο, ς luxd e«] respectively."," Now let us return to the strange phenomenon displayed in \ref{zetaFig} and \ref{aptaOapcFig}, i.e. $\zeta<1$ and $\frac{a_{p,ta}}{a_{p,c}}<1$ respectively."
" We have explained that these two things take place when e< Land O,,554, or O,,9 takes too siuall values."," We have explained that these two things take place when $w<-1$ and $\Omega_{mb,ta}$ or $\Omega_{m0}$ takes too small values."
 Tt can be checked that when =Ouid<7 1. we must have¢< land the kinetic of cnereythe virialized matter svstei will be less than zero.see eq(53)).," It can be checked that when $\frac{a_{p,ta}}{a_{p,c}}<1$ we must have $\zeta<1$ and the kinetic energy of the virialized matter system will be less than zero,see \ref{vMrelation}) )."
 We think such a “cluster” cau not cuit N-ravs.," We think such a ""cluster"" can not emit X-rays."
star formation activity and relatively low gas metal content. compared to the mean properties of the complete. galaxy »opulation at à given z.,"star formation activity and relatively low gas metal content, compared to the mean properties of the complete galaxy population at a given $z$."
 Regarding the mean specific SER (SSETU. defined. as he ratio between the SER. and the stellar mass of a given galaxy (Fig. 4)).," Regarding the mean specific SFR (SSFR), defined as the ratio between the SFR and the stellar mass of a given galaxy (Fig. \ref{gssfr}) ),"
 host galaxies are predicted to show SSERs similar to those in the low metallicity sample. anc higher han those in the complete galaxy population. for z« 2.," host galaxies are predicted to show SSFRs similar to those in the low metallicity sample, and higher than those in the complete galaxy population, for $z < 2$ ."
 Between z—2 and z~6. there are no significant dillerences in mean SSERs among the three samples. which iive larger SSElLHs that low redshift) galaxies.," Between $z \sim 2$ and $z \sim 6$, there are no significant differences in mean SSFRs among the three samples, which have larger SSFRs that low redshift galaxies."
 This can oe understood. because. at. higher redshift.. galaxies have arger gas reservoirs which can feed stronger star formation activity and are. on average. less chemically enriched.," This can be understood because, at higher redshift, galaxies have larger gas reservoirs which can feed stronger star formation activity and are, on average, less chemically enriched."
 At ow redshift. host. galaxies seem to be particularly efficient al transforming gas into stars.," At low redshift, host galaxies seem to be particularly efficient at transforming gas into stars."
 Note. however. that the mean SSER. predicted. by scenario 1.3 at low redshift is half an order of magnitude lower than the mean observed SSETL," Note, however, that the mean SSFR predicted by scenario II.3 at low redshift is half an order of magnitude lower than the mean observed SSFR."
 Observations show that host galaxies tend to be bluer than the general population of galaxies observed at à given redshift. and. fainter than a typical L galaxy.," Observations show that host galaxies tend to be bluer than the general population of galaxies observed at a given redshift, and fainter than a typical $L^*$ galaxy."
 In fact. this trend can be nicely reproduced by our scenario L3. as shown in Fig. 5..," In fact, this trend can be nicely reproduced by our scenario II.3, as shown in Fig. \ref{colours}."
 Phe luminosities and colours of the predicted host ealaxies are in excellent. agreement. with the observations compiled by Savaglioetal.(2009)., The luminosities and colours of the predicted host galaxies are in excellent agreement with the observations compiled by \citet{Sav09}.
. From this figure. we can see that host galaxies are bluer than the complete galaxy population for 2«2. but have similar mean colours for higher redshíits.," From this figure, we can see that host galaxies are bluer than the complete galaxy population for $ z < 2$, but have similar mean colours for higher redshfits."
 Our scenario predicts that host galaxies are more Luminous svstemis in the D-band. compared. to the mean luminosity of the global galaxy. population at all redshilts.," Our scenario predicts that host galaxies are more luminous systems in the $B$ -band, compared to the mean luminosity of the global galaxy population at all redshifts."
 In Fig. 6..," In Fig. \ref{metal},"
 we compare the mean cold. gas metallicity of the host. galaxies predicted. by scenario 11.3 to. dillerent metallicity estimations reported. by Savaglioetal.(2009)., we compare the mean cold gas metallicity of the host galaxies predicted by scenario II.3 to different metallicity estimations reported by \citet{Sav09}.
 Since at 2>0.2 it is very dillicult to distinguish ΕΠΗ regions with enough resolution. these authors generally. measured 1¢ optical luminosity-weightecd mean metallicity in à galaxy.," Since at $z > 0.2$ it is very difficult to distinguish HII regions with enough resolution, these authors generally measured the optical luminosity-weighted mean metallicity in a galaxy."
 For consistency. host galaxies at 2<0.2 were treated by then as the rest of the sample (i.e. integrating [uxes over the whole galaxy).," For consistency, host galaxies at $z<0.2$ were treated by them as the rest of the sample (i.e. integrating fluxes over the whole galaxy)."
 lo this figure. we have included metallicities obtained by using cdillerent. indicators (seeSavaglioetal.109.formore details)..," In this figure, we have included metallicities obtained by using different indicators \citep[see][for more details]{Sav09}."
 In some cases. absorption lines in 16 optical afterglow can be used to obtain the metallicity of neutral cold. gas along the line of sight of the GRB he so-called ΟΙAs).," In some cases, absorption lines in the optical afterglow can be used to obtain the metallicity of neutral cold gas along the line of sight of the GRB (the so-called GRB-DLAs)."
 This is the case of 9 GRD-DLA systems studied by Savaglio(2006)... all of them at >1.6.," This is the case of 9 GRB-DLA systems studied by \citet{Sav06}, all of them at $z > 1.6$."
 In this case. the metallicity could. be associated more clirectly to the metallicity of the host galaxy. contrary o QSO-DL which are associated to LIL clouds in the intergalactic Asmedium.," In this case, the metallicity could be associated more directly to the metallicity of the host galaxy, contrary to QSO-DLAs which are associated to HI clouds in the intergalactic medium."
 At z<I. measurements of metallicity w Savaglioetal.(2009) are derived. [rom hot σας and. in this case. the lower branch solution is preferred. for the rosts.," At $z<1$, measurements of metallicity by \citet{Sav09} are derived from hot gas and, in this case, the lower branch solution is preferred for the hosts."
 As shown in Fie. 6.," As shown in Fig. \ref{metal},"
 the predicted. host galaxies metallicities are systematically higher than the CdtB-DLA metallicities., the predicted host galaxies metallicities are systematically higher than the GRB-DLA metallicities.
 This might indicate that LORBs occur in regions of even lower metallicity than the mean metallicity of the cold gas of the host galaxies., This might indicate that LGRBs occur in regions of even lower metallicity than the mean metallicity of the cold gas of the host galaxies.
 In this sense. Nuzaetal. 2007).. adopting similar hypotheses to generate synthetic ΕΙ populations. but using full cosmological simulations where the chemical enrichment of barvons was consistently ollowed with redshift. claimed. a metallicity threshold. of L3Z. [or the progenitor stars in order to reproduce observations.," In this sense, \citet{Nuz07}, adopting similar hypotheses to generate synthetic LGRB populations, but using full cosmological simulations where the chemical enrichment of baryons was consistently followed with redshift, claimed a metallicity threshold of $0.3
Z_{\odot}$ for the progenitor stars in order to reproduce observations."
 More detailed information on the metallicity of individual stellar populations. which also takes into account he inhomogeneities of the interstellar medium. are needed o improve our understanding of this issue (see Pontzen and Artale ct al.," More detailed information on the metallicity of individual stellar populations, which also takes into account the inhomogeneities of the interstellar medium, are needed to improve our understanding of this issue (see \citealt{Pon09} and Artale et al."
 in. preparation), in preparation).
 Also along, Also along
"for Z—0.1Zo, Zo, and 10Zo, respectively.","for $Z = 0.1 Z_{\odot}$ , $Z_{\odot}$ , and $10 Z_{\odot}$, respectively."
" Thus, even for extreme metallicities the maximum difference between the estimated and true rates is well within a factor of two."," Thus, even for extreme metallicities the maximum difference between the estimated and true rates is well within a factor of two."
" These maxima are reached near the 0.1 dex exclusion zone, so the maximum errors for temperatures that differ substantially from the equilibrium values are much smaller."," These maxima are reached near the 0.1 dex exclusion zone, so the maximum errors for temperatures that differ substantially from the equilibrium values are much smaller."
" We have also tabulated the combined cooling rates of all elements heavier than helium, assuming solar relative abundances."," We have also tabulated the combined cooling rates of all elements heavier than helium, assuming solar relative abundances."
" While scaling all heavy elements simultaneously reduces the accuracy (relative to scaling the contribution of each element individually), these tables may be convenient in the absence of a complete set of elemental abundances."," While scaling all heavy elements simultaneously reduces the accuracy (relative to scaling the contribution of each element individually), these tables may be convenient in the absence of a complete set of elemental abundances."
" In this case, the total cooling rate becomes: Although cooling rates including photo-ionization have not yet been tabulated, CIE cooling rates have been published by various authors."," In this case, the total cooling rate becomes: Although cooling rates including photo-ionization have not yet been tabulated, CIE cooling rates have been published by various authors."
" In Figure 1 we compare our CIE results (ie., version 07.02) with those of ? (who used version 06.02), ? (who used MAPPINGS)) and also with (versionr;?).."," In Figure \ref{fig:codecomparison} we compare our CIE results (i.e., version 07.02) with those of \cite{Gnat2007}
 (who used version 06.02), \cite{Sutherland1993} (who used ) and also with \citep[version r;][]{Groves2008}."
" The calculations generally differ in terms of the code, the atomic rates, and the solar abundances that were used."," The calculations generally differ in terms of the code, the atomic rates, and the solar abundances that were used."
" In order to focus the comparison on codes and rates, we used the solar abundances assumed by ? when computing the cooling rates for all curves in thisfigure?."," In order to focus the comparison on codes and rates, we used the solar abundances assumed by \cite{Gnat2007} when computing the cooling rates for all curves in this."
. Note that these abundances differ somewhat from the solar abundances that we use in the rest of this paper., Note that these abundances differ somewhat from the solar abundances that we use in the rest of this paper.
" The differences in the cooling rates shown in Figure 1 are typically smaller than 0.3 dex suggesting that the cooling rates are known to better than a factor of two, at least for CIE."," The differences in the cooling rates shown in Figure \ref{fig:codecomparison} are typically smaller than 0.3 dex suggesting that the cooling rates are known to better than a factor of two, at least for CIE."
" The differences are largest for T~10?K, with giving higher cooling rates thanCLOUDY."," The differences are largest for $T\sim
10^5\,\K$, with giving higher cooling rates than."
". 'The cooling rates in photo-ionization equilibrium are not proportional to the density squared, as is the case for CIE."," The cooling rates in photo-ionization equilibrium are not proportional to the density squared, as is the case for CIE."
" As a consequence, the cooling curve changes dramatically with density."," As a consequence, the cooling curve changes dramatically with density."
 This is illustrated in Fig., This is illustrated in Fig.
" 2 which shows normalized, net cooling, rates (|A/nà|) as a function of temperature for solar abundances."," \ref{fig:photodensity} which shows normalized, net cooling, rates $\vert \Lambda/n_{\rm H}^2\vert$ ), as a function of temperature for solar abundances."
" Different curves correspond to different densities, as indicated in the legend."," Different curves correspond to different densities, as indicated in the legend."
 The calculation includes the CMB and the ΗΜΟΙ background at redshift three., The calculation includes the CMB and the HM01 background at redshift three.
 The z=3 HMO1 background corresponds to a hydrogen photo-ionization rate D/10?s=1.1 and an ionization parameter U=1.6x 107?/ng.," The $z=3$ HM01 background corresponds to a hydrogen photo-ionization rate $\Gamma_{12} \equiv \Gamma / 10^{-12}~\s^{-1} =
1.1$ and an ionization parameter $U = 1.6 \times 10^{-5}/n_{\rm
 H}$ ."
" We stress that in the vicinity of ionizing sources the radiation field may be much more intense, which would enhance its effect on the cooling rates compared to the results presented here."," We stress that in the vicinity of ionizing sources the radiation field may be much more intense, which would enhance its effect on the cooling rates compared to the results presented here."
 As the density decreases the gas becomes more highly ionized and the cooling peaks due to collisional excitation of various ions disappear., As the density decreases the gas becomes more highly ionized and the cooling peaks due to collisional excitation of various ions disappear.
" For very low densities and high temperatures the normalized cooling rates actually increase as they become dominated by Compton cooling off the CMB, which scales as Aοςπε’."," For very low densities and high temperatures the normalized cooling rates actually increase as they become dominated by Compton cooling off the CMB, which scales as $\Lambda \propto n_{\rm e}T$ ."
" For the two lowest densities shown, the equilibrium temperature, for which the net cooling rate A—0, exceeds 10*K."," For the two lowest densities shown, the equilibrium temperature, for which the net cooling rate $\Lambda \rightarrow 0$, exceeds $10^4\,\K$."
" In these cases, curves corresponding to net heating appear to the left of the thermal equilibrium temperature."," In these cases, curves corresponding to net heating appear to the left of the thermal equilibrium temperature."
 Figure 3 shows how the presence of heavy elements and radiation affects the radiative cooling time., Figure \ref{fig:coolingtimecontours} shows how the presence of heavy elements and radiation affects the radiative cooling time.
 Each panel shows contours of constant cooling time in the density-temperature plane for two models., Each panel shows contours of constant cooling time in the density-temperature plane for two models.
" The top panels illustrate well known results, while the bottom panels demonstrate the importance of radiation on the cooling due to metal lines."," The top panels illustrate well known results, while the bottom panels demonstrate the importance of radiation on the cooling due to metal lines."
" Here and throughout the cooling time refers to the absolute value of the net radiative cooling time at a fixed hydrogen density, For temperatures below the thermal equilibrium temperature, tcoo1 corresponds to a heating timescale."," Here and throughout the cooling time refers to the absolute value of the net radiative cooling time at a fixed hydrogen density, For temperatures below the thermal equilibrium temperature, $t_{{\rm cool}}$ corresponds to a heating timescale."
" The calculation includes the CMB and, optionally, the HMO01 background at redshift three."," The calculation includes the CMB and, optionally, the HM01 background at redshift three."
" Note that adiabatic cooling due to the expansion of the Universe is not included, but would dominate over radiative cooling for sufficiently low densities."," Note that adiabatic cooling due to the expansion of the Universe is not included, but would dominate over radiative cooling for sufficiently low densities."
" For example, the universal Hubble expansion (appropriate for densities around the cosmic mean, ngc10οι? at 3) corresponds to an adiabatic cooling time 1/(2H)zz1.6x10? yr at z—3."," For example, the universal Hubble expansion (appropriate for densities around the cosmic mean, $n_{\rm H} \sim 10^{-5}\,\cm^{-3}$ at $z=3$ ) corresponds to an adiabatic cooling time $t_{\rm cool, adiab} = 1/(2H) \approx 1.6\times
10^9$ yr at $z=3$."
" The top-left panel shows that for a gas, ionizing radiation drastically reduces the cooling rates for 10K«T<10°K (?).."," The top-left panel shows that for a gas, ionizing radiation drastically reduces the cooling rates for $10^4\,\K < T \la
10^5 \K$ \citep{Efstathiou1992}."
 This happens because the peaks in the cooling rate due to collisional excitation of neutral hydrogen and singlyionizedhelium (followed by Lya emission) areremoved when the gas is photo-ionized., This happens because the peaks in the cooling rate due to collisional excitation of neutral hydrogen and singlyionizedhelium (followed by $\alpha$ emission) areremoved when the gas is photo-ionized.
" In the presence of ionizing radiation (solid curves) there are actually two contours for each net cooling time,"," In the presence of ionizing radiation (solid curves) there are actually two contours for each net cooling time,"
of Figure EMi)),of Figure \ref{fig:e_all}) ).
 The spectra show a softening at low energies. the extra flux coming frou: Compton-scattered pliotous that were originally directed. downward.," The spectra show a softening at low energies, the extra flux coming from Compton-scattered photons that were originally directed downward."
 This effect can be secu most clearly in the last panel of Figure 3.Mi du which we show the resIts with Compton scattering turned ou and off.," This effect can be seen most clearly in the last panel of Figure \ref{fig:e_all}, in which we show the results with Compton scattering turned on and off."
 As expected. this effect is most significant when the electron clistribution is most cdowmward.," As expected, this effect is most significant when the electron distribution is most downward."
 Figure Lo shows the eamuna-ray spectrmm recorded at different values of the outgoing anele . between the ploton direction aud outward solar normal., Figure \ref{fig:a_all} shows the gamma-ray spectrum recorded at different values of the outgoing angle $\beta$ between the photon direction and outward solar normal.
 The two traces in cach panel represent a disk flare (solid) aud a Luh flare (dashed)., The two traces in each panel represent a disk flare (solid) and a limb flare (dashed).
 There are two xocess tha affect the production rate at ditfereut outgoing aneles: relativistic beaming iu a dowmvard electron distribuion will texd to put out more photois af aree 2. while. ou the other haud. photous coming out at large > have louecr paths iu the Sun aud are more Iikelv ο scatter.," There are two process that affect the production rate at different outgoing angles: relativistic beaming in a downward electron distribution will tend to put out more photons at large $\beta$, while, on the other hand, photons coming out at large $\beta$ have longer paths in the Sun and are more likely to scatter."
 At lower energies. the second process is more iuportant and will mase disk flares appear brighter.," At lower energies, the second process is more important and will make disk flares appear brighter."
 At Heh enerev. however. the beaming effect is more important aud will cause iub brieliteing.," At high energy, however, the beaming effect is more important and will cause limb brightening."
 This result may expaln the discovery of limb brightening at > 0.5 MeV but not over the range 55O0 keVow uch 15Is (lonunated by much lower energy photous 1995).," This result may explain the discovery of limb brightening at $>$ 0.3 MeV \citep{vestrand87} but not over the range 5–500 keV, which is dominated by much lower energy photons \citep{li94,li95}."
. The same effec can cause a spectral] reax. witliia given flare: our simulations show spectral hardening for limb flares iu the hiehi«erev baud (higher theura O11 LO! keV) but not below. iu agreement with the observations of Li(1995).," The same effect can cause a spectral break within a given flare: our simulations show spectral hardening for limb flares in the high-energy band (higher than about 400 keV) but not below, in agreement with the observations of \citet{li95}."
 For the simmlated isoropic distribution. most photoas observed are direct breimsstralilung. which is also isotropic. so there is no significant sjρουτα] evolution with view!ic angle. as shown in panel E of Figure £L.," For the simulated isotropic distribution, most photons observed are direct bremsstrahlung, which is also isotropic, so there is no significant spectral evolution with viewing angle, as shown in panel E of Figure \ref{fig:a_all}."
 For paucake distributions. it is still true that the Mad οςupolelr observed 1s directly from breiusstraliluug. but beaming to lieh 3 is visible at all energies. as shown i1i panel F of Figure 1..," For pancake distributions, it is still true that the main component observed is directly from bremsstrahlung, but beaming to high $\beta$ is visible at all energies, as shown in panel F of Figure \ref{fig:a_all}."
 Tn Table 1.. we sunnarize the ratio OTWECL1 511 keV line flux and flux at 200 keV as well as the ratio between the 511 keV line ane the δ15 MeV coutiumua froni our simulations.," In Table \ref{tab:e}, we summarize the ratio between 511 keV line flux and flux at 200 keV as well as the ratio between the 511 keV line and the 8–15 MeV continuum from our simulations."
 Iu order to compare these ratios withRIES data. we convolved tli| Spectra from our siuations with the spectral respotrise inatrix of the iustrumnenut5 (Swithetal.2002): both the «lirect output of the sinilatious and the ratio iu the “count space” of he instrument after cuvolution are srown in Table L..," In order to compare these ratios with data, we convolved the spectra from our simulations with the spectral response matrix of the instrument \citep{smith02}; both the direct output of the simulations and the ratio in the “count space” of the instrument after convolution are shown in Table \ref{tab:e}."
 It is iuterestiis to note that the ratios can either decrease Or lucrease from the convolution process. depending ou the overall sipe of the spectruui.," It is interesting to note that the ratios can either decrease or increase from the convolution process, depending on the overall shape of the spectrum."
. When the Ισοπου renmisstral1.mug escapes the Sun easily. (such as for au isotropic electroi1 cüstribution). not only does it overwhelm the solar anuilation line |mt also the un]ti-MeV. bremsstrallune ploteris pair produce in the spacecraft. so that the count spectruni has a amore prominent 511 keV line than the photon ssectrmm.," When the high-energy bremsstrahlung escapes the Sun easily (such as for an isotropic electron distribution), not only does it overwhelm the solar annihilation line but also the multi-MeV bremsstrahlung photons pair produce in the spacecraft, so that the count spectrum has a more prominent 511 keV line than the photon spectrum."
 For flare spectra in which little MeV xenisstralimug escapes. on the other haud. the most iuportaut mstruueutal effect is that the solar 511 keV photous (which are sjenificaut in this case) often Compton scatter out of FIIESSTs detectors afcra single juteraction. so hat thev xxester as continuum photons instead of Lue photous. causing the cotut spectrum to have a less siguificaut ine than t16 photon spectrum.," For flare spectra in which little MeV bremsstrahlung escapes, on the other hand, the most important instrumental effect is that the solar 511 keV photons (which are significant in this case) often Compton scatter out of 's detectors after a single interaction, so that they register as continuum photons instead of line photons, causing the count spectrum to have a less significant line than the photon spectrum."
 A solar gauunuaray προςrometer with a heavy auticoiucideuce shield. such as the Canmuna-Rayv Spectrometer on the (Forrestctal.1980).. would be ess susceptible to all these lustrimental effects. aud the lne-to-contiunuui ratios wou«d be much more siniar in the count aud photon spectra.," A solar gamma-ray spectrometer with a heavy anticoincidence shield, such as the Gamma-Ray Spectrometer on the \citep{forrest80}, would be less susceptible to all these instrumental effects, and the line-to-continuum ratios would be much more similar in the count and photon spectra."
 We also simulated tιο dateraction |vetween acceleratec protons aud the solar ati»osphere., We also simulated the interaction between accelerated protons and the solar atmosphere.
 The siunulated solar atmosphere was the same as in the electron siuulations., The simulated solar atmosphere was the same as in the electron simulations.
 As discussed above. we are at this time simulating ouly the production of pions aud their secoudarics. not nuclear excitation. spallation. and radioactive decay.," As discussed above, we are at this time simulating only the production of pions and their secondaries, not nuclear excitation, spallation, and radioactive decay."
 We simulated dowisvard beamed ane downward isotropic proton distrinitions. with results shown in Table 20 and Figure 5..," We simulated downward beamed and downward isotropic proton distributions, with results shown in Table \ref{tab:p}
 and Figure \ref{fig:proton_out}."
 A pancake distribution o: protons is uo included. since it has been ruled out for at least one gzunuerayv flare by observations of strong 1edshifts in the mclear de-excitatio1 lines (Suuthetal.2003).," A pancake distribution of protons is not included, since it has been ruled out for at least one gamma-ray flare by observations of strong redshifts in the nuclear de-excitation lines \citep{smith03}."
. The shape of the οιteoius spectrum changes little when the aneular aud spectral distributions of the protous are varied. but the owall eanunuaseray hDnuuunositv is ereater for harder spectral indices and for the more isotropic distribution.," The shape of the outgoing spectrum changes little when the angular and spectral distributions of the protons are varied, but the overall gamma-ray luminosity is greater for harder spectral indices and for the more isotropic distribution."
 This is exoected. suce pious are produced oulv by the highest-cnerey protons aud since the distribution will produce some pious at shallower column depths where plotous are better able to escape (sce below).," This is expected, since pions are produced only by the highest-energy protons and since the downward-isotropic distribution will produce some pions at shallower column depths where photons are better able to escape (see below)."
 The spectra observed at 0.2«cos3<0.fL extend to higher energy because more photons emerge without scatterie., The spectra observed at $0.2<\cos\beta<0.4$ extend to higher energy because more photons emerge without scattering.
 Dious are produced very deep in the Sun. at column depths of τοις of g/cmr. as shown in Figure 6..," Pions are produced very deep in the Sun, at column depths of tens of $^2$, as shown in Figure \ref{fig:piproduct}."
 The production rate faIs off niore quickly with depth for the «oxcuvaurd isotropic distribution. since protous at a shallow angle cau go through a large cohuun of solar atinosphere axd still produce pious at relatively s1uall depth.," The production rate falls off more quickly with depth for the downward isotropic distribution, since protons at a shallow angle can go through a large column of solar atmosphere and still produce pions at relatively small depth."
 Pious have very short lifetimes «10 SN* Or üx and 110! s for xU). so they decay where they are produced.," Pions have very short lifetimes $\times 10^{-8}$ s for $\pi^{\pm}$ and $\times 10^{-17}$ s for $\pi^0$ ), so they decay where they are produced."
 The positrous produceL bv ü decay have to travel some distance before they slow down and auuihilate., The positrons produced by $\pi^{+}$ decay have to travel some distance before they slow down and annihilate.
 Figure 7 shows he depth distributious of positron aunihilation events for both injected protous and electrons when both have a spectral index of 2.2 arc energv ranges of 1X).10000. ATeW and 0.1.100 MeV. respectively., Figure \ref{fig:annidepth} shows the depth distributions of positron annihilation events for both injected protons and electrons when both have a spectral index of 2.2 and energy ranges of 100–10000 MeV and 0.1–100 MeV respectively.
 Each proton in this case IS MOL| than 200 times as likely to prodice a positron as an electron. aud they tend to be produced deeper in the solar amosphere.," Each proton in this case is more than 200 times as likely to produce a positron as an electron, and they tend to be produced deeper in the solar atmosphere."
 Among )ositrons orieluating with protons. we found that originate from στ]ü decay. from. pair-production of the gamma-rays produced il EMü decay. and frou more indirect cascade processes (for example. πa»breimisstralilungpairproductio i," Among positrons originating with protons, we found that originate from $\pi^{+}$ decay, from pair-production of the gamma-rays produced in $\pi^0$ decay, and from more indirect cascade processes (for example, $\pi^{-} \rightarrow e^{-} \rightarrow {\rm bremsstrahlung}
\rightarrow {\rm pair~production}$ )."
" Most of the annihilation photous that leave the Sun in the simulations experieuced Compton scattering. so that they are observed m a continuii below the li1ο,"," Most of the annihilation photons that leave the Sun in the simulations experienced Compton scattering, so that they are observed in a continuum below the line."
" In Figure δ., we plot the depth distributions of ouly those annihilation events corresponding fc| photous that escape the Sun."," In Figure \ref{fig:outannidepth}, we plot the depth distributions of only those annihilation events corresponding to photons that escape the Sun."
 As expected. the deeper the annihilation happens. the fewer plotous escape without scattering.," As expected, the deeper the annihilation happens, the fewer photons escape without scattering."
 More than of the gamma-ray photons we observed experienced: Compton scattering., More than of the gamma-ray photons we observed experienced Compton scattering.
 The resultuis Compton contimuni can ninidc two other spectral components just below 511 keV: the, The resulting Compton continuum can mimic two other spectral components just below 511 keV: the
(1.7)) is optimal in the sense that oue can uot replace it by auy smaller power.,\ref{cpMSW}) ) is optimal in the sense that one can not replace it by any smaller power.
 However. it seems that little is known about the sharp coustaut in (1.7)).," However, it seems that little is known about the sharp constant in \ref{cpMSW}) )."
 Comiug back to inequalities (1.1)). (1.5)) and (1.6)). the natural question that arises is the following: why does the inequality (1.1)) seems to be the parabolic extension of (1.5)) although the proof is inspired (as mentioned above) from that of (1.6)) given by Ogawa [17]??," Coming back to inequalities \ref{eq1:IM}) ), \ref{eq2:KT}) ) and \ref{eq3:O}) ), the natural question that arises is the following: why does the inequality \ref{eq1:IM}) ) seems to be the parabolic extension of \ref{eq2:KT}) ) although the proof is inspired (as mentioned above) from that of \ref{eq3:O}) ) given by Ogawa \cite{Og03}?"
 The answer to this question is partially contained in [13.Remark2.14] where the authors pointed out that the well-known relation between elliptic/isotropic Lizorkin-Triebel aud BALO spaces (see 2.3])) will not be used in the proof of (1.1)) even though it seems to be valid (without giving a proof) in the parabolic/anisotropic framework., The answer to this question is partially contained in \cite[Remark 2.14]{IM09} where the authors pointed out that the well-known relation between elliptic/isotropic Lizorkin-Triebel and $BMO$ spaces (see \cite[Proposition 2.3]{Og03}) ) will not be used in the proof of \ref{eq1:IM}) ) even though it seems to be valid (without giving a proof) in the parabolic/anisotropic framework.
The relation is the following: where FI is the homogeneous parabolic Lizorkiu-Triebel space (see Defiuition 2.3)).,"The relation is the following: where $\dot{F}^{0,a}_{\infty,2}$ is the homogeneous parabolic Lizorkin-Triebel space (see Definition \ref{LT_defi}) )."
 Iu this paper. we show a parabolie version of the logaritlinic Sobolev inequality (1.6)) basically uxing the equivaleuce (1.8)) that is shown to be true (see Lemna 3.1)).," In this paper, we show a parabolic version of the logarithmic Sobolev inequality \ref{eq3:O}) ) basically using the equivalence \ref{eq4:equiv}) ) that is shown to be true (see Lemma \ref{lem1}) )."
 This answers the question raised above., This answers the question raised above.
" Our study takes place on the whole space IE""land on the bounded domain Qy.", Our study takes place on the whole space $\R^{n+1}$ and on the bounded domain $\O_T$.
 A Comparison (in some special cases) of our inequality with (1.1)) is also discussed., A comparison (in some special cases) of our inequality with \ref{eq1:IM}) ) is also discussed.
 Before stating our main results. we celine some terminology.," Before stating our main results, we define some terminology."
" A generic element in £ will be denoted by z=Gc./)€E"" Ilovhere e=PIENEr4)€Ig"" ds the spatial variable. aud /€Ε is the ime variable."," A generic element in $\R^{n+1}$ will be denoted by $z=(x,t)\in
\R^{n+1}$ where $x=(x_{1},\ldots,x_{n})\in \R^{n}$ is the spatial variable, and $t\in \R$ is the time variable."
 For a eiven fuuctiou g. the notation O;g stands for the partial derivative with respect o the spatial variable: Jig=Ong:— 4.7=1...n.," For a given function $g$, the notation $\partial_{i}g$ stands for the partial derivative with respect to the spatial variable: $\partial_{i}g =
\partial_{x_{i}} g := \frac{\partial g}{\partial x_{i}}$, $i=1,...,
n$."
" In this case O,1g=Og:—St."," In this case $\partial_{n+1}g = \partial_{t} g:= \frac{\partial
g}{\partial
 t}$."
 We also denote Og. s€FN. auy derivative with respect tor of order s.," We also denote $\partial^{s}_{x} g$, $s\in \N$, any derivative with respect to $x$ of order $s$ ."
" Moreover. we denote the space-time graclient w Vgum(Gu...O,g.0,τα)."," Moreover, we denote the space-time gradient by $\nabla g := (\partial_{1}g, \ldots,
\partial_{n}g, \partial_{n+1}g)$."
" Finally. we denote ||f|[y:=maxt|filix...Wallyfsalla) for any vector-valued function f—(fy.....foetna)€X"".1 where X is any Banach space."," Finally, we denote $\|f\|_{X}:=
\max (\|f_{1}\|_{X},\ldots,\|f_{n}\|_{X}, \|f_{n+1}\|_{X})$ for any vector-valued function $f=(f_{1},\ldots,f_{n}, f_{n+1})\in X^{n+1}$ where $X$ is any Banach space."
" Throughout this j»iper and for the sakeof simplicity. we will drop the superscript 1+ from X"". +. Following the above notations. our first theorem reads:"," Throughout this paper and for the sakeof simplicity, we will drop the superscript $n+1$ from $X^{n+1}$ Following the above notations, our first theorem reads:"
 ~5 (e.g.Strometal. (Ammannetal.1981).. etal.2001:Laureijs2002).. (e.g.Z," $\sim$ \citep[e.g.][]{1993prpl.conf..837S, 2001ApJ...553L.153H}, \citep{1984ApJ...278L..23A}. \citep{1993prpl.conf.1253B, 1999ApJ...520..215F,
1999ApJ...510L.131G, 1999A&A...343..496P, 2001A&A...365..545H,
2002A&A...387..285L}. \citep[e.g.,][]{2001ARA&A..39..549Z}."
uckerman2001). 2200 (Habiugetal.2001:Laureijset2002).. (fz10 (dX100 ((zN Zuckermanetal.2001a)) (2:20 Jeffries (e.g.Wadlara&Russell2000)..," $\gtrsim$ \citep{1999Natur.401..456H, 2001A&A...365..545H, 2001ApJ...555..932S,
2002A&A...387..285L}, $t\approx10$ $d\lesssim100$ $\approx$ \citealp{2001ApJ...562L..87Z}) $\approx$ \citealp{1995MNRAS.273..559J,
2001MNRAS.328...45M}) \citep[e.g.][]{2000prpl.conf..995W},"
[function with redshift is matched by the relevant increase in (he mean separation at hieh redshift (lower cluster abundance).,function with redshift is matched by the relevant increase in the mean separation at high redshift (lower cluster abundance).
" The same mass clusters shift upwards along the f—d relation as the redshilt increases: both the comoving clustering scale and the cluster mean separation increase with redshift so that the 2,—d relation remains essentially unchanged.", The same mass clusters shift upwards along the $R_0 - d$ relation as the redshift increases: both the comoving clustering scale and the cluster mean separation increase with redshift so that the $R_0 - d$ relation remains essentially unchanged.
" Ab zZ2. the LCDM relation follows approximately Ly)(2)22.6 (comoving scales),"," At $z \la 2$, the LCDM relation follows approximately $R_0 (z) \simeq 2.6 \sqrt{d(z)}$ (comoving scales)."
 The evolution of the 2y—d relation to high redshift provides an important new cosmological tool., The evolution of the $R_0 - d$ relation to high redshift provides an important new cosmological tool.
 The observed evolution of the relation from zc0 to z~3 can be used to break degeneracies (hat exist al 2O and thus allow a precise determination of cosmological parameters., The observed evolution of the relation from $z \simeq 0$ to $z \sim 3$ can be used to break degeneracies that exist at $z \sim 0$ and thus allow a precise determination of cosmological parameters.
" No evolution in the £2,—d relation is expected (using a correlation slope 5=2) for 2 2if the current LCDSM model is correct.", No evolution in the $R_0 - d$ relation is expected (using a correlation slope $\gamma = 2$ ) for $z \la 2$ if the current LCDM model is correct.
the time evolutions change significantly.,the time evolutions change significantly.
" The temporal slope of 74, turns over quickly [rom Vyxda2 (BAM) to the [ar steeper ST slope 1,cx!.", The temporal slope of $\nu_m$ turns over quickly from $\nu_m \propto t^{-3/2}$ (BM) to the far steeper ST slope $\nu_m \propto t^{-3}$.
" The temporal slope lor 74 is not only less steep al late times. its late time ST asvinptote also lies sienilicantly higher (han the early Gime DM asyimptote. and as a result vy, actually lor some (time alter the jet break."," The temporal slope for $\nu_c$ is not only less steep at late times, its late time ST asymptote also lies significantly higher than the early time BM asymptote, and as a result $\nu_c$ actually for some time after the jet break."
" This effect will be less severe for larger opening angles. since p.xEy”D in the DM regime and 5.xFE,°° dn (the ST regime. where E; the total energy in both jets (and therefore in the final ST sphere)."," This effect will be less severe for larger opening angles, since $\nu_c \propto E_{iso}^{-3/5}$ in the BM regime and $\nu_c \propto E_j^{-3/5}$ in the ST regime, where $E_j$ the total energy in both jets (and therefore in the final ST sphere)."
" The two energies are related via 2;£z£5,,05/2.", The two energies are related via $E_j \approx E_{iso} \theta_0^2 / 2$.
 It is also worth noting that. before rising. the temporal slope οἱ v. temporarily bevond —1/2.," It is also worth noting that, before rising, the temporal slope of $\nu_c$ temporarily beyond $-1/2$."
 A steepening of the cooling break frequency tov. x117. has recently been observed in GRB 091127 bv comparing optical ancl X-ray data (Fileasetal.2011)., A steepening of the cooling break frequency to $\nu_c \propto t^{-1.2}$ has recently been observed in GRB 091127 by comparing optical and X-ray data \citep{Filgas2011}.
. Our plot shows that Chis is. in principle. not inconsistent with simulations (aud therefore with (he standard model. since we do not expand upon the standard svuchrotvon lBramnework by including features like evolving nucrophvsics parameters such as €e5).," Our plot shows that this is, in principle, not inconsistent with simulations (and therefore with the standard model, since we do not expand upon the standard synchrotron framework by including features like evolving microphysics parameters such as $\epsilon_B$ )."
 Hlowever. we caution against overinterpretation of the post-break 7 evolution because our approach to electron cooling (based on 1993)) relies on a single global cooling time approximation rather than on tracing the local accelerated. electron. distribution (for a comparison between the (wo approaches. see al. 2010..," However, we caution against overinterpretation of the post-break $\nu_c$ evolution because our approach to electron cooling (based on \citealt{Sari1998}) ) relies on a single global cooling time approximation rather than on tracing the local accelerated electron distribution (for a comparison between the two approaches, see \citealt{vanEerten2010offaxis}. ."
 In the example there. 7 lor local cooling is typically higher by a factor e» 5).," In the example there, $\nu_c$ for local cooling is typically higher by a factor $\sim 5$ )."
" Given (his caveat for 7. a clear sleepening of 174, and » immediately post jet break is a general prediction of our studs. with the steepening of 4, being more robust."," Given this caveat for $\nu_c$, a clear steepening of $\nu_m$ and $\nu_c$ immediately post jet break is a general prediction of our study, with the steepening of $\nu_m$ being more robust."
" The final feature in all three evolution plots is the onset of the counterjet around ~250 davs. resulting in a relative increase of P,,,; and η and a decrease in p."," The final feature in all three evolution plots is the onset of the counterjet around $\sim 250$ days, resulting in a relative increase of $F_{peak}$ and $\nu_m$ and a decrease in $\nu_c$."
 This effect is strongest around. ~1500 clays., This effect is strongest around $\sim 1500$ days.
" Using both the on-axis baselines shown in Fig 3. and the baselines [or @)=0.2 rad. Poy,=209/3. we have generated spectra (excluding svnchrotron sell-absorption) for a cdilferent sel of explosion and radiation parameters and compare these to spectra calculated directly from simulations."," Using both the on-axis baselines shown in Fig \ref{criticals_figure} and the baselines for $\theta_0 = 0.2$ rad, $\theta_{obs} = 2 \theta_0 / 3$, we have generated spectra (excluding synchrotron self-absorption) for a different set of explosion and radiation parameters and compare these to spectra calculated directly from simulations."
 The results are shown in Fig 4.., The results are shown in Fig \ref{spectra_figure}.
" The off-axis angle is equal to the average observer angle assuming randomly oriented jets and no detection if 8,4,>84.", The off-axis angle is equal to the average observer angle assuming randomly oriented jets and no detection if $\theta_{obs} > \theta_0$.
 The scaling approach correctly captures (he peak flux ancl break Irequencies., The scaling approach correctly captures the peak flux and break frequencies.
 The scalings-based spectra can be further improved upon by including smooth power law transitions between different spectral regimes., The scalings-based spectra can be further improved upon by including smooth power law transitions between different spectral regimes.
 Fig 39. suggests that some dependency on Gy.Is lobe expected., Fig \ref{criticals_figure} suggests that some dependency on $\theta_{obs}$is tobe expected.
 We show that gamma-ray burst afterglow spectra and light curves above the svnchrotron sell-absorption break can be generated for arbitrary explosion audradiation parameters by scaling the values of a lew Κον parameters (Freak. Ye Yer) rom a given baseline.," We show that gamma-ray burst afterglow spectra and light curves above the synchrotron self-absorption break can be generated for arbitrary explosion andradiation parameters by scaling the values of a few key parameters $F_{peak}$ , $\nu_c$ , $\nu_m$ ) from a given baseline."
 The baseline, The baseline
"In this work we investigate the reason why coronal loop systems, or entire active regions, look fuzzier in warm ~2—3 MK spectral lines than in cooler €1 MK lines.","In this work we investigate the reason why coronal loop systems, or entire active regions, look fuzzier in warm $\sim 2-3$ MK spectral lines than in cooler $\leq 1$ MK lines."
" This evidence has been well known since the first X-ray and UV missions, e.2. Skylab, but it has been recently put on a more established ground from Hinode/EIS spectral observation (?).."," This evidence has been well known since the first X-ray and UV missions, e.g. Skylab, but it has been recently put on a more established ground from Hinode/EIS spectral observation \citep{Tripathi_2009}."
" Our basic scenario is that coronal loops consist of bundles of thin strands, cach of thickness below the instrumental spatial resolution, and that each strand is heated up to about 10 MK by a strong and fast heat pulse, i.c. the loops are heated by a storm of nanoflares."," Our basic scenario is that coronal loops consist of bundles of thin strands, each of thickness below the instrumental spatial resolution, and that each strand is heated up to about 10 MK by a strong and fast heat pulse, i.e. the loops are heated by a storm of nanoflares."
" The plasma is confined in cach strand, so that it evolves as an independent atmosphere, and can be modeled with loop hydrodynamics (see also ?) for a conceptually similar approach)."," The plasma is confined in each strand, so that it evolves as an independent atmosphere, and can be modeled with loop hydrodynamics (see also \cite{Patsourakos_Klimchuk_2007} for a conceptually similar approach)."
" Our choice has been to assume that the strands are all heated once and by the same heat pulse, lasting 60 s, occurring at a different random time for each strand, with a cadence and an intensity adequate to maintain the loop at ~3 MK on average."," Our choice has been to assume that the strands are all heated once and by the same heat pulse, lasting 60 s, occurring at a different random time for each strand, with a cadence and an intensity adequate to maintain the loop at $\sim 3$ MK on average."
 This model fits well the observational constraint of hot/underdense-cool/overdense cycles., This model fits well the observational constraint of hot/underdense-cool/overdense cycles.
" We have then collected 2000 different strands to form a loop system, and derived synthetic images of the loop system when it reaches steady state in several relevant spectral lines."," We have then collected $2000$ different strands to form a loop system, and derived synthetic images of the loop system when it reaches steady state in several relevant spectral lines."
" In our opinion, the images synthesized from our model unequivocally show the same ""fuzziness"" in the same warm lines as observed with EIS. and the same better definition in the cool lines as observed with EIS."," In our opinion, the images synthesized from our model unequivocally show the same “fuzziness” in the same warm lines as observed with EIS, and the same better definition in the cool lines as observed with EIS."
" 1n other words, our model is able to explain the evidence."," In other words, our model is able to explain the evidence."
" Of course, it explains also the effect as observed in narrow-band XUV instruments such as the normal-incidence imaging telescopes. TRACE and SoHO/EIT."," Of course, it explains also the effect as observed in narrow-band XUV instruments such as the normal-incidence imaging telescopes, TRACE and SoHO/EIT."
 We have also provided quantitative figures to this effect., We have also provided quantitative figures to this effect.
" The basic reason why this model works is that, in spite of the short heat pulse, the strands spend a long time with a high emission measure at a temperature around 3 MK, much less time when plasma is hotter and long time, but with much less emission measure when the plasma is cooler."," The basic reason why this model works is that, in spite of the short heat pulse, the strands spend a long time with a high emission measure at a temperature around 3 MK, much less time when plasma is hotter and long time, but with much less emission measure when the plasma is cooler."
" So the loop systems appear more uniform around 3 MK, and this higher filling factor gives the impression of “fuzziness”, as described in ?).."," So the loop systems appear more uniform around 3 MK, and this higher filling factor gives the impression of “fuzziness"", as described in \citet{Tripathi_2009}."
 In cooler lines we are able to resolve better the, In cooler lines we are able to resolve better the
"Figure | shows the CO(J—1 0) integrated intensity distributions between Vi, of 0 and 30 km l| in the region (/.b)~(57.5 17.5.207.8 0.7).","Figure \ref{largemap} shows the $^{12}$ $J$ =1–0) integrated intensity distributions between $V_{\rm{lsr}}$ of 0 and 30 km $^{-1}$ in the region $(l, b) \sim (5^\circ.5$ $7^\circ.5, -0^\circ.8$ $0^\circ.7)$."
 M20 is denoted by a cross and is located at ~075.6 [rom the supernova remnant (SNR) W28., M20 is denoted by a cross and is located at $\sim0^\circ.6$ from the supernova remnant (SNR) W28.
 The distribution of molecular clouds is verv complicated. and includes an elongated feature running from south-west to north-east throughout the region.," The distribution of molecular clouds is very complicated, and includes an elongated feature running from south-west to north-east throughout the region."
 Dense molecular clouds associated with W28 are found around. (1.5)e(67.4 67.8.207.4 07.0) in this velocity range (e.g..Arikawaοἱal.1999).," Dense molecular clouds associated with W28 are found around $(l,b) \sim (6^\circ.4$ $6^\circ.8, -0^\circ.4$ $0^\circ.0)$ in this velocity range \citep[e.g.,][]{ari1999}."
 The reeion shown in Figure 2. corresponds to the box drawn in solid lines in Figure L.., The region shown in Figure \ref{iimap} corresponds to the box drawn in solid lines in Figure \ref{largemap}.
 Figures aa 2ec show the integrated intensity distributions of 2CO(J—2 1) over three different velocity ranges. Figures 2dd. 2[[ show comparisons between the I|CO(J—2 1) and the Spitzer vin data. and Figures 2ee 23i show comparisons between the |àCO(J—2 1) and the IRAS 25 jm data.," Figures \ref{iimap}a \ref{iimap}c c show the integrated intensity distributions of $^{12}$ $J$ =2–1) over three different velocity ranges, Figures \ref{iimap}d \ref{iimap}f f show comparisons between the $^{12}$ $J$ =2–1) and the Spitzer 8¦Ìm data, and Figures \ref{iimap}g \ref{iimap}i i show comparisons between the $^{12}$ $J$ =2–1) and the IRAS 25 $\mu$ m data."
 The large cross depicts the central star., The large cross depicts the central star.
" Class 0/I objects and cold dust cores (cloudcoresTCOOTCL?Leflochetal.2008). are shown bv circles ancl small crosses, respectively."," Class 0/I objects and cold dust cores \citep[cloud cores TC00--TC17][]{lef2008} are shown by circles and small crosses, respectively."
 These objects indicate recent star formation ancl pre-star formation of the second generation of stars in M20., These objects indicate recent star formation and pre-star formation of the second generation of stars in M20.
 In Figures 2aa. 2dd and 2ge. we find a cloud with its peak position near (he central star and well aligned with the center of the Trifid dust lanes (hereafter 2 kms ! cloud).," In Figures \ref{iimap}a a, \ref{iimap}d d and \ref{iimap}g g, we find a cloud with its peak position near the central star and well aligned with the center of the Trifid dust lanes (hereafter 2 km $^{-1}$ cloud)."
 The distribution of the molecular gas shows a triangle shape and each of its corners appears io trace the three dust lanes., The distribution of the molecular gas shows a triangle shape and each of its corners appears to trace the three dust lanes.
 The molecular gas around 8 km |. shown in Figures 2bb. 2ee and 2hh. consists of a central cloud and three surrounding elouds to the northeast. northwest and south of (hereafter clouds C. NW. NE and 5. respectively).," The molecular gas around 8 km $^{-1}$, shown in Figures \ref{iimap}b b, \ref{iimap}e e and \ref{iimap}h h, consists of a central cloud and three surrounding clouds to the northeast, northwest and south of (hereafter clouds C, NW, NE and S, respectively)."
 Ir addition. we list three small clouds named clouds NEL. NE? and NES. respectively. as indicated in Figure 3bb. The peak," In addition, we list three small clouds named clouds NE1, NE2 and NE3, respectively, as indicated in Figure \ref{co+noao}b b. The peak"
can be put on a colour-colour diagram (Caballero-Nievesal.2010). for additional understanding of the system.,can be put on a colour-colour diagram \citep{caballero-nieves2010} for additional understanding of the system.
 Most adaptive optics observations have been focused on specific projects such as multiplicity surveys (e.g. Turner et al., Most adaptive optics observations have been focused on specific projects such as multiplicity surveys (e.g. Turner et al.
 2008). but there is a great. benefit to using AO for ong term monitoring of binary stars.," 2008), but there is a great benefit to using AO for long term monitoring of binary stars."
 Phe increased cvnamic range of XO allows it to be used in the study of systems that he speckle interferometry has been unable to observe., The increased dynamic range of AO allows it to be used in the study of systems that the speckle interferometry has been unable to observe.
 Many of these svstems were discovered. decades ago with visual methods (e.g. Burnham 1894) and the published astrometey las large errors., Many of these systems were discovered decades ago with visual methods (e.g. Burnham 1894) and the published astrometry has large errors.
 Between 2001 ancl 2006. the Acdsyanced Electro-Optical System (ALOS) telescope and. AO system (Roberts&evman2002) were used. to observe binary stars in {-- in order to collect astrometric data to improve orbit determination and to provide photometric data for spectral class determination.," Between 2001 and 2006, the Advanced Electro-Optical System (AEOS) telescope and AO system \citep{roberts2002} were used to observe binary stars in -band in order to collect astrometric data to improve orbit determination and to provide photometric data for spectral class determination."
 This paper presents the measurements rom data collected in 2002., This paper presents the measurements from data collected in 2002.
 The other observations will be »e presented in subsequent. papers., The other observations will be be presented in subsequent papers.
 Most. AO systems have science cameras that observe in he near-IH1t. only a handful of systems have operated in the visible.," Most AO systems have science cameras that observe in the near-IR, only a handful of systems have operated in the visible."
 Phese include the Mt. Wilson svstem (Sheltonctal.1905) and the systems at the U.S. Air Force telescopes at the Starfire Optical Ranee (Fugatehirneetal.1998) viel on Maui. (Roberts&Nevman 2002).," These include the Mt. Wilson system \citep{shelton1995} and the systems at the U.S. Air Force telescopes at the Starfire Optical Range \citep{fugate1994, spinhirne1998} and on Maui \citep{roberts2002}."
. During the last decade. only the U.S. Air Foree’s AEOS telescope on Maui was available for astronomical observations and is currently unavailable for astronomical observations.," During the last decade, only the U.S. Air Force's AEOS telescope on Maui was available for astronomical observations and is currently unavailable for astronomical observations."
 As such. photometric measurements from the AEOS telescope are unique and. unlikely to be repeated in the near future.," As such, photometric measurements from the AEOS telescope are unique and unlikely to be repeated in the near future."
 Photometric measuremetns in the visible are especially useful when combined with near-H3. photometric measurements., Photometric measuremetns in the visible are especially useful when combined with near-IR photometric measurements.
 The addition of visible measurements. to near-IH measurements. decreases the uncertainty in spectral classification of stars.(Llinkleyetal.2010).," The addition of visible measurements to near-IR measurements, decreases the uncertainty in spectral classification of \citep{hinkley2010}."
.. Of. course. since the binary systems are dynamic. the astrometric measurements can not be duplicated.," Of course, since the binary systems are dynamic, the astrometric measurements can not be duplicated."
 Observations were made using the ALOS 3.6 m telescope and its AO system., Observations were made using the AEOS 3.6 m telescope and its AO system.
 Lhe AEOS telescope is located at the Maui Space Surveillance System at the summit of Laleakala (Dracdleyetal.2006)., The AEOS telescope is located at the Maui Space Surveillance System at the summit of Haleakala \citep{bradley2006}.
.. The AEOS AO system is a natural euide star system using a Shack-Hartmann wavelront sensor (Roberts&revi2002)., The AEOS AO system is a natural guide star system using a Shack-Hartmann wavefront sensor \citep{roberts2002}.
.. The individual subapertures rave a diameter of 11.9 em projected onto the primary., The individual subapertures have a diameter of 11.9 cm projected onto the primary.
 The deformable mirror has 941 actuators., The deformable mirror has 941 actuators.
 The svstem's closed oop bandwidth is adjustable and can run up to 200 112. although the normal bandwidth is approximately 50 Hz.," The system's closed loop bandwidth is adjustable and can run up to 200 Hz, although the normal bandwidth is approximately 50 Hz."
 In he configuration used for these observations. the light [rom 500-540 nm is sent to the tip/tilt detector svstem. the light rom 540-700 nm is sent to the wavelront sensor and. the ight longer than 700 nm is sent to the Visible Imager CCD sclence camera.," In the configuration used for these observations, the light from 500-540 nm is sent to the tip/tilt detector system, the light from 540-700 nm is sent to the wavefront sensor and the light longer than 700 nm is sent to the Visible Imager CCD science camera."
 The observing list was created from the Washington Double Star Catalog (WDS) by selecting., The observing list was created from the Washington Double Star Catalog (WDS) by selecting.
 ALL objects had |cS and 525°., All objects had $V<8$ and $\delta>-25^\circ$.
 The list included a number of παν stars with well measured astrometry. for comparison purposes.," The list included a number of binary stars with well measured astrometry, for comparison purposes."
 “These were the stars with the smallest. cynanic range in the observing Dist., These were the stars with the smallest dynamic range in the observing list.
 Ho also includes stars with larger dynamic ranges than what speckle interferometry can do., It also includes stars with larger dynamic ranges than what speckle interferometry can do.
 Phe intent was to gather additional astrometric measurements which could be used for eventual orbit calculation., The intent was to gather additional astrometric measurements which could be used for eventual orbit calculation.
 Special attention was paid to binaries that had no recent published astrometry., Special attention was paid to binaries that had no recent published astrometry.
 Many of these binaries have separations of several areseconds. but their dynamic range is too large for speckle interferometry observations to detect.," Many of these binaries have separations of several arcseconds, but their dynamic range is too large for speckle interferometry observations to detect."
 AO is well suited to observe these., AO is well suited to observe these.
 During testing and characterisation of the AQ system a number of stars were observed that were not in the WDS., During testing and characterisation of the AO system a number of stars were observed that were not in the WDS.
 L report on the results of these stars in addition to the observations of the known binaries., I report on the results of these stars in addition to the observations of the known binaries.
 Each data set consists of 250 [frames using a Dessel I--band filter., Each data set consists of 250 frames using a Bessel -band filter.
 After collection. any saturated. frames are discarded. and the remaining frames are debiased. dark subtracted and Dat fielded.," After collection, any saturated frames are discarded and the remaining frames are debiased, dark subtracted and flat fielded."
 Phe frames are weighted by their peak pixel. which is proportional to their Strehl ratio and then co-adeled using a shift-and-add. routine.," The frames are weighted by their peak pixel, which is proportional to their Strehl ratio and then co-added using a shift-and-add routine."
 The resulting image is analysed with the program FIPSTARS: it uses an iterative blind-deconvolution that fits the location of delta functions and their relative intensity to the data., The resulting image is analysed with the program FITSTARS; it uses an iterative blind-deconvolution that fits the location of delta functions and their relative intensity to the data.
 The co-adding technique and the analysis with ΕΕ. presented in tenBrununelaaretal.(1996). and tenDrum-melaarctal. (2000)., The co-adding technique and the analysis with FITSTARS was presented in \citet{tenBrummelaar1996} and \citet{tenBrummelaar2000}.
. Observations were made in a queue scheduling moce and as such. observations were mace during a wide range of observing conditions.," Observations were made in a queue scheduling mode and as such, observations were made during a wide range of observing conditions."
 Error bars on the astrometry and photometry were assigned using the method in Robertsetal.(2005)., Error bars on the astrometry and photometry were assigned using the method in \citet{roberts2005}.
.. For the photometry. simulated binary stars were createc from observations of single stars.," For the photometry, simulated binary stars were created from observations of single stars."
 The photometry of these simulated: binaries was measured ancl used to create a eric of measurement errors as à function of separation (p) ane iferential magnitudes., The photometry of these simulated binaries was measured and used to create a grid of measurement errors as a function of separation $\rho$ ) and differential magnitudes.
" For astrometryv. the separation error bar is 40002 for p x17.. ΟΕ for 1 « p <4""... ane 407002 [or p > 4.."," For astrometry, the separation error bar is $\pm$ 02 for $\rho$ $\leq$, $\pm$ 01 for 1 $<$ $\rho$ $\leq$, and $\pm$ 02 for $\rho$ $>$ ."
 HooThe error in. positione. angle (6) cause by errors in determining the centroid of the secondary. star location will be larger for svstems with small separations : ⇂↓⋯⊔∖∖⊽⊔⇂⋖⋅↓⋅⊳∖∢⊾↓≻⋜⊔, The error in position angle $\theta$ ) caused by errors in determining the centroid of the secondary star location will be larger for systems with small separations than wider separations.
⋅⋜∐↓∪⊔⊳∖⊳↓↓↕⋜↧∖⇁∢⊾⋯⇂∪↓≻∩⊾∠⇂∶∶⇉⇂∪↓⋅∕⇂∖∕↓⋜⋯∠. ∣⋅ ∣⋅ ∶∶↓⇂∪↓⋅∕⇂↙⇁↓⋜↧≱∖↥↓↕⋖⊾↓≻∪⊳∖↓↿↓∪⊔⋜⋯⋏∙≟↓∢⊾⋖⋅↓⋅↓⋅∪↓⋅⊳ ↔, I have adopted $\pm2^\circ$ for $\rho < 1$ and $\pm1^\circ$ for $\rho > 1$ as the position angle error.
 The astrometry and photometry of all resolved: systems are listed in ‘Table 1.., The astrometry and photometry of all resolved systems are listed in Table \ref{binaries2}.
 For cach star. I list the Washington Double Star (WDS) number. the discovery designation. the LD Catalogue number. the Hipparcos Catalogue number. the Besselian cate of the observation. the separation in areseconds. the position angle in degrees and finally the cillerential magnitude measured in Bessel f--band.," For each star, I list the Washington Double Star (WDS) number, the discovery designation, the HD Catalogue number, the Hipparcos Catalogue number, the Besselian date of the observation, the separation in arcseconds, the position angle in degrees and finally the differential magnitude measured in Bessel -band."
 Since the ALEOS telescope is an alt-az design. it requires a Dove prism image derotator in the science camera to keep the orientation of the image fixed.," Since the AEOS telescope is an alt-az design, it requires a Dove prism image derotator in the science camera to keep the orientation of the image fixed."
 E carried out some tests of the derotator. in which the derotator was turned olf.," I carried out some tests of the derotator, in which the derotator was turned off."
 In. these. cases. it was not possible to make an accurate measurement of the position angle of the stars.," In these cases, it was not possible to make an accurate measurement of the position angle of the stars."
 Phe separation and differential magnitude are still published. while the separation. will be of marginal value without a position angle. the differential magnitude is still valuable.," The separation and differential magnitude are still published, while the separation will be of marginal value without a position angle, the differential magnitude is still valuable."
 The Ustedastrometry was compared. with the latest published. astrometry in the WDS., The listedastrometry was compared with the latest published astrometry in the WDS.
 The astrometry for all but two systems was consistent with the published. data., The astrometry for all but two systems was consistent with the published data.
"where the potential terms have been neglected because | [T V®,| t£. αξ ensured by (19)).","where the potential terms have been neglected because $\mid~\mbox{\boldmath $ $}_{i_{\alpha}, 0 } \mid \gg \mid \mbox{\boldmath $ $} \Phi_{\gamma}
\mid t $ , as ensured by \ref{timeint}) )."
" The total energy change of the £a peuticke during pheyime interval (0,δ8) is easily caleulated by integrating ei "," The total energy change of the $i_{\alpha}$ particle during the time interval $(0, \delta t)$ is easily calculated by integrating eq. \ref{dEidt}) )."
We will be interested] in the average value of this quantity., Summing up on $i_{\alpha}$ we get the total energy variation of class $\alpha$ particles due to the fluctuating forces caused by $\beta$ particles in this time interval: We will be interested in the average value of this quantity.
 The presence and motion of the ἐς satellite particle perturbs he background., The presence and motion of the $i_S$ satellite particle perturbs the background.
 As a result. while the statistical (ensemble) average of the background I[uctuating forces acting on the satellite vanishes in the unperturbed state. (FF(19=0. hey do not vanish anymore in the real perturbed svstenm. FP(iyAl ," As a result, while the statistical (ensemble) average of the background fluctuating forces acting on the satellite vanishes in the unperturbed state, $ \langle \mbox{\boldmath $ $}^{B}_{i_S}(t) \rangle _{0} = 0$, they do not vanish anymore in the real perturbed system, $ \langle \mbox{\boldmath $ $}^{B}_{i_S}(t) \rangle \neq 0$."
"‘The same is true in general for the stochastic Orces caused by class 3 particles ancl acting on class à xwiicles: GP;(0=0. but F,(0D=0). )0cause the yhase density and the number of microstates available to he system has changed due to the perturbation."," The same is true in general for the stochastic forces caused by class $\beta$ particles and acting on class $\alpha$ particles: $\langle \mbox{\boldmath $ $}^{\beta}_{i_{\alpha}}(t) \rangle_{0} = 0$, but $\langle \mbox{\boldmath $ $}^{\beta}_{i_{\alpha}}(t) \rangle \neq 0$, because the phase density and the number of microstates available to the system has changed due to the perturbation."
 Following BAI92 ancl M93. we assume that the probability of finding a dynamical variable. Q. with a given value. PQ). is »oportional to the change in the number of microstates available to the whole system.," Following BM92 and M93, we assume that the probability of finding a dynamical variable, $Q$, with a given value, $P[Q]$ , is proportional to the change in the number of microstates available to the whole system."
" This change is given by the ""ACLOE: where 59 is the entropy. change of the system as a result of the distortion.", This change is given by the factor: where $\delta S$ is the entropy change of the system as a result of the distortion.
 The expected. value of a dynamical function. Q. can now be written as: where E are the variables defining the phase space of the Vp|Ns particles and. ος) is the distribution function for the unperturbed state.," The expected value of a dynamical function, $Q$, can now be written as: where $\Gamma$ are the variables defining the phase space of the $N_B + N_S$ particles and $ f_{0}(\Gamma)$ is the distribution function for the unperturbed state."
" As a result ofthe Ductuations. a generic particle initially withenergy σε will. change to an energy ο;=55,|ὅτι- o—D.5."," As a result of the fluctuations, a generic particle initially withenergy $\varepsilon_{i_{\alpha}}$, will change to an energy $\varepsilon_{i_{\alpha}}' = \varepsilon_{i_{\alpha}}+
\delta \varepsilon_{i_{\alpha}}$, $\alpha = B,S$."
 Recalling the definition of entropy: with Sy a constant. this energy change results into a total entropy variation given by: where [ος is the class a one particle distribution function for the unperturbed: state corresponding to an energy σεν," Recalling the definition of entropy: with $S_0$ a constant, this energy change results into a total entropy variation given by: where $f^{\alpha}(\varepsilon_{i_{\alpha}})$ is the class $\alpha$ one particle distribution function for the unperturbed state corresponding to an energy $\varepsilon_{i_{\alpha}}$."
" Most two-body encounters are weak. and then δει,Xf;"," Most two-body encounters are weak, and then $\delta \varepsilon_{i_{\alpha}} \ll \varepsilon_{i_{\alpha}}$."
 Expanding the ros., Expanding the r.h.s.
" of eq.(25)) and then the exponential in eq.(22)). we obtain that the change in the probability function is given approximately by: For most astronomical applications it is justified to use an isothermal Alaxwellian one-particle distribution function. where wi is the velocity vector. o, is the velocity dispersion of class à. particles and 3,=—L is an inverse temperature."," of \ref{varS}) ) and then the exponential in \ref{defK}) ), we obtain that the change in the probability function is given approximately by: For most astronomical applications it is justified to use an isothermal Maxwellian one-particle distribution function, where $\mbox{\boldmath $ $}$ is the velocity vector, $\sigma_{\alpha}$ is the velocity dispersion of class $\alpha$ particles and $\beta_{\alpha} = {1 \over m_{\alpha} \sigma_{\alpha}^2}$ is an inverse temperature."
 Introducing this expression fornau the distribution function in eq. (26)).," Introducing this expression for the distribution function in eq. \ref{expK}) ),"
 the factor of change becomes: The next step is to find out an expression for the energy variation., the factor of change becomes: The next step is to find out an expression for the energy variation.
" Phe total energy of the svstem must be conserved. so that we have: Moreover. for one given particle. 4,. its energy. variation can be expressed as: where (05, ids the fraction of the total class a autointeraction energy. ALNuu. absorbed. by particle 4. and b; Cds the fraction of the total interaction energy between class a and à particles. caused by the Uuetuating forces of the à subsystem. absorbed by 4, particle."," The total energy of the system must be conserved, so that we have: Moreover, for one given particle, $i_{\alpha}$ , its energy variation can be expressed as: where $a_{i_{\alpha}}$ is the fraction of the total class $\alpha$ autointeraction energy, $\Delta E_{\alpha, tot}^{\alpha}$, absorbed by particle $i_{\alpha}$, and $b_{i_{\alpha}}$ is the fraction of the total interaction energy between class $\alpha$ and $\tilde{\alpha}$ particles, caused by the fluctuating forces of the $\alpha$ subsystem, absorbed by $i_{\alpha}$ particle."
 Summing on £4 in eq. (300).," Summing on $i_{\alpha}$ in eq. \ref{deltE}) ),"
 we get the total energy change of subsystem o: compatible with energv conservation (eq. (29)))., we get the total energy change of subsystem $\alpha$: compatible with energy conservation (eq. \ref{Econs}) )).
 ‘Lo write down eq. (81)), To write down eq. \ref{sumE}) )
 from (30)). it has been taken into account that $7.oa=Mob1," from \ref{deltE}) ), it has been taken into account that $\sum_{i_{\alpha}}
a_{i_{\alpha}} = \sum_{i_{\alpha}} b_{i_{\alpha}} = 1$."
 Energy signs are such that Ad;0 if particle ὃν gains energy due to the Huetuating forces caused by class ~ particles and conversely., Energy signs are such that $\Delta E_{i_{\alpha}}^{\gamma} > 0$ if particle $i_{\alpha}$ gains energy due to the fluctuating forces caused by class $\gamma$ particles and conversely.
" With this convention. if energy [lux is from subsystem a to subsystem à. then AR’),«0 (subsystem à. loses energy). and ALS,20 (subsystemà gains energy). so that Yde;«O and SM,de),2 O."," With this convention, if energy flux is from subsystem $\alpha$ to subsystem $\tilde{\alpha}$, then $ \Delta E_{\alpha, tot}^{\tilde{\alpha}} < 0$ (subsystem $\alpha$ loses energy), and $ \Delta 
E_{\tilde{\alpha}, tot}^{\alpha}>0$ (subsystem$\tilde{\alpha}$ gains energy), so that $\sum_{i_{\alpha}} \delta \varepsilon_{i_{\alpha}} < 0$ and $\sum_{i_{\tilde{\alpha}}} \delta \varepsilon_{i_{\tilde{\alpha}}} > 0$ ."
 Lnserting eq. (31)), Inserting eq. \ref{sumE}) )
 in eq. (28)), in eq. \ref{Kfinal}) )
 and recalling eq. (2.1).," and recalling eq. \ref{deltaEtot}) ),"
 we obtain: Ίσα. (23)), we obtain: Eq. \ref{aver}) )
allows us now to write the ensemble average of the instantaneous energv variation at time / of ageneric class yo particle due to the stochastic forces caused by class v particles:,allows us now to write the ensemble average of the instantaneous energy variation at time $t$ of ageneric class $\mu$ particle due to the stochastic forces caused by class $\nu$ particles:
and ellicientlv. depleted: lithium in a substantial fraction of the early Lalo barvonic matter (Piauetal.2006).. mocifications to the BBN considering the decay of unstable particles (c.g.Cyburtetal.2010)... modifications to the reaction Cross sections for the Li production during BBN (e.g.Chakrabortyetal.2011)... or deep! turbulent. mixing during the MS that connects the convective envelope to inner. Li-depleted regions (e.g.Richareletal.2005:Muc-ciarellictal. POLL).,"and efficiently depleted lithium in a substantial fraction of the early Halo baryonic matter \citep{piau06}, modifications to the BBN considering the decay of unstable particles \citep[e.g.][]{cyburt10}, modifications to the reaction cross sections for the Li production during BBN \citep[e.g.][]{chak11}, or 'deep' turbulent mixing during the MS that connects the convective envelope to inner, Li-depleted regions \citep[e.g.][]{richard05, muc}."
.. Our result. lor RGB stars provides an additional robust constraint on the clliciency of this turbulent mixing., Our result for RGB stars provides an additional robust constraint on the efficiency of this turbulent mixing.
" Independently of its. parametrization. during the ALS any additional element. transport needs to bring into the Li burning region an amount of initial lithium 2N,,,, L1)20.3-0.4. dex. in order to eliminate the cliscrepaney with BBN calculations (the turbulence mocel denoted as T6.25 or 6.28 by. Richardctal.(2005). appearc to burn approximately the right amount of Li in models with Fe/ll]2 -2.31)."," Independently of its parametrization, during the MS any additional element transport needs to bring into the Li burning region an amount of initial lithium $\Delta_{burn}$ (Li)=0.3-0.4 dex, in order to eliminate the discrepancy with BBN calculations (the turbulence model denoted as T6.25 or T6.28 by \citet{richard05} appear to burn approximately the right amount of Li in models with [Fe/H]= -2.31)."
" The value of Apr, (Li) appears to be roughly the same for both Halo field ancl globular cluster stars.", The value of $\Delta_{burn}$ (Li) appears to be roughly the same for both Halo field and globular cluster stars.
 The use of lower RGB stars will allow estimates of the Li content in stellar populations more distant that those usually observed. to. investigate thePlateau., The use of lower RGB stars will allow estimates of the Li content in stellar populations more distant that those usually observed to investigate the.
" The obvious benefits are: (1) an enlarged. sample of field. stars and. clusters to study the primordial Li abundance within he Galaxy. and (ii) a better chance to assess whether a 7""cosmoloeical lithium problem? exists also in extragalactic systems with a cilferent and a dillerent star formation ustory (seeMonacoctoriginal.consideredO11.forafirststudy.ofthedwarfgalaxyacerctedbytheMilkv.Way ).."," The obvious benefits are: (i) an enlarged sample of field stars and clusters to study the primordial Li abundance within the Galaxy, and (ii) a better chance to assess whether a “cosmological lithium problem” exists also in extragalactic systems with a different origin and a different star formation history \citep[see][for a first study of the initial Li in $\omega$ Cen, widely considered as the remnant of 
a dwarf galaxy accreted by the Milky Way ]{mona}."
 For instance. he current. generation of high resolution spectrographs mounted on S metre-class telescopes allows to reach down o one magnitude fainter than the RGB bump level for stars in M 54 and the old stellar population of Sagittarius dwarf galaxy.," For instance, the current generation of high resolution spectrographs mounted on 8 metre-class telescopes allows to reach down to one magnitude fainter than the RGB bump level for stars in M 54 and the old stellar population of Sagittarius dwarf galaxy."
 In. principle. also stars at the RGB bump level in old. clusters belonging to the Large. Alagellanic Cloud can be reached. by using. for example. the VETE. spectrograph X-SHIOOTELH: this possibility(even if expensive in ternis of observing time due to the faintness of the targets) will open a new perspective in the investigation of the Li. problem.," In principle, also stars at the RGB bump level in old clusters belonging to the Large Magellanic Cloud can be reached, by using, for example, the VLT spectrograph X-SHOOTER; this possibility (even if expensive in terms of observing time due to the faintness of the targets) will open a new perspective in the investigation of the Li problem."
 Finally. with the advent of 30 moetre-class telescopes (as the E-ELT) spectroscopy. of lower RGB stars will provide new constraints to the primordial Li abundance in even more distant svstenis.," Finally, with the advent of 30 metre-class telescopes (as the E-ELT) spectroscopy of lower RGB stars will provide new constraints to the primordial Li abundance in even more distant systems."
 The authors warmly thank the anonymous. referee for his/her comments ancl suggestions., The authors warmly thank the anonymous referee for his/her comments and suggestions.
 PB acknowledges support from the Programme Nationale de Physique Stellaire (PNPS) and. the Programme Nationale de Cosmologie ct Galaxies (ΝΟ) of the Institut. Nationale de Sciences de FPUniverse of CNIS., PB acknowledges support from the Programme Nationale de Physique Stellaire (PNPS) and the Programme Nationale de Cosmologie et Galaxies (PNCG) of the Institut Nationale de Sciences de l'Universe of CNRS.
We can define the detection efficiency of a specific huission as the nuuber of observable eveuts divided by the expected iiuuber of coalesceunces in the same time interval.,We can define the detection efficiency of a specific mission as the number of observable events divided by the expected number of coalescences in the same time interval.
 Figure 9 shows the global (MDs|[Bs) detection efficiency for aud the efficiency considering as “detections” oulv MDs.," Figure \ref{eff} shows the global (MBs+IBs) detection efficiency for and the efficiency considering as “detections"" only MBs."
 The huge GW-brightuess of MDBIIDs is such that will observe 290% of all coalescences occurring at 204., The large GW-brightness of MBHBs is such that will observe $\gsim 90$ of all coalescences occurring at $z\lsim 5$.
 The efficiency falls below 0.5 only for MDBIIDs« at 228., The efficiency falls below $0.5$ only for MBHBs at $z\gsim 8$.
 The cfiiciency to MDs ouly is. obviously. lower.," The efficiency to MBs only is, obviously, lower."
 Figure 9 shows that a spacebased interferometer such as cau directly observe the final stage of the spiral-iu phase of about half of all AIBITBs coalescing at 5=5., Figure \ref{eff} shows that a space–based interferometer such as can directly observe the final stage of the spiral-in phase of about half of all MBHBs coalescing at $z\simeq 5$.
 Tn this paper we have characterized the CAV signa produced dy cosmological MDBIIDs. aud we have then folded the signal iuto the performance capabilities.," In this paper we have characterized the GW signal produced by cosmological MBHBs, and we have then folded the signal into the performance capabilities."
 We find that should resolve more than of al cosmiolosical coalescences of MDBIIDs occurring at i5., We find that should resolve more than of all cosmological coalescences of MBHBs occurring at $z\lsim 5$.
 The detection efficiency is already 20.5 for MDBIIDs at Dc8., The detection efficiency is already $\gsim 0.5$ for MBHBs at $z\simeq 8$.
 We showed that the confusion noise frou residua uuresolved MDBIIDs is expected to be at least au order of maenitude below iustrunceutal noise., We showed that the confusion noise from residual unresolved MBHBs is expected to be at least an order of magnitude below instrumental noise.
 We have divided the resolved events iuto mereiues a nespiral binaries., We have divided the resolved events into merging and in-spiral binaries.
 MDs are associated with svstenis a relatively low redshift iuvolviug heavy pairs (LO!107 Ανν , MBs are associated with systems at relatively low redshift involving heavy pairs $10^4-10^7$ $_{\odot}$ ).
Their strong CAV signal can be used to study the orbital evolution of the pair uutil the ISCO. allowing to test CR iu extreme conditions.," Their strong GW signal can be used to study the orbital evolution of the pair until the ISCO, allowing to test GR in extreme conditions."
 Ou the coutrary. IDs are less massive pairs at ligher redshift.," On the contrary, IBs are less massive pairs at higher redshift."
 Such systems can be eoncrally observed. with moderate integrated S/N. ouly for a relatively short amount of time. from few weeks to fex mouths. before the ISCO is reached.," Such systems can be generally observed, with moderate integrated $S/N$, only for a relatively short amount of time, from few weeks to few months, before the ISCO is reached."
 IDs are nevertheless, IBs are nevertheless
"Specifically, because we &-correct following the procedure described in Bernardi et al. (","Specifically, because we $k$ -correct following the procedure described in Bernardi et al. ("
20004). all galaxies at the sale redshift are assigned the same A-correction.,"2003a), all galaxies at the same redshift are assigned the same $k$ -correction."
 This leads to a simall amount of scatter (less than 0.02 mags) in our absolute magitucles aud colors which may well depeud on redshift., This leads to a small amount of scatter (less than 0.02 mags) in our absolute magnitudes and colors which may well depend on redshift.
 Figure 3. shows the color-o relation in the sample., Figure \ref{csig} shows the $\sigma$ relation in the sample.
" The ornat is the same as for the previous figure: top paucls show the raw nieasureiment. aud bottom paucls show the result of accounting for evolution by adding 0.2: mags o the colors. as was required. to model the evolution of ie color mnaguitnde relation,"," The format is the same as for the previous figure: top panels show the raw measurement, and bottom panels show the result of accounting for evolution by adding $0.3z$ mags to the colors, as was required to model the evolution of the color magnitude relation."
 The left-amost panels show 1¢ color-o relation in the full suuple. aud the other two ouils show the relation for galaxies which are restricted Oa narrow ranee in maeuitucde.," The left-most panels show the $\sigma$ relation in the full sample, and the other two panels show the relation for galaxies which are restricted to a narrow range in magnitude."
 Clearly. at fixed redshitt. re between color aud a is the same for all uaguitude c," Clearly, at fixed redshift, the correlation between color and $\sigma$ is the same for all magnitude bins."
"orrelation ofbius, color-o relation ∙∙ inredshift∙∙ velocityfrom sugeests that the relation is steepening slightlythedifferent with that galaxies with snall velocity dispersions are evolving ολοι more rapidly,", Comparison of the $\sigma$ relation in the different redshift bins suggests that the relation is steepening slightly with redshift: galaxies with small velocity dispersions are evolving slightly more rapidly.
" Because we are no longer maling as at fixed maguitide. oue may wonder if thefcolor|AL) of the color-o relation is affected bv the maguitude- withselection,"," Because we are no longer making measurements at fixed magnitude, one may wonder if the slope of the $\sigma$ relation is affected by the magnitude-limited selection."
 Appendix Bo develops a simple model The demonstrates that this is not the case., Appendix \ref{algebra} develops a simple model which demonstrates that this is not the case.
 We lave also between checked that the slope ehauge does not depend strougly ou our choice of A-correction., We have also checked that the slope change does not depend strongly on our choice of $k$ -correction.
 With the current sample size. this steeping is barely significant: it will be interesting to see if this steepenine persists when the sample is lareer.," With the current sample size, this steeping is barely significant: it will be interesting to see if this steepening persists when the sample is larger."
 Together. Figures 2. and 3) indicate that the colormagnitude relation is entirely a consequence of the color-o and maguitude-o relations.," Together, Figures \ref{cmag} and \ref{csig} indicate that the color-magnitude relation is entirely a consequence of the $\sigma$ and $\sigma$ relations."
 In particulax. the joint distribution of color. magnitude aud velocity dispersion 1s: Appeudix B./— demonstrates that if this expression is correct. then residuals from the magnitude-¢ relation should not correlate with residuals frou the color-o relation.," In particular, the joint distribution of color, magnitude and velocity dispersion is: Appendix \ref{algebra} demonstrates that if this expression is correct, then residuals from the $\sigma$ relation should not correlate with residuals from the $\sigma$ relation."
 This is shown in Figure 1: M—(MU|o) docs not correlate with color.(color|a). but σi|M) does correlate with. color fcolor|AL).," This is shown in Figure \ref{cvmresids}: $M - \langle M|\sigma\rangle$ does not correlate with ${\rm color} - \langle {\rm color}|\sigma\rangle$, but $\sigma - \langle\sigma|M\rangle$ does correlate with ${\rm color} - \langle {\rm color}|M\rangle$ ."
" Morcover. residuals frou, the color-o relation should not correlate with imaguitude. whereas residuals the color-magnitude relation should correlate with Comparison dispersion."," Moreover, residuals from the $\sigma$ relation should not correlate with magnitude, whereas residuals from the color-magnitude relation should correlate with velocity dispersion."
 The two panels in Figure 5 show jns this is indeed the case., The two panels in Figure \ref{agesigma} show that this is indeed the case.
 Note that the slope of the redshitt: between color έσω]»|M)and o is not as steep Slightly for the color-o relation itself., Note that the slope of the correlation between ${\rm color} - \langle {\rm color}|M\rangle$ and $\sigma$ is not as steep as for the $\sigma$ relation itself.
 In effect. this is because ueasureinents correlates with o (because AL itself correlates slope c).," In effect, this is because $\langle {\rm color}|M\rangle$ correlates with $\sigma$ (because $M$ itself correlates with $\sigma$ )."
 inited bottom panel shows that the correlation which color-aguitude residualsofFigure 5(i.c.. age) aud velocity dispersion steepeus systematically with redshift.," The bottom panel of Figure \ref{agesigma} shows that the correlation between color-magnitude residuals (i.e., age) and velocity dispersion steepens systematically with redshift."
 Although, Although
solids with a formallv infinite space density): as the criterion for the onset of GI.,solids with a formally infinite space density): as the criterion for the onset of GI.
 This is clearly a more conservative approach than considering the Roche stability criterion which only requires a hieh but finite midplane space density. equation (2)).," This is clearly a more conservative approach than considering the Roche stability criterion which only requires a high but finite midplane space density, equation \ref{Roche}) )."
 In practice. because saturation is reached so quickly once conditions become appropriate for precipitation. (he (vo criteria are virtually identical. except for the cases when (he gas is a considerable aid to GI.," In practice, because saturation is reached so quickly once conditions become appropriate for precipitation, the two criteria are virtually identical, except for the cases when the gas is a considerable aid to GI."
 In such extreme conditions of massive or very cold disks. we revert to the Toone criterion. Ως«1. to assess the possibility Lor GI.," In such extreme conditions of massive or very cold disks, we revert to the Toomre criterion, $Q_{\rm p}
< 1$, to assess the possibility for GI."
 A disk model which is gravitationally stable at cosmic abundances ean be made unstable in several wavs. as shown for the MSN in Fig. A..," A disk model which is gravitationally stable at cosmic abundances can be made unstable in several ways, as shown for the MSN in Fig. \ref{fig:sd}."
 Holding the gas content fixed. increasing Mp Will vield GI αἱ a value. X4. which is typically “ye.," Holding the gas content fixed, increasing $\Sigma_{\rm p}$ will yield GI at a value, $\Sigma_{\rm p,u}$, which is typically $\Sigma_{\rm p,c}$."
 The amount of enhancement needed for GI is shown Lor various models in Fig. 2..," The amount of enhancement $\mathcal{E}
\equiv \Sigma_{\rm p,u}/\Sigma_{\rm p,\odot}$ needed for GI is shown for various models in Fig. \ref{fig:enh}."
" The inverse process. holding the particle content fixed and lowering X, until GI occurs ab a value My. works equally well."," The inverse process, holding the particle content fixed and lowering $\Sigma_{\rm g}$ until GI occurs at a value $\Sigma_{\rm g,u}$ , works equally well."
" The depletion factors. D=X./X,. delined so that D>1. are plotted in Fig. À.."," The depletion factors, $\mathcal{D} = \Sigma_{\rm
g,\odot}/\Sigma_{\rm g,u}$, defined so that $\mathcal{D} \geq 1$, are plotted in Fig. \ref{fig:dep}."
 One can think of the gas depletion or solid enhancement scenarios as reflecting the mechanism which gives rise to solid/gas ratio enhancements and the physical conditions ab the (ime of planetesimal formation., One can think of the gas depletion or solid enhancement scenarios as reflecting the mechanism which gives rise to solid/gas ratio enhancements and the physical conditions at the time of planetesimal formation.
 There is no essential difference between (he two procedures except. that enhancing solids vields a higher surface densitv., There is no essential difference between the two procedures except that enhancing solids yields a higher surface density.
 The reason that required depletion [actors are larger. D>£. (vpically by [actors of 1.5-2. is the effect. of sell-gravitv represented by the s(6) factor in Y.," The reason that required depletion factors are larger, $\mathcal{D} > \mathcal{E}$, typically by factors of 1.5-2, is the effect of self-gravity represented by the $s(\psi)$ factor in $\Sigma_{\rm p,c}$."
 We find that GI requires augmenting (he particle to gas ratio by factors of two to tens above cosmic. depending on the disk model and radial location.," We find that GI requires augmenting the particle to gas ratio by factors of two to tens above cosmic, depending on the disk model and radial location."
 As expected. colder disks with less pressure support (and (hus less vertical shear) need less enhancement.," As expected, colder disks with less pressure support (and thus less vertical shear) need less enhancement."
 Higher mass disks also require smaller enhancement factors. but the effect is weaker.," Higher mass disks also require smaller enhancement factors, but the effect is weaker."
 We find that GI without enhancement is possible only in the outer regions (>10 AU) of cool disks which are 10 to 15 times more massive than the MSN in these regions., We find that GI without enhancement is possible only in the outer regions $>10$ AU) of cool disks which are 10 to 15 times more massive than the MSN in these regions.
 Two caveats exist in (he interpretation of these results., Two caveats exist in the interpretation of these results.
 If only rocky materials. chondrules. are enhanced and not ices. then the fractional enhancement of solids is actually (14-W)8—W. where WO=3.2 (or 0) is the cosmic ice to rock ratio outside (or inside) the iceline.," If only rocky materials, chondrules, are enhanced and not ices, then the fractional enhancement of solids is actually $(1+W)\mathcal{E} - W$, where $W=3.2$ (or 0) is the cosmic ice to rock ratio outside (or inside) the iceline."
" Also. if planetesimal formation occurs in one of the high X, scenarios. the totalamount of solids need not exceed the MSN if the enhancement is local."," Also, if planetesimal formation occurs in one of the high $\Sigma_{\rm p}$ scenarios, the totalamount of solids need not exceed the MSN if the enhancement is local."
"Before determining the parameters involved in the RM effect, an orbital model has to be obtained.","Before determining the parameters involved in the RM effect, an orbital model has to be obtained."
" To derive the radial-velocities of the components out of eclipse, we fitted two Gaussians to the two peaks in the BFs."," To derive the radial-velocities of the components out of eclipse, we fitted two Gaussians to the two peaks in the BFs."
 A x? fit was applied to extract the orbital parameters., A $\chi^{2}$ fit was applied to extract the orbital parameters.
" In this work, we adopted the orbital period (716407568+6x 1077) for all fits, since it is derived at much higher accuracy from eclipse photometry than from radial-velocity variations (Giménez&Margrave 1985))."," In this work, we adopted the orbital period $7\fd6407568
\pm 6\times10^{-7}$ ) for all fits, since it is derived at much higher accuracy from eclipse photometry than from radial-velocity variations \citeauthor{Gimenez1985} \citeyear{Gimenez1985}) )."
" The inclination of the orbit (87.0+ 0.1°), and the sizes of the components 1.346+0.023Ro and 1.323+0.023 have been adopted from Andersenetal.(1987);; these are needed for later analysis."," The inclination of the orbit $87.0 \pm 0.1 ^{\circ}$ ), and the sizes of the components $1.346 \pm 0.023 R_{\odot}$ and $1.323 \pm 0.023 R_{\odot}$ have been adopted from \cite{Andersen1987}; these are needed for later analysis."
 The fitted parameters are shown in the second column of Table 2 with their 1-c uncertainties., The fitted parameters are shown in the second column of Table \ref{tab:fit} with their $\sigma$ uncertainties.
" In addition, the orbital parameters given by Andersenetal.(1987) and GiménezMargrave(1985) are shown for comparison in column five."," In addition, the orbital parameters given by \citet{Andersen1987} and \cite*{Gimenez1985} are shown for comparison in column five."
 The tomography algorithm of Bagnuolo&Gies(1991) is used to disentangle the primary and secondary spectra., The tomography algorithm of \citet*{Bagnuolo1991} is used to disentangle the primary and secondary spectra.
" This algorithm uses, the spectra obtained at different phases of the orbit, and the orbital parameters of the system, as input."," This algorithm uses, the spectra obtained at different phases of the orbit, and the orbital parameters of the system, as input."
 It starts with two synthetic spectra without spectral lines for the two components in CCyg., It starts with two synthetic spectra without spectral lines for the two components in Cyg.
" For all observations taken outside the eclipses, it shifts the observed spectra in the rest-frames of each component using the newly obtained orbital parameters."," For all observations taken outside the eclipses, it shifts the observed spectra in the rest-frames of each component using the newly obtained orbital parameters."
" Subsequently, the synthetic spectra are compared with the observed spectra."," Subsequently, the synthetic spectra are compared with the observed spectra."
 The mean of all the differences between the synthetic and observed spectra is added to the synthetic spectra., The mean of all the differences between the synthetic and observed spectra is added to the synthetic spectra.
" This complete process is repeated 50 times, but in our case it converged after only a few iterations."," This complete process is repeated 50 times, but in our case it converged after only a few iterations."
" In the next step, the spectrum of the foreground star is subtracted."," In the next step, the spectrum of the foreground star is subtracted."
" For an observation out of eclipse this is straightforward, using the spectrum shifted in velocity space to the appropriate position."," For an observation out of eclipse this is straightforward, using the spectrum shifted in velocity space to the appropriate position."
" During eclipses, one has to incorporate the change in the light ratio of the two stars due to the eclipses."," During eclipses, one has to incorporate the change in the light ratio of the two stars due to the eclipses."
 For this we assumed a linear limb-darkening law with a limb-darkening coefficient (u) of 0.6 for both stars., For this we assumed a linear limb-darkening law with a limb-darkening coefficient $u$ ) of $0.6$ for both stars.
" Subsequently, the BF was calculated with only one star in the spectrum."," Subsequently, the BF was calculated with only one star in the spectrum."
 Figs., Figs.
" 2 and 3 show the BFs of the primary and secondary stars during their eclipses, after subtraction of the foreground star."," \ref{fig:beta_bf_primary} and \ref{fig:beta_bf_secondary} show the BFs of the primary and secondary stars during their eclipses, after subtraction of the foreground star."
" Note that, for computational reasons, the continua of the observed spectra were set to zero and the signs of the spectra have been changed; this results in positive BFs."," Note that, for computational reasons, the continua of the observed spectra were set to zero and the signs of the spectra have been changed; this results in positive BFs."
" The center of gravity of the absorption lines can now be extracted from the BFs and used to calculate the radial-velocity of the eclipsed star, including the radial-velocity anomaly introduced by the RM effect."," The center of gravity of the absorption lines can now be extracted from the BFs and used to calculate the radial-velocity of the eclipsed star, including the radial-velocity anomaly introduced by the RM effect."
" Using the orbital model and the formula by Kopal(1959) and Hosokawa(1953) to calculate the rotation anomaly, the orbital parameters and the parameters relevant for the RM effect of the two stars can be"," Using the orbital model and the formula by \cite{Kopal1959}
 and \cite{Hosokawa1953} to calculate the rotation anomaly, the orbital parameters and the parameters relevant for the RM effect of the two stars can be"
The dynamical evolution of gravitationally bouud stellar clusters lias been exteusively studied for decades. aud the basic theory is thought to be secure.,"The dynamical evolution of gravitationally bound stellar clusters has been extensively studied for decades, and the basic theory is thought to be secure."
 Populous systems evolve. over many Crossing times. through the processes kuown collectively as dynamical relaxation 2008.Chapter 7)..," Populous systems evolve, over many crossing times, through the processes known collectively as dynamical relaxation \citep[][Chapter~7]{bt08}."
 The inner core of the cluster contracts. ellectively trausferring euergy to the outer halo. which expaucs as a result.," The inner core of the cluster contracts, effectively transferring energy to the outer halo, which expands as a result."
 Concurrently. stars of relatively high mass sink toward the cluster center.," Concurrently, stars of relatively high mass sink toward the cluster center."
 Theory predicts further that the interior contraction leads eventually to core collapse. a catastrophic rise in central density (Lyiden-Bell&Wood19605).," Theory predicts further that the interior contraction leads eventually to core collapse, a catastrophic rise in central density \citep{lw68}."
.. As first suggested by Hills (1975).," As first suggested by \citet{hi75}, ,"
extragalactic surveys.,extragalactic surveys.
 To be totally confusion limited. a 3.6 pun. that the incompleteness would. be due only to confusion. LPs of approximately 50 ksec (14 hours) woutle be needed.," To be totally confusion limited at 3.6 $\umu$ m, that the incompleteness would be due only to confusion, ITs of approximately 50 ksec (14 hours) would be needed."
" This is within the scope of a Legacy Science tvpe project. where a ""noise map) of unresolved backgrouim sources [rom a reasonable size of area could be obtained for IIuctuation stucies."," This is within the scope of a Legacy Science type project, where a `noise map' of unresolved background sources from a reasonable size of area could be obtained for fluctuation studies."
 On the other hand. as far as direct source counts are concerned. much shorter PVs are adequate.," On the other hand, as far as direct source counts are concerned, much shorter ITs are adequate."
 Consider a 500 s exposure., Consider a 500 s exposure.
" At 6 μ.]ν, sources would still be detected to the confusion limit: that is sources would be lost at. 20. per cent rate due to confusion only."," At 6 $\umu$ Jy, sources would still be detected to the confusion limit; that is sources would be lost at 20 per cent rate due to confusion only."
 Halt of all 4 gy. objects would. be undetected: ~50 per cent of these are lost. due to confusion and the other half cue to sky noise., Half of all 4 $\umu$ Jy objects would be undetected; $\sim50$ per cent of these are lost due to confusion and the other half due to sky noise.
" This + wy level corresponds to approximately 1565,44 as calculated [rom Iq. τι.", This 4 $\umu$ Jy level corresponds to approximately $15\sigma_{\rm conf}$ as calculated from Eq. \ref{eq6-5}.
 Moreover. it is easy to see that the confusion limit is approached: if the VP is increased by a factor of 10. sources only 1.5 times fainter would be detected with the same confidence level.," Moreover, it is easy to see that the confusion limit is approached; if the IT is increased by a factor of 10, sources only 1.5 times fainter would be detected with the same confidence level."
 Η only the 3.6 jum band. were considered. we would conclude that it does not make much sense to extend the integration time bevond 1 hour.," If only the 3.6 $\umu$ m band were considered, we would conclude that it does not make much sense to extend the integration time beyond 1 hour."
 With this EL 3 jy sources are well detected., With this IT 3 $\umu$ Jy sources are well detected.
 Llowever. one is pushing confusion already since only 60 per cent of all sources at that Dux level could be extracted. (it becomes unreliable to interpret and moclel the count slopes if completeness corrections exceed a factor of 2).," However, one is pushing confusion already since only $\sim60$ per cent of all sources at that flux level could be extracted (it becomes unreliable to interpret and model the count slopes if completeness corrections exceed a factor of 2)."
" This limit corresponds to approximately 25 beams per SOULCE,", This limit corresponds to approximately 25 beams per source.
 ln the longest HLAC' waveband. with the baseline model. integration times exceeding 10 hours would still uncover new sources ab 3.244Jv. level with only modest. completeness corrections of ~1.2.," In the longest IRAC waveband, with the baseline model, integration times exceeding 10 hours would still uncover new sources at $3-4 \umu$ Jy level with only modest completeness corrections of $\sim 1.2$."
 However. truly confusion limited images ab S tun are much harder to reach than at 3.6 pum they would require nearly 100 hours of integration time.," However, truly confusion limited images at 8 $\umu$ m are much harder to reach than at 3.6 $\umu$ m – they would require nearly 100 hours of integration time."
 A practical S pum confusion limit is reached at a brighter lux level if galaxy counts are better modelled with the ISO-itted counts., A practical 8 $\umu$ m confusion limit is reached at a brighter flux level if galaxy counts are better modelled with the ISO-fitted counts.
 Requiring TO per cent completeness (ith z10m ideal photometric detections). sources at 4 μ.]ν would »( detected with the ISO-fitted model. while 2 Jy objects could be reached with the baseline model.," Requiring 70 per cent completeness (with $\approx10\sigma$ ideal photometric detections), sources at 4 $\umu$ Jy would be detected with the ISO-fitted model, while 2 $\umu$ Jy objects could be reached with the baseline model."
 However. in the alter case the FE needed. would. exceed. the scope of any realistic project.," However, in the latter case the IT needed would exceed the scope of any realistic project."
 For the δ qun. band. we conclude that an integration ime of about 15 hours would be both sullicient and useful or performing a deep survey (at the same time this would allow truly confusion limited images from the two shortest wavelength. filters)., For the 8 $\umu$ m band we conclude that an integration time of about 15 hours would be both sufficient and useful for performing a deep survey (at the same time this would allow truly confusion limited images from the two shortest wavelength filters).
" Sources at +4 pede would be at. Seoul or lle, depending whether galaxy counts are closer to the ISO-fittecl or baseline. model. respectively."," Sources at 4 $\umu$ Jy would be at $8\sigma_{\rm conf}$ or $11\sigma_{\rm conf}$ depending whether galaxy counts are closer to the ISO-fitted or baseline model, respectively."
 Respective completeness levels would be at 2 60 and SO per cent., Respective completeness levels would be at $\approx$ 60 and 80 per cent.
 The ISO and baseline models give 20 and 40 beanis/source at 4 LJ]y. respectively.," The ISO and baseline models give 20 and 40 beams/source at 4 $\umu$ Jy, respectively."
 ‘Table 1 summarizes the integration times along with the expected: values. of confusion. for the main mocels used in this work., Table 1 summarizes the integration times along with the expected values of confusion for the main models used in this work.
 Lt gives the confusion limit anc noise in the several dillerent. methods. presented. in. this work., It gives the confusion limit and noise in the several different methods presented in this work.
 Specifically. i£. can. be seen that the one-beame-per-source limit is nearly two orders of magnitudeo too low.," Specifically, it can be seen that the one-beam-per-source limit is nearly two orders of magnitude too low."
 Because the faint naitcd-LR counts are Hatter in the 3.6ptn1 band. the overall confusion limit is best clescribed by approximately 15 Tout.," Because the faint mid-IR counts are flatter in the $3.6\umu$ m band, the overall confusion limit is best described by approximately 15 $\sigma_{\rm conf}$."
 ln the longer LRAC waveband the limit is ο10., In the longer IRAC waveband the limit is $\la 10$.
 The steepest counts are the baseline Spun the resulting adopted confusion is approximately 25 beams/source. while for the other two cases in the table confusion could be described as £20 beams per source.," The steepest counts are the baseline $8\umu$ m – the resulting adopted confusion is approximately 25 beams/source, while for the other two cases in the table confusion could be described as $\la 20$ beams per source."
 There are indications that the LRAC resolution might prove to be better than the instrument specifications used, There are indications that the IRAC resolution might prove to be better than the instrument specifications used
to characterize X-ray selected: groups of galaxies up to 2~|.,to characterize X-ray selected groups of galaxies up to $z \sim 1$.
 This enables us not only to fully describe. the galaxy populations of the two fossil groups. but also to characterize their surrounding large-scale structures (LASS). and to speculate on their progenitors.," This enables us not only to fully describe the galaxy populations of the two fossil groups, but also to characterize their surrounding large-scale structures (LSSs), and to speculate on their progenitors."
 In Sect., In Sect.
 2 we describe selection ancl properties of these two groups., 2 we describe selection and properties of these two groups.
 Their galaxy stellar mass functions and colourmagnitude diagrams are determined. in Sect., Their galaxy stellar mass functions and colour–magnitude diagrams are determined in Sect.
 3., 3.
 Discussion of results ancl inference on evolutionary scenarios appear in Sect., Discussion of results and inference on evolutionary scenarios appear in Sect.
 4: conclusions are drawn in Sect., 4; conclusions are drawn in Sect.
 5., 5.
" As in G09. we adopt a ACDAL cosmological moclel (O,,= 0.258, O4= 0.742) with Ly=τὸkms+Alpe1 consistently with results from (Dunkley et al."," As in G09, we adopt a $\mathrm{\Lambda}$ CDM cosmological model $\mathrm{\Omega_m} = 0.258$ , $\mathrm{\Omega_\Lambda} = 0.742$ ) with $\mathrm{H}_0 = 72~\mathrm{km~s}^{-1}~\mathrm{Mpc}^{-1}$, consistently with results from (Dunkley et al."
 2009: lxomatsu et al., 2009; Komatsu et al.
 2009)., 2009).
" Phus. a redshift of 0:2 (0.425) corresponds to a lookback time of 3OSLGyr (4.409 Civr). à Iuminosity distance of 1961.1Alpe (2298.2 Mpc). an angular diameter distance of 1041.8Alpe (1131.5 Alpe). and a scale ol 5.051kpc/"" (5.187 kpc/"")."," Thus, a redshift of 0.372 (0.425) corresponds to a lookback time of $3.981~\mathrm{Gyr}$ $4.409~\mathrm{Gyr}$ ), a luminosity distance of $1961.1~\mathrm{Mpc}$ $2298.2~\mathrm{Mpc}$ ), an angular diameter distance of $1041.8~\mathrm{Mpc}$ $1131.8~\mathrm{Mpc}$ ), and a scale of $5.051~\mathrm{kpc}/^{\prime \prime}$ $5.487~\mathrm{kpc}/^{\prime \prime}$ )."
 Lereafter magnitudes are expressed in the AB system unless otherwise noted., Hereafter magnitudes are expressed in the AB system unless otherwise noted.
 From the composite mosaic of the and X-ray data mapping the 2deg? arca. extended sources (i.e. groups ancl clusters) were detected down to a Dux limit of LO7eres|em (Finoguenov οἱ al.," From the composite mosaic of the and X-ray data mapping the $2~\mathrm{deg}^2$ area, extended sources (i.e., groups and clusters) were detected down to a flux limit of $10^{-15}~\mathrm{erg~s}^{-1}~\mathrm{cm}^{-2}$ (Finoguenov et al."
 in preparation: see also Finoguenov et al., in preparation; see also Finoguenov et al.
 2007)., 2007).
 C09 selected OL groups/poor clusters at 0.1<z«I. which have an X-ray Bux estimate at a significance better than 3o. after point-like source subtraction (see Finoguenov οἱ al.," G09 selected 91 groups/poor clusters at $0.1 < z < 1$, which have an X-ray flux estimate at a significance better than $3 \mathrm{\sigma}$, after point-like source subtraction (see Finoguenov et al."
 2007)., 2007).
 For these groups. the membership of a galaxy (through a precise photometric )) and the total stellar mass in galaxies together with its uncertainty were robustly determined. as described in COO.," For these groups, the membership of a galaxy (through a precise photometric ) and the total stellar mass in galaxies together with its uncertainty were robustly determined as described in G09."
 Phe total mass of cach group was determined from the Lx Moos relation established through weak lensing analysis by Leauthaucl et al. (, The total mass of each group was determined from the $L_{\mathrm{X}}$ $M_{200}$ relation established through weak lensing analysis by Leauthaud et al. (
2010).,2010).
" Uneertainties on Also, are statistical only (Le. they arise from the τις Moos relation)."," Uncertainties on $M_{200}$ are statistical only (i.e., they arise from the $L_{\mathrm{X}}$ $M_{200}$ relation)."
 The elfects of systematics are estimated to be lower than the statisticaluncertainty., The effects of systematics are estimated to be lower than the statistical.
 We searched. for. fossil groups in the C09 sample., We searched for fossil groups in the G09 sample.
 As dn Giocini et al. (, As in Giodini et al. (
in. preparation). we defined as member candidates of a group. those. galaxies within a projected. eroup-centric distance. of fou. and with a photometric redshift consistent with the photometric redshift of the group within two times the uncertainty on the photometric redshift of the group.,"in preparation), we defined as member candidates of a group those galaxies within a projected group-centric distance of $R_{200}$, and with a photometric redshift consistent with the photometric redshift of the group within two times the uncertainty on the photometric redshift of the group."
 Phen we inspected the brightest member-candidate galaxies within a projected eroup-centric distance equal to 0.{ους to minimize the potential bias produced. by uncertainties on Rooy., Then we inspected the brightest member-candidate galaxies within a projected group-centric distance equal to $0.7 R_{200}$ to minimize the potential bias produced by uncertainties on $R_{200}$.
 As for ranking in luminosity. the available band. photometry was considered. since the reference. photometric catalogue is extracted from imaging in this band. (Hbort et al.," As for ranking in luminosity, the available $i$ -band photometry was considered, since the reference photometric catalogue is extracted from imaging in this band (Ilbert et al."
 2009)., 2009).
 This choice avoids the use of template- ancl (photometric) redshift-dependent &-corrections as for the choice of considering rest-frame L-band magnitudes., This choice avoids the use of template- and (photometric) redshift-dependent $k$ -corrections as for the choice of considering rest-frame R-band magnitudes.
 Furthermore. up to z=I. the (filter (observed frame) maps emission at rest-Lrame wavelengths redder than the 4000 -break. which limits the impact of voung stellar populations and. potentially. attenuation by a clusty interstellar medium.," Furthermore, up to $z = 1$, the $i$ -filter (observed frame) maps emission at rest-frame wavelengths redder than the 4000 -break, which limits the impact of young stellar populations and, potentially, attenuation by a dusty interstellar medium."
 A number of groups were initially selected as potential fossil systems. the magnitude cdilference between the BCC and any other bright member-candidate galaxy within 0.7Roo being conservatively chosen to be larger than 1.57- mae.," A number of groups were initially selected as potential fossil systems, the magnitude difference between the BCG and any other bright member-candidate galaxy within $0.7 R_{200}$ being conservatively chosen to be larger than $1.5~i$ -mag."
 We set a larger search racius and a smaller magnitude eap than those required. by. the definition of fossil groups (cl., We set a larger search radius and a smaller magnitude gap than those required by the definition of fossil groups (cf.
 Sect., Sect.
 1) in order to maximize the number of candidates in this first round of the search for fossil groups., 1) in order to maximize the number of candidates in this first round of the search for fossil groups.
 Two groups were successively established. as fossil thanks to the existing spectroscopic information (Lillv et al., Two groups were successively established as fossil thanks to the existing spectroscopic information (Lilly et al.
 2007). limited to sources brighter than 7=22.5mag. which enabled a finer screening against projected foregroundbackground: bright ealaxies.," 2007), limited to sources brighter than $i = 22.5~\mathrm{mag}$, which enabled a finer screening against projected foreground/background bright galaxies."
 On one hand. we Lageccl out. galaxies. classified as member candidates if they were located within {ίουυ [rom the N-ray centroicl of either fossil. group but exhibited a line-of-sight velocity in excess of 3000kms+ plus its 30 with respect to the spectroseopically determine recession velocity of either group.," On one hand, we flagged out galaxies classified as member candidates if they were located within $R_{200}$ from the X-ray centroid of either fossil group but exhibited a line-of-sight velocity in excess of $3000~\mathrm{km~s}^{-1}$ plus its $3 \sigma$ with respect to the spectroscopically determined recession velocity of either group."
 Ehe redshift of cach group was computed. using the median spectroscopic redshifts of the galaxies within ogy through iterative removal of outliers with a recession velocity beyond 1500kms.7 with respec to the recession velocity of the group., The redshift of each group was computed using the median spectroscopic redshifts of the galaxies within $R_{200}$ through iterative removal of outliers with a recession velocity beyond $1500~\mathrm{km~s}^{-1}$ with respect to the recession velocity of the group.
 The starting recdshif! was defined. by the photometric redshifts of galaxics on the red. sequence., The starting redshift was defined by the photometric redshifts of galaxies on the red sequence.
 Contamination was checked. by running a red-sequence-finding algorithm between. redshifts O anc 2 and by using spectroscopic group catalogs (Ixnobel et al., Contamination was checked by running a red-sequence-finding algorithm between redshifts 0 and 2 and by using spectroscopic group catalogs (Knobel et al.
 2009)., 2009).
 On the other hand. the available spectroscopy enabled us to check. in particular. that bright ealaxies within 0.547595 from the X-ray. centroid of either fossil group were actually not cropped as member candidates because of an inaccurate photometric redshift.," On the other hand, the available spectroscopy enabled us to check, in particular, that bright galaxies within $0.5 R_{200}$ from the X-ray centroid of either fossil group were actually not dropped as member candidates because of an inaccurate photometric redshift."
 Additional considerations on size and Luminosity were used to check the goodness of the photometric redshifts of relatively bright. galaxies without spectroscopy (see | 0212.6 in Fig., Additional considerations on size and luminosity were used to check the goodness of the photometric redshifts of relatively bright galaxies without spectroscopy (see $+$ 0212.6 in Fig.
 2)., 2).
" Figures | and 2 show cut-outs of the central regions of the two fossil groups under. study. which encompass the area within 0,0[ους for each svstem."," Figures 1 and 2 show cut-outs of the central regions of the two fossil groups under study, which encompass the area within $0.5 R_{200}$ for each system."
" They reproduce X-rav surface brightness contours overlaid on the ""band HST/ACS images (Ilxoekemoer et al.", They reproduce X-ray surface brightness contours overlaid on the $i$ -band HST/ACS images (Koekemoer et al.
 2007) of the twogalaxy svstems., 2007) of the twogalaxy systems.
 In. particular. member candidates (Le. photometric members) are indicated together with all ealaxies brighter than 7=-mag having a spectroscopic redshift.," In particular, member candidates (i.e., photometric members) are indicated together with all galaxies brighter than $i = 22.5~\mathrm{mag}$ having a spectroscopic redshift."
 Phe BCC of either group can be casily identified at the center of the X-ray emission region., The BCG of either group can be easily identified at the center of the X-ray emission region.
 and that higher huuimositv ACNs tend to be associated with vounger stellar populatious 2007)., and that higher luminosity AGNs tend to be associated with younger stellar populations .
. This connectioi iuav be driven by the fact that both black hole erowth and star formation occur when large amounts of eas are injected iuto the central reeion of a galaxy 2001).. although a inechanisin is necessary fo transport eas from or~100 pe down to sub-pe scales. regardless of the external fuel supply2010).," This connection may be driven by the fact that both black hole growth and star formation occur when large amounts of gas are injected into the central region of a galaxy , although a mechanism is necessary to transport gas from $r\sim100$ pc down to sub-pc scales, regardless of the external fuel supply."
. A more direct connection between uuclear star formation aud ACN activity has also been proposed where mass loss fron evolved stars or augulur-noimentuni loss associated witli sSuperuova-eenerated turbulence supplies the necessary material to the black hole accretion disk., A more direct connection between nuclear star formation and AGN activity has also been proposed where mass loss from evolved stars or angular-momentum loss associated with supernova-generated turbulence supplies the necessary material to the black hole accretion disk.
 Measurements of ongoing star formation in AGN lost ealaxies are uscful for coustrainius tle above models. but standard star-formation rate (SER) diagnostics such as the ultraviolet (UV) continuum. the Πα cussion line. or the infrared (IR) οὐμι are often coutamunated by the ACN itself.," Measurements of ongoing star formation in AGN host galaxies are useful for constraining the above models, but standard star-formation rate (SFR) diagnostics such as the ultraviolet (UV) continuum, the $\alpha$ emission line, or the infrared (IR) continuum are often contaminated by the AGN itself."
 The mid-IR aromatic (also known as PATI) features offer a solution because they probe the streueth of the UV radiation field iu photo-dissociation regious near voung. massive stars2007a).," The mid-IR aromatic (also known as PAH) features offer a solution because they probe the strength of the UV radiation field in photo-dissociation regions near young, massive stars."
. Wwhile higli-energv photons or shocks associated with the ACN could destroy the molecular carriers of the aromatic features1998).. showed that the," While high-energy photons or shocks associated with the AGN could destroy the molecular carriers of the aromatic features, showed that the"
At present time the Universe is essentially inhomogeneous on the scales of about 10-100 Mpc.,At present time the Universe is essentially inhomogeneous on the scales of about 10–100 Mpc.
 The development of initial fluctuations led to an observable large-scale structure., The development of initial fluctuations led to an observable large-scale structure.
 The regions with increased matter density provide an additional attraction of surrounding galaxies., The regions with increased matter density provide an additional attraction of surrounding galaxies.
 The regions with decreased density. e.g. voids. also make an input to the collective large-scale motion of galaxies on the background of Hubble expansion.," The regions with decreased density, e.g. voids, also make an input to the collective large-scale motion of galaxies on the background of Hubble expansion."
 Investigation of such motion on one side allows to map the matter density. including dark matter. in the Local Universe. and on the other side its parameters are linked with cosmological parameters.," Investigation of such motion on one side allows to map the matter density, including dark matter, in the Local Universe, and on the other side its parameters are linked with cosmological parameters."
 All of this makes the study of collective galaxy motions important., All of this makes the study of collective galaxy motions important.
 In recent years a number of articles was published claiming that typical velocities of large-scale collective motions are inconsistent with the standard ACDM model., In recent years a number of articles was published claiming that typical velocities of large-scale collective motions are inconsistent with the standard $\Lambda$ CDM model.
 For example. Watkinsetal.(2009) obtained the value 407+Slims at the scale LOOM+Alpe. whereas the ACDM model gives about 250kms5.," For example, \citet{ref:WFH09} obtained the value $407 \pm 81\,\rmn{km\,s}^{-1}$ at the scale $100h^{-1}\,\rmn{Mpc}$, whereas the $\Lambda$ CDM model gives about $250\,\rmn{km\,s}^{-1}$."
 However. our estimation of 210£S6kms at the same scale. obtained in the article (Parnovsky&Parnowski2010).. is consistent with the XCDM predictions.," However, our estimation of $210 \pm 86\,\rmn{km\,s}^{-1}$ at the same scale, obtained in the article \citep{ref:APSS09}, is consistent with the $\Lambda$ CDM predictions."
" Additionally. in the same article we obtained from the peculiar velocities the constraints on the cosmological parameters ©,,, and oy and their combinations. which match the other more precise constraints like baryonic acoustic oscillations or WMAP observations."," Additionally, in the same article we obtained from the peculiar velocities the constraints on the cosmological parameters $\Omega_m$ and $\sigma_8$ and their combinations, which match the other more precise constraints like baryonic acoustic oscillations or WMAP observations."
 In the article (Parnovsky&Parnowski2010). we used a sumple of RFGC galaxies with measured redshifts and line widths., In the article \citep{ref:APSS09} we used a sample of RFGC galaxies with measured redshifts and line widths.
 The Revised Flat Galaxy Catalogue (RFGC) and its previous version Flat Galaxy Catalogue (FGC) (Karachentsevetal.1993). contain the information about Right Ascension and Declination for the epochs J2000.0 and B1950.0. galactic longitude and latitude. major and minor blue and red diameters in areminutes in the POSS-I diameter system. morphological type of the spiral galaxies according to the Hubble classification. index of the mean surface brightness and some other parameters. which are not used in this article.," The Revised Flat Galaxy Catalogue (RFGC) and its previous version Flat Galaxy Catalogue (FGC) \citep{ref:FGC} contain the information about Right Ascension and Declination for the epochs J2000.0 and B1950.0, galactic longitude and latitude, major and minor blue and red diameters in arcminutes in the POSS-I diameter system, morphological type of the spiral galaxies according to the Hubble classification, index of the mean surface brightness and some other parameters, which are not used in this article."
 The RFGC contains data about 4236 flat edge-on spiral galaxies. almost uniformly covering the celestial sphere and satisfying the conditions 7 and eu010.," The RFGC contains data about 4236 flat edge-on spiral galaxies, almost uniformly covering the celestial sphere and satisfying the conditions $a_b/b_b\ge7$ and $a_b>0\farcm 6$."
" Here a), and 5; are the major and minor axial diameters in the e»; system.", Here $a_b$ and $b_b$ are the major and minor axial diameters in the $a_{25}$ system.
" The original goal of this catalogue was to estimate the distance to galaxies according to the Tully-Fisher relation in the line width — linear diameter"" version without using their redshifts.", The original goal of this catalogue was to estimate the distance to galaxies according to the Tully-Fisher relation in the line width – linear diameter” version without using their redshifts.
 The data about the redshifts and line widths or gas rotation velocities Ἐν were taken from differen sources., The data about the redshifts and line widths or gas rotation velocities $V_{rot}$ were taken from different sources.
 There were a number of graduallyincreasing samples of galaxies with such data (Karachentsev.etal.2000:Parnovskyeal.2001:Parnovsky&Tugay 200-4).," There were a number of graduallyincreasing samples of galaxies with such data \citep{ref:K00,ref:Par01,ref:ParTug04}."
. The latest version of this sample including 1623 galaxies was compiled and described by Parnovsky&Parnowski(2010)., The latest version of this sample including 1623 galaxies was compiled and described by \citet{ref:APSS09}.
. A list of peculiar velocities basec upon this list in the non-relativistic model of motion was assembled by Parnovsky&Parnowski(C2009)., A list of peculiar velocities based upon this list in the non-relativistic model of motion was assembled by \citet{ref:arxiv09}.
. In this article we use the same sample. but with differen model of collective motion of galaxies (Kudrya&Alexandrov2002. 2004).. based upon the general theory of relativity (GTR).," In this article we use the same sample, but with different model of collective motion of galaxies \citep{ref:KudAlex02,ref:KudAlex04}, based upon the general theory of relativity (GTR)."
 This model was applied earlier to the previous version of the sample by Parnovsky&Gaydamaka (2004):: however. the present article offers a much more in-depth analysis.," This model was applied earlier to the previous version of the sample by \citet{ref:ParGayd05}; ; however, the present article offers a much more in-depth analysis."
increase due to albedo.,increase due to albedo.
" Even an initial point source produces a total source with a FWHM peaking around 7"" (Fig.", Even an initial point source produces a total source with a FWHM peaking around $7''$ (Fig.
" 2ff,h). A"," \ref{fig2}f f,h). ("
nisotropy (Fig. 2i-l) -,Fig. \ref{fig2}{ ) -
 The shift in centroid position is larger for a higher initial downward anisotropy (the ratio of downward flux to upward flux) for all u and energies (Fig., The shift in centroid position is larger for a higher initial downward anisotropy (the ratio of downward flux to upward flux) for all $\mu$ and energies (Fig.
 2iik).," \ref{fig2}i i,k)."
 All shifts follow the general trend and tend towards zero at the centre (u= 1.0) and the limb (u= 0.0)., All shifts follow the general trend and tend towards zero at the centre $\mu=1.0$ ) and the limb $\mu=0.0$ ).
" Using y=3 and a primary source of FWHM-4.9"", a directivity of 5 produces a peak difference of ~0.9"" and even an isotropic source produces a peak difference of ~0.4""."," Using $\gamma=3$ and a primary source of $\sim 4.9''$, a directivity of 5 produces a peak difference of $\sim 0.9''$ and even an isotropic source produces a peak difference of $\sim 0.4''$."
" The shift in source position peaks near jj=0.4—0.6 and ~30 keV for a downward anisotropy of 2 and an isotropic source, but the shift peaks at a lower wp=0.4—0.5 for a downward directivity of 5."," The shift in source position peaks near $\mu=0.4-0.6$ and $\sim30$ keV for a downward anisotropy of 2 and an isotropic source, but the shift peaks at a lower $\mu=0.4-0.5$ for a downward directivity of 5."
 The stronger downward beaming of the primary source also leads to larger apparent source sizes for all µ and energies (Fig., The stronger downward beaming of the primary source also leads to larger apparent source sizes for all $\mu$ and energies (Fig.
 2jj.D).," \ref{fig2}j j,l)."
 It should be observed that the total FWHM produced for a directivity of 5 peaks at uw~0.15 (Fig., It should be observed that the total FWHM produced for a directivity of 5 peaks at $\mu\sim0.15$ (Fig.
 2pp) giving an apparent FWHM~13”., \ref{fig2}p p) giving an apparent $\sim 13''$.
" Since the fraction of reflected photons reduces with u the FWHM in perpendicular direction can be expected to slowly decrease from diskcentre to limb,"," Since the fraction of reflected photons reduces with $\mu$ the FWHM in perpendicular direction can be expected to slowly decrease from diskcentre to limb,"
ol the density distribution of the ISM onto the sky.,of the density distribution of the ISM onto the sky.
 The above procedure with the parameters we adopted results in clouds (hat are quite [ull of holes. with ~15% of the projected density distribution being almost blank.," The above procedure with the parameters we adopted results in clouds that are quite full of holes, with $\sim$ of the projected density distribution being almost blank."
" The ISM as shown by IL Lis similar if a low column density of ILI (<5x10! IL atoms 7) is taken to be ""blank"" (ie.. a column densitv much smaller than the average)."," The large-scale ISM as shown by H I is similar if a low column density of H I $<5\times10^{19}$ H atoms $^{-2}$ ) is taken to be “blank” (i.e., a column density much smaller than the average)."
 Elmegreen (1997) has discussed the emptiness of the ISM. with the large-scale structure in mind.," Elmegreen (1997) has discussed the emptiness of the ISM, with the large-scale structure in mind."
 Inages ol actual reflection nebulae (see Selleren. Werner. Dinerstein 1992 for 22023. and το») show strong filaments and structure. but there is material al all points within the nebula.," Images of actual reflection nebulae (see Sellgren, Werner, Dinerstein 1992 for 2023 and 7023) show strong filaments and structure, but there is material at all points within the nebula."
 For this reason. we sometimes add a uniform densitv {ο all cells in the supercube.," For this reason, we sometimes add a uniform density to all cells in the supercube."
 This constant density does not change tlie value of 2. since the Fourier transform of a constant is a Dirac ó-function al the origin. =0.," This constant density does not change the value of $\beta$, since the Fourier transform of a constant is a Dirac $\delta$ -function at the origin, $k=0$."
 Choosing a constant densitv provides a minimum projected density., Choosing a constant density provides a minimum projected density.
 The detailed placement of the clumps of dust also influences the results of our radiative transfer calculations., The detailed placement of the clumps of dust also influences the results of our radiative transfer calculations.
 The clumping is mainiv formed. by the first round of random casting of 32 points that are subsequently spread. by (ree more rounds of casting points in their vicinilies., The clumping is mainly formed by the first round of random casting of 32 points that are subsequently spread by three more rounds of casting points in their vicinities.
 The locations of the first round of points is uniquely determined bx the integer seed of the random nmunbergenerator.. and the locations of all subsequent. points follow rom the initial value of this integer in a complicated but unique way.," The locations of the first round of points is uniquely determined by the integer seed of the random number, and the locations of all subsequent points follow from the initial value of this integer in a complicated but unique way."
 The response of the nodel nebula to the central star is strongly affected bv the precise placement of the dust relative 0o the star and. thereby. to the value of the initial seed.," The response of the model nebula to the central star is strongly affected by the precise placement of the dust relative to the star and, thereby, to the value of the initial seed."
 We considered. suites of nodels that differed only in their initial seeds., We considered suites of models that differed only in their initial seeds.
 Our procedure amounts (o assuming (hat the star does not affect the clensity distribution of the dust in its immediate vicinity. so the initial seed is allowed (o control the placement of the dust both near aud far [rom the star.," Our procedure amounts to assuming that the star does not affect the density distribution of the dust in its immediate vicinity, so the initial seed is allowed to control the placement of the dust both near and far from the star."
 To test (he sensitivity of results to this assumption. we also considered models with a cavity in the dust distribution within the inner of the radius of the sphere.," To test the sensitivity of results to this assumption, we also considered models with a cavity in the dust distribution within the inner of the radius of the sphere."
 The radiative transfer was performed by the Monte Carlo code described by Wood Revnolds (1999)., The radiative transfer was performed by the Monte Carlo code described by Wood Reynolds (1999).
 It involves considering photon packages propagated in a random direction from the central star., It involves considering photon packages propagated in a random direction from the central star.
 We assumed e and g. along with the scattering. phase [function of Tlenvey Greenstein (1941).," We assumed $a$ and $g$, along with the scattering phase function of Henyey Greenstein (1941)."
" In most cases we used 5xLO° photons for each model. alter checking for a few cases that the results were the same as from a model using 2x10"" photons."," In most cases we used $5\times10^6$ photons for each model, after checking for a few cases that the results were the same as from a model using $2\times10^7$ photons."
 Unlike (he situation lor placing the dust. the initial seed for the radiative transfer makes no difference. as expected Irom such a large number of stellar photons propagated in random directions.," Unlike the situation for placing the dust, the initial seed for the radiative transfer makes no difference, as expected from such a large number of stellar photons propagated in random directions."
this- systematic+ uncertainty+ to the formal. Poisson+ error of. cach incazureineut in. quadrature. L6.B 07P=86gD|σας. and defined a statisticονο Iey such that Here. A3 is the standard statistic calculated for cach fit.,"this systematic uncertainty to the formal Poisson error of each measurement in quadrature, i.e., $\sigma^2=\sigma_{\rm formal}^2+ \sigma_{\rm
sys}^2$, and defined a statistic $X^2$ such that Here, $\chi^2$ is the standard statistic calculated for each fit."
 The posterior distribution of the uew statistic X7 may not be the same as that of the \? statistic aud will depend ou the uature of the systematic uncertainties., The posterior distribution of the new statistic $X^2$ may not be the same as that of the $\chi^2$ statistic and will depend on the nature of the systematic uncertainties.
 Iu. order to explore the degree aud nature of systematic uncertainties. we fit for cach source the X7. distribution with the 4? distribution expected for the number of deerces of freedom used in the fits. with © as a free paraicter.," In order to explore the degree and nature of systematic uncertainties, we fit for each source the $X^2$ distribution with the $\chi^2$ distribution expected for the number of degrees of freedom used in the fits, with $\xi$ as a free parameter."
" Note that the expected distribution that we use is formalhy correct if the countrate data in the individual spectral bins have ""correlated errors.", Note that the expected distribution that we use is formally correct if the countrate data in the individual spectral bins have uncorrelated errors.
 The expected \? aud the observed N? distributions for the optimal © value for KS 260. IU 31. aud IU 536 are shown in Figure L..," The expected $\chi^2$ and the observed $X^2$ distributions for the optimal $\xi$ value for KS $-$ 260, 4U $-$ 34, and 4U $-$ 536 are shown in Figure \ref{fig:chi2}."
 The © value required to make the observed N? distributious for KS 260 consistent with the expected ones is 0.55 (see Table 2))., The $\xi$ value required to make the observed $X^2$ distributions for KS $-$ 260 consistent with the expected ones is 0.55 (see Table \ref{chi2table}) ).
 This value corresponds to svstematic uncertainties that are very μπα., This value corresponds to systematic uncertainties that are very small.
 As an cxaple. we cousider a typical 0.25 s integration for NS 260. when its spectra is characterized by a color temperature of 2.5 keV. Iu this case. the average uuuber of counts in cach spectral bin in the 3-10 keV cherev range is LLO ct aud the corresponding Poisson uncertainty is 29.5%.," As an example, we consider a typical 0.25 s integration for KS $-$ 260, when its spectrum is characterized by a color temperature of 2.5 keV. In this case, the average number of counts in each spectral bin in the 3-10 keV energy range is 110 ct and the corresponding Poisson uncertainty is $\simeq 9.5$."
. Multiplviug this bv the interred value κ=0.52 for this source leads to the conchision that the systematic uncertainties required to render the observed spectrum consistent with a blackbody are ~55 ., Multiplying this by the inferred value $\xi=0.52$ for this source leads to the conclusion that the systematic uncertainties required to render the observed spectrum consistent with a blackbody are $\simeq 5$ .
. For the case of IU 31. which is brighter than IS 260. he formal πιοαμ are 26% aud the systematic uncertaiuties amount to 23°," For the case of 4U $-$ 34, which is brighter than KS $-$ 260, the formal uncertainties are $\simeq 6$ and the systematic uncertainties amount to $\simeq 3$."
 Figure d shows that Ίοςthe resulting X? distributions can be well approximated by the 4? distribution but have weak ails extending to ligher values., Figure \ref{fig:chi2} shows that the resulting $X^2$ distributions can be well approximated by the $\chi^2$ distribution but have weak tails extending to higher values.
 These tails most likely arise from the inconsistency of only a small πο of spectra with blackbody fictions eveu though we cannot rule out the possibility that the X? statistic follows a different )oxterior distribution tha X7., These tails most likely arise from the inconsistency of only a small number of spectra with blackbody functions even though we cannot rule out the possibility that the $X^2$ statistic follows a different posterior distribution than $\chi^2$.
 Figure 1. allows us also to identify the X-ray spectra that are statistically imconsisteut with blackbodies., Figure \ref{fig:chi2} allows us also to identify the X-ray spectra that are statistically inconsistent with blackbodies.
 For each source. there is a masiunun value of X? per degree of freedom bevoud which the distribution of Y? values deviates frou he theoretical expectatiou.," For each source, there is a maximum value of $X^2$ per degree of freedom beyond which the distribution of $X^2$ values deviates from the theoretical expectation."
 For the case of NS 260. this lunitine value of the reduced X? is 1.7. for IU 3114 is 1.7. and for LU 536 is 1.9 (see Table 2)).," For the case of KS $-$ 260, this limiting value of the reduced $X^2$ is 1.7, for 4U $-$ 34 it is 1.7, and for 4U $-$ 536 is 1.9 (see Table \ref{chi2table}) )."
 The spectra with high reduced X? values often occur at the late stages of the cooling tails. where the subtraction of the persistent cussion is the most problematic.," The spectra with high reduced $X^2$ values often occur at the late stages of the cooling tails, where the subtraction of the persistent emission is the most problematic."
 However. unacceptable X? values may also be found in other. secuingly raudom places of the cooling tails.," However, unacceptable $X^2$ values may also be found in other, seemingly random places of the cooling tails."
 Nevertheless. the fraction of spectra that is iueonsistent with blackbodies are <3%... <6%. and Z2% for KS 260. for LU 31. and for IU 536. respectively.," Nevertheless, the fraction of spectra that is inconsistent with blackbodies are $\lesssim 3$, $\lesssim 6$, and $\lesssim 2$ for KS $-$ 260, for 4U $-$ 34, and for 4U $-$ 536, respectively."
 Horeafter. we consider only the spectra that we regard to be statistically acceptable. eiveu the values of. the reduced LlX7.," Hereafter, we consider only the spectra that we regard to be statistically acceptable, given the values of the reduced $X^2$."
 Oi second working hypothesis is that. during the cooling tail of cach burst. the eutire neutron star is enitting nuiformly with negligible lateral temperature variations.," Our second working hypothesis is that, during the cooling tail of each burst, the entire neutron star is emitting uniformly with negligible lateral temperature variations."
 This assunption is again expected to be violated at some level for a umber of reasons., This assumption is again expected to be violated at some level for a number of reasons.
" The non-uniformity of accretion outo the neutron star (οιοι, Inogamov Suuvaev 1999). the finite time of propagation of the burning front around the star (sec. c.e.. Nozakura. Ikeuchi. Fujimoto 1981: Bildsten 1995: Spitkovsky. Levin. Ushomirsky 2002). as well as the excitation of non-radial modes ou the stellar surface (Πο 2001: Piro Bildsten 2005: Naravan Cooper 2007) are all expected to lead to some variations m the effective temperature of emission at differcut latitudes aud lougitudes ou the stellar surface."," The non-uniformity of accretion onto the neutron star (e.g., Inogamov Sunyaev 1999), the finite time of propagation of the burning front around the star (see, e.g., Nozakura, Ikeuchi, Fujimoto 1984; Bildsten 1995; Spitkovsky, Levin, Ushomirsky 2002), as well as the excitation of non-radial modes on the stellar surface (Heyl 2004; Piro Bildsten 2005; Narayan Cooper 2007) are all expected to lead to some variations in the effective temperature of emission at different latitudes and longitudes on the stellar surface."
 The characteristics of burst oscillations observed during the cooling tails ofX-ray bursts. however. imply that aux varlatious iu the surface temperatures of neutron stars can only be mareial.," The characteristics of burst oscillations observed during the cooling tails ofX-ray bursts, however, imply that any variations in the surface temperatures of neutron stars can only be marginal."
 Indeed. auy component of the variation," Indeed, any component of the variation"
aas progenitors.,as progenitors.
 The methodology of all these studies was similar., The methodology of all these studies was similar.
" A one-dimensional progenitor model was exploded. somewhat artificially, by micas of a piston or a thermal bomb. and the subsequent evolution followed with a two-dimensional code."," A one-dimensional progenitor model was exploded, somewhat artificially, by means of a piston or a thermal bomb, and the subsequent evolution followed with a two-dimensional code."
 More receutlv. ? and ? have used a different iyproach.," More recently, \citet{Kifonidis:2003} and \citet{Kifonidis:2006} have used a different approach."
 These authors followed a blue superegiaut model from the first seconds of the explosion out to about 5 days after core collapse. using first oue code with neutrino plivsics for the carly times. and another code with mesh refinement for later times.," These authors followed a blue supergiant model from the first seconds of the explosion out to about 5 days after core collapse, using first one code with neutrino physics for the early times, and another code with mesh refinement for later times."
 They saw mixing at the Si-O interface. a location at which uo previous studies had found mixing. and were able to reproduce the high ?9Ni velocities observed in SN LOSTA. something previous studies had not done.," They saw mixing at the Si-O interface, a location at which no previous studies had found mixing, and were able to reproduce the high $^{56}$ Ni velocities observed in SN 1987A, something previous studies had not done."
 While attempts to reproduce observations of 1987À have been uunierous. no multidimensional studies of musing and fallback in very low metallicity πηραπονάς have been done.," While attempts to reproduce observations of 1987A have been numerous, no multidimensional studies of mixing and fallback in very low metallicity supernovae have been done."
 The uucleosvuthetic vields of ποτάπου (Pop III) aud extremely metal-poor (EAIP) stars mueht still be visible iu the abundance patterns observed iu some halo stars in our own galaxy., The nucleosynthetic yields of metal-free (Pop III) and extremely metal-poor (EMP) stars might still be visible in the abundance patterns observed in some halo stars in our own galaxy.
" Of particular interest are the ""ultra-iron-poor (IMP) stars C??2).."," Of particular interest are the “ultra-iron-poor” (HMP) stars \citep{Frebel:2005,Aoki:2006}. ."
 These stars with [Fe/T|< -5. have abuudauce patterus that differ considerably from those observed in stars with near solar metallicity or even other metal-poor stars (7).," These stars with $<$ -5, have abundance patterns that differ considerably from those observed in stars with near solar metallicity or even other metal-poor stars \citep{Cayrel:2004}."
 It is possible that these irou-poor stars were curiched by oulv one or a few supernovae (2).., It is possible that these iron-poor stars were enriched by only one or a few supernovae \citep{Frebel:2005}.
 Iu particular. the two most metal-poor stars known and several other UMP stars display πανκος cuhancement in C. N. aud O relative to Fe.," In particular, the two most metal-poor stars known and several other UMP stars display marked enhancement in C, N, and O relative to Fe."
 Previous studies (22?) have sought to explain these abundance patterns with one-dimensional models for superuovae that parainoetrize the amount of musing aud fallback to match what is observed.," Previous studies \citep{Iwamoto:2005,Tominaga:2007,Heger&Woosley:2008} have sought to explain these abundance patterns with one-dimensional models for supernovae that parametrize the amount of mixing and fallback to match what is observed."
 Simulating mixing and fallback directly. rather than αταιοΊσανι requires a iulti-dimeusional approach.," Simulating mixing and fallback directly, rather than parametrically, requires a multi-dimensional approach."
 Iu this paper. we use two-dimensional axisvninuetric sinulatious to explore directly the amount of Ravleigh-Tavlor-induced mixing that occurs m non-otatiug zero- and solur- metallicity stars.," In this paper, we use two-dimensional axisymmetric simulations to explore directly the amount of Rayleigh-Taylor-induced mixing that occurs in non-rotating zero- and solar- metallicity stars."
 Our methodology is similar to the earlier studies (before Kifonidis) of SN. 105ΤΑ. Tn2. we discuss our initial models. our modifications to the code. aud our simulation setup.," Our methodology is similar to the earlier studies (before Kifonidis) of SN 1987A. In, we discuss our initial models, our modifications to the code, and our simulation setup."
 Iu3.. results are eiven that show the deeree of mixing. the fal velocity distribution of isotopes. aud the ejected vields.," In, results are given that show the degree of mixing, the final velocity distribution of isotopes, and the ejected yields."
 These vields are compared with abundances observed iu IIMP stars in3., These yields are compared with abundances observed in HMP stars in.
1. Finally. we provide a short summary of results aud their interpretation in The preseut work follows the method used in many previous studies of iuixiug in supernovae.," Finally, we provide a short summary of results and their interpretation in The present work follows the method used in many previous studies of mixing in supernovae."
 A ouc-dimensional code was used to evolve aud explode the pre-supernova model aud to follow the first stages of the expansion to the time when the reverse shock was just beeinning to form., A one-dimensional code was used to evolve and explode the pre-supernova model and to follow the first stages of the expansion to the time when the reverse shock was just beginning to form.
 No significan growth of iustabilities is expected before the formation of the reverse shock., No significan growth of instabilities is expected before the formation of the reverse shock.
 The one-dimensional model was then mapped outo a two-dimensional grid and the ensuing instabilities followed., The one-dimensional model was then mapped onto a two-dimensional grid and the ensuing instabilities followed.
 While ?/— reproduced the observations of SN 1987À somewhat better than previous attempts. possibly by following the carly stages of the explosion. this paper does not do that.," While \citet{Kifonidis:2006} reproduced the observations of SN 1987A somewhat better than previous attempts, possibly by following the early stages of the explosion, this paper does not do that."
 The plysics of the initial explosion relnaus uncertain and our goal is to isolate the differences in post-explosive musing that arise as a direct consequence of the differences in initial structure of the pre-supernova models., The physics of the initial explosion remains uncertain and our goal is to isolate the differences in post-explosive mixing that arise as a direct consequence of the differences in initial structure of the pre-supernova models.
 Exploding the star with a piston in the same location aud with the same energv in all models allows us to accomplish this., Exploding the star with a piston in the same location and with the same energy in all models allows us to accomplish this.
 The choice of piston mass location is constrained by observational paramicters., The choice of piston mass location is constrained by observational parameters.
 The pistou cannot be located within the iron core or the resulting explosion will produce far too πιο of 51.58 Fe and other neutrou-rich species to be iu agreement with observations of these isotopes.," The piston cannot be located within the iron core or the resulting explosion will produce far too much of 54,58 Fe and other neutron-rich species to be in agreement with observations of these isotopes."
 On the other hand. the renmaut mass will be too large to agree with observations if the explosion site is located outside the base of the oxveen shell.," On the other hand, the remnant mass will be too large to agree with observations if the explosion site is located outside the base of the oxygen shell."
 There are reasons to believe the location site is located at the base of the oxveen shellthe large density decrease associated with this location is dynamically importaut. and successful explosion calculations often fud the mass cut there.," There are reasons to believe the location site is located at the base of the oxygen shell–the large density decrease associated with this location is dynamically important, and successful explosion calculations often find the mass cut there."
 The papers frou which our models are taken also reported on models in which the stars were exploded with a piston at the edge of the ni core., The papers from which our models are taken also reported on models in which the stars were exploded with a piston at the edge of the ni core.
 These explosious experience sleltly less fallback. aud produce more wickel. by a factor of 2 or so. than the models preseuted in this paper.," These explosions experience slightly less fallback, and produce more nickel, by a factor of 2 or so, than the models presented in this paper."
 luitial models were taken from the surveys of ? aud ?.., Initial models were taken from the surveys of \citet{Heger&Woosley:2008} and \citet{Woosley&Heger:2007}.
 Both of these papers used the code (77). to evolve stars through all stable stages of unclear burning uutil their iron cores became unstable to collapse.," Both of these papers used the code \citep{Weaver:1978,Woosley:2002} to evolve stars through all stable stages of nuclear burning until their iron cores became unstable to collapse."
 At this poiut. pistous located at or near the base of the oxveen shell were used to explode the stars.," At this point, pistons located at or near the base of the oxygen shell were used to explode the stars."
 2. simulated the evolution and explosion of 10 to 100 sstars with zero initial metallicity., \citet{Heger&Woosley:2008} simulated the evolution and explosion of 10 to 100 stars with zero initial metallicity.
 Explosion energies ranged from 0.3 to 10. D. where 1 Bethe = 1 B = 10° e," Explosion energies ranged from 0.3 to 10 B, where 1 Bethe = 1 B = $10^{51}$ ergs."
"ves, 7T exiundined solar-imetallicity stars from 12 to LOO wwhich were exploded by pistons simular to the other survey. but for a 1nore limited sot of masses aud cucreics."," \citet{Woosley&Heger:2007} examined solar-metallicity stars from 12 to 100 which were exploded by pistons similar to the other survey, but for a more limited set of masses and energies."
 Both surveys were limited to non-rotatiug progenitors., Both surveys were limited to non-rotating progenitors.
 The zero-iuetallicity stars were assumed to lave uo lass loss. while the solu-inetallicitv inodels took mass loss iuto account.," The zero-metallicity stars were assumed to have no mass loss, while the solar-metallicity models took mass loss into account."
 Tere ouly two representative stars from cach survey are studied: Models z15D aud z25D from ? anc Models S15À and s25A from ?.., Here only two representative stars from each survey are studied: Models z15D and z25D from \citet{Heger&Woosley:2008} and Models s15A and s25A from \citet{Woosley&Heger:2007}.
" The letter ""z indicates zero initial wetallicity. while ""s iudieates solu metallicity."," The letter “z” indicates zero initial metallicity, while “s” indicates solar metallicity."
 The uunbers m the models correspond to the initial mass of the star in aand the final letter is the explosion energv. 1.2 D in each case.," The numbers in the models correspond to the initial mass of the star in and the final letter is the explosion energy, 1.2 B in each case."
 The pistou was located at the place in the star where the eutropy was equal to LOApfbarvon.," The piston was located at the place in the star where the entropy was equal to $4.0
k_B/$ baryon."
 This correspouded to the base of the oxvecu shell., This corresponded to the base of the oxygen shell.
 Series sA and zD are thus directly comparable in all respects save their initial metallicity., Series sA and zD are thus directly comparable in all respects save their initial metallicity.
 15 and 25 rrepreseut the “canonical” Supernova cases with the most conunonly eimiploved explosion energy aud piston location., 15 and 25 represent the “canonical” supernova cases with the most commonly employed explosion energy and piston location.
 15 and 25 stars are also in the same lass range as previous studies of Ravleigh-Tavlor mixing in supernovae. allowing for easy comparison.," 15 and 25 stars are also in the same mass range as previous studies of Rayleigh-Taylor mixing in supernovae, allowing for easy comparison."
 The one-dimensional progenitor models used iu this study lead to spherically sauuuetzic explosions., The one-dimensional progenitor models used in this study lead to spherically symmetric explosions.
 Mappiug the models from one to two diuensious after theexplosion has taken place has the effect of suppressing low-order departures from spherical svnuuetry., Mapping the models from one to two dimensions after theexplosion has taken place has the effect of suppressing low-order departures from spherical symmetry.
 This work oulv addresses spherically svuuuetric explosions witl, This work only addresses spherically symmetric explosions with
 This work oulv addresses spherically svuuuetric explosions witli, This work only addresses spherically symmetric explosions with
primary nitrogen [rom rapidly evolving massive stars (M > 8 AL. ).,primary nitrogen from rapidly evolving massive stars (M $>$ 8 $_\odot$ ).
 In contrast. Henryοἱal. and Chiappiniοἱal.(2003). concluded that these objects are dominated by primary nitrogen [rom intermediate mass stars. which have masses in (he range 4-3 M. and evolve much slower.," In contrast, \cite{henry00} and \cite{chiappini03} concluded that these objects are dominated by primary nitrogen from intermediate mass stars, which have masses in the range 4-8 $_\odot$ and evolve much slower."
 In order (o correctly. interpret (the plateau properties. it is important (ο up-date the techniques emploved to determine the N/O values.," In order to correctly interpret the plateau properties, it is important to up-date the techniques employed to determine the N/O values."
 This can be accomplished (through modeling., This can be accomplished through modeling.
 In particular. simulations are required to obtain N/O for two reasons.," In particular, simulations are required to obtain N/O for two reasons."
 Firstly. they. are necessary for [finding parameterizations for the electron temperatures ol the regions where and — are emitting. i.e.. and).," Firstly, they are necessary for finding parameterizations for the electron temperatures of the regions where $^+$ and $^+$ are emitting, i.e., and."
. Unfortunately. because the strengths of the auroral features A5755 and AA7320.7230. are commonlv unavailable im observational data. (hie above temperatures cannot be obtained from emission-line [Iux ratios of the Form. nebular line(s) / auroral line(s). although thev are required in order to determine (he abundances of (he above (wo ions.," Unfortunately, because the strengths of the auroral features $\lambda5755$ and $\lambda\lambda7320,7230$ are commonly unavailable in observational data, the above temperatures cannot be obtained from emission-line flux ratios of the form, nebular line(s) / auroral line(s), although they are required in order to determine the abundances of the above two ions."
 Since photoionization models can provide the auroral lines missing [rom observations. these lines can be used in (urn to compute)..LO). and 7). independent of each other.," Since photoionization models can provide the auroral lines missing from observations, these lines can be used in turn to compute, and , independent of each other."
 Because objects with oxygen abundances below 8.1 usually have sufficient strength in the auroral line [O II] A4363. can be directly determined [rom the observed temperature sensitive line flux ratio (συ+Lso07)τι (Shieldsetal.1981).," Because objects with oxygen abundances below 8.1 usually have sufficient strength in the auroral line [O III] $\lambda4363$, can be directly determined from the observed temperature sensitive line flux ratio $(I_{4959}+I_{5007})/I_{4363}$ \citep{shields81}."
. In general. a parameterization of the form = = 7)]]. inferred from models. is used to compute N/O αἱ low Ο/Η (e.g.. IXobulnickv&Skillman1996:Izotovetal.1999;Melbourne 2004)).," In general, a parameterization of the form = = ], inferred from models, is used to compute N/O at low O/H (e.g., \citealt{kobulnicky96,izotov99,melbourne04}) )."
 Examples of (his (wpe of relation. based on photoionization models by Stasinska (1990).. can be found in Pageletal.(1992). or Ivotovetal.(1994).," Examples of this type of relation, based on photoionization models by \cite{stasinska90}, can be found in \cite{pagel92} or \cite{izotov94}."
. A more recent parameterization based on models by Stasiüska&Leitherer(1996) is used in Stasitska&Izotov(2003).. although the stellar spectra used as input to these models reflect (he stale-ol-(he-art in 1995.," A more recent parameterization based on models by \cite{stasinska96} is used in \cite{stasinska03}, although the stellar spectra used as input to these models reflect the state-of-the-art in 1995."
 In addition. the lowest stellar atmosphere metallicity (hat they. used is solar/10.," In addition, the lowest stellar atmosphere metallicity that they used is solar/10."
 Ever since. more complete svnthetic stellar spectra have been published [or A as low as solar/20 (e.g.. Smithetal. 2002)).," Ever since, more complete synthetic stellar spectra have been published for metallicities as low as solar/20 (e.g., \citealt{smith02}) )."
" Parameterizations of the form — τη and = 2)]] for svstems with metallicities as low as "" M I Zw 18 should be obtained andcompared to each other. using results from up-to-date stellar and nebular models."," Parameterizations of the form = ] and = ] for systems with metallicities as low as that of I Zw 18 should be obtained and compared to each other, using results from up-to-date stellar and nebular models."
 secondly. models are required lor finding (he ionization correction factor ICE) necessary for obtaining N/O from .," Secondly, models are required for finding the ionization correction factor (ICF) necessary for obtaining N/O from $^+$ $^+$."
 Dased on simulations descrbed in Garnett Shields (1987). which make use of Mihalas (1972) and IXurucz (1975. 1979) stellar atmospheres with effective temperatures ranging rom 38 klx to 55 Κἰν. Garnett(1990) showed that 0.8 <(N/OJ/(N )) € 1.0 in ionized nebulae with one-tenth (Anders&Grevesse1989) solar abundances.," Based on simulations described in Garnett Shields (1987), which make use of Mihalas (1972) and Kurucz (1975, 1979) stellar atmospheres with effective temperatures ranging from 38 kK to 55 kK, \cite{garnett90} showed that 0.8 $\lesssim$ ) $\lesssim$ 1.0 in ionized nebulae with one-tenth \citep{anders89} solar abundances."
 More recently.Izotovetal.(2004) confirmed (hat N/Ozz isa," More recently,\cite{izotov04} confirmed that N/O $\approx $ is a"
ucasureiieuts of the prineval abundance of deuterims (sce ce. O'Meara ct al. 2001) with accurate theoretical xedietious of the leht-clement abundances (see e$. Durles et al. 2001).,"measurements of the primeval abundance of deuterium (see e.g., O'Meara et al, 2001) with accurate theoretical predictions of the light-element abundances (see e.g., Burles et al, 2001)."
 I follow the aualvsis of Durles et al (2001) in adopting O55?=(0.02+0.001.," I follow the analysis of Burles et al (2001) in adopting $\Omega_Bh^2 =
0.02\pm 0.001$."
 Iere oo. there are still issues to be resolved: possible unidentified svstematics in the determination of the xiuneval ceuterimm abundance: reliable values for the xiueval HIe aud “Li abundances to compare with the values predicted from the deuteriuu-determuned barvon density.," Here too, there are still issues to be resolved: possible unidentified systematics in the determination of the primeval deuterium abundance; reliable values for the primeval $^4$ He and $^7$ Li abundances to compare with the values predicted from the deuterium-determined baryon density."
" Over the next decade. as mere deuteriun svstenis are found and the Πο and ""Li abundances are better understood. the accuracy aud reliability. of the BBN baryon density| should improve."," Over the next decade, as more deuterium systems are found and the $^4$ He and $^7$ Li abundances are better understood, the accuracy and reliability of the BBN baryon density should improve."
 The barvou-to-matter ratio in clusters can be determined by x-ray measurements alone and by ineasurenjents of the Sunvaey Zel'dovich (SZ) distortion of the CMD combined with x-ray mcasurements., The baryon-to-matter ratio in clusters can be determined by x-ray measurements alone and by measurements of the Sunyaev – Zel'dovich (SZ) distortion of the CMB combined with x-ray measurements.
 For x-ray measurements alone. I adopt the cluster barvou fraction determined. from a sample of 15: clusters by Moli ct al (1998).O08). :and for the SZ/N-rayλος determinationὲ D use the cluster sample of Grego et al 2001).," For x-ray measurements alone, I adopt the cluster baryon fraction determined from a sample of 45 clusters by Mohr et al (1998), and for the SZ/X-ray determination I use the cluster sample of Grego et al (2001)."
 Potential sources of systematic error remain., Potential sources of systematic error remain.
" There is ""Cne clumping of cluster eas. Which could lead to an overestimation of the amount of gas."," There is some clumping of cluster gas, which could lead to an overestimation of the amount of gas."
 The baryon-to-total Inass ratio does vary with radius. and the calibrations are done by comparison with numerical simulations.," The baryon-to-total mass ratio does vary with radius, and the calibrations are done by comparison with numerical simulations."
 The treatineut of eas cdvnenics in these sinulatious still involves approxinatious and assmuptious., The treatment of gas dynamics in these simulations still involves approximations and assumptions.
 Better simulations. more observations of clusters with the SZ echuique and x-ray should address the key issues and nuprove the reliability of this sampling techuique.," Better simulations, more observations of clusters with the SZ technique and x-ray should address the key issues and improve the reliability of this sampling technique."
" The seuxitivitv of the abundance of clusters. both as a ction of cluster mass and redshift. to the matter deusity las been used to estimate Qa, (see c. Dalicall Fa. 1998: Blanchard et al. 2000: Παιν. 2000)."," The sensitivity of the abundance of clusters, both as a function of cluster mass and redshift, to the matter density has been used to estimate $\Omega_M$ (see e.g., Bahcall Fan, 1998; Blanchard et al, 2000; Henry, 2000)."
 Tlowever. the range in inferred values is broad. O34;=0.1/—1. largely jcause of the exponentially important. but uncertain relation between cluster mass and x-ray temperature.," However, the range in inferred values is broad, $\Omega_M =0.1 - 1$, largely because of the exponentially important, but uncertain relation between cluster mass and x-ray temperature."
 For his reason. I do not include these measurements dn niv determination ofthe matter deusitv.," For this reason, I do not include these measurements in my determination of the matter density."
 Finally. the value of the ITubble constant is inportant iu converting physical deusities to fractious of critical deusity: Iadopt the value determined by the ITubble Kev Project: h—042430407 (Freedinan et al. 20013.," Finally, the value of the Hubble constant is important in converting physical densities to fractions of critical density; I adopt the value determined by the Hubble Key Project: $h=0.72\pm 0.07$ (Freedman et al, 2001)."
 The error is almost cutirely due to systematics (the statistical eror is only σι= £0.02)., The error is almost entirely due to systematics (the statistical error is only $\sigma_h = \pm 0.02$ ).
 The largest part of the svsteniatie error budget is iu the distance to the Large Magellanic Cloud., The largest part of the systematic error budget is in the distance to the Large Magellanic Cloud.
 Possible dependence of the Cepheid period — minosity relation ou metallicitv mav also be au issue., Possible dependence of the Cepheid period – luminosity relation on metallicity may also be an issue.
 Taving: adopted these plivsical: iieasureiments as iuput: data. it is straightforward to deduce the fractious of critical deusity contributed by iatter aud by barvous. as well as the Eibble constant.," Having adopted these physical measurements as input data, it is straightforward to deduce the fractions of critical density contributed by matter and by baryons, as well as the Hubble constant."
 But first. consider the cousistency of these 1002sreimeuts.," But first, consider the consistency of these measurements."
 The plivsical baryou deusity (05/2) is determined by BBN. CMD anisotropy and the power spectrum | Hubble constant: These three. independent determinations of the barvon density are clearly cousisteut. eiviug one coufideuce in the case for a low barvou deusity (ppzἐν107en7).," The physical baryon density $\Omega_Bh^2$ ) is determined by BBN, CMB anisotropy and the power spectrum + Hubble constant: These three, independent determinations of the baryon density are clearly consistent, giving one confidence in the case for a low baryon density $\rho_B \approx 4\times 10^{-31} \,{\rm g\ cm^{-3}}$ )."
 They involve very different plhivsices — nuclear reactions when the Universe was secouds old. eravity-driven acoustic oscillations when the Universe was around: 100.000 vrs old. and the inhomogeneity iu the distribution of matter in the Universe today and thus also provide au iportaut test the consistency of the bie-bang framework iud general relativity.," They involve very different physics – nuclear reactions when the Universe was seconds old, gravity-driven acoustic oscillations when the Universe was around 400,000 yrs old, and the inhomogeneity in the distribution of matter in the Universe today – and thus also provide an important test the consistency of the big-bang framework and general relativity."
 Next. consider the ratio of the total matter density to the barvon density: Again. all four measurements are clearly consisteut and involve different plysics eravitv driven acoustic oscillations. iuhomoegencity in the distribution of matter today. and cluster dyaanics.," Next, consider the ratio of the total matter density to the baryon density: Again, all four measurements are clearly consistent and involve different physics – gravity driven acoustic oscillations, inhomogeneity in the distribution of matter today, and cluster dynamics."
: Using staudard techniques (and flat priors) [have the likelihood fuiction for Oar. Op aud constructed.h.," Using standard techniques (and flat priors) I have constructed the likelihood function for $\Omega_M$, $\Omega_B$ and $h$."
 Frou this. a posteriori probability distributions aud credible are calculated W nnreinalizius over one or two ofranges these quautities in the usual wav.," From this, a posteriori probability distributions and credible ranges are calculated by marginalizing over one or two of these quantities in the usual way."
 The 17 ruuges are: While the one-dimensional probability distributions are rot perfectly Gaussian. the and credible ranges natch pretty well with these lo env flags.," The $1-\sigma$ ranges are: While the one-dimensional probability distributions are not perfectly Gaussian, the and credible ranges match pretty well with these $1\sigma$ error flags."
" The value for the baryon fraction is largely (riven. by .BBN aud Πως alone they implyὩς=0.0385c0.0077,", The value for the baryon fraction is largely driven by BBN and $H_0$; alone they imply$\Omega_B = 0.0385\pm 0.0077$.
 Likewise. the Dibble coustaut is largely driven by its direct determination.," Likewise, the Hubble constant is largely driven by its direct determination."
" The different scaliugs of the barvon-to-uatter ratios with IInubble coustaut also provide important everage. Which can be seen in two wavs: (1) the joiut determination of  has a sliehtlv smaller uncertainty thu he direct 1neasureimnent alone. £0.06 vs. £0.07: (2) if one arbitrarily doubles the nucertaiutv in the ITubble coustaut. f=072Hd0.1-L and carries: ont the sane analysis,1 the results do not change dramatically: To investigate the robustuess of my estimates for the matter aud barvon deusities I have studied their sensitivity to the individual iput data."," The different scalings of the baryon-to-matter ratios with Hubble constant also provide important leverage, which can be seen in two ways: (1) the joint determination of $h$ has a slightly smaller uncertainty than the direct measurement alone, $\pm 0.06$ vs. $\pm 0.07$; (2) if one arbitrarily doubles the uncertainty in the Hubble constant, $h=0.72\pm 0.14$, and carries out the same analysis, the results do not change dramatically: To investigate the robustness of my estimates for the matter and baryon densities I have studied their sensitivity to the individual input data."
 To iuvestigate sensitivity to scale-dependeut bias on Q4;/ T increased σον by a factorfac⋅ of L, To investigate sensitivity to scale-dependent bias on $\Omega_Mh$ I increased $\sigma_{\Omega_Mh}$ by a factor of 4.
" TheHe eeeutral» Aτς forΕξω QjO and; [eOp werMN uuchanged and their errors valuesincreased to EO.OLL aud £00076 respectively,.", The central values for $\Omega_M$ and $\Omega_B$ were unchanged and their errors increased to $\pm 0.044$ and $\pm 0.0076$ respectively.
" One.. by one I doubled the errors for the other data: the ceutral values for O3; aud Op changed little iuputaud grew fo at lost 0.5 and 0.008 respectively,", One by one I doubled the errors for the other input data; the central values for $\Omega_M$ and $\Omega_B$ changed little and the errors grew to at most $\pm 0.05$ and $\pm 0.008$ respectively.
 theOne errorsmünor trend was observed: cularging the error flags on both the N-rav aud SZ cluster fractions by a factor of {. to reduce the baryonweight eiveu to the cluster barvon fraction. siguificautlydecreased the estimate for the matter deusitv bv about lo. 0.05.," One minor trend was observed: enlarging the error flags on both the X-ray and SZ cluster baryon fractions by a factor of 4, to significantly reduce the weight given to the cluster baryon fraction, decreased the estimate for the matter density by about $1\sigma$ , $\Omega_M =0.29\pm 0.05$ ."
"(Jasperelal.2007:Moseset2011). the dominant forward/reverse reaction pair [or the formation/destruction of the €ο bond is either OII+Cll,M.=CIL4OIIM or Oll+CIL=CHO4IL depending upon local temperature aid pressure conditions near the quench level.","\citep{jasper2007,moses2011} the dominant forward/reverse reaction pair for the formation/destruction of the C–O bond is either $\textrm{OH} + \textrm{CH}_{3} + \textrm{M} \rightleftarrows \textrm{CH}_{3}\textrm{OH} + \textrm{M}$ or $\textrm{OH} + \textrm{CH}_{3} \rightleftarrows \textrm{CH}_{2}\textrm{OH} + \textrm{H}$, depending upon local temperature and pressure conditions near the quench level."
 However. because of their similar rates. both reaction patliwavs should be considered together when calculating Τρ lor CO=CII; quenching in brown dw or hot-Jupiter atmospheres.," However, because of their similar rates, both reaction pathways should be considered together when calculating $\tau_{chem}$ for $\textrm{CO}\rightleftarrows \textrm{CH}_{4}$ quenching in brown dwarf or hot-Jupiter atmospheres."
" This reaction mechanism differs from (he forwardreverse reaction pair ll»+CIL,O=CIL,OILIL proposed by Visscheretal.(2010).. the lorward/reverse reaction pair HE+Π.ΟM=CII4O adopted by Yungetal.(1988). ancl subsequent authors (e.g..Griffith&Yelle1999:Bézardetal.2002:CooperShowman2006:Saumonοἱal.2006:IIDubeny&Burrows2007:Lineet2010:\ladhusudhanSeager 2011).. or the original suggestion of Hs + II4CO = CIL; + OL by Prinn&Barshay(1977). and subsequent authors (e.g..Feeley&Prinn1935.1988:FeglevLodders1996:Lodclers1994.2002:Saumonetal.2003:Visscher&Feeley2005:ItibenyBurrows2007) because of recent updates in reaction rate coefficients."," This reaction mechanism differs from the forward/reverse reaction pair $\textrm{H}_{2} + \textrm{CH}_{3}\textrm{O} \rightleftarrows \textrm{CH}_{3}\textrm{OH} + \textrm{H}$ proposed by \citet{visscher2010icarus}, , the forward/reverse reaction pair $\textrm{H}+\textrm{H}_{2}\textrm{CO}+\textrm{M}\rightleftarrows 
\textrm{CH}_{3}\textrm{O}+\textrm{M}$ adopted by \citet{yung1988} and subsequent authors \citep[e.g.,][]{griffith1999,bezard2002,cooper2006,saumon2006,hubeny2007,line2010,madhusudhan2011}, or the original suggestion of $_2$ + $_2$ CO $\rightleftarrows$ $_3$ + OH by \citet{prinn1977} and subsequent authors \citep[e.g.,][]{fegley1985apj,fegley1988,fegley1996,lodders1994,lodders2002,saumon2003iau,visscher2005,hubeny2007} because of recent updates in reaction rate coefficients."
 These revisions also have implications for estimates of the water abundance in Jupiter's deep troposphere using the CO observational constraint., These revisions also have implications for estimates of the water abundance in Jupiter's deep troposphere using the CO observational constraint.
 Using updated kinetics. our model results along with a lower limit provided by entry probe measurements suggest a water abundance of approximately 0.51-2.6 limes the solar abundance. corresponding to ΠΟ Πο22(4.9—25)x10.! in Jupiter's deep atmosphere.," Using updated kinetics, our model results along with a lower limit provided by entry probe measurements suggest a water abundance of approximately 0.51-2.6 times the solar abundance, corresponding to $_{2}$ $_{2}\approx(4.9-25)\times10^{-4}$ in Jupiter's deep atmosphere."
 The transport-induced quenching behavior of CO therefore implies lower Ε.Ο abundances than have been predicted [rom several giant. planet. formation scenarios Visscheretal. 2010)..," The transport-induced quenching behavior of CO therefore implies lower $_{2}$ O abundances than have been predicted from several giant planet formation scenarios \citep[e.g., see][]{lodders2004apj,visscher2010icarus}."
 For each substellar object. the rate of vertical transport (characterized bv eddy diffusion coellicient Jv...) will strongly. affect the quenched abundance of a given species: [or higher [νι values. quenching occurs al deeper. hotter altitudes. whereas for lower A.. values. «quenching occurs at higher. cooler altitudes.," For each substellar object, the rate of vertical transport (characterized by eddy diffusion coefficient $K_{zz}$ ) will strongly affect the quenched abundance of a given species: for higher $K_{zz}$ values, quenching occurs at deeper, hotter altitudes, whereas for lower $K_{zz}$ values, quenching occurs at higher, cooler altitudes."
 Moreover. the equilibrium abundance of any atmospheric constituent at its quench level depends upon the bulk composition aud thermal profile of the atinosphere(7.¢.. the prevailing conditions at the quench point).," Moreover, the equilibrium abundance of any atmospheric constituent at its quench level depends upon the bulk composition and thermal profile of the atmosphere, the prevailing conditions at the quench point)."
 The detection and characterization of quench species may therefore provide constraints on the chemistry. structure. and mixing rates of substellar atinosphleres (e.g..Feglev&Lodders1996: 2002).," The detection and characterization of quench species may therefore provide constraints on the chemistry, structure, and mixing rates of substellar atmospheres \citep[e.g.,][]{fegley1996,lodders2002}."
. For Gliese 229D. our results suggest significantly higher A.. rates near the CO quench level than have been previously inferred.," For Gliese 229B, our results suggest significantly higher $K_{zz}$ rates near the CO quench level than have been previously inferred."
" For IID 189733b. the terminator CII,; detection by Swainetal.(2008) and the corresponding analysis bv Seager(2009) suggest high values of Wve. C7105 em? 1) at the CO=CIL, quench point. whereas Cll; upper limits [ου the davside atmosphere as observed. during secondary eclipse (Charbonneauetal.2008:Maclhusuchan&Seager2009;Swain2008.2009) suggest lower values of A. (<107 cm? +)."," For HD 189733b, the terminator $_{4}$ detection by \citet{swain2008} and the corresponding analysis by \citet{madhusudhan2009} suggest high values of $K_{zz}$ $\gtrsim 10^{8}$ $^{2}$ $^{-1}$ ) at the $\textrm{CO} \rightleftarrows \textrm{CH}_{4}$ quench point, whereas $_{4}$ upper limits for the dayside atmosphere as observed during secondary eclipse \citep{charbonneau2008,madhusudhan2009,swain2008,swain2009} suggest lower values of $K_{zz}$ $\lesssim 10^{8}$ $^{2}$ $^{-1}$ )."
 These differences imply that disequilibriumchemistry.local A. differences. or other processes are complicating the simple picture of," These differences imply that disequilibriumchemistry,local $K_{zz}$ differences, or other processes are complicating the simple picture of"
The peak of the GCLE is the same in the eEs and a composite dE. modulo uncertainties in background subtraction for the dlIs.,"The peak of the GCLF is the same in the gEs and a composite dE, modulo uncertainties in background subtraction for the dEs."
 This observation may be difficult (o square with theoretical expectations that dvnamical fielion should deplete massive GCs in less (han a ]Iubble time. and with the properties of dE nuclei.," This observation may be difficult to square with theoretical expectations that dynamical friction should deplete massive GCs in less than a Hubble time, and with the properties of dE nuclei."
 There appear to be two classes of nuclei: small bright red nuclei consistent with formation bv dynamical friction of GCs. and larger [aint blue nuclei which appear to have formed by a dissipative process with little contribution from GCs.," There appear to be two classes of nuclei: small bright red nuclei consistent with formation by dynamical friction of GCs, and larger faint blue nuclei which appear to have formed by a dissipative process with little contribution from GCs."
 Though dominated by blue GCs. many dEs appear to have bimodal color distributions. wilh significant red GC subpopulations.," Though dominated by blue GCs, many dEs appear to have bimodal color distributions, with significant red GC subpopulations."
 The colors of these GC's form a continuity will those of more massive galaxies: both the mean blue and του GC colors of dEs appear consistent with extrapolations of the GC colorgalaxy huminosity relations for luminous ellipticals., The colors of these GCs form a continuity with those of more massive galaxies; both the mean blue and red GC colors of dEs appear consistent with extrapolations of the GC color–galaxy luminosity relations for luminous ellipticals.
 We confirm (hese relations for both blue and red GC subpopulations., We confirm these relations for both blue and red GC subpopulations.
 While previous works found an inverse correlation between dI Sy and galaxy. Iuminositw. we find little support for such a relation.," While previous works found an inverse correlation between dE $S_N$ and galaxy luminosity, we find little support for such a relation."
 There is a large scatter in $ among dEs and some evidence [or two separate groups of galaxies: dEs with Sy~2. and dEs with large GC svstems that have Sy ranging [rom ~5—20 with median Sy~10.," There is a large scatter in $S_N$ among dEs and some evidence for two separate groups of galaxies: dEs with $S_N \sim 2$, and dEs with large GC systems that have $S_N$ ranging from $\sim 5-20$ with median $S_N \sim 10$."
 However. these 5 variations do not appear to be connected to the presence of a nucleus or the lraction of red GCs.," However, these $S_N$ variations do not appear to be connected to the presence of a nucleus or the fraction of red GCs."
 Our findings suggest multiple formation channels for Virgo dEs., Our findings suggest multiple formation channels for Virgo dEs.
 We thank an anonvamous referee lor comments that considerably improved (he manuscript., We thank an anonymous referee for comments that considerably improved the manuscript.
 We acknowledge support by the National Science Foundation through Grant AST-0206139 and a Graduate Research Fellowship (J. οι)., We acknowledge support by the National Science Foundation through Grant AST-0206139 and a Graduate Research Fellowship (J. S.).
 This research has made use of the NASA/IPAC Extragalactic Database (NED). which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Xeronautics and Space Achuinistration.," This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."
 We thank Graeme Smith for useful conversations., We thank Graeme Smith for useful conversations.
these modes in such simulations also determines the nature of the galaxy mass profile on scales within z10—IO0pe.,"these modes in such simulations also determines the nature of the galaxy mass profile on scales within $\lesssim10-100\,$ pc."
 As such. it is also particularly interesting to understand whether or not such modes could arise generically.," As such, it is also particularly interesting to understand whether or not such modes could arise generically."
 There are many candidate nuclear disks in such systems (2222222). ," There are many candidate nuclear disks in such systems \citep{lauer:ngc4486b,
 lauer:centers,
 houghton:ngc1399.nuclear.disk,
 thatte:m83.double.nucleus,debattista:vcc128.binary.nucleus,
 afanasiev:2002.ngc5055.nuclear.disk,
 seth:ngc404.nuclear.disk}."
There is considerable literature discussing the mode structure. pattern. speeds. and evolution of general self-gravitating disk instabilities (seee.g. 222?2).. ," There is considerable literature discussing the mode structure, pattern speeds, and evolution of general self-gravitating disk instabilities \citep[see e.g.][]{lin.shu:spiral.wave.dispersion,
goldreichtremaine:spiral.excitement,goldreichtremaine:spiral.resonances,
toomre:spiral.group.velocity,toomre:spiral.structure.review}. ."
But these m7=| modes are less well-understood. especially in collisionless (stellar or planetary) disks.," But these $m=1$ modes are less well-understood, especially in collisionless (stellar or planetary) disks."
 For example. there remains considerable debate regarding the stability of such modes (e.g.2222).," For example, there remains considerable debate regarding the stability of such modes \citep[e.g.][]{tremaine:slow.keplerian.modes,
salow:nuclear.disk.models,jacobs:longlived.lopsided.disk.modes,
touma:keplerian.instabilities}."
 These works describe many interesting behaviors of n2| modes in a disk in a nearly Keplerian potential. but their conclusions rely on specitic assumptions.," These works describe many interesting behaviors of $m=1$ modes in a disk in a nearly Keplerian potential, but their conclusions rely on specific assumptions."
 ? show that such modes are linearly stable. but only in the limit where Ma<Muy at all radit.," \citet{tremaine:slow.keplerian.modes} show that such modes are linearly stable, but only in the limit where $M_{d}\ll M_{\rm BH}$ at all radii."
 And much of the insight from the study of protostellar and planetary disks focuses on either the same limit (for planetary disks) or the opposite limit (for early-stage protostellar disks) in which the system is really just a self-gravitating disk (seeandreferencestherein) But in simulations or observations of galactic nuclei (2222?) and protostellar evolution (222).. much of the interesting behavior involves disks over a range of radii where thedisk is not completely negligible in mass.," And much of the insight from the study of protostellar and planetary disks focuses on either the same limit (for planetary disks) or the opposite limit (for early-stage protostellar disks) in which the system is really just a self-gravitating disk \citep[see][and references therein]{laughlin:1994.protostar.disk.instabilities,
laughlin:1996.protostar.disk.instabilities.inflow}
 But in simulations or observations of galactic nuclei \citep{levine2008:nuclear.zoom,
 escala:nuclear.gas.transport.to.msigma,mayer:bh.binary.sph.zoom.sim,
 hopkins:maximum.surface.densities,hopkins:zoom.sims}
 and protostellar evolution \citep{laughlin:1994.protostar.disk.instabilities,
bate:1995.protobinary.accretion.vs.frag,
nelson:1998.circumstellar.disk.instabilities}, much of the interesting behavior involves disks over a range of radii where thedisk is not completely negligible in mass."
 The mode structure outlined in 2. is used in ?. to estimate the effects on a one or two low-mass planet system. but assuming mode stability and undersimilar mass and radius restrictions (and not allowing for a large collisionless disk component).," The mode structure outlined in \citet{tremaine:slow.keplerian.modes} is used in \citet{papaloizou:2002.m1.modes} to estimate the effects on a one or two low-mass planet system, but assuming mode stability and undersimilar mass and radius restrictions (and not allowing for a large collisionless disk component)."
" ? and ??. reach opposite conclusions to ?.. but they focus on ""fast modes"" (O,,— ©) in the regime M,7My Cor Maj~ M. and consider only pure fluid disks with a hard and reflecting outer edge. in which case the resulting mode growth rates depend sensitively on the structure and nature of reflection at the disk edge (and can be dramatically modified — in fact. completely eliminated — allowing any flow ""through? or outside the edge. the most probable configuration)."," \citet{adams89:eccentric.instab.in.keplerian.disks}
 and \citet{ostriker:eccentric.waves.via.forcing,shu:gas.disk.bar.tscale} reach opposite conclusions to \citet{tremaine:slow.keplerian.modes}, but they focus on “fast modes” $\Omega_{p}\sim \Omega$ ) in the regime $M_{d}\sim M_{\rm BH}$ (or $M_{d}\sim M_{\ast}$ ), and consider only pure fluid disks with a hard and reflecting outer edge, in which case the resulting mode growth rates depend sensitively on the structure and nature of reflection at the disk edge (and can be dramatically modified – in fact, completely eliminated – allowing any flow “through” or outside the edge, the most probable configuration)."
 In general. collisionless disks ean have very different mode structure from fluid systems.," In general, collisionless disks can have very different mode structure from fluid systems."
 ?. consider instabilities of narrow torus annuli (us opposed to disks) but with similar restrictions., \citet{christodoulou:fast.mode.torii.stability} consider instabilities of narrow torus annuli (as opposed to disks) but with similar restrictions.
 Also. because the mode growth is sensitive to motion of the center of mass. most numerical studies to date have lacked the resolution to determine whether mode growth is real or artificial in the limit where the disk mass is smaller than the BH/star mass (seethediscussionin2)..," Also, because the mode growth is sensitive to motion of the center of mass, most numerical studies to date have lacked the resolution to determine whether mode growth is real or artificial in the limit where the disk mass is smaller than the BH/star mass \citep[see the discussion in][]{nelson:1998.circumstellar.disk.instabilities}."
 Moreover. these studies have largely been restricted to very specitic mass profiles tthe Kuzmin disk. with X *constant at small radii? and/or systems with sharp “edges.” where in fact the profiles seen in interesting phases in simulations and in sstar-forming systems and the centers of real “cusp” elliptical galaxies resemble a range of power-law slopes with smooth declines at large radii and significant variation in profile shape (222).," Moreover, these studies have largely been restricted to very specific mass profiles the Kuz'min disk, with $\Sigma\rightarrow$ constant at small radii) and/or systems with sharp “edges,” where in fact the profiles seen in interesting phases in simulations and in star-forming systems and the centers of real “cusp” elliptical galaxies resemble a range of power-law slopes with smooth declines at large radii and significant variation in profile shape \citep{gebhardt96,
hopkins:msigma.scatter,hopkins:sb.ir.lfs}."
 As such. the origin of these modes. where observed. and many of their properties have remained ambiguous.," As such, the origin of these modes, where observed, and many of their properties have remained ambiguous."
 Given claims of the stability of such modes. alternative suggestions for their origin have ranged from their being induced by an external collision/passage (ingalacticnuclei.frome.g.anuclearstarcluster:see2). to their being excited by substantial populations of stars on retrograde orbits (2)..," Given claims of the stability of such modes, alternative suggestions for their origin have ranged from their being induced by an external collision/passage \citep[in galactic nuclei, from e.g.\ a nuclear star cluster; see][]{sambhus:m31.nuclear.disk.model}, to their being excited by substantial populations of stars on retrograde orbits \citep{touma:keplerian.instabilities}."
 But these explanations pertain only to very specitic systems or regimes. and do not explain the ubiquity of such modes in astrophysical systems.," But these explanations pertain only to very specific systems or regimes, and do not explain the ubiquity of such modes in astrophysical systems."
 Showing that they can in fact be self-generating via gravitational instability would have profound implications., Showing that they can in fact be self-generating via gravitational instability would have profound implications.
 Moreover. in systems with star or planet formation as an ongoing process. these modes will evolve in time. as quantities such as the disk gas fraction. mass profile. dispersion profile. and total disk mass are affected by these processes.," Moreover, in systems with star or planet formation as an ongoing process, these modes will evolve in time, as quantities such as the disk gas fraction, mass profile, dispersion profile, and total disk mass are affected by these processes."
 Similarly. the modes in the collisionless disk can drive very strong inflows and outflows in gus. changing the properties of the host disks in turn (see191).," Similarly, the modes in the collisionless disk can drive very strong inflows and outflows in gas, changing the properties of the host disks in turn \citep[see][]{nelson:1998.circumstellar.disk.instabilities,
bournaud:2005.lopsided.disk.inflow,
hopkins:zoom.sims}."
 Therefore it is of great importance to both survey a range of analvtie profile shapes and dispersion levels. and to compare with simulations that can incorporate non-linear effects on the mode evolution.," Therefore it is of great importance to both survey a range of analytic profile shapes and dispersion levels, and to compare with simulations that can incorporate non-linear effects on the mode evolution."
 It is also particularly interesting to examine the level of inflow generated by such modes. if the disks have some gs.," It is also particularly interesting to examine the level of inflow generated by such modes, if the disks have some gas."
 In this paper we expand upon the investigation of globa a=| modes in nearly Keplerian. predominantly collisionless disks.," In this paper we expand upon the investigation of global $m=1$ modes in nearly Keplerian, predominantly collisionless disks."
" In particular, we focus on the question of whether or no such modes can. in fact. be unstable and self-generating. anc if so how they propagate throughout such disks."," In particular, we focus on the question of whether or not such modes can, in fact, be unstable and self-generating, and if so how they propagate throughout such disks."
 After defining some terms 2). we consider modes in the local (WKB») limi 3). which allows us to analytically derive approximate stability criteria and discuss conditions for efficient mode propagation. in both gaseous and stellar disks.," After defining some terms \ref{sec:definitions}) ), we consider modes in the local (WKB) limit \ref{sec:wkb}) ), which allows us to analytically derive approximate stability criteria and discuss conditions for efficient mode propagation, in both gaseous and stellar disks."
 In 4. we discuss exac numerical solutions which allow us to extend this discussion to linear global normal modes. and outline under what conditions these modes are unstable cand what their characteristic frequencies are). and how this depends on a variety of disk properties including mass profile shape. mass. and disk thickness.," In \ref{sec:exact}, we discuss exact numerical solutions which allow us to extend this discussion to linear global normal modes, and outline under what conditions these modes are unstable (and what their characteristic frequencies are), and how this depends on a variety of disk properties including mass profile shape, mass, and disk thickness."
 We discuss the structure of such modes. and the conditions under which they will drive shocks in collisionless+gaseous systems and corresponding inflow/outflow. and the radii over which the modes can act.," We discuss the structure of such modes, and the conditions under which they will drive shocks in collisionless+gaseous systems and corresponding inflow/outflow, and the radii over which the modes can act."
 In 5. we compare to the results from high-resolution hydrodynamic simulations which include self-gravity. gas cooling. star formation. shocks. inflow/outflow. and non-linear effects all not captured in an analytic formulation. and discuss how this compares to our analytic insight.," In \ref{sec:sims}, we compare to the results from high-resolution hydrodynamic simulations which include self-gravity, gas cooling, star formation, shocks, inflow/outflow, and non-linear effects all not captured in an analytic formulation, and discuss how this compares to our analytic insight."
 Finally. in 6.. we summarize our conclusions and their implications for astrophysical systems.," Finally, in \ref{sec:discussion}, we summarize our conclusions and their implications for astrophysical systems."
 Adopt a cylindrical coordinate frame. (8. o. z). and consider an initially axisymmetric. thin. planar disk with an arbitrary spherical (BH+bulgethalo} component.," Adopt a cylindrical coordinate frame, $R$, $\phi$, $z$ ), and consider an initially axisymmetric, thin, planar disk with an arbitrary spherical (BH+bulge+halo) component."
 The coordinate center is located at the BH., The coordinate center is located at the BH.
 The initial potential in thedisk plane can be written <bo(R). and other properties are defined in standard terms: where V. is the cireular velocity. €) the angular velocity. and 4 the epicyclic frequency.," The initial potential in thedisk plane can be written $\Phi_{0} = \Phi_{0}(R)$ , and other properties are defined in standard terms: where $V_{c}$ is the circular velocity, $\Omega$ the angular velocity, and $\kappa$ the epicyclic frequency."
" We use c, to denote the sound speed in a gaseous disk and @- the vertical dispersion in a stellar disk.", We use $c_{s}$ to denote the sound speed in a gaseous disk and $\sigma_{z}$ the vertical dispersion in a stellar disk.
 Consider a perturbation in the plane and detine the perturbed surfacedensity field by We consider a frame rotating with the perturbation pattern speed ©., Consider a perturbation in the plane and define the perturbed surfacedensity field by We consider a frame rotating with the perturbation pattern speed $\Omega_{p}$ .
" We can represent the perturbed system as a sum of linearly independent modes m. X,=» Ns "," We can represent the perturbed system as a sum of linearly independent modes $m$ , $\Sigma_{1}\equiv \sum_{m=1}^{\infty}\,\Sigma_{m}$ ."
Since we will focus on the behavior of these modes individually. consider (without loss," Since we will focus on the behavior of these modes individually, consider (without loss"
measured one. and the reasonable amount of K-band light produced. (figure 2)) makes us confident that we co not over-produce either stars or metals.,"measured one, and the reasonable amount of K-band light produced (figure \ref{figopt}) ) makes us confident that we do not over-produce either stars or metals."
 However note that at low redshift. the agreement is only for non-dust-corrected data. so the contribution of our spirals (which closely match the non corrected. Macau curve at.a££ redshifts) might be uncerestimated in our model.," However note that at low redshift, the agreement is only for non-dust-corrected data, so the contribution of our spirals (which closely match the non corrected Madau curve at redshifts) might be underestimated in our model."
 From the perspective of metals only. the star formation rate could be higher. provided that a fair fraction of the heavy elements is ejected into the IGM.," From the perspective of metals only, the star formation rate could be higher, provided that a fair fraction of the heavy elements is ejected into the IGM."
 The model however predicts a peak in star formation around redshift ~ 3.5 (this is also true for the οςΔΙ case). sensibly hisher than what is usually assumed. current data. being compatible with a Lat star formation rate at recishifts 1l.," The model however predicts a peak in star formation around redshift $\sim$ 3.5 (this is also true for the SCDM case), sensibly higher than what is usually assumed, current data being compatible with a flat star formation rate at redshifts $z>$ 1."
 A more detailed. comparison with the SCDAL cosmology used in Silk Devriendt (2000) reveals that the. comoving star formation rate increase from 2=0 to z&3 is steeper in the ΑςΟΝΕ moclel. due to the fact that fewer galaxies tend to form on average at low reclshilts in such a model.," A more detailed comparison with the SCDM cosmology used in Silk Devriendt (2000) reveals that the comoving star formation rate increase from $z = 0$ to $z \approx 3$ is steeper in the $\Lambda$ CDM model, due to the fact that fewer galaxies tend to form on average at low redshifts in such a model."
 More specilically. this increase in the steepness of the SER. results froma: This explains why the cliscrepancy mainly shows up in 1e spiral population and that. in contrast. the contribution [elliptical galaxies which form much earlier is very. similar in both cosmologies (Silk Devriendt 2000).," More specifically, this increase in the steepness of the SFR results from: This explains why the discrepancy mainly shows up in the spiral population and that, in contrast, the contribution of elliptical galaxies which form much earlier is very similar in both cosmologies (Silk Devriendt 2000)."
 We argue that 1f amount of star formation occurring in. dust-shirouced objects cannot be much greater than our model predicts in order to avoid overestimating the subnim dilfuse background (sce figure 6))., We argue that the amount of star formation occurring in dust-shrouded objects cannot be much greater than our model predicts in order to avoid overestimating the submm diffuse background (see figure \ref{figback}) ).
 Therefore. we emphasize that cosmic star ormation has to decrease at redshifts 2 3.5., Therefore we emphasize that cosmic star formation has to decrease at redshifts $z \ge$ 3.5.
 Note that his result is strengthened. if dust-shrouded. AGNs are a major contributor to the submm emission. even though this does not appear to be the case if N-ray characteristics are a reliable αλ monitor (e.g. Barger οἱ al.," Note that this result is strengthened if dust-shrouded AGNs are a major contributor to the submm emission, even though this does not appear to be the case if X-ray characteristics are a reliable AGN monitor (e.g. Barger et al."
 2001)., 2001).
 We have implemented. the model of BSSOS within. the simple semi-analvtic model of DCOO0 in order to describe galaxy collisions on a physical basis., We have implemented the model of BSS98 within the simple semi-analytic model of DG00 in order to describe galaxy collisions on a physical basis.
 We find that such a combination: Our results qualitatively agree with the model of the infrared. universe presented in Tan. Silk Ballance (1999).," We find that such a combination: Our results qualitatively agree with the model of the infrared universe presented in Tan, Silk Balland (1999)."
 We also note good agreement. of the main conclusions of the present work with the collisional starburst model. of Somerville et al. (, We also note good agreement of the main conclusions of the present work with the collisional starburst model of Somerville et al. (
2001).,2001).
 Phis agreement is examplified in the comparison between ou SER plot (figure Sof the present paper) and the SER. predicted by their collisiona starburst model (their figure 9)., This agreement is examplified in the comparison between our SFR plot (figure \ref{figsfr} of the present paper) and the SFR predicted by their collisional starburst model (their figure 9).
 Lt is satisfving that these two approaches give consistent results as it supports the view that galaxv-galaxw collisions in the high redshif universe might have plaved a dominant role in trigecring star formation., It is satisfying that these two approaches give consistent results as it supports the view that galaxy-galaxy collisions in the high redshift universe might have played a dominant role in triggering star formation.
 Note however that Somerville et al., Note however that Somerville et al.
 fail to accoun for the subnum counts (Somerville private communication)., fail to account for the submm counts (Somerville private communication).
 Thev find too few highly obscurecl luminous galaxies., They find too few highly obscured luminous galaxies.
 Our model gives satisfactory agreement both in the restframe, Our model gives satisfactory agreement both in the restframe
report correspond to the observed spectrum along a tangent occurring at various impact parameters through the shell away from the star cluster.,report correspond to the observed spectrum along a tangent occurring at various impact parameters through the shell away from the star cluster.
" In this way we closely mimic the observations, which place a spectrometer slit at various positions."," In this way we closely mimic the observations, which place a spectrometer slit at various positions."
 There are at present no reliable dielectronic recombination rate coefficients for recombination from S? to S*!., There are at present no reliable dielectronic recombination rate coefficients for recombination from $^{+2}$ to $^{+1}$.
" We reply on empirical estimates of the rate coefficient based on photoionization modeling of astronomical observations, as wasdone by Alietal.(1991)."," We reply on empirical estimates of the rate coefficient based on photoionization modeling of astronomical observations, as wasdone by \citet{ali91}."
. Based on such models we would judge our current estimates to be uncertain by about30%., Based on such models we would judge our current estimates to be uncertain by about.
. This introduces roughly a uuncertainty in the balance between [S II] and [S III]., This introduces roughly a uncertainty in the balance between [S II] and [S III].
 This produces an uncertainty that enters as an unknown scale factor that affects all models., This produces an uncertainty that enters as an unknown scale factor that affects all models.
 This represents a basic uncertainty that affects all observations by this scale factor., This represents a basic uncertainty that affects all observations by this scale factor.
" It may shift the model predictions by an unknown systematic amount, but will not produce object to object fluctuations in the spectrum."," It may shift the model predictions by an unknown systematic amount, but will not produce object to object fluctuations in the spectrum."
" To demonstrate the validity of the method employed in this paper to Barnard's Loop, we first made calculations that simulate the H II region M 43 (NGC 1982), which is dominated by a single cool star."," To demonstrate the validity of the method employed in this paper to Barnard's Loop, we first made calculations that simulate the H II region M 43 (NGC 1982), which is dominated by a single cool star."
 We then used the results of that study to guide the calculations of the conditions for Barnard's Loop., We then used the results of that study to guide the calculations of the conditions for Barnard's Loop.
" M 43 lies to the immediate northeast of the much brighter Orion Nebula (M 42, NGC 1976) and was included in the recent comprehensive spectroscopic mapping of (2010)."," M 43 lies to the immediate northeast of the much brighter Orion Nebula (M 42, NGC 1976) and was included in the recent comprehensive spectroscopic mapping of \citet{od10}."
". The central star is NU Ori, which is spectral type B0.5 V (Schild& 2008).."," The central star is NU Ori, which is spectral type B0.5 V \citep{sh71,pen75,sd08}. ."
 The total Lyman continuum, The total Lyman continuum
sufficient) criterion for fragmentation.,sufficient) criterion for fragmentation.
 As noted in Section 2. there is tentative evidence from Figure 2 that the points at the highest NV fall below the solid line - in other words we have simulations that are not fragmenting even though they are in the regime where the artificial viscosity contribution is less than 54.," As noted in Section 2, there is tentative evidence from Figure 2 that the points at the highest $N$ fall below the solid line - in other words we have simulations that are not fragmenting even though they are in the regime where the artificial viscosity contribution is less than $5 \%$."
 We interpret this result as evidence that there is indeed a physical mechanism preventing fragmentation for small cooling rates., We interpret this result as evidence that there is indeed a physical mechanism preventing fragmentation for small cooling rates.
 In addition to the thermal effects described above. artificial viscosity might also dynamically stabilize the disc.," In addition to the thermal effects described above, artificial viscosity might also dynamically stabilize the disc."
 The specific effect of viscosity in this regard depends on how viscosity scales with surface density and might also lead to a secular instability (2).., The specific effect of viscosity in this regard depends on how viscosity scales with surface density and might also lead to a secular instability \citep{schmit95}.
 While this is beyond the scope of the present paper. such effects should be further investigated.," While this is beyond the scope of the present paper, such effects should be further investigated."
 Since we find it rather surprising that artifical viscosity should suppress fragmentation when it contributes such a minor component to the dise’s thermal balance. we also explore the iypothesis that the effect of under resolution is one of artificially smoothing density enhancements over the SPH smoothing length h.," Since we find it rather surprising that artifical viscosity should suppress fragmentation when it contributes such a minor component to the disc's thermal balance, we also explore the hypothesis that the effect of under resolution is one of artificially smoothing density enhancements over the SPH smoothing length $h$."
 In poorly resolved simulations. where / is not much smaller han the length scale of density peaks (A). then this will suppress he peak amplitude of the resulting density fluctuations by a factor of 1|hA (assuming that gravitational instabilities generate oredominantly linear structures).," In poorly resolved simulations, where $h$ is not much smaller than the length scale of density peaks $\lambda$ ), then this will suppress the peak amplitude of the resulting density fluctuations by a factor of $1 + h/\lambda$ (assuming that gravitational instabilities generate predominantly linear structures)."
 According to ?.. the gravitational jeating rate associated. with modes of r.m.s.," According to \citet{CLC09}, the gravitational heating rate associated with modes of r.m.s."
 fractional amplitude AMN ds proportional to. (ANMY and therefore in thermal equilibrium this quantity scales with the cooling rate Gx3 74)., fractional amplitude $\Delta \Sigma/\Sigma$ is proportional to $(\Delta \Sigma/\Sigma)^2$ and therefore in thermal equilibrium this quantity scales with the cooling rate $\propto \beta^{-1}$ ).
 If we assume that in a perfectly resolved calculation the peak amplitude would scale with the r.m.s., If we assume that in a perfectly resolved calculation the peak amplitude would scale with the r.m.s.
 amplitude (but be degraded by a faetor 1|hfA in the case of finite /) and if we furthermore associate fragmentation with the peak fluctuations achieving a critical value of ANY (of order unity) then it follows that the cooling rate required for fragmentation is increased in the case of simulations of finite ., amplitude (but be degraded by a factor $1 + h/\lambda$ in the case of finite $h$ ) and if we furthermore associate fragmentation with the peak fluctuations achieving a critical value of $\Delta \Sigma/\Sigma$ (of order unity) then it follows that the cooling rate required for fragmentation is increased in the case of simulations of finite $h$.
 Specifically we have where Jj is the value required for fragmentation in the case of a well resolved simulation (i.e. small /)., Specifically we have where $\beta_0$ is the value required for fragmentation in the case of a well resolved simulation (i.e. small $h$ ).
 In estimating A we note that the Jeans length in a dise with Toomre €2 parameter close to unity is just the vertical scale height //: it therefore seems logical that A should scale with // and this motivates the form of equation (a2»., In estimating $\lambda$ we note that the Jeans length in a disc with Toomre $Q$ parameter close to unity is just the vertical scale height $H$; it therefore seems logical that $\lambda$ should scale with $H$ and this motivates the form of equation \ref{eq:bquadfit}) ).
 We note that both our resolution criteria do not abandon the notion that (in a well resolved simulation) there is a critical cooling rate associated with fragmentation but take into account that the fact that more vigorous cooling (lower :7) is required in the case of poorly resolved simulations., We note that both our resolution criteria do not abandon the notion that (in a well resolved simulation) there is a critical cooling rate associated with fragmentation but take into account that the fact that more vigorous cooling (lower $\beta$ ) is required in the case of poorly resolved simulations.
 In this paper we have shown that the results of ?. (concerning the location at which fragmentation occurs in SPH simulations of cooling self-gravitating discs) are quantitatively consistent Cf interpreted as being driven by resolution effects) with the results of ? in which it is shown that the critical cooling rate for fragmentation depends on the number of particles JN., In this paper we have shown that the results of \cite{meru10a} (concerning the location at which fragmentation occurs in SPH simulations of cooling self-gravitating discs) are quantitatively consistent (if interpreted as being driven by resolution effects) with the results of \cite{meru10b} in which it is shown that the critical cooling rate for fragmentation depends on the number of particles $N$ .
 Indeed the results of each paper imply the results of the other and both imply that the measured cooling rate for fragmentation is a function of ffif (where h is the SPH smoothing length and // is the dise scale height)., Indeed the results of each paper imply the results of the other and both imply that the measured cooling rate for fragmentation is a function of $h/H$ (where $h$ is the SPH smoothing length and $H$ is the disc scale height).
 It is difficult to assign a precise functional form for the way that the critical cooling rate depends on resolution. given the scatter in the simulation data and the relatively small range in ///h for which simulations are currently available.," It is difficult to assign a precise functional form for the way that the critical cooling rate depends on resolution, given the scatter in the simulation data and the relatively small range in $H/h$ for which simulations are currently available."
 We have explored two possibilities for effects that may explain the simulation results., We have explored two possibilities for effects that may explain the simulation results.
 In one case we explore the possibility that a necessary criterion for fragmentation to be detected is that the artificial viscosity contributes less than a certain fraction of the thermal energy input (and associated angular momentum transport) in the disc., In one case we explore the possibility that a necessary criterion for fragmentation to be detected is that the artificial viscosity contributes less than a certain fraction of the thermal energy input (and associated angular momentum transport) in the disc.
 We find that the results at low resolution can be explained in these terms but that the requirement on the contribution from artifical viscosity is suprisingly stringent (1.e. fragmentation occurs only where this contributes less than 54 of the energy input to the disc)., We find that the results at low resolution can be explained in these terms but that the requirement on the contribution from artifical viscosity is suprisingly stringent (i.e. fragmentation occurs only where this contributes less than $5 \%$ of the energy input to the disc).
 Alternatively. we consider the possibility that finite resolution just smooths out density peaks so that fluctuations that would collapse if well resolved do not achieve a critical amplitude at finite /.," Alternatively, we consider the possibility that finite resolution just smooths out density peaks so that fluctuations that would collapse if well resolved do not achieve a critical amplitude at finite $h$."
 Irrespective of how one explains how resolution affects the cooling requirements for fragmentation. an important issue - as stressed by ? is whether there is indeed a convergence in the required cooling rate at high resolution.," Irrespective of how one explains how resolution affects the cooling requirements for fragmentation, an important issue - as stressed by \citet{meru10b} - is whether there is indeed a convergence in the required cooling rate at high resolution."
 In other words. is there a level of resolution above which one recovers the result that has been assumed hitherto - i.e. that there is ap/rvsicalt condition on the cooling rate required for fragmentation?," In other words, is there a level of resolution above which one recovers the result that has been assumed hitherto - i.e. that there is a condition on the cooling rate required for fragmentation?"
 We evidently cannot answer this question with calculations that have not attained convergence (see Figure 2 where Jus. rises mildly with NV even at the highest jV. values studied)., We evidently cannot answer this question with calculations that have not attained convergence (see Figure 2 where $\beta_{\rm frag}$ rises mildly with $N$ even at the highest $N$ values studied).
 However. Figure 2 contains hints of approaching convergence.," However, Figure 2 contains hints of approaching convergence."
 One way to see this is to compare the simulation data with the solid line whieh corresponds to requirement of a 5% contribution from arititical viscosity., One way to see this is to compare the simulation data with the solid line which corresponds to requirement of a $5 \%$ contribution from aritifical viscosity.
 The fact that the right hand points le below this solid line (where «Ίων scales with Nt?) is evidence that this condition may be necessary but not sufficient for fragmentation., The fact that the right hand points lie below this solid line (where $\beta_{\rm frag}$ scales with $N^{1/3}$ ) is evidence that this condition may be necessary but not sufficient for fragmentation.
 Similarly. the simulation data is consistent with the dashed line in which the actual «2 required for fragmentation converges to a value of oje14.7 at high resolution.," Similarly, the simulation data is consistent with the dashed line in which the actual $\beta$ required for fragmentation converges to a value of $\beta_0\approx 14.7$ at high resolution."
 Clearly the question of ultimate convergence will only be settled by further simulations at higher A’., Clearly the question of ultimate convergence will only be settled by further simulations at higher $N$.
 If convergence is ultimately. attained then it would involve a radical re-think of all our understanding of gravitationally unstable discs since it would imply that self-gravitating dise (however slowly cooling) should in reality fragment., If convergence is ultimately attained then it would involve a radical re-think of all our understanding of gravitationally unstable discs since it would imply that self-gravitating disc (however slowly cooling) should in reality fragment.
 This would be surprising because. in the case of very slow cooling. the r.m.s.," This would be surprising because, in the case of very slow cooling, the r.m.s."
 mode amplitude required to achieve thermal balance should be very low and it would be unexpected (though possible in principle) that such a dise nevertheless exhibited locally non-linear density fluctuations giving rise to collapsing fragments., mode amplitude required to achieve thermal balance should be very low and it would be unexpected (though possible in principle) that such a disc nevertheless exhibited locally non-linear density fluctuations giving rise to collapsing fragments.
 The more conservative. conclusion (if. convergence is ultimately attained) is that we have simply under-estimated the critical 3 value hitherto., The more conservative conclusion (if convergence is ultimately attained) is that we have simply under-estimated the critical $\beta$ value hitherto.
 This would involve some quantitative adjustment of previous conclusions., This would involve some quantitative adjustment of previous conclusions.
 For example. if the critical cooling time for fragmentation is roughly a factor 2 higher than had been previously thought then this affects the location at which giant jxlanets ean form through gravitational instability (2: in the regime of ice cooling appropriate to the outer parts of protostellar discs. his change would bring in the minimum radius for fragmentation by a factor ~27/7 (22).," For example, if the critical cooling time for fragmentation is roughly a factor $2$ higher than had been previously thought then this affects the location at which giant planets can form through gravitational instability \citep{meru10b}: in the regime of ice cooling appropriate to the outer parts of protostellar discs, this change would bring in the minimum radius for fragmentation by a factor $\sim 2^{2/9}$ \citep{clarke09,CLC10}."
 Although this change is quite modest. it may be important to the discussion of whether recently imaged dane around HR 8799. ?.. around 5 Pic. 2? or around Fomahault. 11) could have been formed by gravitational instability.," Although this change is quite modest, it may be important to the discussion of whether recently imaged planets (e.g., around HR 8799, \citealt{marois08}, around $\beta$ Pic, \citealt{lagrange09} or around Fomahault, \citealt{kalas08}) ) could have been formed by gravitational instability."
 ote. however. that — for a given critical cooling time — the uncertainty in the determination of the fragmentation radius due © uncertainties in the relevant opacities. in the detailed vertical structure of thedisc and due to the effects of magnetic fields are orobably larger than the modest change discussed above.," Note, however, that — for a given critical cooling time — the uncertainty in the determination of the fragmentation radius due to uncertainties in the relevant opacities, in the detailed vertical structure of thedisc and due to the effects of magnetic fields are probably larger than the modest change discussed above."
 More in general. we might ask which ones of the properties," More in general, we might ask which ones of the properties"
"is always unimportant for thin disks. as 74,~| is suggested. however. the advection of magnetic fields may be efficient for a geometrically thick aceretion disk with H~R (e.g..Fer-reira&Petrucci 2011).","is always unimportant for thin disks, as ${\cal P}_{\rm m}\sim 1$ is suggested, however, the advection of magnetic fields may be efficient for a geometrically thick accretion disk with $H\sim R$ \citep*[e.g.,][]{2011arXiv1101.2292F}."
. An alternativemodel was suggested by Spruit&Uzdensky(2005) for advection of the external field in the disk. in which turbulent diffusion is reduced by bundles of the large-scale magnetic field (Stehle&Spruit 2001)..," An alternativemodel was suggested by \citet{2005ApJ...629..960S} for advection of the external field in the disk, in which turbulent diffusion is reduced by bundles of the large-scale magnetic field \citep{2001MNRAS.323..587S}."
 Lovelaceetal.(2009) suggested that the field can be efficiently advected inward based on the assumption of the surface layer of the accretion disk to be nonturbulent., \citet{2009ApJ...701..885L} suggested that the field can be efficiently advected inward based on the assumption of the surface layer of the accretion disk to be nonturbulent.
 The general relativistic magnetohydrodynamic (GRMHD) simulation of an accretion torus embedded in a large-scale magnetic field showed that the mass is accreted mainly within the accretion disk. and the magnetic field flux is carried by the motions in the low-density corona (Beckwithetal.2009).," The general relativistic magnetohydrodynamic (GRMHD) simulation of an accretion torus embedded in a large-scale magnetic field showed that the mass is accreted mainly within the accretion disk, and the magnetic field flux is carried by the motions in the low-density corona \citep{2009ApJ...707..428B}."
 Low mass accretion rate ἡ may lead to the aceretion flows to be advection-dominated (Narayan&Yi1994.1995)..," Low mass accretion rate $\dot{m}$ may lead to the accretion flows to be advection-dominated \citep{1994ApJ...428L..13N,1995ApJ...452..710N}."
 Advection dominated accretion flows (ADAFs) are suggested to be present in low-luminosity active galactic nuclei (AGNs) (seeNarayan2002.forareviewandreferencestherein).. FR I radio galaxies (e.g..Ghisellint&Celotti2001:CaoRawl-ings 2004).. or BL Lae objects (e.g.Cao2003)..," Advection dominated accretion flows (ADAFs) are suggested to be present in low-luminosity active galactic nuclei (AGNs) \citep*[see][for a
review and references therein]{2002luml.conf..405N}, FR I radio galaxies \citep*[e.g.,][]{2001A&A...379L...1G,2004MNRAS.349.1419C}, or BL Lac objects \citep*[e.g.][]{2003ApJ...599..147C}."
 The ADAF model can successfully explain most observational features of low-luminosity AGNs and black hole X-ray binaries in the low/hard state (e.g..Lasotaetal.1996:Gammie1999:Quataertetal.1999;Xu&Cao 2009).. ," The ADAF model can successfully explain most observational features of low-luminosity AGNs and black hole X-ray binaries in the low/hard state \citep*[e.g.,][]{1996ApJ...462..142L,1999ApJ...516..177G,1999ApJ...525L..89Q,2009RAA.....9..401X}. ."
ADAFs are hot and geometrically thick. which have relatively higher radial velocities than thin accretion disks (Narayan&Y11994. 1995)..," ADAFs are hot and geometrically thick, which have relatively higher radial velocities than thin accretion disks \citep{1994ApJ...428L..13N,1995ApJ...452..710N}."
 This implies that the advection of the external fields in ADAFs may be more efficiently than that in thin disks., This implies that the advection of the external fields in ADAFs may be more efficiently than that in thin disks.
 In this work. we explore the advection/diffusion of the large-scale magnetic fields threading an ADAE. in which the compression of the accretion flow in the vertical direction by the magnetic field is properly considered.," In this work, we explore the advection/diffusion of the large-scale magnetic fields threading an ADAF, in which the compression of the accretion flow in the vertical direction by the magnetic field is properly considered."
" The dynamies of a steady ADAF with large-scale magnetic fields are described by a set of differential equations. namely. the continuity equation, the radial and azimuthal momentum equations. and the energy equation."," The dynamics of a steady ADAF with large-scale magnetic fields are described by a set of differential equations, namely, the continuity equation, the radial and azimuthal momentum equations, and the energy equation."
 The continuity equationo. is where mass loss rate in the winds from the ADAF ts neglected., The continuity equation is where mass loss rate in the winds from the ADAF is neglected.
 The radial momentum equation is where is the radial component of the large-scale magnetic fieldsBj at the disk surface. and the pseudo-Newtonian potential is adopted to simulate the gravity of a non-rotating black hole (Paczyfisky&Wiita1980)..," The radial momentum equation is where $B_R^{\rm S}$ is the radial component of the large-scale magnetic fields at the disk surface, and the pseudo-Newtonian potential is adopted to simulate the gravity of a non-rotating black hole \citep{1980A&A....88...23P}."
" Keplerian angular velocity is given by 3 where Κι22GM/c"".", The Keplerian angular velocity is given by where $R_{\rm g}=2GM/c^2$.
 The radial magnetic fields will be sheared into azimuthal fields by the differential rotation of the flow. which leads to magnetorotational instability (MRI) and the MRI-driven turbulence (Balbus&Hawley1991.1998)..," The radial magnetic fields will be sheared into azimuthal fields by the differential rotation of the flow, which leads to magnetorotational instability (MRI) and the MRI-driven turbulence \citep{1991ApJ...376..214B,1998RvMP...70....1B}."
 For simplicity. we assume that the conventional o-viscosity can. describe the angular momentum transportation in the aceretion. flow caused by MRI-driven turbulence.," For simplicity, we assume that the conventional $\alpha$ -viscosity can describe the angular momentum transportation in the accretion flow caused by MRI-driven turbulence."
" The angular momentum equation Is where / is the specific angular momentum of the flow. jj, 1s the specific angular momentum of the gas swallowed by the black hole. and the o-viscosity. is adopted."," The angular momentum equation is where $j$ is the specific angular momentum of the flow, $j_{\rm in}$ is the specific angular momentum of the gas swallowed by the black hole, and the $\alpha$ -viscosity, is adopted."
 The angular momentum equation (4)) reduces to an algebraic equation. assuming dQ /dR=-O/R.," The angular momentum equation \ref{azimuthal_1}) ) reduces to an algebraic equation, by assuming $d\Omega/dR\simeq -\Omega/R$."
The energy equation is where 7 is the temperature and s is the entropy of the gas in the ADAF., The energy equation is where $T$ is the temperature and $s$ is the entropy of the gas in the ADAF.
 Equation (7)) can be re-written as where  is the ratio of specific heats. and the parameter f describes the fraction of the dissipated energy advected 1n the flow.," Equation \ref{energy_1}) ) can be re-written as where $\gamma$ is the ratio of specific heats, and the parameter $f$ describes the fraction of the dissipated energy advected in the flow."
 Substituting the continuity equation (1)) into Equation (8)). we have The vertical structure of the accretion flow is significantly altered in the presence of large-scale magnetic fields.," Substituting the continuity equation \ref{continuity_1}) ) into Equation \ref{energy_2}) ), we have The vertical structure of the accretion flow is significantly altered in the presence of large-scale magnetic fields."
 In this work. we calculate the vertical structure of the ADAF following the approach given in Cao&Spruit(2002)..," In this work, we calculate the vertical structure of the ADAF following the approach given in \citet{2002A&A...385..289C}."
 Assuming the aceretion flow to be isothermal m the vertical direction. we can calculate the vertical structure of the ADAF with provided the shape of the magnetic field lines in. the accretion. flow is known.," Assuming the accretion flow to be isothermal in the vertical direction, we can calculate the vertical structure of the ADAF with provided the shape of the magnetic field lines in the accretion flow is known."
 An additional term. containing OB-/OR. is included. because H~R holds at least in the outer region of ADAFs.," An additional term containing $\partial B_z/\partial R$, is included, because $H\sim R$ holds at least in the outer region of ADAFs."
 In principle. the field line shape is computable by solving the radial and vertical momentum equations with suitable boundary conditions (seeCao&Spruit2002.forthede- diseussion).. ," In principle, the field line shape is computable by solving the radial and vertical momentum equations with suitable boundary conditions \citep*[see][for the detailed
discussion]{2002A&A...385..289C}. ."
For the isothermal case. an approximate analytical expression is proposed for the shape of the field linesin the flow:," For the isothermal case, an approximate analytical expression is proposed for the shape of the field linesin the flow:"
Tsolated neutron stars (NSs) being nou-sphlierical bodies are expected to demonstrate free precession (for a byief review see. for example. Link 20033).,"Isolated neutron stars (NSs) being non-spherical bodies are expected to demonstrate free precession (for a brief review see, for example, \citealt{l2003}) )."
 however. exanples of this phenomena are less than few. iud even inrare cases When a precessiou-like behavior is observed different interpretations can be discussed (even nof related to precession. see for example RudermanaudCul (200633).," However, examples of this phenomena are less than few, and even in rare cases when a precession-like behavior is observed different interpretations can be discussed (even not related to precession, see for example \cite{rg2006}) )."
 The problem of long period free precession iu NSs is a long staucing one., The problem of long period free precession in NSs is a long standing one.
 A NS can precess if it is nou-spherical aud rotation axis docs uot coincide with a principal axis, A NS can precess if it is non-spherical and rotation axis does not coincide with a principal axis.
 Typically. biaxial objects are discussed. so deviation from spherical Αποταν can be described by one parameter oblateuess (see Akeünetal.(2006) for a discussion of triaxial model).," Typically, biaxial objects are discussed, so deviation from spherical symmetry can be described by one parameter – oblateness (see \cite{alw2006} for a discussion of triaxial model)."
 Expected values of NS oblatencss (due to rotation or influence of strong magnetic fields) can naturally lead to precession periods about one vear., Expected values of NS oblateness (due to rotation or influence of strong magnetic fields) can naturally lead to precession periods about one year.
 The precession period is equal to Dao=Pie., The precession period is equal to $P_\mathrm{prec}=P/\epsilon$.
 Were P is the spin period of a NS. € its oblateness. and Pypr recession period.," Here $P$ is the spin period of a NS, $\epsilon$ – its oblateness, and $P_\mathrm{pres}$ – precession period."
 Measured precession periods require oblateuess about 10N, Measured precession periods require oblateness about $10^{-8}$.
 ILowever. discussing dvuanies of NSs it is necessary to take into accout the uetwork of suporfluid vortices inside them.," However, discussing dynamics of NSs it is necessary to take into accout the network of superfluid vortices inside them."
 The neutron superfiuid Lquicd im the interior of a NS participates in rotation via formatio- of quautized vortex lines., The neutron superfluid liquid in the interior of a NS participates in rotation via formation of quantized vortex lines.
 The deusitv of these lines per unit area isn=20., The density of these lines per unit area is $n=2\Omega / k$.
" Tere ο=2a/P is spi- frequency. and &—2205, where nn, is a neutron mass (sec. for exaunple. ShapiroaudTeukolsky1983.. Ch."," Here $\Omega=2\pi /P$ is spin frequency, and $k=h/2m_\mathrm{n}$, where $m_\mathrm{n}$ is a neutron mass (see, for example, \citealt{st1983}, Ch."
 10)., 10).
 The vortices exist iu the core of à NS. where they can interact with superfluid (superconducting) protons anca normal electrons. aud in the crust. where they cam pin toit.," The vortices exist in the core of a NS, where they can interact with superfluid (superconducting) protons and normal electrons, and in the crust, where they can pin toit."
 Coupling of superfluid neutron vortices with clectrousf in a core results in diiupiug of free precession (AlparandOvchnan 1987)., Coupling of superfluid neutron vortices with electrons in a core results in damping of free precession \citep{ao1987}.
. But the time scale of this damping is long enoush. according to these authors.," But the time scale of this damping is long enough, according to these authors."
 For spin period about 1l second it is —LOO 104 Das (AlparandOvemia LOST)., For spin period about 1 second it is $\sim 400$ – $10^4$ $P_\mathrm{prec}$ \citep{ao1987}.
 Still. this fime scale is much shorter than a NS age. so some excitation mechanisin is necessary for precession.," Still, this time scale is much shorter than a NS age, so some excitation mechanism is necessary for precession."
 As it is discussed below. iu he presented model excitation is due to a elitch.," As it is discussed below, in the presented model excitation is due to a glitch."
 A kind of unie (ΠιοΙαλάπο} of vortices can also happen in the core due to interactions with uaenetic flux tubes (see discussion. for example. iu Link 2007)).," A kind of pinning (“immobilization”) of vortices can also happen in the core due to interactions with magnetic flux tubes (see discussion, for example, in \citealt{l2007}) )."
 Iu this case. the moment of inertia of “pinned” neutrons (wlich is about 7) is about 10 times arecr. than the moment of the remaining parts of a NS. Lo.," In this case, the moment of inertia of “pinned” neutrons (which is about $I$ ) is about 10 times larger, than the moment of the remaining parts of a NS, $I_\mathrm{c}$ ."
 9Ο. Pa NLP.," So, $P_\mathrm{prec}\sim 0.1 P$ ."
Very high redshilt supernovae can be equite interesting for astrophysical issues (which in (urn might impact cosmology). to be discussed in relsec:svs..,"Very high redshift supernovae can be quite interesting for astrophysical issues (which in turn might impact cosmology), to be discussed in \\ref{sec:sys}."
 Llere we consider (he measurement aspects of such a sample. and the implementation of observations characterizing (he sources. as a practical counterpoint to the theoretical considerations of (hie previous section.," Here we consider the measurement aspects of such a sample, and the implementation of observations characterizing the sources, as a practical counterpoint to the theoretical considerations of the previous section."
 Thousands of supernovae should exist. and be detected by SNAP. at 2> 1.7.," Thousands of supernovae should exist, and be detected by SNAP, at $z>1.7$ ."
 See Figure 7 lor estimates of both rates: the intrinsic SNe Ia rates are [rom a fit of observed Supernova Legacy Survey (SNLS: Astierοἱal. (2006))) rates at 0.3<2« (Sullivanetal.2006b) to the model of Scannapieco&Bildsten(2005).., See Figure \ref{fig:ratesn} for estimates of both rates; the intrinsic SNe Ia rates are from a fit of observed Supernova Legacy Survey (SNLS: \citet{astier06}) ) rates at $0.3 < z <0.8$ \citep{sullivanrates} to the model of \citet{scannapieco05b}.
 In this model. each of two SN Ia populations has rates proportional either to (hie star formation rate (SER) or the total stellar mass.," In this model, each of two SN Ia populations has rates proportional either to the star formation rate (SFR) or the total stellar mass."
 Core-collapse supernova rates are basedon LST GOODS rates al 0.3<2«0.7 , Core-collapse supernova rates are basedon HST GOODS rates at $0.3 < z < 0.7$ 
of the parameters of their. populations of binaries and blue stragelers (DS).,of the parameters of their populations of binaries and blue stragglers (BS).
 Dynamical models are needed for the design and interpretation of observational programmes: how is the period. distribution ancl the spatial distribution of binaries allected by dynamical evolution?, Dynamical models are needed for the design and interpretation of observational programmes: how is the period distribution and the spatial distribution of binaries affected by dynamical evolution?
 Another problem is the abundance and spatial distribution of blue stragelers. which can only be answered by a technique which follows simultaneously both their cdvnamies and internal evolution.," Another problem is the abundance and spatial distribution of blue stragglers, which can only be answered by a technique which follows simultaneously both their dynamics and internal evolution."
 While N-body techniques may. ultimately be the method of choice for such studies. svstems with the size of a elobular cluster are likely to remain beyond reach for some vears. simply. because of the number of stars and the population of binaries.," While $N$ -body techniques may ultimately be the method of choice for such studies, systems with the size of a globular cluster are likely to remain beyond reach for some years, simply because of the number of stars and the population of binaries."
 After all. it is only recently that the “hardest” open clusters have been modelled. at the necessary level of sophistication. and even then the tvpical simulation takes one month (LIurleyetal.2005).," After all, it is only recently that the “hardest"" open clusters have been modelled at the necessary level of sophistication, and even then the typical simulation takes one month \citep{hurleyetal2005}."
.. These authors focused on the old open cluster M67. which has been chosen by the MIODEST international collaboration (MOcelling. DEnse S'Tellar svstems) (Sillsetal.2003) as a target. cluster [or comparison between observations and. various techniques of numerical simulation.," These authors focused on the old open cluster M67, which has been chosen by the MODEST international collaboration (MOdelling DEnse STellar systems) \citep{sillsetal2003}
 as a target cluster for comparison between observations and various techniques of numerical simulation."
 We also focus on this cluster. partly for the purpose of refining our calibration of the Monte Carlo method.," We also focus on this cluster, partly for the purpose of refining our calibration of the Monte Carlo method."
 This paper begins in Sec.2 with a summary of the features which have been acleled to the Monte Carlo scheme., This paper begins in Sec.2 with a summary of the features which have been added to the Monte Carlo scheme.
 We also show there how we calibrate the Monte. Carlo technique with N-body simulations., We also show there how we calibrate the Monte Carlo technique with $N$ -body simulations.
 Next (Sec., Next (Sec.
 3) we apply the technique to construct à dynamical evolutionary mocel of the old open cluster M67. and compare our results with observations.," 3) we apply the technique to construct a dynamical evolutionary model of the old open cluster M67, and compare our results with observations."
 We give predictions for the initial parameters of the old open cluster M67., We give predictions for the initial parameters of the old open cluster M67.
 The final section summarises our conclusions. and discusses some of the main limitations of our mocdels.," The final section summarises our conclusions, and discusses some of the main limitations of our models."
 From the dynamical point of view our Monte Carlo code is almost exactly as described. in. Giersz(2006)., From the dynamical point of view our Monte Carlo code is almost exactly as described in \citet{giersz2006}.
.. In. this technique a star. cluster is (treated. as a collection. of spherical shells. cach one representing a single star with a certain energv and angular. momentum.," In this technique a star cluster is treated as a collection of spherical shells, each one representing a single star with a certain energy and angular momentum."
 Neighbouring shells are allowed to interact ancl exchange energy and angular momentum at a rate determined by the theory of relaxation., Neighbouring shells are allowed to interact and exchange energy and angular momentum at a rate determined by the theory of relaxation.
 Escapers are removed according to a prescription which mimics the effect of a tide., Escapers are removed according to a prescription which mimics the effect of a tide.
 Shells corresponding to binary stars also interact with sinele stars. ancl other binary stars. at rates determined by cross sections drawn from the literature (CGiersz2001).," Shells corresponding to binary stars also interact with single stars, and other binary stars, at rates determined by cross sections drawn from the literature \citep{giersz2001}."
. The only cynamical alterations deal with tightly. bound: subsvstems. which often arise in systems with a large mass range (e.g. those including both stellar-mass black holes and stars at the hvdrogen-burning limit of the main sequence).," The only dynamical alterations deal with tightly bound subsystems, which often arise in systems with a large mass range (e.g. those including both stellar-mass black holes and stars at the hydrogen-burning limit of the main sequence)."
 The introduction of stellar and. binary evolution has been greatly facilitated: by the development. of the “AleSeatter” interlace (Llegeic.PortegiesZwart&IHurlev2006).. which provides subroutines for initialising the stellar evolution of single and binary stars. and for retrieving the results of subsequent evolution. mass loss. merging of binary components. etc.," The introduction of stellar and binary evolution has been greatly facilitated by the development of the “McScatter"" interface \citep{heggieetal2006}, which provides subroutines for initialising the stellar evolution of single and binary stars, and for retrieving the results of subsequent evolution, mass loss, merging of binary components, etc."
 At present two such packages for stellar evolution can be emploved., At present two such packages for stellar evolution can be employed.
 One of these is SeBa (PortegiesZwart&Verbunt 1996)... which is incorporated. within the STARLAB environment (Hut.2003).," One of these is SeBa \citep{pzv1996}, which is incorporated within the STARLAB environment \citep{hut2003}."
. Phe other is referred (ο as “BSE” (binary star evolution)) and is based on the extensive formulae for the evolution of single stars of a range of metallicities given by Hurley.Pols&Tout(2000).. along with the treatment of binaries presented by. Hurley.Tout&Pols (2002).," The other is referred to as “BSE"" (binary star evolution), and is based on the extensive formulae for the evolution of single stars of a range of metallicities given by \citet{hurleyetal2000}, along with the treatment of binaries presented by \citet{hurleyetal2002}."
. Most of our effort has been conducted with BSE. partly to minimise any development. problems with mixcd-language progranuuing. and partly because SeDa is at oesent restricted to solar metallicity. whereas our interest is mainly. directed to globular clusters.," Most of our effort has been conducted with BSE, partly to minimise any development problems with mixed-language programming, and partly because SeBa is at present restricted to solar metallicity, whereas our interest is mainly directed to globular clusters."
 Gencrally speaking. he use of the Mescatter interface poses few problems: During a time step of the Monte Carlo code. the changes caused by relaxation and dynamical interactions between jnaries and single stars are performed. and then the stellar evolution of all stars and binaries is updated.," Generally speaking, the use of the McScatter interface poses few problems: During a time step of the Monte Carlo code, the changes caused by relaxation and dynamical interactions between binaries and single stars are performed, and then the stellar evolution of all stars and binaries is updated."
 The associated oss of mass (if any) is incorporated into the data for each star and binary in the Monte Carlo code. and any mergers are dealt with by altering the numbers of single and binary stars and adjusting the parameters of the bodies allected.," The associated loss of mass (if any) is incorporated into the data for each star and binary in the Monte Carlo code, and any mergers are dealt with by altering the numbers of single and binary stars and adjusting the parameters of the bodies affected."
 In a Monte. Carlo simulation. it is usual το adopt units such that the constant of gravitation. the initial total mass ancl the initial virial racius are 1.," In a Monte Carlo simulation it is usual to adopt units such that the constant of gravitation, the initial total mass and the initial virial radius are 1."
 In order to, In order to
"by geochemical exchanges between these different reservoirs, tectonics, atmospheric escape, photochemistry, and biology if present.","by geochemical exchanges between these different reservoirs, tectonics, atmospheric escape, photochemistry, and biology if present."
" Therefore, the expected diversity of exoplanet atmospheres, and terrestrial planets in particular, covers a wide parameter space, and our current understanding of the origin and evolution of planetary atmospheres provides very few constraints to guide us in this exploration."," Therefore, the expected diversity of exoplanet atmospheres, and terrestrial planets in particular, covers a wide parameter space, and our current understanding of the origin and evolution of planetary atmospheres provides very few constraints to guide us in this exploration."
" Although the use of detailed atmosphere models and synthetic spectra is essential, in particular to interpret spectral observations, it is equally important to allow ourselves to explore a much broader parameter space than the one covered today by self-consistent models."," Although the use of detailed atmosphere models and synthetic spectra is essential, in particular to interpret spectral observations, it is equally important to allow ourselves to explore a much broader parameter space than the one covered today by self-consistent models."
" This is why we chose to base this study on a different, “model-less” approach, which is complementary to the use of detailed atmosphere models, which remains necessary to refine the actual S/N for a specific close-up in the parameter space (for instance RAU10, based on self-consistent habitable planet atmosphere models)."," This is why we chose to base this study on a different, “model-less” approach, which is complementary to the use of detailed atmosphere models, which remains necessary to refine the actual S/N for a specific close-up in the parameter space (for instance RAU10, based on self-consistent habitable planet atmosphere models)."
" Because of the reasons above, we chose here to examine the S/N of features of species, freeing us from any a priori on the atmospheric composition and structure."," Because of the reasons above, we chose here to examine the S/N of features of species, freeing us from any a priori on the atmospheric composition and structure."
" Moreover, what interests us here is not the absolute planetary signal flux, but the the of a spectral feature."," Moreover, what interests us here is not the absolute planetary signal flux, but the the of a spectral feature."
" Therefore, we model the detection by estimating the difference of the planetary flux between two appropriately chosen binned channels, one measuring the continuum, and the other the flux in the absorption band of the feature."," Therefore, we model the detection by estimating the difference of the planetary flux between two appropriately chosen binned channels, one measuring the continuum, and the other the flux in the absorption band of the feature."
" Of course, when a given (photo)spectroscopical observation comprising up to tens of channels will be fitted with synthetic spectra, the S/N on the detection of species will be much higher."," Of course, when a given (photo)spectroscopical observation comprising up to tens of channels will be fitted with synthetic spectra, the S/N on the detection of species will be much higher."
" With this definition, an S/N of 3 is a safe 3o detection (also see Section below)."," With this definition, an S/N of 3 is a safe $3\,\sigma$ detection (also see Section \ref{s:spec-feat-sig} below)."
" In general, we chose to compute the S/N for a fiducial signature defined by a given spectral resolution, and a contrast necessary for its detection."," In general, we chose to compute the S/N for a fiducial signature defined by a given spectral resolution, and a contrast necessary for its detection."
 The way the signature contrast (or depth) is defined is described in the next section., The way the signature contrast (or depth) is defined is described in the next section.
" However, we also wish to particularly emphasize the case of the habitable super-earths."," However, we also wish to particularly emphasize the case of the habitable super-earths."
" As such, we consider some of the strongest infrared signatures of species present in the terrestrial atmosphere: We measure this feature relative to a region redward ofum."," As such, we consider some of the strongest infrared signatures of species present in the terrestrial atmosphere: We measure this feature relative to a region redward of."
". Therefore, we consider in the calculation a mean working wavelength ofum.. ("," Therefore, we consider in the calculation a mean working wavelength of. ("
"and an effective width ofum,, soA= 10).","and an effective width of, so $R\,=\,10$ )."
" Since this a filter observation forJWST., the modeled width of the feature will be specified in the appropriate section below (Section 4.1.2))."," Since this a filter observation for, the modeled width of the feature will be specified in the appropriate section below (Section \ref{s:miri-first}) )."
 The considered width is (so R= 20).," The considered width is (so $R\,=\,20$ )."
" Depending of the type of transit, we use several assumptions to compute the planetary spectral feature depth."," Depending of the type of transit, we use several assumptions to compute the planetary spectral feature depth."
 We use the same formulas as ? for the planetary spectral feature photon count (we consider the additional background and instrumental noises as indicated in Eq. 2))., We use the same formulas as \citet{beckwith} for the planetary spectral feature photon count (we consider the additional background and instrumental noises as indicated in Eq. \ref{eq:s2n}) ).
" We chose the difference in atmospheric opacity height between the in- and out-of-band channels to be n=3 atmospheric scale heights H=kT.q/ug (Figure 1)), k being the Boltzmann constant."," We chose the difference in atmospheric opacity height between the in- and out-of-band channels to be $n\,=\,3$ atmospheric scale heights $H = k\,T_{\RM{eq}} /\mu{}\,g$ (Figure \ref{f:primary}) ), $k$ being the Boltzmann constant."
" Consequently, the S/N scales with V, and n."," Consequently, the S/N scales with $^1/_\mu$ and $n$."
" This value has been observed for hot jupiters between adjacent spectral bins (even though larger differences in the apparent radius have been measured over entire spectra, see previous discussion on S/N definition on this page)."," This value has been observed for hot jupiters between adjacent spectral bins (even though larger differences in the apparent radius have been measured over entire spectra, see previous discussion on S/N definition on this page)."
" Another way of seeing our modeling is as an achievable ""resolution in amplitude"".", Another way of seeing our modeling is as an achievable “resolution in amplitude”.
" A “n=3 sampling"" should actually enable to detect opacity-radius variations of the planet over extended wavelength ranges (i.e. spectra) with a “bit depth"" that could be handy if disentanglement of the signatures of multiple species is required)."," A $n\,=\,3$ sampling” should actually enable to detect opacity-radius variations of the planet over extended wavelength ranges (i.e. spectra) with a “bit depth” that could be handy if disentanglement of the signatures of multiple species is required)."
" n=3 is also a high value for the Earth case, where greatest opacity height difference is 4H for the CO, and the"," $n\,=\,3$ is also a high value for the Earth case, where greatest opacity height difference is $4\,H$ for the $_2$ and the"
monentuni to eravitational radiation aud eventually coalesce.,momentum to gravitational radiation and eventually coalesce.
 The final iuspirals of MDIT pairs take about 10! seconds. and are the most luminous eravitational wave events in the Universe.," The final inspirals of MBH pairs take about $10^4$ seconds, and are the most luminous gravitational wave events in the Universe."
 These eveuts are one of the chief targets of the Laser Interferometer Space Auteuna (LISA) CAV interferometer satellite., These events are one of the chief targets of the Laser Interferometer Space Antenna (LISA) GW interferometer satellite.
 Du. this paper. we concentrate on the quiesceut evolution leading up to this state.," In this paper, we concentrate on the quiescent evolution leading up to this state."
 Before the final inspiral. the GW auplitucde is where fis the strain or metric perturbation. My is the total mass of the binary in της of LOSAL... 4 is the mass ratio (y< 1). Py is the observed CAV period in vears (the orbital period divided bv 2 for the expected nearly-circular orbits}. aud Dee is the distance in Cope.," Before the final inspiral, the GW amplitude is where $h$ is the strain or metric perturbation, $M_8$ is the total mass of the binary in units of $10^8 M_\odot$, $q$ is the mass ratio $q<1$ ), $P_{\rm yr}$ is the observed GW period in years (the orbital period divided by 2 for the expected nearly-circular orbits), and $D_{\rm Gpc}$ is the distance in Gpc."
 The lifetime of the svstem is The precision of the rotation periods of uullisecond period pulsars which is established: via pulse arrival time measurements allows detection of the stochastic MDII-MDIT backeround spectrum at ullz frequencies (22?)..," The lifetime of the system is The precision of the rotation periods of millisecond period pulsars which is established via pulse arrival time measurements allows detection of the stochastic MBH-MBH background spectrum at nHz frequencies \citep{Sazhin78, Detweiler79, Rajagopal95}."
 The detection process is very similar to that of the laser interferometers—passage of an electromagnetic signal through distorted space-timeexcept that in the case of pulsars no mirrors are needed as we have a distant precision clock. the rotating neutron star. sending us a periodic pulse train.," The detection process is very similar to that of the laser interferometers—passage of an electromagnetic signal through distorted space-time—except that in the case of pulsars no mirrors are needed as we have a distant precision clock, the rotating neutron star, sending us a periodic pulse train."
 Measurements of a single pulsar can place an upper lait ou the presence of a spectrum of gravitational radiation (??)..," Measurements of a single pulsar can place an upper limit on the presence of a spectrum of gravitational radiation \citep{Kaspi94,
 Lommen01b}."
 In short. the limit ou strain is eiven by the ratio of the timine precision aud the measurement duration: 1 ps/10 vr ~ὃν10H5," In short, the limit on strain is given by the ratio of the timing precision and the measurement duration; 1 $\mu$ s/10 yr $\sim~3\times 10^{-14}$."
 While pulsar timine caunot detect individual eveuts of the small wuplitude given in equation (1)). these measurements have a good prospect for detection of the stochastic backerouud of CAVS froii the euseiuble of these MDBII-MDBIT coalesccuce events throughout tlheU," While pulsar timing cannot detect individual events of the small amplitude given in equation \ref{eq:gwamp}) ), these measurements have a good prospect for detection of the stochastic background of GWs from the ensemble of these MBH-MBH coalescence events throughout the."
niverse? The CAV perturbs pulse arrival times of a spatial array of pulsars in a correlated manner that is distinct from other known perturbations such as atomic time and ephemeris errors;, The GW perturbs pulse arrival times of a spatial array of pulsars in a correlated manner that is distinct from other known perturbations such as atomic time and ephemeris errors.
 A Pulsar Timingo Array then acts as a nlIz exavitational wave telescope capable of direct detection of the stochastic background raciation., A Pulsar Timing Array then acts as a nHz gravitational wave telescope capable of direct detection of the stochastic background radiation.
 Questions remain., Questions remain.
 Are there dynamical processes that drive the MDBII pair iuto the CW reeime?, Are there dynamical processes that drive the MBH pair into the GW regime?
 Does this happen frequeuthy?, Does this happen frequently?
 If so. can we observe the eravitational raciation via pulsar tinune?," If so, can we observe the gravitational radiation via pulsar timing?"
 If not. do we then see evidence of close binary MBIIs πιο up in the centers of may. or most. galaxies?," If not, do we then see evidence of close binary MBHs “hung up” in the centers of many, or most, galaxies?"
 If we observe ucither the GW signal via precision pulsar timiue nor inactive close pairs via high aneular resolution studies. docs this imply that some part of the paradigii.the ubiquity of black holes at all redshifts aud the importance of πιασος in galaxy evolutionis flawed?," If we observe neither the GW signal via precision pulsar timing nor inactive close pairs via high angular resolution studies, does this imply that some part of the paradigm—the ubiquity of black holes at all redshifts and the importance of mergers in galaxy evolution—is flawed?"
 Some of these questious have been taken up by other groups over the vears., Some of these questions have been taken up by other groups over the years.
 In their iuportaut paper. ?.hereafterRR.. discussed several mechanisius driving the MDBIT pair iuto the CAV regiae. and calculated the GA spectrum πάσα: various assunptions.," In their important paper, \citet[hereafter RR]{Rajagopal95}, discussed several mechanisms driving the MBH pair into the GW regime, and calculated the GW spectrum under various assumptions."
 More recenutlv. ? follow up on the gas-cdyuamical mechauisi for driving the MDBII coalesccuce first mentioned by 7..," More recently, \citet{Gould99} follow up on the gas-dynamical mechanism for driving the MBH coalescence first mentioned by \cite{Begelman80}."
 7? explore the detailed interaction of the MIBIT binary with the accretion disk., \citet{ArmitageNatarajan02} explore the detailed interaction of the MBH binary with the accretion disk.
 Meauhile. ? aud ?. have investigated the stellaz-dyaizunuical schemes.," Meanwhile, \citet{MilMer01} and \citet{Yu01} have investigated the stellar-dynamical schemes."
 Finally. ? have investigated the effect that a time-dependent cliauge in MDIT “demographics” might have ou the merger history of galaxies. and ? las shown an alternative method for calculating the CAV spectrum for generic sources.," Finally, \citet{Menou01}
 have investigated the effect that a time-dependent change in MBH “demographics” might have on the merger history of galaxies, and \citet{Phinney01}
 has shown an alternative method for calculating the GW spectrum for generic sources."
 The advances in our uuderstaudiusgC» of MDBIIs alongOo with steady progressC» in precision pulsar ήπιοOo have led us to this paper., The advances in our understanding of MBHs along with steady progress in precision pulsar timing have led us to this paper.
 Iu, In
"Values of 0, aud q, are larger than those of the unaberrated angles 0, aud Que",Values of $\hat \theta_r$ and $\hat \varphi_r$ are larger than those of the unaberrated angles $\theta_r$ and $\varphi_r$.
 For the special case of points Ixiug on the meridian including the rotational and maguetie axes the formmlac are simpler., For the special case of points lying on the meridian including the rotational and magnetic axes the formulae are simpler.
" In this case we confine atteution tothe y: plauc. Le. ο=yy,7/2."," In this case we confine attention to the $y-z$ plane, i.e., $\varphi_e = \varphi_r = \pi/2$."
 Consequently. aud After iucludiug aberration the impact angle ο needs care in its definition.," Consequently, and After including aberration the impact angle $\beta$ needs care in its definition."
" Iu absence of aberration the usual definition is 3=0,a where y,=7/2 is understood.", In absence of aberration the usual definition is $\beta = \theta_r - \alpha$ where $\varphi_r = \pi/2$ is understood.
" Now we cau define it for example as JJ—0,a with ο=7/2 understood.", Now we can define it for example as $\beta = \hat \theta_r - \alpha$ with $\hat \varphi_r = \pi/2$ understood.
" The relation of jj with the locations (0,..42,)is then not simple."," The relation of $\beta$ with the locations $(\hat \theta_{r}, \hat \varphi_{r})$is then not simple."
" With the desired. definition of |J. its relation with 0, and y, can be derived using Eqs."," With the desired definition of $\beta$ , its relation with $\hat \theta_{r}$ and $\hat \varphi_{r}$ can be derived using Eqs."
 1 aud 2 or Eqs., \ref{tab1} and \ref{pab1} or Eqs.
 8 aud 9..," \ref{tab2}
 and \ref{pab2}."
 IIeuceforth. we consider the longitude offset ouly for tle simple case of the direction of the magnetic axis.," Henceforth, we consider the longitude offset only for the simple case of the direction of the magnetic axis."
 Firstly this should suffice for waderstancding the eross properties of the offsets which is our ain here. aud secondly because the correspondingifs offsets are available only for this case (Shitov 1983).," Firstly this should suffice for understanding the gross properties of the offsets which is our aim here, and secondly because the corresponding offsets are available only for this case (Shitov 1983)."
" Therefore. iu addition to 44=ον7/2 we also have 0,=a."," Therefore, in addition to $\varphi_e = \varphi_r = \pi/2$ we also have $\theta_e = \theta_r = \alpha$."
 Now e=sina and then Eqs.," Now $v = \xi \, sin \, \alpha$ and then Eqs."
 9 and 11. in the uourclativistic limit reduce to the often used efe formula.," \ref{pab2} and \ref{pab3}, in the nonrelativistic limit reduce to the often used $v/c$ formula."
 The offset in longitude iutroduced by aberration is Equating the pulsar braking torque to the product of stellar magnetic moment and the toroidal component of the iiagnetie field caused by the stellar maguctic dipole radiation Shitov (1983. 1985) derived the toroidal magnetic field component By as where By is the polar surface magnetic field.," The offset in longitude introduced by aberration is Equating the pulsar braking torque to the product of stellar magnetic moment and the toroidal component of the magnetic field caused by the stellar magnetic dipole radiation Shitov (1983, 1985) derived the toroidal magnetic field component $B_t$ as where $B_0$ is the polar surface magnetic field."
 The magnitude of the magnetic field at a distance ris Br)., The magnitude of the magnetic field at a distance $r$ is $B(r)$ .
" Presence of By changes the azimuth of the aud radiating charges by anamount 42,54 such that", Presence of $B_t$ changes the azimuth of the co-rotating and radiating charges by anamount $\varphi_{mfs}$ such that
null hypothesis by carrving out FAP estimates aud other tests.,null hypothesis by carrying out FAP estimates and other tests.
 These safeguards will eusure coutinued coufidence and credibility⋅⋅⋅ of; the profound: aud extraordinary. claims. of: the detections of low-mass plaucts., These safeguards will ensure continued confidence and credibility of the profound and extraordinary claims of the detection of low-mass planets.
spectral indexes. Eq. (,"spectral indexes, Eq. ("
4).,4).
 Phe model was calculated similarly o the CDM. model anc was also used. to estimate. the cosmic variance of the correlation function. (see Section 6)., The model was calculated similarly to the CDM model and was also used to estimate the cosmic variance of the correlation function (see Section 6).
 The model is designated as DPS.6., The model is designated as DPS.6.
 Phe. oscillatory »shaviour of the double power-law model is less regular: he first minimum of the correlation function. has much arecr amplitude., The oscillatory behaviour of the double power-law model is less regular; the first minimum of the correlation function has much larger amplitude.
 Amplitudes of maxima are approximately as high as in the case of the mixed model. the mean period of oscillations is also similar. but the scatter of individual »eriods is larger.," Amplitudes of maxima are approximately as high as in the case of the mixed model, the mean period of oscillations is also similar, but the scatter of individual periods is larger."
 We shall use the following parameters to. characterise oscillations of the correlation function: the mean separation of the first. minimum from zero. rast the position and amplitude of the first secondary maximum. 74; and zl: ilferences between the subsequent maxima. AG)—Fuss; Fuse ane the mean value of dilferences. derived. from. the first 4 dillerences between maxima and from the first + dillerences between minima. Aye.," We shall use the following parameters to characterise oscillations of the correlation function: the mean separation of the first minimum from zero, $r_{min}$; the position and amplitude of the first secondary maximum, $r_{max}$ and $A_{max}$; differences between the subsequent maxima, $\Delta_{ij}=r_{maxi} - r_{maxj}$ ; and the mean value of differences, derived from the first 4 differences between maxima and from the first 4 differences between minima, $\Delta_{mean}$."
 Scaling parameters can be used to derive the value of the true period of oscillations. P. which we take to be equal to the grid step of the net of the uasi-regular mocel. and to the wavelength of the maximum of the spectrum. Ag=2a/ho.," Scaling parameters can be used to derive the value of the true period of oscillations, $P$, which we take to be equal to the grid step of the net of the quasi-regular model, and to the wavelength of the maximum of the spectrum, $\lambda_0=2\pi/k_0$."
 Values of these parameters for models with at least one secondary minimum and maximum are given in Table 1., Values of these parameters for models with at least one secondary minimum and maximum are given in Table 1.
 They are derived. from the mean smoothed correlation function of the particular model. calculated from ten realizations.," They are derived from the mean smoothed correlation function of the particular model, calculated from ten realizations."
 “To avoid the decrease by smoothing the amplitude has been estimated from unsmoothed claI, To avoid the decrease by smoothing the amplitude has been estimated from unsmoothed data.
n This Table shows that these parameters. vary only within rather narrow limits., This Table shows that these parameters vary only within rather narrow limits.
 The position of the first secondary maximum is almost the same for all ecometrical models with identical grid step (ancl period P)., The position of the first secondary maximum is almost the same for all geometrical models with identical grid step (and period $P$ ).
 Dillerences between maxima and minima are larger. but not much.," Differences between maxima and minima are larger, but not much."
 ‘These cillerences are rather systematic: in all our ecometric tov models As)2 P. and Ags«P.," These differences are rather systematic: in all our geometric toy models $\Delta_{21} > P$ , and $\Delta_{32} < P$."
 The characteristic scale of the supercluster-void network. P. can be caleulated from. the above parameters using the mean values of the following paranielers: and As we see the most accurate determination of P comes from the last equation.," The characteristic scale of the supercluster-void network, $P$, can be calculated from the above parameters using the mean values of the following parameters: and As we see the most accurate determination of $P$ comes from the last equation."
 1n this Section we continue the analysis of the correlation unction. anc the power spectrum. for cillerent cluster distributions., In this Section we continue the analysis of the correlation function and the power spectrum for different cluster distributions.
 Our main goal is to find which geometric xoperties of the distribution of superclusters can. be detected. on the basis of the correlation function ancl the power spectrum alone., Our main goal is to find which geometric properties of the distribution of superclusters can be detected on the basis of the correlation function and the power spectrum alone.
 We investigate the influcnee of the shape of the volume occupied. with clusters., We investigate the influence of the shape of the volume occupied with clusters.
 Phe available observed. samples are generally not cubical in shape. and 16 shape of sample can. in principle. influence statistical properties of the samples.," The available observed samples are generally not cubical in shape, and the shape of sample can, in principle, influence statistical properties of the samples."
 The correlation functions with their error corridors and the respective power spectra with their error corridors are plotted. for several models in. Figs 2 4., The correlation functions with their error corridors and the respective power spectra with their error corridors are plotted for several models in Figs 2 – 4.
 On small scales all correlation. functions have a large maximum which reflects the fact that our. models have clustering properties., On small scales all correlation functions have a large maximum which reflects the fact that our models have clustering properties.
 On large scales the correlation functions are different., On large scales the correlation functions are different.
 Phey have one of three principal forms: they become flat on large seales cirectly from the maximum on small scales (random supercluster model): have a minimum on intermediate scales followed by one secondary maximum. and then smoothly. become Fat (Voronoi model): or obey an oscillatory behaviour with alternating secondary maxima and minima of decreasing amplitude (models with a built-in regular structure of the tvpe of a rectangular Lattice).," They have one of three principal forms: they become flat on large scales directly from the maximum on small scales (random supercluster model); have a minimum on intermediate scales followed by one secondary maximum, and then smoothly become flat (Voronoi model); or obey an oscillatory behaviour with alternating secondary maxima and minima of decreasing amplitude (models with a built-in regular structure of the type of a rectangular lattice)."
 Geometric interpretation of the correlation function of the first twpe is simple: here superclusters are distributed randomly ancl peaks from: numbers of objects at. various separations cancel each other out., Geometric interpretation of the correlation function of the first type is simple: here superclusters are distributed randomly and peaks from numbers of objects at various separations cancel each other out.
 Superclusters separated. bv. large voids. produce. a correlation function with a minimum. whose location corresponds to the mean separation between superclusters and. voids.," Superclusters separated by large voids produce a correlation function with a minimum, whose location corresponds to the mean separation between superclusters and voids."
 The minimum ids [followed by a secondary maximum corresponding to the distance between superclusters across voids., The minimum is followed by a secondary maximum corresponding to the distance between superclusters across voids.
 On still larger scales. there are no regularities in the supercluster-voicl network (voids are spaced randomly). and the correlation function on very large scales is close to zero since superclusters at various separations cancel cach other out as in the previous case.," On still larger scales there are no regularities in the supercluster-void network (voids are spaced randomly), and the correlation function on very large scales is close to zero since superclusters at various separations cancel each other out as in the previous case."
 This distribution is realized in the Voronoi moclel., This distribution is realized in the Voronoi model.
 The interpretation of the oscillating correlation function is also straightforward., The interpretation of the oscillating correlation function is also straightforward.
 In. all models. which produce an oscillating correlation function the distribution of clusters on large scales is quasi-regular in the sense that high-density regions form a fairly regular network with an approximately constant &rid length., In all models which produce an oscillating correlation function the distribution of clusters on large scales is quasi-regular in the sense that high-density regions form a fairly regular network with an approximately constant grid length.
 In order to get regular oscillations the geometric structure must not be too regular., In order to get regular oscillations the geometric structure must not be too regular.
 An example of very regular structure with superclusters located only in corners of the grid. shows that the correlation function has a number of small maxima and minima without anv regular oscillations., An example of very regular structure with superclusters located only in corners of the grid shows that the correlation function has a number of small maxima and minima without any regular oscillations.
 Quasi-regtiar oscillations are generated in all models with certain reguarity and certain irregularity: the supercluster-void. network must havea constant overall, Quasi-regular oscillations are generated in all models with certain regularity and certain irregularity: the supercluster-void network must havea constant overall
Progress in the study of QSO absorption line svstems has &one hand in hand with the advancement of technology over the past. few vears.,Progress in the study of QSO absorption line systems has gone hand in hand with the advancement of technology over the past few years.
 During the 19808. developments in echelle spectroscopy with sensitive electronic detectors increased the attainable resolution by à [factor of ten., During the 1980's developments in echelle spectroscopy with sensitive electronic detectors increased the attainable resolution by a factor of ten.
 The detailed. analysis of the absorption systems in these spectra was possible through absorption line profile fitting., The detailed analysis of the absorption systems in these spectra was possible through absorption line profile fitting.
 The increase in spectral dispersion coupled with the need to obtain a respectable S/N. however. forced. astronomers to observe the same object for many. nights on 4 me-class telescopes. restricting the number of objects ibi was possible to observe.," The increase in spectral dispersion coupled with the need to obtain a respectable S/N, however, forced astronomers to observe the same object for many nights on $\,$ m-class telescopes, restricting the number of objects it was possible to observe."
 In the 1990s the 10mm Week telescope together with its powerful instrument HESS enabled. us to obtain optical spectra of faint. high redshift QSOs at unprecedented spectral resolution (7 kms 1) and a signal-to-noise ratio in excess of a hundred in a single night.," In the 1990's the $\,$ m Keck telescope together with its powerful instrument HIRES enabled us to obtain optical spectra of faint, high redshift QSOs at unprecedented spectral resolution $\sim 7\,$ $\,$ $^{-1}$ ) and a signal-to-noise ratio in excess of a hundred in a single night."
 Meanwhile. ultra-violet spectroscopy using the Llubhle Space Telescope opened a window on QSO absorbers at low redshift.," Meanwhile, ultra-violet spectroscopy using the Hubble Space Telescope opened a window on QSO absorbers at low redshift."
 Using these data. very detailed studies of the chemical properties of the largest. absorbers. danmipec Lyman-alpha svstenis (DLAs). have provided a wealth of information about the formation of structure.," Using these data, very detailed studies of the chemical properties of the largest absorbers, damped Lyman-alpha systems (DLAs), have provided a wealth of information about the formation of structure."
 Understanding the chemical evolutionary history of galaxies. seen here in absorption. is fundamental to the study of galaxy. formation.," Understanding the chemical evolutionary history of galaxies, seen here in absorption, is fundamental to the study of galaxy formation."
 Phe study of DLAs has sullered from the small number of objects. approximately one hundred. that are currently known.," The study of DLAs has suffered from the small number of objects, approximately one hundred, that are currently known."
 Although detailed studies of individual objects are very revealing. LIST imaging of QSO fields has revealed a wide range of luminosities ancl morphologies for DLA counterparts.," Although detailed studies of individual objects are very revealing, HST imaging of QSO fields has revealed a wide range of luminosities and morphologies for DLA counterparts."
 Hence to determine the evolution in the absorption properties ofa such mixed population of galaxies. much larger samples of QSO absorbers will be required.," Hence to determine the evolution in the absorption properties of a such mixed population of galaxies, much larger samples of QSO absorbers will be required."
 With the recent release of the 20P QSO IHedshift Survey (207) Lok Catalogue (Croom ct al., With the recent release of the 2dF QSO Redshift Survey (2QZ) 10k Catalogue (Croom et al.
 20012) the number of known QSOs has suddenly and dramatically increased., 2001a) the number of known QSOs has suddenly and dramatically increased.
 With he 2QZ rapidly approaching its target of 25000 QSOs. ogether with Sloan Digital Sky Survey observations (Lan et al.," With the 2QZ rapidly approaching its target of 25000 QSOs, together with Sloan Digital Sky Survey observations (Fan et al."
 1999). unprecedented: numbers of new QSO spectra will soon be available from which we can identify and study arge numbers of new heavy clement absorption svstenis.," 1999), unprecedented numbers of new QSO spectra will soon be available from which we can identify and study large numbers of new heavy element absorption systems."
 As the 207 spectra were taken primarily to confirm the identity of QSOs. and determine their redshift. they have a vpical signal-to-noise ratio (S/N) —10. and a resolution of ~SA..," As the 2QZ spectra were taken primarily to confirm the identity of QSOs, and determine their redshift, they have a typical signal-to-noise ratio (S/N) $\sim$ 10, and a resolution of $\sim$."
 Although this is not ideal for absorption line analysis.," Although this is not ideal for absorption line analysis,"
of them lie at distances larger than 250Mpe.,of them lie at distances larger than 250.
. The closest of them is located at about 90Μρο.. and their median distance is about 200Μρο.," The closest of them is located at about 90, and their median distance is about 200."
. As mentioned above. owing to the sample geometry. the nearby superclusters may not be fully included in the sample volume and their small clumpiness may be due to this selection effect.," As mentioned above, owing to the sample geometry, the nearby superclusters may not be fully included in the sample volume and their small clumpiness may be due to this selection effect."
 Some nearby poor superclusters are located in low-density filaments between us and more distant superclusters. and their shape and small clumpiness may be real 2).," Some nearby poor superclusters are located in low-density filaments between us and more distant superclusters, and their shape and small clumpiness may be real ."
. The closest more elongated superclusters with the shape parameter ΚιΚΟ«0.6 are about 170 away from us. their mean and median distances almost coincide and are about 254 ((this is approximately the distance to the rich superclusters in the SGW).," The closest more elongated superclusters with the shape parameter $K_1/K_2 < 0.6$ are about 170 away from us, their mean and median distances almost coincide and are about 254 (this is approximately the distance to the rich superclusters in the SGW)."
 Below. we give a short description of individual superclusters in our sample.," Below, we give a short description of individual superclusters in our sample."
 In the figures of this section. and in Appendix AppendixD: we show for each supercluster (except for those for which Ἐν=| over the whole mass fraction interval) the sky distribution of supercluster members. the values of the fourth Minkowski functional Vi vs. the mass fraction af and the morphological signature for each supercluster.," In the figures of this section and in Appendix \ref{sec:MFfig} we show for each supercluster (except for those for which $V_3 = 1$ over the whole mass fraction interval) the sky distribution of supercluster members, the values of the fourth Minkowski functional $V_3$ vs. the mass fraction $mf$ and the morphological signature for each supercluster."
 Panels in these figures are as follows., Panels in these figures are as follows.
 The left panels show the sky distributions of galaxies in superclusters, The left panels show the sky distributions of galaxies in superclusters
lower energies (han curvature photons. we have not included (his mechanism in the model in (his study.,"lower energies than curvature photons, we have not included this mechanism in the pair-starved model in this study."
 The CH. emission model below the CR pair death line used in (his study is developed [rom the work by ILuding.Usov.&Muslimov(2005)., The CR emission model below the CR pair death line used in this study is developed from the work by \citet{Hard05}.
. The inclination angle a and the viewing angle ¢ determine which open field lines are sampled by the line of sight., The inclination angle $\alpha$ and the viewing angle $\zeta$ determine which open field lines are sampled by the line of sight.
 As illustrated in Figure 3. the line of sight intersects tangentially a particular open field line with a radius of curvature p. at a radial distance r and polar angle 9.," As illustrated in Figure 3, the line of sight intersects tangentially a particular open field line with a radius of curvature $\rho_c$ at a radial distance r and polar angle $\theta$."
 The open field lines are defined within the polar cap angle given by (he expression where P is the pulsar period in seconds. H is the neutron star radius (105 em) and c is the speed of lisht.," The open field lines are defined within the polar cap angle given by the expression where P is the pulsar period in seconds, $R$ is the neutron star radius $10^6$ cm) and c is the speed of light."
" We partition the open field lines through a dimensionless parameter. €. that varies between 0 and 1 and is defined as where 0, is the polar angele of the open field line at the intersection with (he surface of the star."," We partition the open field lines through a dimensionless parameter, $\xi$, that varies between 0 and 1 and is defined as where $\theta_s$ is the polar angle of the open field line at the intersection with the surface of the star."
" The particle emits curvature photons along the line of sight at an angle 6,=30/2 given bv where ó is (he phase angle. a is the magnetic inclination and ¢ is (he viewing angle."," The particle emits curvature photons along the line of sight at an angle $\theta_\gamma\ =\ {3\theta / 2}$ given by where $\phi$ is the phase angle, $\alpha$ is the magnetic inclination and $\zeta$ is the viewing angle."
 We approximate the accelerating electric field from Equation 1H of (1993) using the expression where & = 0.15 is the general relativistic inertial [rame dragging [actor. D» is the surface magnetic field in units of 1077 C. 5 =r/R is the dimensionless radius and y is the azimuth angle around the magnetic pole given bx the expression The eain in energy of the accelerating primary electron is compensated bv the CH losses," We approximate the accelerating electric field from Equation 14 of \citet{Hard98} using the expression where $\kappa$ = 0.15 is the general relativistic inertial frame dragging factor, $B_{12}$ is the surface magnetic field in units of $10^{12}$ G, $\eta$ =r/R is the dimensionless radius and $\varphi$ is the azimuth angle around the magnetic pole given by the expression The gain in energy of the accelerating primary electron is compensated by the CR losses"
major axis of the galaxy. as seen in Figure 1..,"major axis of the galaxy, as seen in Figure \ref{fig:ima}."
 We have specifically. chosen this carly-type spiral in order to avoid the presence of complex structural components ancl dust. which can make the stellar population analysis very tricky.," We have specifically chosen this early-type spiral in order to avoid the presence of complex structural components and dust, which can make the stellar population analysis very tricky."
 The galaxy distance is 31.6 AIpe (Erwin2004)... which corresponds to 7150 +.," The galaxy distance is 31.6 Mpc \citep{2004A&A...415..941E}, which corresponds to $\sim$ 150 $^{-1}$."
 The relevant. properties of 3357 are shown in Table 1.., The relevant properties of 357 are shown in Table \ref{tab:n357}.
 Although some studies claim this galaxy is isolated (ος...Gadottictal.2007).. vandenDergh(2002) finds it belongs to a group with at. least. six other members.," Although some studies claim this galaxy is isolated \citep[e.g.,][]{2007MNRAS.381..943G}, \citet{2002AJ....124..782V} finds it belongs to a group with at least six other members."
 However. it shows no signatures of interaction with its closer companions.," However, it shows no signatures of interaction with its closer companions."
 3357 is classified as à LINER. (Cacottietal. 2007).., 357 is classified as a LINER \citep{2007MNRAS.381..943G}.
 The structural properties of 3357. have been studied: photometrically by several authors., The structural properties of 357 have been studied photometrically by several authors.
 In. this way. Aguerrictal.(2005). perform a photometric decomposition of an /--band image of this galaxy along its outer bar major axis. getting the main photometric parameters. of its structural components. namely. bulge. outer bar. and cise: they do not take into account the inner bar since its contribution to the radial surface brightness along the main bar is negligible.," In this way, \citet{2005A&A...434..109A} perform a photometric decomposition of an -band image of this galaxy along its outer bar major axis, getting the main photometric parameters of its structural components, namely bulge, outer bar and disc; they do not take into account the inner bar since its contribution to the radial surface brightness along the main bar is negligible."
 Pheir main conclusion is that the bulge of 3357 follows the same fundamental plane than the ellipticals and other bulges of SO galaxies., Their main conclusion is that the bulge of 357 follows the same fundamental plane than the ellipticals and other bulges of S0 galaxies.
 The spectroscopic observations of 3357. were carried out with the 3.5-m New Technology. Telescope (NTL) at the European Southern Observatory (ESO) in La Silla (Chile) on 5-18 October 2002., The spectroscopic observations of 357 were carried out with the 3.5-m New Technology Telescope (NTT) at the European Southern Observatory (ESO) in La Silla (Chile) on 5-13 October 2002.
 The ESO Alulti-Alode Instrument (IMMI was operated both in blue (BLMD) and red. medium-dispersion spectroscopic (IMDB) mode., The ESO Multi-Mode Instrument (EMMI) was operated both in blue (BLMD) and red medium-dispersion spectroscopic (REMD) mode.
 The NEP mounted EXIAIL in DLMD using the grating 38 blazed at with 1200 groovesmmnm+ in first order in combination with a 1.3 aresec 5.5 arcmiün slit., The NTT mounted EMMI in BLMD using the grating 3 blazed at with 1200 $^{-1}$ in first order in combination with a 1.3 arcsec $\times$ 5.5 arcmin slit.
 The detector was the 331 ‘Tektronix TIx1024«; ED CCD with 1024.1024 pixels of 24« pni., The detector was the 31 Tektronix TK1024 EB CCD with $1024\times1024$ pixels of $24\times24$ $\mu$ $^2$.
 Lt vielded a wavelength coverage between about and wwith a reciprocal dispersion of ppixel|., It yielded a wavelength coverage between about and with a reciprocal dispersion of $^{-1}$.
 The spatial seale was 0.37 ppixcl1., The spatial scale was 0.37 $^{-1}$.
 The instrumental resolution was (ΑΛΛΗ) corresponding to aint40 kim , The instrumental resolution was (FWHM) corresponding to $\sigma_{\rm inst}\sim40$ km $^{-1}$ .
Six spectra of 45 min cach were taken aligning the slit with the major axis of the inner bar (PA=45°)., Six spectra of 45 min each were taken aligning the slit with the major axis of the inner bar $\rm PA = 45^\circ$ ).
 Two more spectra of 45 min each were obtained aligning the slit with the major axis of the outer bar (VA=1207)., Two more spectra of 45 min each were obtained aligning the slit with the major axis of the outer bar $\rm PA = 120^\circ$ ).
 All the spectra were obtained using the guiding TY camera tocenter the slit on the galaxy. nucleus., All the spectra were obtained using the guiding TV camera tocenter the slit on the galaxy nucleus.
 The NIP mounted EMMLEin RIMD using the erating 66 blazed at with 1200 grooves mmJ| in first order., The NTT mounted EMMI in REMD using the grating 6 blazed at with 1200 grooves $^{-1}$ in first order.
 A 1.0 aresec 5.5 avemin slit was adopted., A 1.0 arcsec $\times$ 5.5 arcmin slit was adopted.
 The mosaiced. MET/LL CCDs 662 and 63 with 2048.-4096 pixels o£ 15.15 fmi? covered the wavelength range between about aandAA., The mosaiced MIT/LL CCDs 62 and 63 with $2048\times4096$ pixels of $15\times15$ $\mu$ $^2$ covered the wavelength range between about and.
 The on-chip 2 pixel binning provided a reciprocal dispersion and spatial scale of ppixel+ and 0.332 aresee |., The on-chip $2\times2$ pixel binning provided a reciprocal dispersion and spatial scale of $^{-1}$ and 0.332 arcsec $^{-1}$ .
 The instrumental resolution was ((FWHIIAL) corresponding to σι30 kim t, The instrumental resolution was (FWHM) corresponding to $\sigma_{\rm inst}\sim30$ km $^{-1}$.
" After centering the slit on the galaxy nucleus. two spectra of 30 min cach were obtained along the cise major axis (VA= 20"")."," After centering the slit on the galaxy nucleus, two spectra of 30 min each were obtained along the disc major axis $\rm PA =
20^\circ$ )."
 The range of the secing FWLIAL during the observing runs was 0.6-1.4 arcsec as measured bv the ESO Dillerential Image Motion. Monitor., The range of the seeing FWHM during the observing runs was 0.6-1.4 arcsec as measured by the ESO Differential Image Motion Monitor.
 A comparison lamp exposure was obtained after cach object. integration to allow accurate wavelength. calibration., A comparison lamp exposure was obtained after each object integration to allow accurate wavelength calibration.
 Quartz lamp and twilight sky Ilatfields were used to remove pixel-to-pixel variations and larec-scale illumination patterns., Quartz lamp and twilight sky flatfields were used to remove pixel-to-pixel variations and large-scale illumination patterns.
 Several G and Ix stars and spectrophotometric standard. stars were observed with the sane set-up to serve as templates in measuring the stellar kinematics and in Dux calibration. respectively.," Several G and K stars and spectrophotometric standard stars were observed with the same set-up to serve as templates in measuring the stellar kinematics and in flux calibration, respectively."
 All the spectra were overscan and bias subtracted. Hatfield) corrected. corrected. for bad. pixels ancl columns. and wavelength calibrated using standard routines.," All the spectra were overscan and bias subtracted, flatfield corrected, corrected for bad pixels and columns, and wavelength calibrated using standard routines."
 The cosmic ray. removal is a critical step since any residual might allect the spectral lines. measured. to. derive. the properties of the stellar populations., The cosmic ray removal is a critical step since any residual might affect the spectral lines measured to derive the properties of the stellar populations.
 It was performed with the RIEDUCEALE package(C'ardiel 1999).. that assures a careful and accurate inspection. ancl interpolation of thespectra.," It was performed with the REDUCEME package\citep{1999PhDT........12C}, , that assures a careful and accurate inspection and interpolation of thespectra."
 We checked that the wavelength rebinning was done, We checked that the wavelength rebinning was done
"we can rewrite the right hand side of (21)) Finally. we find the relation between the current helicity spectrum. Ak) and the helicity spectrum R,, by identifying the antisymmetric part of the left hand side of (21)) with the antisymmetric part of the right hand side: From now on. although we mostly speak of helicity. we actually deal with current helicity for convenience and bear in mind that H(&) is easily convertible to ΑΚ) using (24))","			we can rewrite the right hand side of \ref{MR}) ): 			Finally, we find the relation between the current helicity spectrum $\hat{H}(k)$ and the helicity spectrum $\hat{R}_{H}$ by identifying the antisymmetric part of the left hand side of \ref{MR}) ) with the antisymmetric part of the right hand side: 			From now on, although we mostly speak of helicity, we actually deal with current helicity for convenience and bear in mind that $\hat{H}(k)$ is easily convertible to $\hat{R}_{H}(k)$ using \ref{finalcurhel}) )."
 A more detailed analysis of all these relations can be found in?.., 			A more detailed analysis of all these relations can be found in \citet{1978mfge.book.....M}.
 For the magnetic energy density in 1D Fourier space. a broken power-law is assumed in the following in our examples by adopting usually with =2 and Κα=I if not stated otherwise. but with differentspectral indices a.," 			 			For the magnetic energy density in 1D Fourier space, a broken power-law is assumed in the following in our examples by adopting 			usually with $\beta=2$ and $k_{0}=1$ if not stated otherwise, but with different spectral indices $\alpha$."
 The low-X asymptotic egxK corresponds to a white noise spectrum without correlations on scales larger than 1/Ko., The $k$ asymptotic $\epsilon_{B}\approx k^2$ corresponds to a white noise spectrum without correlations on scales larger than $1/k_{0}$.
 For large k. we find ep«K. eventually becoming a Kolmogorov-spectrum for @=5/3.," For large $k$, we find $\epsilon_{B}\propto k^{-\alpha}$, eventually becoming a Kolmogorov-spectrum for $\alpha=5/3$."
 When ever necessary. we can alw.ays: model the helicity power spectrum as H(k)=-ἄτεμ)canEq)€p(k). where AK) is a function between —] and 1.," 			 			When ever necessary, we can always model the helicity power spectrum as $\hat{H}(k)=-\frac{\pi^2}{k^3} \epsilon_{H}(k)=\frac{\pi^2}{k^3} h(k) \epsilon_{B}(k)$, where $h(k)$ is a function between $-1$ and $1$."
 This be seen from and the fact that the matrix A;; must be positive definite., This can be seen from 			and the fact that the matrix $A_{ij}$ must be positive definite.
 We adopt k=Κον without loss of generality and find the characteristic polynomial of A;; to be This yields that //€[-1.1].," We adopt $\fe{k}=k e_{x}$ without loss of generality and find the characteristic polynomial of $A_{ij}$ to be 			This yields that $h \in \left[-1,1 \right]$."
 The correlation functions of our observables can be calculated ina general and consistent way which we want to present now., 			The correlation functions of our observables can be calculated in a general and consistent way which we want to present now.
 Before we start. some general remarks about the mathematics are in place.," 			 			Before we start, some general remarks about the mathematics are in place."
 Throughout this study an expression such as JB relates to a multidimensional scalar product: This definition. includes a discrete summation. over indices as well as a continuous integral over position space., 			Throughout this study an expression such as $\textbf{J}^{\dagger}\textbf{B}$ relates to a multidimensional scalar product: 			This definition includes a discrete summation over indices as well as a continuous integral over position space.
 ihe ;ssnfpytétrié properties of matrix objects defined over a SPARSE AR à pealar product (28)) reflect the appearance of discrete summation and continous integration., The symmetric properties of matrix objects defined over a space with a scalar product \ref{multiscalar}) ) reflect the appearance of discrete summation and continous integration.
 Therefore. a matrix element M;;(x.v) is called symmetric (or hermitian for complex quantities). if 1t is symmetric under a transposition of its indices under an interchange of its vectors r: Thus. a symmetrised element is expressed as where r2y—x.," Therefore, a matrix element $M_{ij}(\fe{x},\fe{y})$ is called symmetric (or hermitian for complex quantities), if it is symmetric under a transposition of its indices under an interchange of its vectors $\fe{r}$: 			Thus, a symmetrised element is expressed as 			where $\fe{r}=\fe{y}-\fe{x}$."
 In the case where a matrix element is only symmetrised for index transposition. we call itsynnetric:: This distinction between symmetric and index-symmetric is important. because it takes care of subtleties that could easily generate confusion.," In the case where a matrix element is only symmetrised for index transposition, we call it: 			This distinction between symmetric and index-symmetric is important, because it takes care of subtleties that could easily generate confusion."
 We like to emphasize the difference between both symmetry operations. when applied to the magnetic correlation. tensor (8)).," We like to emphasize the difference between both symmetry operations, when applied to the magnetic correlation tensor \ref{al:M}) )."
 The tensor contains an intrinsic symmetric and an intrinsic antisymmetric element., The tensor contains an intrinsic symmetric and an intrinsic antisymmetric element.
 Regarding (30)). the intrinsic antisymmetric part is preserved. whereas regarding (31)) it is not.," Regarding \ref{al:sym}) ), the intrinsic antisymmetric part is preserved, whereas regarding \ref{al:insym}) ) it is not."
 This is of paramount relevance. since information on the helical power spectrum is only preserved. if the intrinsic antisymmetric parts do not cancel out during calculations.," This is of paramount relevance, since information on the helical power spectrum is only preserved, if the intrinsic antisymmetric parts do not cancel out during calculations."
 Furthermore. we like to introduce the functional derivative. which is the natural generalisation of a derivative to function. vector spaces.," 			 			Furthermore, we like to introduce the functional derivative, which is the natural generalisation of a derivative to function vector spaces."
 Its precise definition Is (see ?):: For convenience and to avoid confusion with the delta function. we sometimes adopt easier notations: Now we proceed. presenting the framework of the calculations.," Its precise definition is \citep[see][]{1995iqft.book.....P}: : 			For convenience and to avoid confusion with the delta function, we sometimes adopt easier notations: 			 			Now we proceed, presenting the framework of the calculations."
 The general evaluation of the expectation value of a function X of observables forGaussian magnetic. field statistics with covariance matrix M and its determinant [M] is, The general evaluation of the expectation value of a function $X$ of observables forGaussian magnetic field statistics with covariance matrix $M$ and its determinant $|M|$ is
Figure 7 illustrates how the meclian lifetimes of planets «M4 various masses. all formed. at rs=LOAU in the MMSN aud in the alpha disk. are allectec by Changes iu the uormalizatiou of torque fluctuations. e.,"Figure \ref{fig:medlMp} illustrates how the median lifetimes of planets of various masses, all formed at $r_S=10\au$ in the MMSN and in the alpha disk, are affected by changes in the normalization of torque fluctuations, $\epsilon$."
 For the nominal e=0.5 vaue. ¢iffusio1 jostly affects the orbital evolution of the lower mass planets. and reduces somewhatt reir ineclian lietimes.," For the nominal $\epsilon =0.5$ value, diffusion mostly affects the orbital evolution of the lower mass planets, and reduces somewhat their median lifetimes."
 This resilts from the larger values Of finie at lower planet mass. whereas /clill ls] Ldepeucdent o[ planet mass.," This results from the larger values of $t_{\rm mig}$ at lower planet mass, whereas $t_{\rm diff}$ is independent of planet mass."
 As e is increased. cifsion progressively dominates and the cistictiOL anolg jxanets of variot5 lasses 8‘actually disaypears.," As $\epsilon$ is increased, diffusion progressively dominates and the distinction among planets of various masses gradually disappears."
" For large enough values of e. the meciai lifetime of all planets wilh masses AL,τς104 formed at ry=10AU Is reduced below typic:il diskX lifetimes."," For large enough values of $\epsilon$, the median lifetime of all planets with masses $M_p \lesssim 10 M_\oplus$ formed at $r_S=10 \au$ is reduced below typical disk lifetimes."
 As in the previous figure. |owevel. the lifetimes for e>>1 in the alpha disk are dominaed by the diffiinion time at the inner bouudary.," As in the previous figure, however, the lifetimes for $\epsilon\gg 1$ in the alpha disk are dominated by the diffusion time at the inner boundary."
 As anticipated by1)..[).. and (2005).. w Fokker-Plauck treatment confirms that (fusion driveu by urbuleut torque fluctuations iu ‘oto-planetary disks cau grealy iulluence tie. orbital evolutio1 of embedded: low-mass ," As anticipated by, and , our Fokker-Planck treatment confirms that diffusion driven by turbulent torque fluctuations in proto-planetary disks can greatly influence the orbital evolution of embedded low-mass proto-planets."
Coutrary to some expec‘ations. cliffusion does not promoe planetary survival but insteact systematically reduces the lifetime of most platets in the disk.," Contrary to some expectations, diffusion does not promote planetary survival but instead systematically reduces the lifetime of most planets in the disk."
 However. it does help a small fraction jxlanets diffuse to large radii where they ca1 survive [or extened periods. (," However, it does help a small fraction of planets diffuse to large radii where they can survive for extended periods. ("
We consider that a ret “survives” if its orbit remaius lareer thau the inner edge o “tle disk.),We consider that a planet “survives” if its orbit remains larger than the inner edge of the disk.)
 Our 'esults poiut to a potentialy ---uportal1 role for uou-deterijiinistic effects iu planet formation sce141105., Our results point to a potentially important role for non-deterministic effects in planet formation scenarios.
 Iu models with a siguificant evel of diffusion. most proto-plane siu the Earth-mass rauge could eud up being accreted by their stalls. while only a small fr:iction of them would survive by Πας ) arge radii.," In models with a significant level of diffusion, most proto-planets in the Earth-mass range could end up being accreted by their stars, while only a small fraction of them would survive by diffusing to large radii."
 Iu scelarios wlere all proto-plauetary disks a'e elficieut at formiug planets. his could be interpreted as leacdii& τς) ouly a fractiou of all potenti allost stars beiug successtul in keeping a system of surviving planes.," In scenarios where all proto-planetary disks are efficient at forming planets, this could be interpreted as leading to only a fraction of all potential host stars being successful in keeping a system of surviving planets."
 Even systens startie with very similar iuitial concditious may eud up with very differeiit planetary orbital configuratios once their gaseous clisss disappear., Even systems starting with very similar initial conditions may end up with very different planetary orbital configurations once their gaseous disks disappear.
 Neelecting the effects ο irect. gravitational iueractios between proto-plaues. which are ikely to |appeu trom clilferertla Iies of migrallon alcL diffusiοι is one of many mocel litmitatious in OUL woT.," Neglecting the effects of direct gravitational interactions between proto-planets, which are likely to happen from differential rates of migration and diffusion, is one of many model limitations in our work."
 We have already mentioned that «UL stucy dns resqcted to proto-plauets «of low enough jasses that they do not alfect iv way the structwe of the ‘host disk., We have already mentioned that our study is restricted to proto-planets of low enough masses that they do not affect in any way the structure of their host disk.
 This exeuces the late stages of plant planet formation. 'hic1 are obviously of considerabe interest.," This excludes the late stages of giant planet formation, which are obviously of considerable interest."
 La particular. it has een suggested that migration a iTISLOLL. eac1 iuclepencdently. edlId accelerate the rate of growth of cores uutil they reach the criical 1lass al whicl -—Ullaway elvelcype accretion occursb).," In particular, it has been suggested that migration and diffusion, each independently, could accelerate the rate of growth of cores until they reach the critical mass at which runaway envelope accretion occurs."
. Studyiugtjese possibilities within the context of global models such as ours would be iterest]ug., Studying these possibilities within the context of global models such as ours would be interesting.
 Even within the strict regime of aj»plicability of our models. sigificant uncertainties exist.," Even within the strict regime of applicability of our models, significant uncertainties exist."
 Let us mention a few., Let us mention a few.
 We have focused our work on strictly circular orbits., We have focused our work on strictly circular orbits.
 We have assumed that the uucerlyiug proto-planetary disk structwe does not evolve with time. aud that the amplitude 9X/X ," We have assumed that the underlying proto-planetary disk structure does not evolve with time, and that the amplitude $\delta\Sigma/\Sigma$ "
of dark matter halos. the divergence of X for 8:0.,"of dark matter halos, the divergence of $\Sigma$ for $\theta \longrightarrow 0$."
" One simple modification is to cut olf the distribution at small distances as follows: where 6, is a core radius within which the surface mass density [lattens olf to a value αυ=Ge/26.: it can be seen that the projected mass distribution behaves like the SIS for 9x»8.", One simple modification is to cut off the distribution at small distances as follows: where $\theta_c$ is a core radius within which the surface mass density flattens off to a value $\kappa_0=\theta_E/2\theta_c$; it can be seen that the projected mass distribution behaves like the SIS for $\theta \gg \theta_c$.
" Phe Hexion due to this distribution is For 6x6, the Dexion is approximately equal to that of the SIS.", The flexion due to this distribution is For $\theta \gg \theta_c$ the flexion is approximately equal to that of the SIS.
 Llowever. at small separations the Ilexion goes to zero. as should be expected as the convergence is tending to a maximuni.," However, at small separations the flexion goes to zero, as should be expected as the convergence is tending to a maximum."
" The second Hexion is more complicated: but may reaclily be fit to observed data. and can again be seen to reduce to the SIS second Hexion when 6δρ6, and goes to zero at the centre of the lens."," The second flexion is more complicated: but may readily be fit to observed data, and can again be seen to reduce to the SIS second flexion when $\theta \gg \theta_c$ and goes to zero at the centre of the lens."
 Using N-bods simulations. Navarro. Erenk White (1995. 1996. 1997) have shown that the equilibrium density. profiles of cold dark matter (CDAI) halos ean be well fitted over two orders of magnitude in radius by the formula where the radial coordinate ος is the radius in units of a scaling radius r; such that we—rfr; posu(2) is the critical densitv for closure at the epoch of the halo. and A. is a dimensionless scaling density.," Using N-body simulations, Navarro, Frenk White (1995, 1996, 1997) have shown that the equilibrium density profiles of cold dark matter (CDM) halos can be well fitted over two orders of magnitude in radius by the formula where the radial coordinate $x$ is the radius in units of a scaling radius $r_s$ such that $x \equiv r/r_s$, $\rho_{crit}(z)$ is the critical density for closure at the epoch of the halo, and $\Delta_c$ is a dimensionless scaling density."
 VPhis profile describes the simulation halos accurately over a broad. mass range 3.10cAbuΔΙ.<321077. Mono being the total mass of the halo contained within the sphere encompassing a mean overdensity. of 200 times the critical density. gos;(2).," This profile describes the simulation halos accurately over a broad mass range $3 \times 10^{11}
< M_{200}/M_{\odot} < 3 \times 10^{15}$, $M_{200}$ being the total mass of the halo contained within the sphere encompassing a mean overdensity of 200 times the critical density $\rho_{crit}(z)$."
 The racius of this sphere. designated by. reoy. is used to define a second dimensionless scaling parameter. for the NEW profile. namely the concentration e=ουςrs.," The radius of this sphere, designated by $r_{200}$, is used to define a second dimensionless scaling parameter for the NFW profile, namely the concentration $c=r_{200}/r_s$."
 However. the details of the NEW cdelinitions have been implemented. in several wavs in theliterature: Appendix A presents further discussion of the various definitions.," However, the details of the NFW definitions have been implemented in several ways in theliterature; Appendix A presents further discussion of the various definitions."
 A procedure for finding values of A. and c which agree with the numerical simulations is detailed by Navarro et al. C, A procedure for finding values of $\Delta_c$ and $c$ which agree with the numerical simulations is detailed by Navarro et al. (
Xppendix. 1997): the parameters are somewhat complicated. functions of the halo redshift and. Aooo. along with the background. cosmology.,"Appendix, 1997): the parameters are somewhat complicated functions of the halo redshift and $M_{200}$, along with the background cosmology."
 A routine. (charden.f) which carries out these caleulations ancl outputs values for these scaling parameters has been mace available by Julio Navarro athttp://pinot., A routine ) which carries out these calculations and outputs values for these scaling parameters has been made available by Julio Navarro at.
phys.uvic.ca/jfn/charden.. The NEW density profile implies the following form for the cimensionless surface mass density (Bartclmann 1996): where we define &;=poutz)hNor;/Mu and g=£fr.. with £ defined as for equation (24)).," The NFW density profile implies the following form for the dimensionless surface mass density (Bartelmann 1996): where we define $\kappa_s=\rho_{crit}(z)\Delta_c r_s/\Sigma_{crit}$ and $y\equiv \xi/r_s$, with $\xi$ defined as for equation \ref{sigsis}) )."
" The function. f(y) is eiven by The flexion for the NEW density. profile is then given by Delining JF.—ας{λ we then have with jy—ον,=06/0.. and where. from equation (38)) The analvtical form ofthe second. [lexion can also be found. using the fact that for axially symmetric. projected mass profiles the magnitude of the shear can be caleulated from |s(0)]=&(9)R(OÓ). where &(06) is the mean surface mass clensity within a circle of radius 6 from the lens centre (see e.g. Bartelmann Schneider 2001)."," The function $f(y)$ is given by The flexion for the NFW density profile is then given by Defining $\mathcal F \it _s \equiv \kappa_s D_l / r_s $ we then have with $y=\theta D_l/r_s = \theta / \theta_s$, and where, from equation \ref{fnfw}) ), The analytical form ofthe second flexion can also be found, using the fact that for axially symmetric projected mass profiles the magnitude of the shear can be calculated from $|\gamma(\theta)|=\bar{\kappa}(\theta)-\kappa(\theta)$, where $\bar{\kappa}(\theta)$ is the mean surface mass density within a circle of radius $\theta$ from the lens centre (see e.g. Bartelmann Schneider 2001)."
" Wrieht Brainerd (2000) used this method to find an expression for the magnitude of shear due to an NEW halo. ancl their result. can be used. to lind the derivatives of shear 541,4. 515 etc."," Wright Brainerd (2000) used this method to find an expression for the magnitude of shear due to an NFW halo, and their result can be used to find the derivatives of shear $\gamma_{1,1}$, $\gamma_{1,2}$ etc."
 Combining these derivatives as directed. by equation (20)) we see that. the second [exion takes the form To illustrate these results. we calculate the first. and second Dexion signals we might expect to measure for a ealaxv-sized. halo with an NEN. profile.," Combining these derivatives as directed by equation \ref{eqn:fg}) ) we see that the second flexion takes the form where To illustrate these results, we calculate the first and second flexion signals we might expect to measure for a galaxy-sized halo with an NFW profile."
 We choose a lens redshift z;=0.35 and the halo Aou)=11075.AL. this lens redshift being the median of the lens galaxy sampleused by Llockstra et al. (," We choose a lens redshift $z_l =0.35$ and the halo $M_{200}=1\times 10^{12} h^{-1}M_{\odot}$, this lens redshift being the median of the lens galaxy sampleused by Hoekstra et al. ("
2004). and the mass having been found to be roughly typical for galaxy halos in weak lensing analyses bv Brainerd οἱ al. (,"2004), and the mass having been found to be roughly typical for galaxy halos in weak lensing analyses by Brainerd et al. ("
1996) and Llockstra et al. (,1996) and Hoekstra et al. (
2004).,2004).
" We also choose 1ο.=0.5 (corresponding to a source redshift of z,2 OLS) and mocdel the lensing within a standard. Lat ACDAL cosmology. setting the present-day matter density parameter Q,,.5= 0.3. Oy= 0.7.the Hubble. parameter h=0.72 and ox= 0.5."," We also choose $D_{ls}/D_s = 0.5$ (corresponding to a source redshift of $z_s \approx 0.8$ ) and model the lensing within a standard, flat $\Lambda$ CDM cosmology, setting the present-day matter density parameter $\Omega_{m,0}=0.3$ , $\Omega_\Lambda = 0.7$ ,the Hubble parameter $h=0.72$ and $\sigma_8 = 0.8$ ."
 Using these values and. Navarro’s we find a concentration of e=7.20 and a corresponding climensionless, Using these values and Navarro's we find a concentration of $c=7.20$ and a corresponding dimensionless
"Their measured wavelengths are respectively 4865.7, 4963.5 and 5011.4A.","Their measured wavelengths are respectively 4865.7, 4963.5 and 5011.4."
" Comparing with their respective rest frame wavelength of 4861.3, 4958.9 and 5006.7A (e.g.Grovesetal.2002;Dopita&Sutherland2003,andreferences therein),, we deduce the heliocentric radial velocity for the interstellar gas surrounding the SNR to be 275+4 km s~!."," Comparing with their respective rest frame wavelength of 4861.3, 4958.9 and 5006.7 \citep[e.g.][and references therein]{Groves02, Dopita2003}, we deduce the heliocentric radial velocity for the interstellar gas surrounding the SNR to be $\pm$ 4 km $^{-1}$."
" Our measured LMC radial velocity is consistent with the previously observed value of ~260 km s-! (see,e.g.Staveley-Smith1997;vanderMarel,Alves,Hardy&Suntzeff 2002)."," Our measured LMC radial velocity is consistent with the previously observed value of $\sim$ 260 km $^{-1}$ \citep[see, e.g.][]{Staveley-Smith97,Marel02}."
". Clearly, the de-blended spectrum Figure 2 panel (c) is free of any 4959 [O III] line contribution."," Clearly, the de-blended spectrum Figure \ref{fig:spectrum} panel (c) is free of any 4959 [O III] line contribution."
 The main issue here though is that the line is also affected by this procedure., The main issue here though is that the $\beta$ line is also affected by this procedure.
" In our dynamical analysis presented in Section ??,, we have used the raw data cube to examine the velocity structure in the Hf line, and the de-blended cube for the analysis of the [O III] line."," In our dynamical analysis presented in Section \ref{sec:orich}, we have used the raw data cube to examine the velocity structure in the $\beta$ line, and the de-blended cube for the analysis of the [O III] line."
 In Fig., In Fig.
 3 we present a velocity map of SNR N132D using the [O III] A 5007 forbidden line., \ref{fig:vmap} we present a velocity map of SNR N132D using the [O III] $\lambda$ 5007 forbidden line.
" Each panel covers a velocity range of Av,;=425 km s-!, with exception to the zero velocity panel, which covers the smaller range of Av,—240 km s~!."," Each panel covers a velocity range of $\Delta v_r$ =425 km $^{-1}$ , with exception to the zero velocity panel, which covers the smaller range of $\Delta v_r$ =240 km $^{-1}$."
 Several individual O-rich knots can be identified in the various panels., Several individual O-rich knots can be identified in the various panels.
" In the zero-velocity panel, the so-called (Morseetal.1996) feature associated with the interaction of the SNR. with a large cloud in the surrounding ISM is clearly seen in the NE sector of the remnant (the extended and very bright curved structure)."," In the zero-velocity panel, the so-called \citep[][]{Morse96} feature associated with the interaction of the SNR with a large cloud in the surrounding ISM is clearly seen in the NE sector of the remnant (the extended and very bright curved structure)."
 The western rim of the remnant associated with the blast wave can be identified to the NW., The western rim of the remnant associated with the blast wave can be identified to the NW.
" As for the other panels, blue-shifted material is detected with velocities up to ~-2800 km s-!, while red-shifted velocities range up to ~+1800 km s~!."," As for the other panels, blue-shifted material is detected with velocities up to $\sim$ -2800 km $^{-1}$, while red-shifted velocities range up to $\sim$ +1800 km $^{-1}$."
 The different clumps tend to trace elongated filaments with a small curvature along them., The different clumps tend to trace elongated filaments with a small curvature along them.
" In that respect, the Lasker's Bowl feature at <Av, >= 0 to 332 km s! is an exception - being of comparatively larger size and unconnected with the system of high velocity filaments."," In that respect, the Lasker's Bowl feature at $<\Delta v_r>$ = 0 to 332 km $^{-1}$ is an exception - being of comparatively larger size and unconnected with the system of high velocity filaments."
 'The O-rich clumps do not cover the whole velocity space., The O-rich clumps do not cover the whole velocity space.
" On the blue side especially, the panel with Av, >= -757 km s! shows a gap in the the distribution of strong emitting knots, while they are apparent once again in the panels with <Av, >= -1182, -1607, -2032 and -2457 km s~!."," On the blue side especially, the panel with $<\Delta v_r>$ = -757 km $^{-1}$ shows a gap in the the distribution of strong emitting knots, while they are apparent once again in the panels with $<\Delta v_r>$ = -1182, -1607, -2032 and -2457 km $^{-1}$."
 There exists a general trend for the O-rich filaments to spread along the NE-SW direction., There exists a general trend for the O-rich filaments to spread along the NE-SW direction.
" In the rest of this paper, we will adopt the labeling convention of Morse,Winkler&Kirshner(1995) to refer to the various O-rich clumps."," In the rest of this paper, we will adopt the labeling convention of \cite{Morse95} to refer to the various O-rich clumps."
" These knots are labelled with the names given by Morse,WinklerKirshner(1995) in the left-hand panel of Fig. 4..", These knots are labelled with the names given by \cite{Morse95} in the left-hand panel of Fig. \ref{fig:above}.
" Although the oxygen-rich ejecta show a systemic blueshift of ~—400 km s-!, this is not thought to be significant."," Although the oxygen-rich ejecta show a systemic blueshift of $\sim -400$ km $^{-1}$, this is not thought to be significant."
 The instantaneous and accidental spatial distribution of the clumpy ejecta that happen to be passing through the reverse shock will determine whether there is a systematic line shift., The instantaneous and accidental spatial distribution of the clumpy ejecta that happen to be passing through the reverse shock will determine whether there is a systematic line shift.
" Since the fast-moving clumps do not cover the whole velocity space, it is clear that their spatial distribution is very patchy and incomplete."," Since the fast-moving clumps do not cover the whole velocity space, it is clear that their spatial distribution is very patchy and incomplete."
" In the velocity map of Fig. 3,, ["," In the velocity map of Fig. \ref{fig:vmap}, ["
O III] A5007 emission is plotted.,O III] $\lambda$ 5007 emission is plotted.
" However, several knots within N132D have already been identified as also containing hydrogen (e.g.Morseetal.1996)."," However, several knots within N132D have already been identified as also containing hydrogen \citep[e.g.][]{Morse96}."
". Unlike some other young SNR, such as 1E 0102.2-7219 in the SMC (Vogt&Dopita2010a), SNR N132D appears to be experiencing strong interactions with a highly clumpy surrounding interstellar medium."," Unlike some other young SNR, such as 1E 0102.2-7219 in the SMC \citep{Vogt10a}, SNR N132D appears to be experiencing strong interactions with a highly clumpy surrounding interstellar medium."
" Whether these clumps are fragments of the ISM which surrounded the supernova progenitor at its birth, or whether they arose from stellar mass-loss and subsequent interactions with a fast pre-supernova Wolf-Rayet wind, or a combination of the two, is yet to be determined."," Whether these clumps are fragments of the ISM which surrounded the supernova progenitor at its birth, or whether they arose from stellar mass-loss and subsequent interactions with a fast pre-supernova Wolf-Rayet wind, or a combination of the two, is yet to be determined."
" In the X-ray, the clumpy nature of these interactions can be seen in the broken structure of the outer shell (e.g. 2008)."," In the X-ray, the clumpy nature of these interactions can be seen in the broken structure of the outer shell \citep[e.g.][]{Borkowski07,Xiao08}."
". Here, we have used the presence of H emission to identify and locate knots excited by ISM cloud shocks rather than being the result of high-velocity stellar ejecta."," Here, we have used the presence of $\beta$ emission to identify and locate knots excited by ISM cloud shocks rather than being the result of high-velocity stellar ejecta."
" T'his line is conveniently located close from the [O III] A 5007 line and can only be emitted in the shocked ISM, not the oxygen-rich ejecta."," This line is conveniently located close from the [O III] $\lambda$ 5007 line and can only be emitted in the shocked ISM, not the oxygen-rich ejecta."
" In the left hand panel of Fig. 4,,"," In the left hand panel of Fig. \ref{fig:above},"
 we plot the oxygen emission., we plot the oxygen emission.
" In this plot, the intensity scale is scaled linearly from 18 counts per pixel (blue) - up to 60 counts per pixel (green)."," In this plot, the intensity scale is scaled linearly from 18 counts per pixel (blue) - up to 60 counts per pixel (green)."
" Low velocity gas, with radial velocity -100 km s! € v, < 100 km s! has been removed in order avoid filling the plane and obscuring the O-rich knots."," Low velocity gas, with radial velocity -100 km $^{-1}$ $\leq$ $_r$ $\leq$ 100 km $^{-1}$ has been removed in order avoid filling the plane and obscuring the O-rich knots."
" The Morse,Winkler&Kirshner(1995) names of each of the O-rich knots are also shown.", The \cite{Morse95} names of each of the O-rich knots are also shown.
 The right plot also includes the Hj emission using a red-yellow color ramp., The right plot also includes the $\beta$ emission using a red-yellow color ramp.
" For this too, the counts per pixel range from 18 to 60."," For this too, the counts per pixel range from 18 to 60."
" Each point is given a transparency of 0.1, so as torender visible superimposed knots."," Each point is given a transparency of 0.1, so as torender visible superimposed knots."
" We have alsoidentified the field stars from the continuum image as black rings, to avoid confusion with small emission knots."," We have alsoidentified the field stars from the continuum image as black rings, to avoid confusion with small emission knots."
" We also plot for information the two suggested centers of the SNR. from Morse,Winkler&Kirshner : the black star, located at (a= 52502.57; ὃ= —69?38'34""), marks the center of the O-rich knots"," We also plot for information the two suggested centers of the SNR from \cite{Morse95} : the black star, located at $\alpha=5^h25^m02.^s7$ ; $\delta=-69^{\circ}38^\prime34^{\prime\prime}$ ), marks the center of the O-rich knots"
as fji obtained in a sinele componcut fit. but the temperature of the second component is found to be very πια (less than 0.1. keV. at 30 level).,"as that obtained in a single component fit, but the temperature of the second component is found to be very small (less than 0.1 keV at $3\sigma$ level)."
 Thus. we recover the previous results based on the PSPC data reported iu Lima Neto ct al. (," Thus, we recover the previous results based on the PSPC data reported in Lima Neto et al. ("
1997). in particular their 2-tceuperatiure fit o| the central region. with the cooler component at T=10c0.03 keV (see Table 2 iu their paper).,"1997), in particular their 2-temperature fit of the central region, with the cooler component at $T=0.10\pm0.03$ keV (see Table 2 in their paper)."
 Since the ceutral cD galaxy is also a radio source (as can be seen in Fig. 1)), Since the central cD galaxy is also a radio source (as can be seen in Fig. \ref{fig:regionsBeppo}) )
 we have tried a ft with a thermal component aud a power law. in order to model an eventual non-thermal XN-rav source (e.g. an Iuverse Compton scattering of relativistic clectrous with the nücrowave backerouud photons).," we have tried a fit with a thermal component and a power law, in order to model an eventual non-thermal X-ray source (e.g. an Inverse Compton scattering of relativistic electrons with the microwave background photons)."
 However. the inclusion," However, the inclusion"
reactor mixing angle 644 |11].,reactor mixing angle $\theta_{13}$ \cite{11}.
". Recently. the T2Ik collaboration has observed possible indications of the rj,—r, appearance and reported the following ranges for 645 [12] αἱ 90% C.L.. Moreover. the best fit value of 644 is found to be θ229.77 for NIL and 0458211 of ILE. thus. implying large deviations from 644=0 in the above mentioned mixing scenarios."," Recently, the T2K collaboration has observed possible indications of the $\nu_{\mu}\rightarrow\nu_{e}$ appearance and reported the following ranges for $\theta_{13}$ \cite{12}
 at $90\%$ C.L.. Moreover, the best fit value of $\theta_{13}$ is found to be $\theta_{13}\approx9.7^o$ for NH and $\theta_{13}\approx11^o$ of IH, thus, implying large deviations from $\theta_{13}=0^o$ in the above mentioned mixing scenarios."
 Therefore. it becomes important to develop a parametrization of the lepton mixing matrix in which such deviations are manifest.," Therefore, it becomes important to develop a parametrization of the lepton mixing matrix in which such deviations are manifest."
 A natural possibility to obtain a phenomenologically viable neutrino mixing matrix aud to generate non-zero θ and non-maximal 854 is to assiune that these deviations come [rom the charged lepton sector., A natural possibility to obtain a phenomenologically viable neutrino mixing matrix and to generate non-zero $\theta_{13}$ and non-maximal $\theta_{23}$ is to assume that these deviations come from the charged lepton sector.
 Such an assumption has been mace earlier to generate deviations [rom bimaximal mixing |13.14) and tribimaximal mixing |15.16.17.Ls).," Such an assumption has been made earlier to generate deviations from bimaximal mixing \cite{13,14} and tribimaximal mixing \cite{15,16,17,18}."
 A general 3x3 matrix contains 3 moduli and 6 phases [19] and can be represented as where P = diag(1.e*.62) and Q = diag(Loe’.6/72) are diagonal phase matrices having (wo phases each. U is the matrix containing 3 angles and one phase and has the form of C (except for the phase matrix o) in Eq.(2).," A general $\times$ 3 matrix contains 3 moduli and 6 phases \cite{19} and can be represented as where $P$ = $(1,e^{i \phi_1},e^{i \phi_2})$ and $Q$ = $(1,e^{i \rho_1},e^{i \rho_2})$ are diagonal phase matrices having two phases each, $\tilde{U}$ is the matrix containing 3 angles and one phase and has the form of $U$ (except for the phase matrix $\wp$ ) in Eq.(2)."
 In general. when charged leptons also contribute to the mixing. the lepton mixing matrix contains 6 real parameters and six phases |14].," In general, when charged leptons also contribute to the mixing, the lepton mixing matrix contains 6 real parameters and six phases \cite{14}."
". As pointed out earlier the two Majorana phases are unlikelv to be measured in (he present and the forthcoming experiments. so that we may dispense with the Majorana phases at least for the present by considering (he Hermitian products AbAt and M,Mj."," As pointed out earlier the two Majorana phases are unlikely to be measured in the present and the forthcoming experiments, so that we may dispense with the Majorana phases at least for the present by considering the Hermitian products $M_l M_l^{\dagger}$ and $M_\nu M_\nu^{\dagger}$."
 Here. (wo points are in 1.)," Here, two points are in 1.)"
" Since we are considering mass independent textures of the neutrino mass matrix. thus. M, and 1M,MZ are diagonalized by the same diagonalizing matrix. so we can consider the product A,A. 2.)"," Since we are considering mass independent textures of the neutrino mass matrix, thus, $M_\nu$ and $M_\nu M_\nu^{\dagger}$ are diagonalized by the same diagonalizing matrix, so we can consider the product $M_\nu M_\nu^{\dagger}$ 2.)"
 The deviations of the charged lepton mass matrix from diagonal matrix are in any case considered to be arbitrary so the choice of product MMJ can be, The deviations of the charged lepton mass matrix from diagonal matrix are in any case considered to be arbitrary so the choice of product $M_l M_l^{\dagger}$ can be
"ας Εν which expresses how much perturbations of a eiven mass have grown at time /. and a geometrical function Gmi)dm, whieh encodes how many fragments of a given mass will fit on the shell.","$I_{\rm f}(m_{\rm f},t)$ ), which expresses how much perturbations of a given mass have grown at time $t$, and a geometrical function $\mathcal{G}(m_{\rm f})$ $m_{\rm f}$ which encodes how many fragments of a given mass will fit on the shell."
 We may then write The fragmentation integral is simply. defined as no. ∖∖⋎↓↥∢⊾↓⋅⋖⋅∣⇜∩↿∖⋯↓⊳∣∃↓⊳∖↿↓↥⋖⋅↓⊔⊳∖↿⋜⋯↿⋜⋯⋖⊾∪⊔⊳∖. erowth rale οἱ the mode corresponding to mg and fy is the time at which fragmentation The derivation of the function G(r Jey is the point at which we depart from the methodology of ?..," We may then write The fragmentation integral is simply defined as where $\omega(m_{\rm f},t^{\prime})$ is the instantaneous growth rate of the mode corresponding to $m_{\rm f}$ and $t_{0}$ is the time at which fragmentation The derivation of the function $\mathcal{G}(m_{\rm f})$ $m_{\rm f}$ is the point at which we depart from the methodology of \cite{2001A&A...374..746W}."
 It is not clear to us that an analytic expression for G(mi)dmi may be founcl since. on the reasonable assumption that fragments may not overlap cach other. the number of objects of any given wavenumber that may be accommodated by the shell depends on how much. space has already. been consumed. by other fragments.," It is not clear to us that an analytic expression for $\mathcal{G}(m_{\rm f})$ $m_{\rm f}$ may be found since, on the reasonable assumption that fragments may not overlap each other, the number of objects of any given wavenumber that may be accommodated by the shell depends on how much space has already been consumed by other fragments."
 We therefore. adopted. a Alonte Carlo approach in an attempt to derive a analvtic approximation to Gry dmi. We assume that fragments are circles., We therefore adopted a Monte Carlo approach in an attempt to derive a semi--analytic approximation to $\mathcal{G}(m_{\rm f})$ $m_{\rm f}$ We assume that fragments are circles.
 We took a unit square (the shape of the area to be filled is largely irrelevant. since circles do not tesselate) and populated it with circles chosen uniformly in main.asas]. my being the mass of a circle ancl proportional to its area.," We took a unit square (the shape of the area to be filled is largely irrelevant, since circles do not tesselate) and populated it with circles chosen uniformly in $\left[m_{\rm min},m_{\rm max}\right]$, $m_{\rm f}$ being the mass of a circle and proportional to its area."
 We forbade overlapping and continued. until the square was covered up to a factor f by circles., We forbade overlapping and continued until the square was covered up to a factor $f$ by circles.
 We then constructed histograms of the population of circles., We then constructed histograms of the population of circles.
 In Figure. 1. we show the result. of one. such experiment in which f=0.8 ancl miis.Mines are 10? and 10I respectively.," In Figure \ref{fig:circles} we show the result of one such experiment in which $f=0.8$ and $m_{\min},m_{\rm max}$ are $\times10^{-5}$ and $\times10^{-1}$ respectively."
 In Figure 2.. we show the power laws resulting from. hundreds. of such experiments in which we varied f.," In Figure \ref{fig:circles_mf}, we show the power laws resulting from hundreds of such experiments in which we varied $f$."
 Varving the covering factor allects the lowmass end of the mass spectrum. which turns over at small masses due to underrepresentation of small circles.," Varying the covering factor affects the low–mass end of the mass spectrum, which turns over at small masses due to underrepresentation of small circles."
 Achieving higher covering factors requires more small circles ancl pushes the turnover towards smaller masses., Achieving higher covering factors requires more small circles and pushes the turnover towards smaller masses.
 At the high.mass end of the mass function. the mass function. becomes noisy.," At the high–mass end of the mass function, the mass function becomes noisy."
 Llowever. in between these limits. the slope of the function is very robust.," However, in between these limits, the slope of the function is very robust."
" We find that the population of circles can be well approximated by LNxmj7πας, Armed. with this result we may write An analytic expression for the fragmentation integral itself can be derived for the infinitesimally thin shell and is given in Appendix A in a climensionless form that can be applied to any thin shell.", We find that the population of circles can be well approximated by $N\propto m_{\rm f}^{-2.0}$ $m_{\rm f}$ Armed with this result we may write An analytic expression for the fragmentation integral itself can be derived for the infinitesimally thin shell and is given in Appendix A in a dimensionless form that can be applied to any thin shell.
 However. i0. ds somewhat cumbersome and we compute fragmentation integrals from. numerically integrating Equation 5r— using analvtic wavenumber growth rates for the thinshell and DAGLI models and compare the result to that computed from our ΙΤ simulations.," However, it is somewhat cumbersome and we compute fragmentation integrals from numerically integrating Equation \ref{eqn:if} using analytic wavenumber growth rates for the thin–shell and PAGI models and compare the result to that computed from our SPH simulations."
 We make use of the same SPILL code used in Paper Ll. a variant of that described in 2. but more recently updated ancl described in ?..," We make use of the same SPH code used in Paper I, a variant of that described in \cite{1990nmns.work..269B} but more recently updated and described in \cite{1995MNRAS.277..362B}."
 Phe fluid. equations are solved: using the SPIEL technique implementing the standard artificial viscosity. prescription described in νι with a=1. 3= 2.," The fluid equations are solved using the SPH technique implementing the standard artificial viscosity prescription described in \cite{1992ARA&A..30..543M}, with $\alpha=1$, $\beta=2$ ."
 The self gravity of the gas is included. using a binary tree., The self gravity of the gas is included using a binary tree.
 Crucially for these calculation. the code allows very high density regions to be replaced by pointmass sink particles. as described in ?..," Crucially for these calculation, the code allows very high density regions to be replaced by point–mass sink particles, as described in \cite{1995MNRAS.277..362B}."
 Once the density of a particle exceeds a threshold. set to 10.7 &g in these simulations. it ancl its =50 neighbours are considered. candidates for sink creation.," Once the density of a particle exceeds a threshold, set to $10^{-19}$ g $^{-3}$ in these simulations, it and its $\approx 50$ neighbours are considered candidates for sink creation."
 In order for a dense particle and its neighbours to be replaced by à sink. the group of particles must (a) constitute more than a thermal Jeans mass: (b) be contracting: (c) be bound.," In order for a dense particle and its neighbours to be replaced by a sink, the group of particles must (a) constitute more than a thermal Jeans mass; (b) be contracting; (c) be bound."
 Cas particles may subsequently be accreted by sink particles if they pass within the sink particles accretion radius and (a) are bound to the sink: (b) are more bound to that sink than to any other sink: (ο) do not have enough angular momentum to achieve a circular orbitaround. the, Gas particles may subsequently be accreted by sink particles if they pass within the sink particle's accretion radius and (a) are bound to the sink; (b) are more bound to that sink than to any other sink; (c) do not have enough angular momentum to achieve a circular orbitaround the
The distance to IACPN was estimated using two different methods.,The distance to IACPN was estimated using two different methods.
" Firstly. we used the extinction-distance technique (A,—D: c.f. ?2))"," Firstly, we used the extinction–distance technique $A_v - D$; c.f. \citealt{gathier86}) )"
 as implemented by ? for IPHAS data., as implemented by \cite{sale09} for IPHAS data.
" The A,— method is currently the only one which is capable of determining accurate (~ 30%) distances for a large number of PNe. being independent of statistical assumptions about the physies of the nebulae and/or of their central stars (2).."," The $A_v - D$ method is currently the only one which is capable of determining accurate $\sim 30\%$ ) distances for a large number of PNe, being independent of statistical assumptions about the physics of the nebulae and/or of their central stars \citep{giammanco11}."
 GAIA will hopefully improve this situation m the near future by providing hundreds of trigonometric PN distances., GAIA will hopefully improve this situation in the near future by providing hundreds of trigonometric PN distances.
" The A,—D curve towards the sightline of IACPN ο.=178.13. 4.04) was calculated using photometry of 3629 stars in a 10x10° box centred on the position of the PN and is shown in Fig. 4.."," The $A_v - D$ curve towards the sightline of IACPN $l,b = 178.13, -4.04$ ) was calculated using photometry of 3629 stars in a $10 \arcmin \times 10\arcmin$ box centred on the position of the PN and is shown in Fig. \ref{fig:4}."
 Most of the interstellar extinction builds up within the first kiloparsee. beyond which it remains roughly constant at 2.," Most of the interstellar extinction builds up within the first kiloparsec, beyond which it remains roughly constant at $A_V \sim 2$ ."
 We note that this behaviour is consistent with the extinction map of ? which gives anintegrated. Galactic extinction. of, We note that this behaviour is consistent with the extinction map of \citet{schlegel98} which gives anintegrated Galactic extinction of
to be one half thesfellar disc scale length.,to be one half the disc scale length.
 Because the gas is so much more raclially extended than the stars. this still resulted. in very thin disces.," Because the gas is so much more radially extended than the stars, this still resulted in very thin discs."
 One might think that as Long as fe ds small compared to the radial size of the dises its exact value would not be important., One might think that as long as $h_z$ is small compared to the radial size of the discs its exact value would not be important.
 However. as explained in (2000b) very thin clises have an increased cross section to being nearly edegc-on. which changes their kinematic properties.," However, as explained in \nocite{mspp:00}{ (2000b) very thin discs have an increased cross section to being nearly edge-on, which changes their kinematic properties."
 Thus the INS probabilities change non-trivially when we consider thinner discs with ὃν=0.14.., Thus the KS probabilities change non-trivially when we consider thinner discs with $h_z=0.1R_*$.
" We favour the model with 5h.=0.5/2, because these large discs are very likely to be warped bv interactions. and (1998) have shown that using a larger scale height has an cllect similar to including warps in the discs."," We favour the model with $h_z=0.5R_*$ because these large discs are very likely to be warped by interactions, and \nocite{pw:98}{ (1998) have shown that using a larger scale height has an effect similar to including warps in the discs."
 Increasing the disc thickness to 5h.=A; also has a non-neeligible clleet on the kinematics because thicker clises create a larger Ar for a single disc encounter., Increasing the disc thickness to $h_z=R_*$ also has a non-negligible effect on the kinematics because thicker discs create a larger $\delv$ for a single disc encounter.
 Fhus there is a Uracde-olL. and we see that we can reproduce the kinematics either with thinner disces with larger racial extent. or thicker dises with smaller racial extent.," Thus there is a trade-off, and we see that we can reproduce the kinematics either with thinner discs with larger radial extent, or thicker discs with smaller radial extent."
 We have assumed. that all the satellites are on circular orbits within the halo. which is clearly unrealistic.," We have assumed that all the satellites are on circular orbits within the halo, which is clearly unrealistic."
 To test the importance of this assumption we explore the opposite extreme. which is to assume that all satellites are on racial orbits.," To test the importance of this assumption we explore the opposite extreme, which is to assume that all satellites are on radial orbits."
" The potential of a SIS is (ir)=VqIn(r) so conservation of energy gives us πο where rj, is the maximum radius the satellite reaches.", The potential of a SIS is $\Phi(r)=V^2_c \ln(r)$ so conservation of energy gives us V_c where $r_m$ is the maximum radius the satellite reaches.
" From this one can compute that the time it takes for a satellite to travel from 7, to r is given by ra", From this one can compute that the time it takes for a satellite to travel from $r_m$ to $r$ is given by ).
"i and that the orbital period is 2=er,[Vo", and that the orbital period is $P=2\sqrt{2\pi}{{r_m}/{V_c}}$.
" We Line that the expression r(f)=9,(1THA£P) forO< bePSA is a reasonable fit to the true function (satellites spend less than of their time in the inner fourth of the orbit).", We find that the expression $r(t)=r_m(1-.75(4t/P))$ for $0<t<P/4$ is a reasonable fit to the true function (satellites spend less than of their time in the inner fourth of the orbit).
 We therefore use it to determine the probability distribution of satellites along their racial orbits., We therefore use it to determine the probability distribution of satellites along their radial orbits.
 From Table 3 we see tha assuming all racial orbits slightly. improves the statistics of our model and thus considering a true distribution of orbits will probably only increase the agreement between the data and our model. but not enough to rescue any of the unsuccessful mocdels.," From Table \ref{tbdep} we see that assuming all radial orbits slightly improves the statistics of our model and thus considering a true distribution of orbits will probably only increase the agreement between the data and our model, but not enough to rescue any of the unsuccessful models."
 As explained in section 3.1.. when halos merge the satellite galaxies are placed at a distance ον in units of the virial radius. from the centre of the new halo.," As explained in section \ref{sams}, when halos merge the satellite galaxies are placed at a distance $f_{mrg}$, in units of the virial radius, from the centre of the new halo."
 One might worry that this parameter. by influencing the position of satellite galaxies in the halo. may be crucial to our DLAS modeling.," One might worry that this parameter, by influencing the position of satellite galaxies in the halo, may be crucial to our DLAS modeling."
 To test this we try a model with firey set to 1.0 (instead. of the 0.5 as i has been up to now), To test this we try a model with $f_{mrg}$ set to 1.0 (instead of the 0.5 as it has been up to now).
 ‘This requires us to change the free parameters of the SAAIs to maintain the normalization of the reference galaxy. as described in SP.," This requires us to change the free parameters of the SAMs to maintain the normalization of the reference galaxy, as described in SP."
 The results of this model are shown in Table 3.., The results of this model are shown in Table \ref{tbdep}.
 Doubling this parameter results in only a modest change in the kinematic properties of DLAS., Doubling this parameter results in only a modest change in the kinematic properties of DLAS.
 Phis is because the important factor is the number of galaxies in the inner part of the halo (which will give rise to multiple intersections): satellites that start their infall from farther out still spend, This is because the important factor is the number of galaxies in the inner part of the halo (which will give rise to multiple intersections); satellites that start their infall from farther out still spend
We have obtained the first FUV (L000 9 1150 A)) spectra of the dilfuse radiation in an external galaxy using serendipitousFUSE observations of targets in the LMC.,We have obtained the first FUV (1000 – 1150 ) spectra of the diffuse radiation in an external galaxy using serendipitous observations of targets in the LMC.
 Most of these observations are near OD associations and the diffuse emission is bright. ranging from to of the total flux in the region.," Most of these observations are near OB associations and the diffuse emission is bright, ranging from to of the total flux in the region."
 This fraction is much less than the corresponding fraction emitted at 1500 suggesting that the largest part of the heating of the interstellar dust occurs in the FUV., This fraction is much less than the corresponding fraction emitted at 1500 suggesting that the largest part of the heating of the interstellar dust occurs in the FUV.
 We are now building a more detailed model to use the wealth of data now available in the LMC. particularly the data fromSpitzer (Meixneretal.2006).," We are now building a more detailed model to use the wealth of data now available in the LMC, particularly the data from \citep{Meixner06}."
. The UV and IR. data are complementary in (hat thev probe different. aspects of the radiative transler between stus and the dust with the part of the radiation not scattered in the UV radiated in the I and an understanding of the absorption and subsequent re-emission of the starlight in a nearby ealaxv such as the LAIC will provide templates for more distant. galaxies where only the convolution of the two is seen., The UV and IR data are complementary in that they probe different aspects of the radiative transfer between stars and the dust with the part of the radiation not scattered in the UV radiated in the IR and an understanding of the absorption and subsequent re-emission of the starlight in a nearby galaxy such as the LMC will provide templates for more distant galaxies where only the convolution of the two is seen.
 This research has made use ofExplorer data., This research has made use of data.
FUSE was operated by Johns Hopkins University for NASA., was operated by Johns Hopkins University for NASA.
 We acknowledge the use of NASA Astrophysics Data System (ADS)., We acknowledge the use of NASA Astrophysics Data System (ADS).
 AP is supported by a Department of Science and. Technology (DST) research erant., AP is supported by a Department of Science and Technology (DST) research grant.
 Part of this work was supported through funding from ISRO through the Office of Space Science., Part of this work was supported through funding from ISRO through the Office of Space Science.
"durations would be equal to the time taken for the relative lens ancl source positions to change by L(a.g). Let this time be denoted by 1,4... In most cases. however. the events will be significantly shorter. because orbital motion plays an important role.","durations would be equal to the time taken for the relative lens and source positions to change by $L(\alpha, q).$ Let this time be denoted by $T_{transverse}.$ In most cases, however, the events will be significantly shorter, because orbital motion plays an important role."
 Iu addition. orbital motion increases the likelihood that a detectable event will occur.," In addition, orbital motion increases the likelihood that a detectable event will occur."
 In the case in which Tipanseerse>2. the probability that a detectable event will occur is wily.," In the case in which $T_{transverse} > P,$ the probability that a detectable event will occur is unity."
 Particularly in cases wilh a«0.5. the orbital period can be comparable (ο or even shorter than. {μολις the (me taken for (he source (o (traverse a distance L(a.q). In such cases. (he orbital motion is very likely (o rotate the perturbed region in [ront of the source.," Particularly in cases with $\alpha < 0.5,$ the orbital period can be comparable to or even shorter than $T_{traverse}$ the time taken for the source to traverse a distance $L(\alpha, q).$ In such cases, the orbital motion is very likely to rotate the perturbed region in front of the source."
" The probability is Z5,4:4(q)/Dus when Tias)<Duo and is unity otherwise.", The probability is $T_{traverse}(q)/P_{orb}$ when $T_{traverse}(q)< P_{orb}$ and is unity otherwise.
 When the probability is larger than unity. deviations repeat on a lime scale roughly equal to με.," When the probability is larger than unity, deviations repeat on a time scale roughly equal to $P_{orb}$."
 If we are monitoring the svstem frequently enough to cateli a deviation in progress. our chance of seeing the deviation can be 10054 if the planet exists.," If we are monitoring the system frequently enough to catch a deviation in progress, our chance of seeing the deviation can be $100\%$ if the planet exists."
" The time duration of a deviation [rom (he point-lens form is In the cases shown in Figures 3. 4. and 5. (his produces deviations of durations 1.1 davs. 0.56 davs. and 0.14 days. which compare well with values of 754, shown in the bottom-left panels of each figure."," The time duration of a deviation from the point-lens form is In the cases shown in Figures 3, 4, and 5, this produces deviations of durations $1.1$ days, $0.56$ days, and $0.14$ days, which compare well with values of $T_{dev}$ shown in the bottom-left panels of each figure."
" The first exoplanet to be discovered orbiting a sun-like star was 51 Peg b (Mavor Queloz 1995). a planet with msin(/)220.5M, in a 4-dav orbit."," The first exoplanet to be discovered orbiting a sun-like star was 51 Peg b (Mayor Queloz 1995), a planet with $m\, sin(i) \approx 0.5\, M_J$ in a 4-day orbit."
" AC present. there are 155 known exoplanets with semimajor axis smaller than 0.5 AU and with msin(;) between 0.5AZ, and LOAL). These planets are generally referred to as “hot Jupiters""."," At present, there are 155 known exoplanets with semimajor axis smaller than $0.5$ AU and with $m\, sin(i)$ between $0.5\, M_J$ and $10\, M_J.$ These planets are generally referred to as “hot Jupiters”."
 The value οἱ msin(i) is larger than (1Mj.2Mj.3 Mj) in (96.57.31) cases. respectively.," The value of $m\, sin(i)$ is larger than $1\, M_J, 2\, M_J, 3\, M_J$ ) in $96, 57, 31$ ) cases, respectively."
 The planet corresponding to Figure 2 i$ a hot Jupiter., The planet corresponding to Figure 3 is a hot Jupiter.
 Its mass is equal to that of Jupiter. and it orbits a star of 0.3M.: a= 1/3.," Its mass is equal to that of Jupiter, and it orbits a star of $0.8\, M_\odot;$ $\alpha=1/3$ ."
" With Dj,25 pe: Dy=8 kpc. we find 25=0.4 AU."," With $D_L=25$ pc; $D_S=8$ kpc, we find $R_E=0.4$ AU."
 Thus. the semimajor axis is a=àAj0.13 AU. and the orbital period is 20 davs.," Thus, the semimajor axis is $a= \alpha\, R_E = 0.13$ AU, and the orbital period is $20$ days."
 With a transverse speed of 20 km/s. the time taken (o cross dtp is Tj4=35 days.," With a transverse speed of $20$ km/s, the time taken to cross $R_E$ is $\tau_{E,1}=35$ days."
 The duration of the deviations is just over a dav. and the deviations repeat.," The duration of the deviations is just over a day, and the deviations repeat."
 This example demonstrates that hot Jupiters can be found through their influence on the low-maenilication portion of lensing light curves., This example demonstrates that hot Jupiters can be found through their influence on the low-magnification portion of lensing light curves.
" Note that 1, for the same lens star and orbit. (he planet had a mass of (31M.6M.10 Mj). then Ty. wouldbe (1.9 days. 2.7 davs. 3.5 davs)."," Note that if, for the same lens star and orbit, the planet had a mass of $3\, M_J, 6\, M_J, 10\, M_J$ ), then $T_{dev}$ wouldbe $1.9$ days, $2.7$ days, $3.5$ days)."
"found that the best solution depends on the adopted mass for the central star, and even for a fixed value of m4 there may be many different configurations compatible with the observations.","found that the best solution depends on the adopted mass for the central star, and even for a fixed value of $m_A$ there may be many different configurations compatible with the observations."
" This is expected, since the radial velocity data covers less than one orbital period of the system."," This is expected, since the radial velocity data covers less than one orbital period of the system."
" However, we have also found that the dynamics of small planetesimals appears to be only weakly dependent on the particular solution adopted for the binary."," However, we have also found that the dynamics of small planetesimals appears to be only weakly dependent on the particular solution adopted for the binary."
" A comparative study of the evolution of planetesimals under the effects of gas drag from a circumstellar (m, centered) gas disk shows similar evolutionary paths.", A comparative study of the evolution of planetesimals under the effects of gas drag from a circumstellar $m_A$ centered) gas disk shows similar evolutionary paths.
" Although our integrations have not covered many initial conditions or disk parameters, we suspect that the accretional process of a planetesimal swarm should be practically equivalent in any case."," Although our integrations have not covered many initial conditions or disk parameters, we suspect that the accretional process of a planetesimal swarm should be practically equivalent in any case."
" Finally, we also presented a curious case of resonant trapping in divergent migration."," Finally, we also presented a curious case of resonant trapping in divergent migration."
" There is practically no reference to this behavior in the literature and, although its importance in planetary formation is difficult to evaluate, we nevertheless believe the phenomena is intrinsically interesting and merits further analysis."," There is practically no reference to this behavior in the literature and, although its importance in planetary formation is difficult to evaluate, we nevertheless believe the phenomena is intrinsically interesting and merits further analysis."
 This work was supported by the Argentinian Research Council -CONICET- and by the Cérrdoba National University -UNC-., This work was supported by the Argentinian Research Council -CONICET- and by the Córrdoba National University -UNC-.
 A.M.L. is a postdoctoral fellow of SECYT/UNC., A.M.L. is a postdoctoral fellow of SECYT/UNC.
in the simulation data set is much higher than fraction of cool clusters in the AIMIE99 sample.,in the simulation data set is much higher than fraction of cool clusters in the MME99 sample.
 For example. im he AIATE99 sample of 15. clusters. only one cluster has a temperature below 3 keV. In the Dialek ct al. (," For example, in the MME99 sample of 45 clusters, only one cluster has a temperature below 3 keV. In the Bialek et al. ("
2001) SG set. however. 5 of the 12 clusters have temperatures low 3 keV. Iu addition. the mean temperature of clusters in the MALIE99 sample is z 5.5 keV. while it is oulv about 3.8 keV in the Dialek et al. (,"2001) S6 set, however, 5 of the 12 clusters have temperatures below 3 keV. In addition, the mean temperature of clusters in the MME99 sample is $\approx$ 5.5 keV, while it is only about 3.8 keV in the Bialek et al. ("
2001) SG data set.,2001) S6 data set.
 As xeviouslv mentioned. preheating prefercutially affects low cluperature svstenus aud. therefore comparisons between heorv aud observations should be done over the same range in temperatures.," As previously mentioned, preheating preferentially affects low temperature systems and, therefore comparisons between theory and observations should be done over the same range in temperatures."
 To illustrate the problems of comparing theoretical models auc observations that span different temperature ranges. we tried to reproduce the fit of Bialelk et al. (," To illustrate the problems of comparing theoretical models and observations that span different temperature ranges, we tried to reproduce the fit of Bialek et al. ("
2001) to their S6 data set.,2001) to their S6 data set.
 We used data presented in their Table 2 for clusters with Py>2 keV (ve use their preferred. “processed” temperatures) aud fit it with a linear model aud found. M;xRHUL," We used data presented in their Table 2 for clusters with $T_X > 2$ keV (we use their preferred “processed” temperatures) and fit it with a linear model and found $M_{gas} 
\propto T_X^{2.42 \pm 0.17}$."
 This is slightly different from the value listed iu Tttheir Table 3. prestunably because Table 2 is based on data within rogo while Table 3 is based ou data within rsyy (they note that a change of up to in the predicted slope cai occur when switching between the two}.," This is slightly different from the value listed in their Table 3, presumably because Table 2 is based on data within $r_{200}$ while Table 3 is based on data within $r_{500}$ (they note that a change of up to in the predicted slope can occur when switching between the two)."
" To match the conditions of the present work. we then discarded all simulated cluster data below 3 keV (the mean temperature for the remaiming 7 clusters was then 5.1 keV. similar to the NME?)9 data) and found a best fit of M4,κμμ..."," To match the conditions of the present work, we then discarded all simulated cluster data below 3 keV (the mean temperature for the remaining 7 clusters was then $5.1$ keV, similar to the MME99 data) and found a best fit of $M_{gas} \propto T_X^{1.99 \pm 0.30}$."
 This is excellent agreement with the results of MATE99 aud oulv mareiually inconsistent with the DDBLP02 models of similar cutropy imjectiou., This is excellent agreement with the results of MME99 and only marginally inconsistent with the BBLP02 models of similar entropy injection.
 What about their favored models?, What about their favored models?
 We have tried the same type of test ou their S3 data set (INz100 keV cu? )., We have tried the same type of test on their S3 data set $K_0 \approx 100$ keV $^2$ ).
" Fitting all simulated clusters with Ty2 keV (uean temiperature of 3.8 keV) we find MouXTOTO, which is in good aerecment with the results of MMIE99."," Fitting all simulated clusters with $T_X \gtrsim 2$ keV (mean temperature of 3.8 keV) we find $M_{gas} \propto T_X^{1.86 
\pm 
0.12}$, which is in good agreement with the results of MME99."
" When we remove all clusters below 3 keV (mean teniperature of L9 keV). however. the best fit is Maj,xTees, "," When we remove all clusters below 3 keV (mean temperature of 4.9 keV), however, the best fit is $M_{gas} 
\propto T_X^{1.77 \pm 0.38}$."
Iu this case. the best-fit relation is not very coustraiine.," In this case, the best-fit relation is not very constraining."
 It is even iudistinguishable frou the selfsimular result., It is even indistinguishable from the self-similar result.
 It is apparent from them Figure 1. however. that the predicted normalization for this model (and all other low eutropy models) does not match the observations of AIME99.," It is apparent from their Figure 1, however, that the predicted normalization for this model (and all other low entropy models) does not match the observations of MME99."
 This is noted by the authors tlemsclyes., This is noted by the authors themselves.
 Thev clan the difference in the zero poiut may be resolved by reducing the barvon fraction by ~20%., They claim the difference in the zero point may be resolved by reducing the baryon fraction by $\sim 20\%$.
 As we noted earlier. however. a simular normalization offset is also seen in the total cluster mass - temperature (M— Tx) relation and this cannot be resolved bv reducing the xuwvonu fraction.," As we noted earlier, however, a similar normalization offset is also seen in the total cluster mass - temperature $M - T_X$ ) relation and this cannot be resolved by reducing the baryon fraction."
 This suggests that the problem lies with he temperature. rather than the gas mass.," This suggests that the problem lies with the temperature, rather than the gas mass."
 Alternatively. Dialek et al.," Alternatively, Bialek et al."
" also suggest that rescaling their simulatious or I],=το kms. ! Ἰ Gustead of SO kins 3 1 would bring consistency between the normalization of this nodel and the observations.", also suggest that rescaling their simulations for $H_o = 70$ km $^{-1}$ $^{-1}$ (instead of 80 km $^{-1}$ $^{-1}$ ) would bring consistency between the normalization of this model and the observations.
 This would be true only if he harvou fraction was held fixed at 0.1 and not rescaled or the new cosmologv., This would be true only if the baryon fraction was held fixed at 0.1 and not rescaled for the new cosmology.
" Civeu that they assune (2,= L3. this would Παρί Q,=0.01557 which is roughly lower than observed in quasar absorption spectra (Dwles Tytler 1998)."," Given that they assume $\Omega_m = 0.3$ , this would imply $\Omega_b = 0.015 h^{-2}$ which is roughly lower than observed in quasar absorption spectra (Burles Tytler 1998)."
" Thus. while the normalization offset between their theoretical model aud the observations of AIAIE99 is directly reduced by decreasiug the value of /. it ds indirectly increased by roughly the same proportion through the increased value of 95/0,,."," Thus, while the normalization offset between their theoretical model and the observations of MME99 is directly reduced by decreasing the value of $h$, it is indirectly increased by roughly the same proportion through the increased value of $\Omega_b/\Omega_m$."
 lu sununary. as with the Loewenstein (2000) models. we fud that the difference in the results aud couclusious of Dialek et al. (," In summary, as with the Loewenstein (2000) models, we find that the difference in the results and conclusions of Bialek et al. ("
2001) and the present work cau be explained on the basis that differeut temperature ranges were exanuimned.,2001) and the present work can be explained on the basis that different temperature ranges were examined.
 In particular. we have shown that the fraction of cool clusters in Dialek et al," In particular, we have shown that the fraction of cool clusters in Bialek et al."
s simulated data set is much larger than that found in the MME99 sample aud this has likely l]ed to aun underestimation of the eutropv floor in these clusters.,'s simulated data set is much larger than that found in the MME99 sample and this has likely led to an underestimation of the entropy floor in these clusters.
 Iu order to safely aud accurately compare the preheated mo0dels of BBLP02 with observations we have paid special attention to ouly those hot clusters with Ty23 keV. As such. we believe our COMpAarIsOl is more appropriate.," In order to safely and accurately compare the preheated models of BBLP02 with observations we have paid special attention to only those hot clusters with $T_X \gtrsim 3$ keV. As such, we believe our comparison is more appropriate."
" Motivated by a number of observational studies that wave suggested that the M4;—Ty velatiou of clusters of galaxies is inconsistent with the sclfsimilar result of πώΊσα. simulations aud bv the lunch of theCherdre and satellites, which will ereath improve he quality of the observed Ayes—Tx relation. we have iuplemieuted the analytic model of BBLPO2 to study he nupact of preheating on ων—Tx relation."," Motivated by a number of observational studies that have suggested that the $M_{gas} - 
T_X$ relation of clusters of galaxies is inconsistent with the self-similar result of numerical simulations and by the launch of the and satellites, which will greatly improve the quality of the observed $M_{gas}-T_X$ relation, we have implemented the analytic model of BBLP02 to study the impact of preheating on $M_{gas} - T_X$ relation."
 The xedietious of the model have previously been shown to be in very good aereeimeut with observations (6.9. LyTx relation aud ὃν0 relation).," The predictions of the model have previously been shown to be in very good agreement with observations (e.g., $L_X - T_X$ relation and $L_X - \sigma$ relation)."
 Tn agreement with the previous theoretical studies of Loeweustein (2000)x aud Bialek et al. (, In agreement with the previous theoretical studies of Loewenstein (2000) and Bialek et al. (
2001). our aualvsis indicates that injecting the iutracluster πουπα with itropy leads to a steeper relationship than predictec o» the selfsimilar result of muuerical simulations of clusters that evolve through the effects of eravity alone.,"2001), our analysis indicates that injecting the intracluster medium with entropy leads to a steeper relationship than predicted by the self-similar result of numerical simulations of clusters that evolve through the effects of gravity alone."
 Loeweustein (2000) aud Dialek et al. (, Loewenstein (2000) and Bialek et al. (
2001) have fom that models that produce au eutropy floor of Ay~100 keV cu. which is cousisteut with measurements of galaxy groups. are capable of reproducing the Aya.—Tx relation of hot clusters.,"2001) have found that models that produce an entropy floor of $K_0 \sim 100$ keV $^2$ , which is consistent with measurements of galaxy groups, are capable of reproducing the $M_{gas} - T_X$ relation of hot clusters."
" This is incousisteut with our ialysis, which indicates that a ""high, level of cutropy injection (AyZ300 keV cm?) is required. to match the observational data of hot clusters of White et al. ("," This is inconsistent with our analysis, which indicates that a “high” level of entropy injection $K_0 \gtrsim 300$ keV $^2$ ) is required to match the observational data of hot clusters of White et al. ("
1997). Peres et al. (,"1997), Peres et al. ("
1998). aud MMEO99.,"1998), and MME99."
 It is also inconsistent with BBLP02's best-fit value of Ayz330 keV cin? found via an investigation of the LyTx relation of both eroups aud rot clusters.," It is also inconsistent with BBLP02's best-fit value of $K_0 \approx 330$ keV $^2$ found via an investigation of the $L_X 
- T_X$ relation of both groups and hot clusters."
 They note that the strougest coustraiuts for a high cutropy floor comes from hot. clusters., They note that the strongest constraints for a high entropy floor comes from hot clusters.
 Moreover. a lieh value of Ay. oue that is inconsistent with the yreclictions of the best-fit models of Loewensteiu. (2000) and Bialek et al. (," Moreover, a high value of $K_0$, one that is inconsistent with the predictions of the best-fit models of Loewenstein (2000) and Bialek et al. ("
2001). has also been reported by Tozzi Norman (2001).,"2001), has also been reported by Tozzi Norman (2001)."
" Finally, da Silva et al. ("," Finally, da Silva et al. ("
2001) used πιοσα smnulatious with a “low” value of Ay~NO cV cu? (which is similar to the predictions of tle best-fit models of Loewenstein 2000 and Dialek et al.,2001) used numerical simulations with a “low” value of $K_0 \sim 80$ keV $^2$ (which is similar to the predictions of the best-fit models of Loewenstein 2000 and Bialek et al.
 2001) and found that theynot reproduce the observed X-rav scaling relations., 2001) and found that they reproduce the observed X-ray scaling relations.
 Our result. ou the other haud. is consistent with the results of BBLP02. Tozzi Norman (2001). aud da Silva et al. (," Our result, on the other hand, is consistent with the results of BBLP02, Tozzi Norman (2001), and da Silva et al. ("
2001).,2001).
 As discussed in 85. we believe the difference between the studies of Loewensteiu (2000) and Dialek et al. (," As discussed in 5, we believe the difference between the studies of Loewenstein (2000) and Bialek et al. ("
2001) and present work can be explained by considering the difference in teniperature ranges studied.,2001) and present work can be explained by considering the difference in temperature ranges studied.
 Iu particular. wehave focused ouly on hot clusters in au attempt to match the majority of the," In particular, wehave focused only on hot clusters in an attempt to match the majority of the"
"results, though, are affected by assumptions on the initial conditions.","results, though, are affected by assumptions on the initial conditions."
 This confirms that we are far away from understanding all characteristics of these objects and any observation would be of paramount importance to improve theoretical models., This confirms that we are far away from understanding all characteristics of these objects and any observation would be of paramount importance to improve theoretical models.
" In this work, we estimated the average number of OAs events originating from Pop III stars that the Gaia mission may observe to be up to 2.28 + 0.88 off-axis afterglows and 2.78 + 1.41 on-axis ones."," In this work, we estimated the average number of OAs events originating from Pop III stars that the Gaia mission may observe to be up to 2.28 $\pm$ 0.88 off-axis afterglows and 2.78 $\pm$ 1.41 on-axis ones."
" In case such events are found among Gaia data, valuable physical properties associated with the primordial stars of our Universe and their environment could be constrained."," In case such events are found among Gaia data, valuable physical properties associated with the primordial stars of our Universe and their environment could be constrained."
"chauge in the rotation velocity. Ae=(6,Co. Taages between 15 to 30 kan + for App=1 to 2. respectively.","change in the rotation velocity, $\Delta v\equiv v_{\phi}-v_{\rm c}$, ranges between $15$ to $30$ km $^{-1}$ for $\lambda_{\rho B}=1$ to $2$, respectively."
 This value for Ac should be regarded as a eeucrous estimate for two reasons., This value for $\Delta v$ should be regarded as a generous estimate for two reasons.
 First. the azimuthal field is uot expected to be approximately constant while the voluue density of gas at 2=(0 varies by a factor of 50 100 (Diplas&Savage1991).," First, the azimuthal field is not expected to be approximately constant while the volume density of gas at $z=0$ varies by a factor of $\sim 50$ $100$ \citep{dip91}."
". Secondly. the adopted equilibrium configuration. nanelv ce,07)=O at anv HomRey. cannot be reached ia practice. starting fro a rotating disk in equilibriun with the eravitational force. due to the conservation of angular womenutium."," Secondly, the adopted equilibrium configuration, namely $v_{\phi}(R)=0$ at any $R>R_{\rm kep}$, cannot be reached in practice, starting from a rotating disk in equilibrium with the gravitational force, due to the conservation of angular momentum."
 In fact. the magnetic field begius to erow in the disk as discussed in &82.2.. creating a magnetic force directed outward bevoud Rig.," In fact, the magnetic field begins to grow in the disk as discussed in \ref{sec:mcp}, creating a magnetic force directed outward beyond $R_{\rm kep}$."
 This region will wudergo a coutinnous outward dift. while the inner disk (Ro« Rey} must be subjected to the required contraction phase. gcnerating a sap in the surface deusitv of the disk.," This region will undergo a continuous outward drift, while the inner disk $R<R_{\rm kep}$ ) must be subjected to the required contraction phase, generating a gap in the surface density of the disk."
 In order to quantity this effect. we assume for simplicity that the outer disk GI Bu) suffers au approsimately sclbsimilar expansion with factor c2 Lie. p(R)=(poοJexploR.) at [Fofü. n the final equilibria coufiguratiou.," In order to quantify this effect, we assume for simplicity that the outer disk $R>R_{\rm kep}$ ) suffers an approximately self-similar expansion with factor $\psi>1$, i.e., $\rho(R)=(\rho_{0}/\psi^{2})
\exp(-R/\psi R_{\rm g})$ at $R>\psi R_{\rm kep}$, in the final equilibrium configuration."
 From the conservation of augular momentum. it can be shown that the right-handside of Eq. (9))," From the conservation of angular momentum, it can be shown that the right-handside of Eq. \ref{eq:ten}) )"
 is now a factor ον.1) smaller (Appendix C)., is now a factor $\psi^{2}/(\psi-1)$ smaller (Appendix C).
" lence. the optimized situation occurs for e=2 and then (02,e2)/02<A, at Ro=30 kpc."," Hence, the optimized situation occurs for $\psi=2$ and then $(v_{\phi}^{2}-v_{\rm c}^{2})/v_{\rm c}^{2}<0.1 \lambda _{\rho B}$ at $R=30$ kpc."
" This implies that Ac,<10 kins Fat he periphery of disks iu normal spiral galaxies uuder he assumption that they coutaied onlv stars aud the observed eas.", This implies that $\Delta v_{\phi} < 10$ km $^{-1}$ at the periphery of disks in normal spiral galaxies under the assumption that they contained only stars and the observed gas.
" Therefore. it is not possible to banish dark iilos by mmaenetic fields because oue would require mach arecr values of Ac,,."," Therefore, it is not possible to banish dark halos by magnetic fields because one would require much larger values of $\Delta v_{\phi}$."
 For disk galaxies with a dark halo. as postulated in the conventional scenario. it is possible to follow the same xocedure to estimate the maxiuun effect of magnetic fields when ος =cte. instead of 2=GAL/R (see Appendix C).," For disk galaxies with a dark halo, as postulated in the conventional scenario, it is possible to follow the same procedure to estimate the maximum effect of magnetic fields when $v_{\rm c}=$ cte, instead of $v_{\rm c}^{2}=GM/R$ (see Appendix C)."
 Simular arguments sugecst that the expected local. and probably trausieut. variations in the rotation speed arger than ~20 kan + are very unlikely even ii models including dark halos (see also 82.2. and Sáuuchez-Salcedo L997).," Similar arguments suggest that the expected local, and probably transient, variations in the rotation speed larger than $\sim 20$ km $^{-1}$ are very unlikely even in models including dark halos (see also \ref{sec:mcp} and Sánnchez-Salcedo 1997)."
" Iu the next subsections. it will be shown that these upper limits for Ae,, also apply even when galaxies are not isolated systems but are embedded ii an ambient medi. thereby makiug these estimates very robust."," In the next subsections, it will be shown that these upper limits for $\Delta v_{\phi}$ also apply even when galaxies are not isolated systems but are embedded in an ambient medium, thereby making these estimates very robust."
 Tt could be argued that the model described by Eq. (11) , It could be argued that the model described by Eq. \ref{eq:vphi}) )
is too simplistic because other terius not considered in that equation. as a radial flow or other components of the magnetic field. müght be iuportaut. regarding the radial confinement. bevoud Ryy?..," is too simplistic because other terms not considered in that equation, as a radial flow or other components of the magnetic field, might be important, regarding the radial confinement, beyond $R_{\rm HI}$."
 In fact. unlike the radial component of the field. the :-componcut may contribute to the radial confinement of the disk aud will be included in our analvsis.," In fact, unlike the radial component of the field, the $z$ -component may contribute to the radial confinement of the disk and will be included in our analysis."
 Iu addition. the lvdrocwnaimical pressure by a radial inflow due to intergalactic accretion of matter may also plav a role.," In addition, the hydrodynamical pressure by a radial inflow due to intergalactic accretion of matter may also play a role."
 Since systems cmbedded in am ambicut meditin usually present sharp boundaries. it is convenicut to use an iuteeral form of the equations as that eiven by the virial theorem.," Since systems embedded in an ambient medium usually present sharp boundaries, it is convenient to use an integral form of the equations as that given by the virial theorem."
 The scalar virial theorem for fields with Byϐ aud strict ονποσα. svuuuetrv (Le. 0/0:=Ojo 0) applied to a finite cylindrical volue V. bounded by a evlinder 5 of height £. can be written as: where Fis the kinetic cenerev of the eas. YV its eravitational cuerey in the eravitational field created by all iiasses in the svstem. 2 the eas pressure as defined in &2.1.. Pa the gas pressure at the boundary surface. is a coordinate vector. J=421/02 with I the trace of the moment of Inertia tensor and Me is given by (c.m. Fiese Pudntz 2000 aud Appendix 9).," The scalar virial theorem for fields with $B_{R}=0$ and strict cylindrical symmetry (i.e., $\partial/\partial z=\partial/\partial\phi=0$ ) applied to a finite cylindrical volume $V$ , bounded by a cylinder $S$ of height $L$, can be written as: where ${\mathcal{T}}$ is the kinetic energy of the gas, ${\mathcal{W}}$ its gravitational energy in the gravitational field created by all masses in the system, $P$ the gas pressure as defined in \ref{sec:oned}, $P_{\rm S}$ the gas pressure at the boundary surface, ${\mbox{\boldmath{$ $}}}$ is a coordinate vector, $\ddot{I}\equiv
d^2 I/dt^2$ with $I$ the trace of the moment of inertia tensor and ${\mathcal{M}}_{\rm cyl}$ is given by (e.g., Fiege Pudritz 2000 and Appendix B)."
 Throughout this paper the subscript 5 refers to quautities valuated at the radial surface of our evliudrical volume with radius Rs. and the subscript ον stauds for the cvliudrical case.," Throughout this paper the subscript $S$ refers to quantities valuated at the radial surface of our cylindrical volume with radius $R_{\rm S}$, and the subscript ${\rm cyl}$ ' stands for the cylindrical case."
 This form for the virial theorem is valid for any arbitrary helical field (B5;=0) provided cylindrical econmoetrv: uo other additional assumption is required., This form for the virial theorem is valid for any arbitrary helical field $B_{R}=0$ ) provided cylindrical geometry; no other additional assumption is required.
 The surface integral ternis including the :=££/2 surfaces are taken iuto account m Eq. (11))., The surface integral terms including the $z=\pm L/2$ surfaces are taken into account in Eq. \ref{eq:magtermtxt}) ).
 The inteeration of the magnetic terms can be found in Appendix D. For αν further details in the derivation. we refer tle reader to the paper by Fiege Pudritz (2000).," The integration of the magnetic terms can be found in Appendix B. For any further details in the derivation, we refer the reader to the paper by Fiege Pudritz (2000)."
 We can identity two new vias of radial coufinement: bv ral pressure last term of LIIS of Eq. (10))], We can identify two new vias of radial confinement: by ram pressure [last term of LHS of Eq. \ref{eq:virialcyltxt}) )]
 or bv an external imagnetie field., or by an external magnetic field.
 The ambient pressure (2s). ou the other haud. oulv produces vertical confinement as discussed in Appendix A. If these new terms are able to produce radial confinement then the constraint elven bv Eq. (7)}) ," The ambient pressure $P_{\rm S}$ ), on the other hand, only produces vertical confinement as discussed in Appendix A. If these new terms are able to produce radial confinement then the constraint given by Eq. \ref{eq:upperlimit}) )"
could be somehow relaxed., could be somehow relaxed.
 The possible role of these teris will be discussed in two separate sections., The possible role of these terms will be discussed in two separate sections.
" So far. we have neglected the terms involviug cp. vecatse observations show that ey is verv simall conrured to ce, for the ealaxies under consideration."," So far, we have neglected the terms involving $v_{R}$, because observations show that $v_{R}$ is very small compared to $v_{\phi}$ for the galaxies under consideration."
 Devoud the edge of the observed disk. the value of eg is uucertain.," Beyond the edge of the observed disk, the value of $v_{R}$ is uncertain."
 We consider now the surface mteeral of the uonmentun stress iun Eq. (10)).," We consider now the surface integral of the momentum stress in Eq. \ref{eq:virialcyltxt}) ),"
 which may have a negative sien for the case of strong mass accretion iuto the disk., which may have a negative sign for the case of strong mass accretion into the disk.
 Iu act. it can be shown that even though Tis expected to © negative. the combination Ij2 foplo- rite. dS) could be still negative. showing the confining effect of he ran pressure. (," In fact, it can be shown that even though $\ddot{I}$ is expected to be negative, the combination $-\ddot{I}/2 -\int_{S}\rho\,
({\mbox{\boldmath{$ $}}}\cdot
{\mbox{\boldmath{$ $}}})({\mbox{\boldmath{$ $}}}\cdot
d{\mbox{\boldmath{$ $}}})$ could be still negative, showing the confining effect of the ram pressure. ("
For example. in the oue-cimensional case of a supersonic flow that slows down to rest by crashing perpendicularly to a rigid plane wall aud forms a strong aciabatic shock. £/2[pte rite dS) (2/3)f.pto re dS).),"For example, in the one-dimensional case of a supersonic flow that slows down to rest by crashing perpendicularly to a rigid plane wall and forms a strong adiabatic shock, $-\ddot{I}/2 -\int_{S}\rho\,
({\mbox{\boldmath{$ $}}}\cdot
{\mbox{\boldmath{$ $}}})({\mbox{\boldmath{$ $}}}\cdot
d{\mbox{\boldmath{$ $}}})=
-(2/3)\int_{S}\rho\,
({\mbox{\boldmath{$ $}}}\cdot
{\mbox{\boldmath{$ $}}})({\mbox{\boldmath{$ $}}}\cdot
d{\mbox{\boldmath{$ $}}})
$ .)"
 Since spherical accretion cannot confine a disk. the inflow should be extremely collimated parallel to the ealactic plane. Le. eR29 coco for which there is no evidence.," Since spherical accretion cannot confine a disk, the inflow should be extremely collimated parallel to the galactic plane, i.e. $v_{R}\gg v_{z}, v_{\phi}$ , for which there is no evidence."
 Moreover. this collumation is verv uulikelv to occur if the disk forms from a sphere of eas.," Moreover, this collimation is very unlikely to occur if the disk forms from a sphere of gas."
 Cas cools aud parcels of gas acquire circular orbits. conserving approximately angular momentum. when they collapse. to settle into a disk. leading to ty»0 (sce Régenvaldssou 1999 for results based on umucricalsinulatiouns).," Gas cools and parcels of gas acquire circular orbits, conserving approximately angular momentum, when they collapse to settle into a disk, leading to $v_{R}\rightarrow 0$ (see Röggnvaldsson 1999 for results based on numericalsimulations)."
 Furthermore. iu the bypothetical case that," Furthermore, in the hypothetical case that"
"CGs MCI629 and MCT697 are within the range of virial masses of local CGs estimated by Tlickson et ((1992): whilst MC13069 has a similar mass to that found in rich clusters of galaxies,",CGs MC4629 and MC7697 are within the range of virial masses of local CGs estimated by Hickson et (1992); whilst MC13069 has a similar mass to that found in rich clusters of galaxies.
 The velocity dispersion aud masses obtained for MC13069 are consequence of the difference in velocity between (his galaxy. aud the other members of (he group: if we exclude (his galaxy [rom suchestimations?.. the values obtained are 281 kins | and log(M) = 46.03 for the velocity dispersion and mass respectively.," The velocity dispersion and masses obtained for MC13069 are consequence of the difference in velocity between this galaxy and the other members of the group; if we exclude this galaxy from such, the values obtained are 281 km $^{-1}$ and $\log (M)$ = 46.03 for the velocity dispersion and mass respectively."
 Both values would fall within the expected range of values [ον CGs., Both values would fall within the expected range of values for CGs.
 The crossing times (Table 3: col., The crossing times (Table 3; col.
 7) are quite short (a few hundredths of the age of the Universe). and below ~1/20 of their cosmological distance.," 7) are quite short (a few hundredths of the age of the Universe), and below $\sim 1/20$ of their cosmological distance."
 The dvnamic crossing times logH4! for the Hickson sample are within the range —2.96.0.94. with the majority of the CCGs having values within —2.5 and —1.5.," The dynamic crossing times $\log H_ot$ for the Hickson sample are within the range $-2.96, +0.94$, with the majority of the CGs having values within $-2.5$ and $-1.5$ ."
" The median of that sample was log44,/=—1.80..", The median of that sample was $\log H_ot=-1.80$.
" The log//,! values estimated lor our three groups ave —1.76. —1.86. and —2.32. which are within the range spanned by most of the CGs in (he Iickson sample."," The $\log H_ot$ values estimated for our three groups are $-1.76$, $-1.86$, and $-2.32$, which are within the range spanned by most of the CGs in the Hickson sample."
 The values found [or the three CG analvzed in (his paper agree also with those [οπής by Pompei et ((2006) in their study of several CGs at redshift —0.12., The values found for the three CG analyzed in this paper agree also with those found by Pompei et (2006) in their study of several CGs at redshift $\sim$ 0.12.
 These short crossing times seem to indicate that. unless a mechanism for stabilization and/or acquisition of new members is established. the three CGs presented here could not have lasted until the present. and so the population of CGs at redshifts 20.3 is different from the local one.," These short crossing times seem to indicate that, unless a mechanism for stabilization and/or acquisition of new members is established, the three CGs presented here could not have lasted until the present, and so the population of CGs at redshifts $\sim$ 0.3 is different from the local one."
 This raises the issue of the generation and fate of CGs., This raises the issue of the generation and fate of CGs.
 The most natural scenario (Mendes cle Oliveira 2006) would be thetransformation of CGs into a relatively, The most natural scenario (Mendes de Oliveira 2006) would be thetransformation of CGs into a relatively
each iteration. the peak of the map is found. and the scaled PRF at the same location is multiplied by a small gain and subtracted from the map: a narrower Gaussian with the same flux is added to a model map.,"each iteration, the peak of the map is found, and the scaled PRF at the same location is multiplied by a small gain and subtracted from the map; a narrower Gaussian with the same flux is added to a model map."
" The residual maps obtained after ""cleaning"" are shown in reffig:cleaned..", The residual maps obtained after “cleaning” are shown in \\ref{fig:cleaned}.
" The starburst emission that we recover from the beam ""cleaning"" process. after adding back to the model maps the underlying residuals (that account for about of the total). amounts to 337. 111. and Jy at 250. 350. and um. respectively. 1.8. between and of the global emission."," The starburst emission that we recover from the beam “cleaning” process, after adding back to the model maps the underlying residuals (that account for about of the total), amounts to 337, 111, and Jy at 250, 350, and $\mu$ m, respectively, i.e. between and of the global emission."
 If we instead sum the emission from the four brightest sources selected from the ὀδθμπι SCUBA map. fitted with fixed positions and widths (~150 ppc) in all maps. then we already account for about of the global emission in each SPIRE band.," If we instead sum the emission from the four brightest sources selected from the $\mu$ m SCUBA map, fitted with fixed positions and widths $\sim 150$ pc) in all maps, then we already account for about of the global emission in each SPIRE band."
 Since there is a smooth transition from the disk to the off-disk emission. the spatial separation between the two is somewhat arbitrary.," Since there is a smooth transition from the disk to the off-disk emission, the spatial separation between the two is somewhat arbitrary."
 We note that the disk of 882 is very thick and turbulent. and that the residual maps are still contaminated by disk emission.," We note that the disk of 82 is very thick and turbulent, and that the residual maps are still contaminated by disk emission."
 We thus masked pixels where the original flux density exceeds the cleaning threshold. as shown in reffig:cleaned..," We thus masked pixels where the original flux density exceeds the cleaning threshold, as shown in \\ref{fig:cleaned}."
 In all the following. we adopt the Galactic emissivity law derived by Reachetal.(1995) from the COBE survey.," In all the following, we adopt the Galactic emissivity law derived by \cite{Reach95}
 from the COBE survey."
 Dust grain opacities vary as a function of environment and are very uncertain., Dust grain opacities vary as a function of environment and are very uncertain.
 However. dust masses can easily be rescaled 1f another value is assumed.," However, dust masses can easily be rescaled if another value is assumed."
 We thus adopt an opacity valid for dust in the diffuse interstellar medium. Kk2 1.62mm-kke7! in the DIRBE 140m band (Li& 2001).," We thus adopt an opacity valid for dust in the diffuse interstellar medium, $\kappa = 1.62$ $^2$ $^{-1}$ in the DIRBE $\mu$ m band \citep{Li01}."
 Converting it to an opacity at 500m... we obtain mm kkew!. in good agreement with what would have been obtained from the um opacity of Jamesetal.(2002).. i.e. (0.20+0.06) mm kkew!.," Converting it to an opacity at $\mu$ m, we obtain $^2$ $^{-1}$ , in good agreement with what would have been obtained from the $\mu$ m opacity of \cite{James02}, i.e. $(0.20 \pm 0.06)$ $^2$ $^{-1}$."
 Cool dust is detected at So significance in. filaments out to kkpe from the center. at 2504. The maximal extensions are to the north-east and to the south-east of the center. Le. in filaments making a large angle with the polar axes of the galaxy and outflow.," Cool dust is detected at $5 \sigma$ significance in filaments out to kpc from the center, at $\mu$ m. The maximal extensions are to the north-east and to the south-east of the center, i.e. in filaments making a large angle with the polar axes of the galaxy and outflow."
" As already remarked by Engelbrachtetal.(2006) for the PAH emission. dust occupies a very extended halo, and is not confined to the edges of what is traditionally called the superwind."," As already remarked by \cite{Engelbracht06} for the PAH emission, dust occupies a very extended halo, and is not confined to the edges of what is traditionally called the superwind."
 Comparison with the HI map of Yunetal.(1994) shows that the densest parts of the tidal streams are associated with some of the extended dust detected in SPIRE maps., Comparison with the HI map of \cite{Yun94} shows that the densest parts of the tidal streams are associated with some of the extended dust detected in SPIRE maps.
 Below. we provide quantitative arguments to support the impression that most of the dust mass outside the disk of 882 has been removed by tidal interaction. rather than entrained by the superwind.," Below, we provide quantitative arguments to support the impression that most of the dust mass outside the disk of 82 has been removed by tidal interaction, rather than entrained by the superwind."
" To approximately match the angular resolution of the maps and examine spatial variations in dust colors of the wind and halo. we convolved the ""cleaned"" maps with Gaussian kernels of appropriate widths. and regridded the resulting maps to the pixel size at the longest wavelength."," To approximately match the angular resolution of the maps and examine spatial variations in dust colors of the wind and halo, we convolved the “cleaned” maps with Gaussian kernels of appropriate widths, and regridded the resulting maps to the pixel size at the longest wavelength."
 reffig:wind.olorsshowsthe250 um to um ratio map and the um to um ratio map., \\ref{fig:wind_colors} shows the $\mu$ m to $\mu$ m ratio map and the $\mu$ m to $\mu$ m ratio map.
 Based on these ratios. the dust temperature in the wind and halo ranges between about KK and KK. and its average value decreases with projected distance from the starburst.," Based on these ratios, the dust temperature in the wind and halo ranges between about K and K, and its average value decreases with projected distance from the starburst."
 Some filaments that are much warmer than their surroundings can be seen: they are located in-between bright dust spurs reftig:wind.olors)). andthusmusthaverelativelylowdensities.," Some filaments that are much warmer than their surroundings can be seen; they are located in-between bright dust spurs \\ref{fig:wind_colors}) ), and thus must have relatively low densities."
T he presente ," The present data do not allow us to test whether these color variations are caused purely by different excitation conditions, or whether they are affected by changes in the dust composition within the wind."
," Assuming that these filaments follow the Galactic emissivity law, we estimate that they have temperatures between K and K, i.e. at least as high as in the starburst."
," They seem to be associated with the starburst wind, rather than with the tidal features traced by the HI map."
We estimate the total dust mass in the wind and halo from the jm and dust temperature maps. the latter derived from the um to um ratio.," We estimate the total dust mass in the wind and halo from the $\mu$ m and dust temperature maps, the latter derived from the $\mu$ m to $\mu$ m ratio."
" We obtain Myyai,=C11+0.5)x MM (nass error map summed linearly. and 2.5c- cut applied to the brightness maps)."," We obtain $M_{\rm d~halo} = (1.1 \pm 0.5) \times 10^6$ $_{\sun}$ (mass error map summed linearly, and $2.5 \sigma$ cut applied to the brightness maps)."
 The mass derived from the global halo fluxes and a single-temperature fit (with Zu22.3 to KK) is similar: Mgpalo=(1.0 to 1.2)x10°MMe., The mass derived from the global halo fluxes and a single-temperature fit (with $T_{\rm dust} = 22.3$ to K) is similar: $M_{\rm d~halo} = (1.0$ to $1.2) \times 10^6$ $_{\sun}$.
 This is much lower than the SCUBA estimate of Alton(1999) (2 to 10x10° ΜΜΑ). even using the same dust opacity.," This is much lower than the SCUBA estimate of \cite{Alton99}
 (2 to $10 \times 10^6$ $_{\sun}$ ), even using the same dust opacity."
 We cannot rule out a cold component undetected by SPIRE. but the discrepancy may predominantly arise from several analysis issues: although the halo is barely detected in the SCUBA maps (because they are only kkpe in diameter. and the chop throw placed the sky reference within the wind). the starburst and disk have not been subtracted with their sidelobes. and the halo emission may thus be severely contaminated by them: the procedure followed by Altonetal.(1999) to estimate the dust temperature also entails large errors.," We cannot rule out a cold component undetected by SPIRE, but the discrepancy may predominantly arise from several analysis issues: although the halo is barely detected in the SCUBA maps (because they are only kpc in diameter, and the chop throw placed the sky reference within the wind), the starburst and disk have not been subtracted with their sidelobes, and the halo emission may thus be severely contaminated by them; the procedure followed by \cite{Alton99} to estimate the dust temperature also entails large errors."
 The combination of the dust temperature and brightness maps shows that dust that is spatially coincident with the superwind (likely to have been entrained by it) is warmer and more diffuse than dust that is associated with the tidal streams. the latter consequently dominant in terms of mass. as illustrated by the dust mass map in reffig:wind. olors.," The combination of the dust temperature and brightness maps shows that dust that is spatially coincident with the superwind (likely to have been entrained by it) is warmer and more diffuse than dust that is associated with the tidal streams, the latter consequently dominant in terms of mass, as illustrated by the dust mass map in \\ref{fig:wind_colors}."
.De fininglargesectorstoexcludethesuperwindregions. and X-ray maps (with opening angles of 74° in the north and 64° in the south). we argue that at à minimum of the halo dust mass is not associated with the superwind.," Defining large sectors to exclude the superwind regions, based on $\alpha$ and X-ray maps (with opening angles of $^{\rm o}$ in the north and $^{\rm o}$ in the south), we argue that at a minimum of the halo dust mass is not associated with the superwind."
 Since tidal features overlap in projection with superwinc features. this fraction is a strict lower limit.," Since tidal features overlap in projection with superwind features, this fraction is a strict lower limit."
 The global dust mass of 882. folding in the mmm measurement of Thumaetal.(2000).. is Mai(4.5+1.4)x10° MMo (with Tus=24 KK. which provides a fit too low by only at ym and by at jm).," The global dust mass of 82, folding in the mm measurement of \cite{Thuma00}, is $M_{\rm d~tot} \sim (4.5 \pm 1.4) \times 10^6$ $_{\sun}$ (with $T_{\rm dust} = 24$ K, which provides a fit too low by only at $\mu$ m and by at $\mu$ m)."
 If our mass estimates are correct. they imply that ~25% of all the dust has been expelled from the disk.," If our mass estimates are correct, they imply that $\sim 25$ of all the dust has been expelled from the disk."
 Either the efficiency of gas and dust ejection by the superwind and the tidal interaction 15 very high. or the dust grain composition and size distribution in the wind and halo significantly differ from those in the starburst.," Either the efficiency of gas and dust ejection by the superwind and the tidal interaction is very high, or the dust grain composition and size distribution in the wind and halo significantly differ from those in the starburst."
 Without data of comparable quality at both shorter and longer wavelengths. we cannot test the second alternative. but we deemit less likely.," Without data of comparable quality at both shorter and longer wavelengths, we cannot test the second alternative, but we deemit less likely."
 Since the interstellar medium of 882 must have become extremely turbulent and porous as a result of the sustained injection of mechanical energy by the successive starbursts. probably enough ultraviolet radiation is leaking out of the disk to provide most of the dust heating necessary to account for the," Since the interstellar medium of 82 must have become extremely turbulent and porous as a result of the sustained injection of mechanical energy by the successive starbursts, probably enough ultraviolet radiation is leaking out of the disk to provide most of the dust heating necessary to account for the"
loop and the stationary atmosphere surrounding it also produces a toroidal field component. but this appears to be much less effective than direct shearing of field lines inside the rotating source.,"loop and the stationary atmosphere surrounding it also produces a toroidal field component, but this appears to be much less effective than direct shearing of field lines inside the rotating source."
 We find that the continuation of the outflow beyond the initial transient depends on the way the magnetic field i5 maintained at the lower boundary., We find that the continuation of the outflow beyond the initial transient depends on the way the magnetic field is maintained at the lower boundary.
 Differential rotation acting on anon-axisymmetric field quickly dissipates the field through convective expulsion. with the result being that the jet is “choked off” at the base.," Differential rotation acting on a non-axisymmetric field quickly dissipates the field through convective expulsion, with the result being that the jet is “choked off” at the base."
 We have compensated for this by adding an inflow of magnetic field at the base., We have compensated for this by adding an inflow of magnetic field at the base.
 This would represent. for example. the emergence of loops of magnetic field into the atmosphere of an accretion disk.," This would represent, for example, the emergence of loops of magnetic field into the atmosphere of an accretion disk."
 Apart from geometric requirements. the most important parameter for efficient jets turned out to be the (differential) speed of rotation of the footpoints.," Apart from geometric requirements, the most important parameter for efficient jets turned out to be the (differential) speed of rotation of the footpoints."
 In the nodels calculated. the necessary speed 1s of the order of the escape velocity from the disk.," In the models calculated, the necessary speed is of the order of the escape velocity from the disk."
 This is more than what is needed in simulations with a long-scale poloidal initial field (e.g. those presented in Paper D., This is more than what is needed in simulations with a long-scale poloidal initial field (e.g. those presented in Paper I).
 Consequently. the critical points (sonic.Alfvén.. fast magnetosonic) and the equipartition point between the magnetic and kinetic energy flow rates are reached at smaller distances.," Consequently, the critical points (sonic, fast magnetosonic) and the equipartition point between the magnetic and kinetic energy flow rates are reached at smaller distances."
 The conversion of magnetic enthalpy (and the components thereof) to kinetic energy is similar apart from that. being fairly efficient.," The conversion of magnetic enthalpy (and the components thereof) to kinetic energy is similar apart from that, being fairly efficient."
 In the adiabatie calculations presented here. thermal energy from hydrodynamic and magnetic dissipation stays in the flow.," In the adiabatic calculations presented here, thermal energy from hydrodynamic and magnetic dissipation stays in the flow."
 This 15 in contrast with our earlier calculations (Papers I&IIL). where we assumed optically thin environments in which much of the dissipated energy is lost by radiation.," This is in contrast with our earlier calculations (Papers II), where we assumed optically thin environments in which much of the dissipated energy is lost by radiation."
 The present models assume no energy loss and are most relevant for optically thick conditions., The present models assume no energy loss and are most relevant for optically thick conditions.
 In the stratified atmosphere of these models. heating contributes to the flow by thermal buoyancy.," In the stratified atmosphere of these models, heating contributes to the flow by thermal buoyancy."
 In some of the cases presented (Sect. 4.4)).," In some of the cases presented (Sect. \ref{sec:singarc}) ),"
 this is the dominant driving mechanism., this is the dominant driving mechanism.
 Though à wound-up magnetic field is also present in these buoyant plume flows. they probably do not qualify as magnetically driven.," Though a wound-up magnetic field is also present in these buoyant plume flows, they probably do not qualify as magnetically driven."
 The non-axisymmetric “stirring” by the rotating magnetic field at the base that drives them may. however. well be relevant for the case of a (rapidly) rotating core inside a dense stellar envelope.," The non-axisymmetric “stirring” by the rotating magnetic field at the base that drives them may, however, well be relevant for the case of a (rapidly) rotating core inside a dense stellar envelope."
" Even though its field configuration is not of the right kind to produce a magnetically powered outflow. dissipation of rotational energy by ""stirring"" may still have powerful etfects on the envelope."," Even though its field configuration is not of the right kind to produce a magnetically powered outflow, dissipation of rotational energy by “stirring” may still have powerful effects on the envelope."
 The magnetic field in the jets presented here is strongly wound. with the field lines making nany turns along the length of the jet. see Fig.," The magnetic field in the jets presented here is strongly wound, with the field lines making many turns along the length of the jet, see Fig."
 8 for an example.," \ref{fig:flinesE}
 for an example."
 Current-driven instabilities. in. particular kink modes. are therefore to be expected and can indeed be found in the simulations.," Current-driven instabilities, in particular kink modes, are therefore to be expected and can indeed be found in the simulations."
 The turbulent wiggling of the jet increases the interaction with the ambient medium. leading to an increased entrainment of material.," The turbulent wiggling of the jet increases the interaction with the ambient medium, leading to an increased entrainment of material."
 At large distances (larger than those covered by the simulations). it 15 possible that the field configuration is affected by instability-induced dissipation of magnetic energy. presumably with dynamical consequences for the jet.," At large distances (larger than those covered by the simulations), it is possible that the field configuration is affected by instability-induced dissipation of magnetic energy, presumably with dynamical consequences for the jet."
 The effect would likely be the same as in jets launched with large- magnetic fields (see Paper II for that)., The effect would likely be the same as in jets launched with large-scale magnetic fields (see Paper II for that).
 Kelvin-Helmholtz instabilities at the interface between the jet and the ambient medium are suppressed by the relatively coarse resolution used in the simulations., Kelvin–Helmholtz instabilities at the interface between the jet and the ambient medium are suppressed by the relatively coarse resolution used in the simulations.
 The final state of the Jet. at large distances from the source. depends on the impact of instabilities in the region beyond the computational volume of the simulations presented here.," The final state of the jet, at large distances from the source, depends on the impact of instabilities in the region beyond the computational volume of the simulations presented here."
 It is reasonable to believe that the jet continues as a ballistic flow when the instabilities cease to be effective (due to the expansion of the jet and a possible decay of the toroidal field)., It is reasonable to believe that the jet continues as a ballistic flow when the instabilities cease to be effective (due to the expansion of the jet and a possible decay of the toroidal field).
" Α ""disruption"" of the jet would require a strong interaction with the medium into which it propagates: the atmosphere at large distances is probably too thin for that.", A “disruption” of the jet would require a strong interaction with the medium into which it propagates; the atmosphere at large distances is probably too thin for that.
 Although the simulations presented here demonstrate possible forms of rotation-induced acceleration. they probably do not represent very realistic models of actual accretion disks.," Although the simulations presented here demonstrate possible forms of rotation-induced acceleration, they probably do not represent very realistic models of actual accretion disks."
 One may wonder what happens i a more realistic scenario with more complicated or chaotically arranged magnetic field loops emerging from the disk., One may wonder what happens in a more realistic scenario with more complicated or chaotically arranged magnetic field loops emerging from the disk.
 Obviously. magnetic reconnection would likely play a major role in such a scenario.," Obviously, magnetic reconnection would likely play a major role in such a scenario."
 Nonetheless. the surviving magnetic field is stretched out in azimuthal direction by the rotation. and the free energy in the toroidal field ts transformed into an outflow.," Nonetheless, the surviving magnetic field is stretched out in azimuthal direction by the rotation, and the free energy in the toroidal field is transformed into an outflow."
 Temporary fluctuations are likely to occur if the supply of magnetic field loops is not continuous., Temporary fluctuations are likely to occur if the supply of magnetic field loops is not continuous.
 The coherent length of the jet will then be determined by the speed with which reconnection processes destroy the initial field by which the flow is produced., The coherent length of the jet will then be determined by the speed with which reconnection processes destroy the initial field by which the flow is produced.
 The jet may flare up anew when new loops emerge., The jet may flare up anew when new loops emerge.
 This effect could be responsible for the temporary fluctuations in gamma ray bursts., This effect could be responsible for the temporary fluctuations in gamma ray bursts.
 Loops of magnetic field can also be found in the solar corona and their evolution there is likely connected with explosive ejections of material (CMEs. see e.g. ? fora review).," Loops of magnetic field can also be found in the solar corona and their evolution there is likely connected with explosive ejections of material (CMEs, see e.g. \citealt{2006Forbes} for a review)."
 One general idea is that the differential rotation as well as convective motions at the solar photosphere produces shearing. and the energy in the sheared/twisted field is set free in an explosive event (e.g.22)..," One general idea is that the differential rotation as well as convective motions at the solar photosphere produces shearing, and the energy in the sheared/twisted field is set free in an explosive event \citep[e.g.][]{1989vanBallegooijen,2009Zuccarello}."
 In contrast to the jet models discussed here. the footpoints of a solar magnetic arcade is unlikely to be twisted by a (pure) azimuthal motion.," In contrast to the jet models discussed here, the footpoints of a solar magnetic arcade is unlikely to be twisted by a (pure) azimuthal motion."
 Non-azimuthal shearing ts not likely to produce an extended helical field (as in Fig. 4)), Non-azimuthal shearing is not likely to produce an extended helical field (as in Fig. \ref{fig:flinesD})
The model selection approach also allows assessment of the relative Bayesian evidence (In2) for the planarity ⊔↓⋯⇂∢⋅↓↿∖≼⇍∪↓⋅↓⋅⋖⋅⇂⋜∐↓∪⊔∣⋡⋖⋅↿∖∖⊽⋖⋅⋖⊾⊔∣∶−≻⊳∆↗≻⊳⊔∣∶∣⊔↓⋯⇂∢⋅⊳∖⊐⋜⋯∠⊓↓↥⋖⋅. ⋅⋅ ∕ m-preference⋅ model (a correlation⋠ between {5.205. om; not restricted).,"The model selection approach also allows assessment of the relative Bayesian evidence $\ln B$ ) for the planarity model (correlation between $\ell=2,3$, $m'=\ell$ modes) and the $m$ -preference model (a correlation between $\ell=2-5$, $m'$ not restricted)."
 This extends the work of Magueijo&Sorkin(2006) where the low-f low-power evidence was assessed. as well as planarity for some data-sets.," This extends the work of \cite{raf} where the $\ell$ low-power evidence was assessed, as well as planarity for some data-sets."
 Using the Bayes factor. anc the BIC approximation. we find that there is substantial evidence for the planarity model. but no evidence for the m-preference model.," Using the Bayes factor, and the BIC approximation, we find that there is substantial evidence for the planarity model, but no evidence for the $m$ -preference model."
 We also ake a frequentist approach to the problem. and. compare he goodness of [it (ff) to those from Gaussian SL simulations.," We also take a frequentist approach to the problem, and compare the “goodness of fit” $H_f$ ) to those from Gaussian SI simulations."
 In agreement with the Bayesian approach. we ind stronger evidence for the planarity model (~98'4 CL). han for the m-preference model (~95% CL).," In agreement with the Bayesian approach, we find stronger evidence for the planarity model $\sim 98$ CL), than for the $m$ -preference model $\sim 95$ CL)."
 These results are in contradiction with the ALC approach which finds evidence for both models. and. generally stronger evidence or the m-preference model.," These results are in contradiction with the AIC approach which finds evidence for both models, and generally stronger evidence for the $m$ -preference model."
 We think this demonstrates a weakness of this crude statistic. that does not appear to »enalize enough for extra parameters.," We think this demonstrates a weakness of this crude statistic, that does not appear to penalize enough for extra parameters."
 The m-preference model is a more general version of he planarity model., The $m$ -preference model is a more general version of the planarity model.
 Ht is therefore not surprising that the evidence for the planarity model is higher. as the parameter space is smaller while still including the best fitting moclel (m= 0).," It is therefore not surprising that the evidence for the planarity model is higher, as the parameter space is smaller while still including the best fitting model $m'=\ell$ )."
 Likewise. we could restrict the m paranieters © positivo mirror parity modes and find a higher. Bayes actor.," Likewise, we could restrict the $m'$ parameters to positive mirror parity modes and find a higher Bayes factor."
 Dut without a theoretical motivation for restricting he m parameters to these values it could. be argued that his approach involves tuning our model (or equivalently: - he priors) to fit the data-, But without a theoretical motivation for restricting the $m'$ parameters to these values it could be argued that this approach involves tuning our model (or equivalently - the priors) to fit the data.
 Therefore. the lower significance (~ 95'4)) result. for the m-preference. model is our more conservative result. for the significance of the AOL in the WALAP third-vear data.," Therefore, the lower significance $\sim 95$ ) result for the $m$ -preference model is our more conservative result for the significance of the AOE in the WMAP third-year data."
 Note that the Daves factor finds no support for this model. in multipoles (=25. nor forjust (=2.3 (see last column of Table 5)).," Note that the Bayes factor finds no support for this model, in multipoles $\ell=2-5$, nor for just $\ell=2,3$ (see last column of Table \ref{Htabm}) )."
 The higher significance. returned. by the simulations. compared to the Daves factor. highlights an important dilference between the Bayesian and frequentist approaches to model comparison.," The higher significance returned by the simulations, compared to the Bayes factor, highlights an important difference between the Bayesian and frequentist approaches to model comparison."
 For some confidence level. the In(£) 77.. (Gorskictal.1998) ," For some confidence level, the $\ln(B)$ \ref{hybrid}, \citep{healp} "
Whether it is due to Galactic dust or svuchrotron. to cosmological backerounds such as the Cosmic Microwave Backeround (CAIB) or to the Cosmic Infrared Backeround (CID). hat traces the integrated radiation of uuresolved ealaxies. diffuse clusion is onumnipresent in infrared aud iillinetrie observations.,"Whether it is due to Galactic dust or synchrotron, to cosmological backgrounds such as the Cosmic Microwave Background (CMB) or to the Cosmic Infrared Background (CIB), that traces the integrated radiation of unresolved galaxies, diffuse emission is omnipresent in infrared and millimetric observations."
 The augular power προςτι of this radiation is one of the main tools used to constraiu the structure of the interstellar uediuu. the clustering of IR ealaxies (CIB). or the cosiological parameters (CMD).," The angular power spectrum of this radiation is one of the main tools used to constrain the structure of the interstellar medium, the clustering of IR galaxies (CIB), or the cosmological parameters (CMB)."
 Iu short. its estimation requires to Fourier transform the nuage and to average the imiodulus square of the Fourier auplitudes iuto frequency bius.," In short, its estimation requires to Fourier transform the image and to average the modulus square of the Fourier amplitudes into frequency bins."
 However. the image has both boundaries aud offen masked regious (c.g. to remove bright poiut sources) that iuduce power aliasing aud biases the estimation of the ΝΟΥ spectrum if not accounted for properly.," However, the image has both boundaries and often masked regions (e.g. to remove bright point sources) that induce power aliasing and biases the estimation of the power spectrum if not accounted for properly."
 The effec beconies quite sienificaut. when the signa has a steep power spectrun such as À5m simular to that measured for Galactic càyus enisson (2) or even steeper than & as for CAIB anisotropy on angular scales siacr than a few arcnüu (e.g.?7)..," The effect becomes quite significant when the signal has a steep power spectrum such as $k^{-3}$, similar to that measured for Galactic cirrus emission \citep{mamd_07} or even steeper than $k^{-4}$ as for CMB anisotropy on angular scales smaller than a few arcmin \citep[e.g.][]{acbar,quad_t}."
 To account for uou-periodic boundaries. % proposed au original apocizing technique that helps us to deconvolve the estimated power spectrum from that of the observed patch bouncdarics.," To account for non-periodic boundaries, \cite{das}
 proposed an original apodizing technique that helps us to deconvolve the estimated power spectrum from that of the observed patch boundaries."
 These authors also iuitisate the impact of holes by applying a pre-whitenimeg technique to data in real space., These authors also mitigate the impact of holes by applying a pre-whitening technique to data in real space.
 Iu the contest of CMD anisotropy. ? developed the method that allows us to correct for mask effects ou the output binned power spectrum.," In the context of CMB anisotropy, \cite{master} developed the method that allows us to correct for mask effects on the output binned power spectrum."
 They analyze data accross the full sky and account for the sky curvature., They analyze data accross the full sky and account for the sky curvature.
 Tustead of classical Fourier analysis. they project the data outo spherical harmonics aud eo through the algebra of angular power spectra (see Sect. 2)).," Instead of classical Fourier analysis, they project the data onto spherical harmonics and go through the algebra of angular power spectra (see Sect. \ref{se:ps_def}) )."
 This idea las been successfully used ia several experiments (e.g.2?) and is also the basis of more refined algorithms used iu ce. WALAP (7) and Archeops (2).," This idea has been successfully used in several experiments \citep[e.g.][]{boomerang,archeops_t1} and is also the basis of more refined algorithms used in e.g. WMAP \citep{hinshaw} and Archeops \citep{archeops_t2}."
 owever. direct use of in the context of infrared observations with a resolution of tvpicallv a few arcsec requires us to estimate Leecudre polynomials up to orders ( of 10.000 or more or which current recurrences and iutegratiou methods are iwuuerically unstable;," However, direct use of in the context of infrared observations with a resolution of typically a few arcsec requires us to estimate Legendre polynomials up to orders $\ell$ of 10,000 or more for which current recurrences and integration methods are numerically unstable."
 Other techuiques developed in the context of CAIB anisotropy such as maxima ikclihood estimation (7) could be transposed to high aneular resolution maps. but the numerical cost XTM is prolübitive for conmuon applications when the analysis xpeliue requires Moute Carlo simulations.," Other techniques developed in the context of CMB anisotropy such as maximum likelihood estimation \citep{bjk} could be transposed to high angular resolution maps, but the numerical cost $\propto n_{pix}^3$ is prohibitive for common applications when the analysis pipeline requires Monte Carlo simulations."
 This paper aius to transpose the pseudo-spectrua approach pioncerc by to high augular resolution observations aud a classical Fourier analysis iu the contest of the Hat skv approximation., This paper aims to transpose the -spectrum approach pioneered by to high angular resolution observations and a classical Fourier analysis in the context of the flat sky approximation.
 Its originality compared to other approaches is that it works exclusively in discrete space and therefore avoids the complexity of resampling the data and inteerating Bessel fictions., Its originality compared to other approaches is that it works exclusively in discrete space and therefore avoids the complexity of resampling the data and integrating Bessel functions.
" Our aleorithui was nicknamedPon. for ""DP. Of k EstinatoR."," Our algorithm was nicknamed, for “P. Of $k$ EstimatoR”."
 The paper is organized as follows., The paper is organized as follows.
 Section 2 provides the definitions aud algebra involved iu and Sect., Section \ref{se:ps_def} provides the definitions and algebra involved in and Sect.
 3 shows its applications to simulations of various astrophysical components spectra aud a complex mask., \ref{se:applis} shows its applications to simulations of various astrophysical components spectra and a complex mask.
 Detailed derivatious of our results are presented im the appendices., Detailed derivations of our results are presented in the appendices.
 Although this work focuses ou temperature power spectrum estimation. we also show in Appendices AppendixD: and Appendix€: how the formalism cau be generalized to the case of polarization.," Although this work focuses on temperature power spectrum estimation, we also show in Appendices \ref{se:app_eb} and \ref{se:app_te} how the formalism can be generalized to the case of polarization."
 We first) briefly state the limits of the flat sky approxiuation. then recall the definitious of both the power spectrum and psesdo--power spectrum of data iu the coutest of continuous Fourier trausforms.," We first briefly state the limits of the flat sky approximation, then recall the definitions of both the power spectrum and -power spectrum of data in the context of continuous Fourier transforms."
 Finally. we consider their counterpart m discrete space and the Huplementation ofPorn.," Finally, we consider their counterpart in discrete space and the implementation of."
 Projecting an observed fraction of the sky onto a plane rather than a sphere alters the image properties in a wav that depends onu the specific reprojection scheme (6.8. enomonic. tangenutial. evliudrical ete).," Projecting an observed fraction of the sky onto a plane rather than a sphere alters the image properties in a way that depends on the specific reprojection scheme (e.g. gnomonic, tangential, cylindrical etc)."
 The angular power, The angular power
"are mostly the result of thermal buoyancy, driven by dissipative heating of the near-disk atmosphere.","are mostly the result of thermal buoyancy, driven by dissipative heating of the near-disk atmosphere."
" Nonetheless, the presence of a magnetic field is required to launch a directed flow."," Nonetheless, the presence of a magnetic field is required to launch a directed flow."
 The simulations cover the same physical range as the one presented in the preceding section., The simulations cover the same physical range as the one presented in the preceding section.
" The resolution is 400x256x 256, so that the diameter of the differentially rotating surface is resolved with about 25 cells."," The resolution is $400\times256\times256$ , so that the diameter of the differentially rotating surface is resolved with about 25 cells."
" The longest simulation, which also produces the most efficient jet, has the parameter values (Bp=1.2,Ms15)."," The longest simulation, which also produces the most efficient jet, has the parameter values $(\betab=1.2,\Mb=15)$."
" It ran for 14 wallclock days on 96 processors and covers almost two jet crossings, the upper boundary being reached at t~62."," It ran for 14 wallclock days on 96 processors and covers almost two jet crossings, the upper boundary being reached at $t\approx 62$."
" In the jet of the preceding section, Poynting flux was the main source of energy to accelerate the jet."," In the jet of the preceding section, Poynting flux was the main source of energy to accelerate the jet."
 This is clearly different here., This is clearly different here.
" The simulation with (By=1.2,My15) attains a momentary quasi-stationary state, with £x«const in the energy flow, at t~80...90."," The simulation with $(\betab=1.2,\Mb=15)$ attains a momentary quasi-stationary state, with $\efrate_\text{tot}\approx\const$ in the energy flow, at $t \approx 80 \ldots
90$ ."
" In sharp contrast to Fig. 11,,"," In sharp contrast to Fig. \ref{fig:eflow},"
" Ciim is the dominating component at the beginning, being a factor of ~3 larger than Emag."," $\efrate_\text{thrm}$ is the dominating component at the beginning, being a factor of $\simm3$ larger than $\efrate_\text{mag}$."
" The equipartition point Exin=Emag is very close to the lower boundary, the radius where kin=Ethrm is larger, at r~15."," The equipartition point $\efrate_\text{kin}=\efrate_\text{mag}$ is very close to the lower boundary, the radius where $\efrate_\text{kin}=\efrate_\text{thrm}$ is larger, at $r\approx15$."
" Emag also diminishes (by about 80%)), but it is only a small fraction of the final &kin."," $\efrate_\text{mag}$ also diminishes (by about ), but it is only a small fraction of the final $\efrate_\text{kin}$."
 The excess temperature responsible for the high Sim turns up near the central axis next to the lower boundary and increases with the speed of rotation., The excess temperature responsible for the high $\efrate_\text{thrm}$ turns up near the central axis next to the lower boundary and increases with the speed of rotation.
" The heat is apparently produced by numerical viscosity, i.e. dissipation of kinetic energy due to the coarse resolution of the rapidly rotating inner part of the disk."," The heat is apparently produced by numerical viscosity, i.e. dissipation of kinetic energy due to the coarse resolution of the rapidly rotating inner part of the disk."
" Unfortunately, a much higher resolution is unfeasible and a large My is needed for an efficient production of B,."," Unfortunately, a much higher resolution is unfeasible and a large $\Mb$ is needed for an efficient production of $B_\varphi$."
 The simulations are therefore relevant for cases in which dissipative heating is of importance., The simulations are therefore relevant for cases in which dissipative heating is of importance.
 The appearance of the flow becomes more jetlike with increasing rotation velocity., The appearance of the flow becomes more jetlike with increasing rotation velocity.
" In a simulation with (Bp=1.2,M= 3), corresponding to a differential rotation velocity of about 1.1 of the outer loops' footpoints, the jet terminates at a few disk radii from the source in a tightly wound helix, similar to the free end of a garden hose."," In a simulation with $(\betab=1.2,\Mb=3)$ , corresponding to a differential rotation velocity of about $1.1$ of the outer loops' footpoints, the jet terminates at a few disk radii from the source in a tightly wound helix, similar to the free end of a garden hose."
" With My=9, the flow has a turbulent, “smoke stack""-like appearance."," With $\Mb=9$, the flow has a turbulent, “smoke stack”-like appearance."
" The jet produced with My=15 is subject to non-axisymmetric perturbations, but much more coherent."," The jet produced with $\Mb=15$ is subject to non-axisymmetric perturbations, but much more coherent."
" Despite the main energy source being thermal, the results depend greatly on whether a magnetic field is present or not."," Despite the main energy source being thermal, the results depend greatly on whether a magnetic field is present or not."
" In a simulation with (y=1078,M,15), i.e. with virtually no magnetic field, there is no unidirectional flow."," In a simulation with $(\betab=10^{28},\Mb=15)$, i.e. with virtually no magnetic field, there is no unidirectional flow."
" Rather, material is ejected sideways as well as in the upward direction, see Fig. 12.."," Rather, material is ejected sideways as well as in the upward direction, see Fig. \ref{fig:vxrho}."
" The simulation soon crashes, presumably due to too much heat accumulating."," The simulation soon crashes, presumably due to too much heat accumulating."
 The same simulation with y=1.2 is well collimated and plows effortlessly through the dense parts of the atmosphere., The same simulation with $\betab=1.2$ is well collimated and plows effortlessly through the dense parts of the atmosphere.
 We produced collimated outflows in numerical simulations by rotating the footpoints of arcade-shaped magnetic loops., We produced collimated outflows in numerical simulations by rotating the footpoints of arcade-shaped magnetic loops.
 The longest of these jets cross a computational domain which is two orders of magnitude larger than the size of the source., The longest of these jets cross a computational domain which is two orders of magnitude larger than the size of the source.
 Flow acceleration via dissipative as well as non-dissipative processes was observed., Flow acceleration via dissipative as well as non-dissipative processes was observed.
" The latter relies on the presence of shear in the form of differential rotation of the footpoints of individual field loops, which results into the development of a toroidal magnetic field component."," The latter relies on the presence of shear in the form of differential rotation of the footpoints of individual field loops, which results into the development of a toroidal magnetic field component."
 The resulting jet has a helical magnetic field structure with field lines running back to the source outside the jet., The resulting jet has a helical magnetic field structure with field lines running back to the source outside the jet.
 The case of uniformly rotating magnetic loops has also been studied., The case of uniformly rotating magnetic loops has also been studied.
" It turns out to be markedly less effective at producing outflows; infact, no jetlike outflows were observed for uniformly rotating arcades within the numerically accessible parameter range."," It turns out to be markedly less effective at producing outflows; infact, no jetlike outflows were observed for uniformly rotating arcades within the numerically accessible parameter range."
 The shear between the rotating, The shear between the rotating
Betelgeuse is a red supergiant star (Betelgeuse. HD 39801. MI-2Ia-Ibe) and is one of the brightest stars in the optical and near infrared.,"Betelgeuse is a red supergiant star (Betelgeuse, HD 39801, M1–2Ia–Ibe) and is one of the brightest stars in the optical and near infrared."
 This star exhibits variations m integrated brightness. surface features. and the depths. shapes. and Doppler shifts of its spectral lines.," This star exhibits variations in integrated brightness, surface features, and the depths, shapes, and Doppler shifts of its spectral lines."
 There is a backlog of visual-wavelength observations of its brightness which covers almost a hundred years., There is a backlog of visual-wavelength observations of its brightness which covers almost a hundred years.
 The irregular fluctuations of its light curve are clearly aperiodic and rather resemble a series of outbursts., The irregular fluctuations of its light curve are clearly aperiodic and rather resemble a series of outbursts.
 ? studied the variability of different red supergiant (RSG) stars including Betelgeuse and they found a strong noise component in the photometric variability. probably caused by the large convection cells.," \cite{2006MNRAS.372.1721K} studied the variability of different red supergiant (RSG) stars including Betelgeuse and they found a strong noise component in the photometric variability, probably caused by the large convection cells."
 In addition to this. the spectral line variations have been analyzed by several authors. who inferred the presence of large granules and high convective velocities (22).," In addition to this, the spectral line variations have been analyzed by several authors, who inferred the presence of large granules and high convective velocities \citep{2007A&A...469..671J,2008AJ....135.1450G}."
 ? also found line bisectors that predominantly have reversed C-shapes. and line shape variations occurring. at the ] ss! level that have no obvious connection to their shifts in wavelength.," \citeauthor{2008AJ....135.1450G} also found line bisectors that predominantly have reversed C-shapes, and line shape variations occurring at the 1 $^{-1}$ level that have no obvious connection to their shifts in wavelength."
 The position of Betelgeuse on the H-R diagram is highly uncertain. due to uncertainty in its effective temperature.," The position of Betelgeuse on the H-R diagram is highly uncertain, due to uncertainty in its effective temperature."
 ?— used one-dimensional MARCS models (??) to fit the incredibly rich TIO. molecular bands in the optical region of the spectrum for several RSGs.," \cite{2005ApJ...628..973L} used one-dimensional MARCS models \citep{2003ASPC..288..331G,1975A&A....42..407G} to fit the incredibly rich TiO molecular bands in the optical region of the spectrum for several RSGs."
 They found an effective temperature of 3650 K for Betelgeuse., They found an effective temperature of 3650 K for Betelgeuse.
 Despite the fact that they obtained a good agreement with the evolutionary tracks. problems remain.," Despite the fact that they obtained a good agreement with the evolutionary tracks, problems remain."
 There 1s a mismatch in the IR colors that could be due to atmospheric temperature inhomogeneities characteristic of convection (2)..., There is a mismatch in the IR colors that could be due to atmospheric temperature inhomogeneities characteristic of convection \citep{2006ApJ...645.1102L}.
 Also the distance of Betelgeuse has large uncertainities because of errors related to the positional movement of the stellar photocenter., Also the distance of Betelgeuse has large uncertainities because of errors related to the positional movement of the stellar photocenter.
 ? derived a distance of (197445 pe) using high spatial resolution. multiwavelength. VLA radio positions combined with Hipparcos Catalogue Intermediate Astrometric Data.," \cite{2008AJ....135.1430H} derived a distance of $\pm$ 45 pc) using high spatial resolution, multiwavelength, VLA radio positions combined with Hipparcos Catalogue Intermediate Astrometric Data."
 Betelgeuse is one of the best studied RSGs in term of multi- imaging because of its large luminosity and angular diameter., Betelgeuse is one of the best studied RSGs in term of multi-wavelength imaging because of its large luminosity and angular diameter.
 The existence of hot spots on 1ts surface has been proposed to explain numerous interferometric observations with WHT and COAST (22?2??) that have detected time-variable inhomogeneities 1n the brightness distribution.," The existence of hot spots on its surface has been proposed to explain numerous interferometric observations with WHT and COAST \citep{1990MNRAS.245P...7B, 1992MNRAS.257..369W, 1997MNRAS.285..529T,
 1997MNRAS.291..819W, 2000MNRAS.315..635Y, 2004young} that have detected time-variable inhomogeneities in the brightness distribution."
 These authors fitted the visibility and closure phase data with a circular limb-darkened disk and zero to three spots., These authors fitted the visibility and closure phase data with a circular limb-darkened disk and zero to three spots.
 A large spot has been also detected by ? with HST., A large spot has been also detected by \cite{1998AJ....116.2501U} with HST.
 The non-spherical shape of Betelgeuse was also detected by ? in the mid-infrared., The non-spherical shape of Betelgeuse was also detected by \cite{2007ApJ...670L..21T} in the mid-infrared.
 ? published à reconstructed image of Betelgeuse in the H band with two spots using the same data às presented 1n this work., \cite{2009A&A...508..923H} published a reconstructed image of Betelgeuse in the H band with two spots using the same data as presented in this work.
 ? resolved Betelgeuse using diffraction-limited adaptive optics in the near-infrared and found an asymmetric envelope around the star with a bright plume extending in the southwestern region., \cite{2009A&A...504..115K} resolved Betelgeuse using diffraction-limited adaptive optics in the near-infrared and found an asymmetric envelope around the star with a bright plume extending in the southwestern region.
 They claimed the plume was either due to the presence of a convective hot spot or was caused by stellar rotation., They claimed the plume was either due to the presence of a convective hot spot or was caused by stellar rotation.
 ? presented VLTI/AMBER observations of Betelgeuse at high spectral resolution and spatially resolved CO gas motions.," \cite{2009A&A...503..183O}
 presented VLTI/AMBER observations of Betelgeuse at high spectral resolution and spatially resolved CO gas motions."
 They claimed that these motions were related to convective motions in the upper atmosphere or to intermittent mass ejections in clumps or ares., They claimed that these motions were related to convective motions in the upper atmosphere or to intermittent mass ejections in clumps or arcs.
 Radiation hydrodynamics (RHD) simulations of red supergiant stars are available (?) to interpret past and future observations., Radiation hydrodynamics (RHD) simulations of red supergiant stars are available \citep{2002AN....323..213F} to interpret past and future observations.
 (?.hereafterPaper1) used these simulations to explore the impact of the granulation pattern on observed visibility curves and closure phases and detected a granulation pattern on Betelgeuse in the K band by fitting the existing interferometric data of ?.., \cite[hereafter Paper~I]{2009A&A...506.1351C} used these simulations to explore the impact of the granulation pattern on observed visibility curves and closure phases and detected a granulation pattern on Betelgeuse in the K band by fitting the existing interferometric data of \cite{2004A&A...418..675P}.
 This paper is the second in the series aimed at exploring the convection in RSGs., This paper is the second in the series aimed at exploring the convection in RSGs.
 The main purpose is to compare RHD simulations to high-angular resolution observations of Betelgeuse covering a wide spectral range from the optical, The main purpose is to compare RHD simulations to high-angular resolution observations of Betelgeuse covering a wide spectral range from the optical
The peak rest-frame brightucss temperature of the rine is 12 Ik (East chump in our map of Fig 1)).,The peak rest-frame brightness temperature of the ring is 12 K (East clump in our map of Fig \ref{EVLA}) ).
 This is similar to what has been seeu iu other 2~lL SALGs. such as GN20 (Carillietal.2010).. althoueh we cannot rule-out lugher Zp chuups that are not resolved by our present observations.," This is similar to what has been seen in other $z~\sim~4$ SMGs, such as GN20 \citep{Cari10}, although we cannot rule-out higher $T_B$ clumps that are not resolved by our present observations."
" While there is a long history of CO) observations from strongly leused. high redshift galaxies (c.g,Al 2010)... MMISI22]5938 is only the second complete Einstein ring seen in CO ciission. after the 2Ξ1.1 quasar host ealaxy PSS J2322|19LL (Carillietal.2003)."," While there is a long history of CO observations from strongly lensed, high redshift galaxies \citep[e.g.][]{Allo97,Barv94, Swin10}, MM18423+5938 is only the second complete Einstein ring seen in CO emission, after the z=4.1 quasar host galaxy PSS J2322+1944 \citep{Cari03}."
 We identified the lens aud derived a magnification factor of ~12 using a preliminary leusing niodel., We identified the lens and derived a magnification factor of $\sim 12$ using a preliminary lensing model.
" We aneasured a luminosity Log),μι: aud correspouding Il; amass. for MMUISI23]5938 that. when corrected for magnification. are simular to the unuleused SALCs."," We measured a luminosity $\rm L'_{CO(1-0)}$, and corresponding $\rm H_2$ mass, for MM18423+5938 that, when corrected for magnification, are similar to the unlensed SMGs."
 However. the relatively huge range for Lp;g iun our present analysis requires further observations to better xuuple the FIR SED iu orderto better coustrain the iurplied star formation rate.," However, the relatively large range for $L_{FIR}$ in our present analysis requires further observations to better sample the FIR SED in orderto better constrain the implied star formation rate."
 As demonstrated by Ricchersetal.(2008). for the molecular BEiustein ring observed towards the QSO PSS J2322|1911. the brighter SAIC 1223|5938 provides a uuique opportunity to study AIMAISthe eas dynamics on plivsical scale as πα as ~LOO pc with further high scusitivity aud high spatial resolution EVLA observations.," As demonstrated by \citet{Riec08} for the molecular Einstein ring observed towards the QSO PSS J2322+1944, the brighter SMG MM18423+5938 provides a unique opportunity to study the gas dynamics on physical scale as small as $\sim 100$ pc with further high sensitivity and high spatial resolution EVLA observations."
 We acknowledge aud sincerely thankpromptly Dr. S. D. J. Carvu (CADC. Victoria. Canada) for stacking the CFEITT £Llivir processed MegaCau data with ALegaPipe.," We acknowledge and sincerely thank Dr. S. D. J. Gwyn (CADC, Victoria, Canada) for promptly stacking the CFHT $Elixir$ processed MegaCam data with $MegaPipe$."
 This work is based on EVLA observations conducted under the auspices of NRAO. WirCam iud \eeaCam observations conducted at CEITT. and on use of data products from the Two Micron All Sky Survey (241ASS). EVLA.. CFIT..," This work is based on EVLA observations conducted under the auspices of NRAO, WirCam and MegaCam observations conducted at CFHT, and on use of data products from the Two Micron All Sky Survey (2MASS). , ."
for the universe as a whole.,for the universe as a whole.
 Fig., Fig.
" 9 shows, as a function of mass, the abundance of objects identified by the SO(180) algorithm in spherical regions centred on the most massive halo at two different redshifts."," \ref{fig:fig9}
 shows, as a function of mass, the abundance of objects identified by the SO(180) algorithm in spherical regions centred on the most massive halo at two different redshifts."
" The left-hand plot is based on the VLS simulation at z—0 and shows results for spheres of radius 80, 40 and 20 times rooo=! 1.5ΗMpc."," The left-hand plot is based on the VLS simulation at $z=0$ and shows results for spheres of radius $80$ , $40$ and $20$ times $r_{200}= 1.5h^{-1}$ Mpc."
" The right-hand plot is based on R4 at z=49 and shows results for spheres with the ""same"" radii, except that now T200= 1.2h!kpc in comoving units."," The right-hand plot is based on R4 at $z=49$ and shows results for spheres with the “same” radii, except that now $r_{200}=1.2h^{-1}$ kpc in comoving units."
 These plots thus correspond to the simulations and redshifts illustrated in Fig. 8.., These plots thus correspond to the simulations and redshifts illustrated in Fig. \ref{fig:fig8}.
 Both panels of Fig., Both panels of Fig.
" 9 also show predictions for the halo mass function in ""typical"" regions of the universe based on the standard Press-Schechter (PS; Press Schechter 1974) and Sheth Tormen (ST; Sheth Tormen 1999) formulae.", \ref{fig:fig9} also show predictions for the halo mass function in “typical” regions of the universe based on the standard Press-Schechter (PS; Press Schechter 1974) and Sheth Tormen (ST; Sheth Tormen 1999) formulae.
" At z—0 these formulae agree moderately well and the ST prediction, in particular, is very close to the fitting function proposed by Jenkins et al. ("," At $z=0$ these formulae agree moderately well and the ST prediction, in particular, is very close to the fitting function proposed by Jenkins et al. ("
2001) as a good representation of the best available simulation data.,2001) as a good representation of the best available simulation data.
" At z—49, however, the two predictions disagree badly — by a factor of about 10 at 1000h!Mc and by a factor of about 100 at 105A!Mo."," At $z=49$, however, the two predictions disagree badly – by a factor of about 10 at $1000h^{-1}{\rm M}_\odot$ and by a factor of about 100 at $10^5h^{-1}{\rm M}_\odot$."
" In this regime there are no reliable simulations with which they can be compared, so it is unclear which (if either) is most correct."," In this regime there are no reliable simulations with which they can be compared, so it is unclear which (if either) is most correct."
" For the largest high-resolution simulation of a ""typical"" region carried out so far, the so-called Millennium Run, the ST formulae continue to fit the high mass tail of the concordance ACDM mass function out to z—10 where the PS formulae already underpredict by about an order of magnitude (Springel et al."," For the largest high-resolution simulation of a “typical” region carried out so far, the so-called Millennium Run, the ST formulae continue to fit the high mass tail of the concordance $\Lambda$ CDM mass function out to $z=10$ where the PS formulae already underpredict by about an order of magnitude (Springel et al."
 2005)., 2005).
" Nevertheless, these results are still a factor of 5 in redshift and 10° in mass from the regime of concern here."," Nevertheless, these results are still a factor of 5 in redshift and $10^6$ in mass from the regime of concern here."
 Both the PS and the ST formula fit the z—0 data well for spheres of radius 80 and 40r2o0 and the simulation results in the two cases are indistinguishable., Both the PS and the ST formula fit the $z=0$ data well for spheres of radius $80$ and $40r_{200}$ and the simulation results in the two cases are indistinguishable.
" For the sphere of radius 20r200, the simulation results are similar at small mass but appear high at the large mass end."," For the sphere of radius $20r_{200}$, the simulation results are similar at small mass but appear high at the large mass end."
" Within the two larger spheres the mean overdensity is close to zero, so no substantial bias is expected theoretically."," Within the two larger spheres the mean overdensity is close to zero, so no substantial bias is expected theoretically."
 The situation is dramatically different at redshift z—49., The situation is dramatically different at redshift $z=49$.
" Even though the ST prediction is much larger than that from PS theory, it still lies far below any of the mass functions measured from the simulation."," Even though the ST prediction is much larger than that from PS theory, it still lies far below any of the mass functions measured from the simulation."
" In addition, the three spheres produce mass functions which differ considerably, with the smallest sphere having the largest abundances."," In addition, the three spheres produce mass functions which differ considerably, with the smallest sphere having the largest abundances."
" As noted above, the overdensities within these spheres are substantial, and as we now show, their mass functions can be predicted surprisingly well by inserting these overdensities into a suitable version of the conditional or extended Press-Schechter model (EPS; Bond et al."," As noted above, the overdensities within these spheres are substantial, and as we now show, their mass functions can be predicted surprisingly well by inserting these overdensities into a suitable version of the conditional or extended Press-Schechter model (EPS; Bond et al."
" 1991; Bower 1991; Lacey Cole 1993, 1994; Mo White 1996)."," 1991; Bower 1991; Lacey Cole 1993, 1994; Mo White 1996)."
" According to the EPS model as worked out by Mo White (1996), the fractionof the material in a large spherical region oftotal mass Mo and linear overdensity extrapolated to the present day óo which, at redshift z, is contained in"," According to the EPS model as worked out by Mo White (1996), the fractionof the material in a large spherical region oftotal mass $M_0$ and linear overdensity extrapolated to the present day $\delta_0$ which, at redshift $z$ , is contained in"
.lux Limited X-ray sample together cover approximately two-thirdsETE theEREet dsαἱ. mE to redshift z~0.3 and contain more than 750 clusters.,Flux Limited X-ray sample together cover approximately two-thirds of the sky out to redshift $z\sim 0.3$ and contain more than 750 clusters.
 The Massive Cluster Survey -— which at this writing contains 126 clusters and covers 55 per cent of the sky — extends these data to z~0.7., The Massive Cluster Survey – which at this writing contains 126 clusters and covers 55 per cent of the sky – extends these data to $z\sim 0.7$.
 The most straightforward mass-observable relation to complement these X-ray flux-limited surveys is the mass—X-ray luminosity relation., The most straightforward mass–observable relation to complement these X-ray flux-limited surveys is the mass--X-ray luminosity relation.
" For sufficiently massive (hot) objects at the relevant redshifts, the conversion from X-ray flux to luminosity is approximately independent of temperature, in which case the luminosities can be estimated directly from the survey flux and the selection function is identical to the requirement of detection."," For sufficiently massive (hot) objects at the relevant redshifts, the conversion from X-ray flux to luminosity is approximately independent of temperature, in which case the luminosities can be estimated directly from the survey flux and the selection function is identical to the requirement of detection."
" In a flux-complete survey further restricted to high luminosities, every cluster should thus be usable in the analysis, without the need for additional observations other than those required to calibrate the mass-luminosity relation."," In a flux-complete survey further restricted to high luminosities, every cluster should thus be usable in the analysis, without the need for additional observations other than those required to calibrate the mass–luminosity relation."
" A disadvantage is that there is a large scatter in cluster luminosities at fixed mass; however, sufficient data allow this scatter to be quantified empirically."," A disadvantage is that there is a large scatter in cluster luminosities at fixed mass; however, sufficient data allow this scatter to be quantified empirically."
" Alternative approaches use cluster [Henry]temperature gas fraction or Yx parameterB004),, to achieve tighter mass—observable relations at etthe al,expense of reducing the size of the samples available for analysis."," Alternative approaches use cluster temperature, gas fraction or $Y_X$ parameter to achieve tighter mass–observable relations at the expense of reducing the size of the samples available for analysis."
 The need to quantify the selection function in terms of both X-ray flux and a second observable additionally complicates these efforts., The need to quantify the selection function in terms of both X-ray flux and a second observable additionally complicates these efforts.
" In this paper, we use the observed X-ray luminosity function to investigate two cosmological scenarios, assuming a spatially flat metric in both cases: the first includes dark energy in the form of a cosmological constant (ACDM)); the second has dark energy with a constant equation-of-state parameter, w (wCDM))."," In this paper, we use the observed X-ray luminosity function to investigate two cosmological scenarios, assuming a spatially flat metric in both cases: the first includes dark energy in the form of a cosmological constant ); the second has dark energy with a constant equation-of-state parameter, $w$ )."
" In the latter case, we account for the evolution of density perturbations in the dark-energy fluid, assuming that the dark-energy sound speed is equal to the speed of light."," In the latter case, we account for the evolution of density perturbations in the dark-energy fluid, assuming that the dark-energy sound speed is equal to the speed of light."
" For each model, our results are in good agreement with findings from independent cosmological data sets, notably type Ia supernovae (SNIa), the cosmic microwave background (CMB), the X-ray gas mass fraction of galaxy clusters (fgas)), and measurements of cosmic shear."," For each model, our results are in good agreement with findings from independent cosmological data sets, notably type Ia supernovae (SNIa), the cosmic microwave background (CMB), the X-ray gas mass fraction of galaxy clusters ), and measurements of cosmic shear."
 The theoretical background for this work is reviewed in2]., The theoretical background for this work is reviewed in.
 details the data used to constrain the mass-luminosity relation and the cluster samples used to measure the X-ray luminosity function., details the data used to constrain the mass–luminosity relation and the cluster samples used to measure the X-ray luminosity function.
 The analysis procedure is described in and the cosmological results are presented inSectionD]., The analysis procedure is described in and the cosmological results are presented in.
 The[] importance of various systematic effects is discussed in[6]., The importance of various systematic effects is discussed in.
" Unless otherwise noted, masses and luminosities quoted in this paper or shown in figures are computed with respect to a spatially flat reference cosmology with Hubble constant h=Ho/100kms!Mpc!0.7 and Qn 0.3."," Unless otherwise noted, masses and luminosities quoted in this paper or shown in figures are computed with respect to a spatially flat reference cosmology with Hubble constant $h=H_0/100\km\second^{-1}\Mpc^{-1}=0.7$ and $\Omegam=0.3$ ."
" Luminosities and fluxes refer specifically to the energy band in the source and observer rest frames, respectively."," Luminosities and fluxes refer specifically to the energy band in the source and observer rest frames, respectively."
 We will consistently use the notation L to denote to the true luminosity of a cluster and L to denote the luminosity inferred from observation., We will consistently use the notation $L$ to denote to the true luminosity of a cluster and $\hat{L}$ to denote the luminosity inferred from observation.
" We will also write, for example, to refer to the present day matter density in units of the critical density, whereas Qm(z) is the same quantity at redshift z."," We will also write, for example, to refer to the present day matter density in units of the critical density, whereas $\Omegam(z)$ is the same quantity at redshift $z$."
" 'The variance of the linearly evolved density field, smoothed by a spherical top-hat window of comoving radius R, enclosing mass M=InoR3/3, is Here Pm is the mean comoving matter density of the universe, P(k) is the linear power spectrum at redshift zero,Wm(k) is the Fourier transform of the window function, and D(z)=σε(2)/σε(θ) is the growth factor of linear perturbations at scales of 85!Mpc, normalized to unity at z—0."," The variance of the linearly evolved density field, smoothed by a spherical top-hat window of comoving radius $R$, enclosing mass $M=4\pi \bar{\rho}_m R^3 / 3$, is Here $\bar{\rho}_m$ is the mean comoving matter density of the universe, $P(k)$ is the linear power spectrum at redshift zero,$W_M(k)$ is the Fourier transform of the window function, and $D(z)=\sigma_8(z)/\sigma_8(0)$ is the growth factor of linear perturbations at scales of $8h^{-1}\Mpc$, normalized to unity at $z=0$."
" We evaluate the transfer function, T(k), and power sietspectrum,αἱ P000)οςk""*T?(k), using the CAMB package of and mainBodyCitationEind771JJenkinsOthave shown that the predicted mass function of galaxy clusters of mass Μ at redshift 2 can be written in terms of a “universal” function of o!(M,z), which can be fit by a simple form, for cosmological-constant models."," We evaluate the transfer function, $T(k)$ , and power spectrum, $P(k)\propto k^{n_s} T^2(k)$, using the CAMB package of and have shown that the predicted mass function of galaxy clusters of mass $M$ at redshift $z$ can be written in terms of a “universal” function of $\sigma^{-1}(M,z)$, which can be fit by a simple form, for cosmological-constant models."
 It has since been verified that this fitting function is approximately universal (within ~20 per cent) among models with E wz-i1 and Denkinssome2003} evolving-w etmodelsa, It has since been verified that this fitting function is approximately universal (within $\sim 20$ per cent) among models with constant $w\neq-1$ and some $w$ models.
"l]⋅"" adopt the valuesLokas A—0.316, B—0.67 and e—ir. JO1,, determined using a spherical overdensity group finder at an overdensity of 324 with respect to the mean matter density (324m)."," We adopt the values $A=0.316$, $B=0.67$ and $\epsilon=3.82$ from , determined using a spherical overdensity group finder at an overdensity of 324 with respect to the mean matter density $324m$ )."
" The number density per unit mass of galaxy clusters of mass M at redshift z is then Following(2007),, we describe the relationship between mass and X-ray luminosity for massive clusters as self-similar1998], modified by an additional redshift-dependent factor where E(z)=H(z)/Ho and Ma is the cluster mass defined at an overdensity of A with respect to the critical density where the edge of the cluster is defined such that the mean density enclosed is a fixed factor A times the critical density)."," The number density per unit mass of galaxy clusters of mass $M$ at redshift $z$ is then Following, we describe the relationship between mass and X-ray luminosity for massive clusters as self-similar, modified by an additional redshift-dependent factor where $E(z)=H(z)/H_0$ and $M_\Delta$ is the cluster mass defined at an overdensity of $\Delta$ with respect to the critical density where the edge of the cluster is defined such that the mean density enclosed is a fixed factor $\Delta$ times the critical density)."
 Our model also includes a log-normal scatter of width 7(z) in luminosity for a given mass., Our model also includes a log-normal scatter of width $\iscatsym(z)$ in luminosity for a given mass.
" There is good theoretical reason to expect that this scatter may evolve with redshift, since some of the variability in cluster luminosities can be attributed to the development of cool cores as well as the influence of merger events al."," There is good theoretical reason to expect that this scatter may evolve with redshift, since some of the variability in cluster luminosities can be attributed to the development of cool cores as well as the influence of merger events ."
"|2007].. Since current data areinsufficient to directly detect evolution in the mass-luminosity scatter and referencestherein), we allow for a generic, linear evolution in the scatter:"," Since current data areinsufficient to directly detect evolution in the mass–luminosity scatter and referencestherein), we allow for a generic, linear evolution in the scatter:"
"The fitted plvsical models demonstrate clearly that the steep clensity gradient observed in the r>30"" region with extinction (Ilarvev et 22003b) does not continue in the inner region that could not be probed in that study.",The fitted physical models demonstrate clearly that the steep density gradient observed in the $r>30''$ region with extinction (Harvey et 2003b) does not continue in the inner region that could not be probed in that study.
 This is consistent with the modeling of single dish dust emission observations by Visser (2000) ancl Talalla et ((2003)., This is consistent with the modeling of single dish dust emission observations by Visser (2000) and Tafalla et (2003).
 The visibilitv profiles of the best fit models shown in Figure |. are remarkably similar to each other. only the power law moclel differing enough to be distinguishable by eve. aud {hen only at loig baselines.," The visibility profiles of the best fit models shown in Figure 1 are remarkably similar to each other, only the power law model differing enough to be distinguishable by eye, and then only at long baselines."
 This provides an interesting demonstration of the degeneracy of the various nuodels for starless core density structure., This provides an interesting demonstration of the degeneracy of the various models for starless core density structure.
 Figure 2 presents a plot of the best-fit density models., Figure 2 presents a plot of the best-fit density models.
 The normalization of the density. assumes an opacity of en? !. which is uncertain by a [actor of ~5 or more (Ossenkopf Henning 1994).," The normalization of the density assumes an opacity of $\kappa_{{\rm 1.3mm}}=0.02$ $^2$ $^{-1}$, which is uncertain by a factor of $\sim 5$ or more (Ossenkopf Henning 1994)."
 At large radii the Donnor-Ebert and Power-law models differ from the PlIummer-like and cylinder models due to the fact that the latter models are assumed (ο be embedded in an extended uniform distribution of gas., At large radii the Bonnor-Ebert and Power-law models differ from the Plummer-like and cylinder models due to the fact that the latter models are assumed to be embedded in an extended uniform distribution of gas.
" The Phummer-like and Bonnor-Ebert models are almost identical. and have central densities that differ bv only (n(IIl5)=1.4x10"" ? with uncertainty e 50%))."," The Plummer-like and Bonnor-Ebert models are almost identical, and have central densities that differ by only $n({\rm H}_2) = 1.4 \times 10^5$ $^{-3}$ with uncertainty $\sim 50$ )."
 The densily profile of the end-on cvlinder departs significantly from the the and Plumner-like profiles., The density profile of the end-on cylinder departs significantly from the the Bonnor-Ebert and Plummer-like profiles.
 The profile is more shallow with much lower central density (n(llo)=5.1x105 oE with uncertainty  3050))., The profile is more shallow with much lower central density $n({\rm H}_2) = 5.1 \times 10^4$ $^{-3}$ with uncertainty $\sim 30$ ).
 This occurs despite the identical form of the expressions for the evlinder and Plummer-like models (with Ry= v841I). and the fact that the evlinder ancl Bonnor-Ebert models both represent a balance between sell-gravity and thermal pressure.," This occurs despite the identical form of the expressions for the cylinder and Plummer-like models (with $R_0=\sqrt{8} H$ ), and the fact that the cylinder and Bonnor-Ebert models both represent a balance between self-gravity and thermal pressure."
 The difference derives [rom the lower dimensionality of the evlindrical model: a given line-ol-sight corresponds to a constant “radius”. and hence there is no radial integration that for the spherically svimnetrie models makes (he column density profiles more shallow than the density profiles.," The difference derives from the lower dimensionality of the cylindrical model; a given line-of-sight corresponds to a constant “radius”, and hence there is no radial integration that for the spherically symmetric models makes the column density profiles more shallow than the density profiles."
 In addition. (he extension of the cxlinder along the means that the densities are correspondinglv lower al a given radius.," In addition, the extension of the cylinder along the line-of-sight means that the densities are correspondingly lower at a given radius."
 The asvimnmetry ol the LGO42 core viewed in extinction provides a basis for preferring the evlindrical model over the others., The asymmetry of the L694–2 core viewed in extinction provides a basis for preferring the cylindrical model over the others.
 A tited cvlinder with //= 13.5. Lsinó=0.14 pe (L~0.2 0.5. and ᾧ~20 15 5°). and central cdeity (n(Ilo)—4xI0!  embedded in a uniform distribution of gas with column density VOU+H5)~6x1001(L/0.5 pe) 7. successfully reproduces the dust emission visibility profile. as well as the profile and asvuumetry of the dust extinction map.," A tilted cylinder with $H=13.5$ , $L \sin{\phi}=0.14$ pc $L \simeq 0.2$ $0.5$, and $\phi \simeq 20$ $45^{\circ}$ ), and central density $n({\rm H}_2) = 4 \times 10^4$ $^{-3}$ embedded in a uniform distribution of gas with column density $N(H+H_2) \sim 6 \times 10^{21} \, (L / 0.5$ $)$ $^{-2}$, successfully reproduces the dust emission visibility profile, as well as the profile and asymmetry of the dust extinction map."
 The instability of the evlindrical model along its axis is also consistent wilh the inward motions in L6942 inferred from molecular spectral lines (Lee. Myers Talalla 2001).," The instability of the cylindrical model along its axis is also consistent with the inward motions in L694–2 inferred from molecular spectral lines (Lee, Myers Tafalla 2001)."
" As already noted. the inner power law index of the fitted. broken power law model (pE0.90.120.16. Fit HD) may be construed both as a “mean” index in the r«30"" region. and as an upper limit on the index in (he innermost regions (due to the trade-off between turl-OVer racius ancl power law index in the inferredvisibility profile)."," As already noted, the inner power law index of the fitted broken power law model $p=0.9 \, {}^{+0.12}_{-0.16}$, Fit II) may be construed both as a “mean” index in the $r<30''$ region, and as an upper limit on the index in the innermost regions (due to the trade-off between turn-over radius and power law index in the inferredvisibility profile)."
 The former is illustrated by the, The former is illustrated by the
with the results of the previous section.,with the results of the previous section.
 Iu order to quantify this evolution. we fit a liue of zero slope to the poluts a mean value for each redshift interval).," In order to quantify this evolution, we fit a line of zero slope to the points a mean value for each redshift interval)."
 Between the first two redshift bins (roughly z£zO.L and zzz0.6). Aw drops by approximaely a factor of two.," Between the first two redshift bins (roughly $z \approx 0.4$ and $z \approx 0.6$ ), $A_w$ drops by approximately a factor of two."
 For the C band measurement. the drop between the secoud aud third. redshi{ intervals (roughly 290.6 and 2z0.8) is approximately 20%. while the B band shows anotler [actor of approximately two decline.," For the $U$ band measurement, the drop between the second and third redshift intervals (roughly $z \approx 0.6$ and $z \approx 0.8$ ) is approximately $20\%$, while the $B$ band shows another factor of approximately two decline."
 This result is not surprising in the context of hierarchical sructtwe formation where oue expects objects to be more strongly. cluster with decreasing redshift flor z1 I|xaufhuannefel.1999) , This result is not surprising in the context of hierarchical structure formation where one expects objects to be more strongly cluster with decreasing redshift for $z < 1$ \citealt{kauffmann99}) ).
Unfortunately. we do not have enough galaxies to definitely test for clustering evolution with 'edshift for a given poptlation with a fixed inrinsie luminosity.," Unfortunately, we do not have enough galaxies to definitely test for clustering evolution with redshift for a given population with a fixed intrinsic luminosity."
 Ou the other laud. our results do seem to indicate that the evolution is not strongly dependent ou intrinsic luminosity as tliere appears o be no clear evidence for variation iu the custeriung amplitude within a giveu redshift interval.," On the other hand, our results do seem to indicate that the evolution is not strongly dependent on intrinsic luminosity as there appears to be no clear evidence for variation in the clustering amplitude within a given redshift interval."
 The differeuce in the drop iu the amplitude between the muddle aud bieh redshift intervals is most ikely clue to the lower. :iverage intrinsic luiilosity of the galaxies in the B band as compared to he C baud.," The difference in the drop in the amplitude between the middle and high redshift intervals is most likely due to the lower, average intrinsic luminosity of the galaxies in the $B$ band as compared to the $U$ band."
 These poiuts will ueed to be add'essed with future datasets., These points will need to be addressed with future datasets.
 Iu this paper. we have preseued several caleulatious of the augular correlation function. as a [uuction of different apparent mariLE.de iuterv.als. as a Function of redshift. aud as a function of both redshift and absolute magnitude.," In this paper, we have presented several calculations of the angular correlation function, as a function of different apparent magnitude intervals, as a function of redshift, and as a function of both redshift and absolute magnitude."
 The technique we have clemoustrated is less sensitive to recshilt distortions than the spatial correlation approa¢Ji due to the width of our redshift bius., The technique we have demonstrated is less sensitive to redshift distortions than the spatial correlation approach due to the width of our redshift bins.
 Furthermore. our technique does not require mocel predictions for the redshift distribution of galaxies as does the apparent 1naguituce interval approach.," Furthermore, our technique does not require model predictions for the redshift distribution of galaxies as does the apparent magnitude interval approach."
 Future work iu this area will incorporate spectroscopic redshifts into the calculation in order to provide limited distance information Phillipps 1985)). as well as wituess tlie application of these tectiniques to larger surveys.," Future work in this area will incorporate spectroscopic redshifts into the calculation in order to provide limited distance information \citealt{phillipps85}) ), as well as witness the application of these techniques to larger surveys."
 While not the main poiut of this paper. the variation ofthe amplitude of the augular correlation with apparent magnitude is in good agreement with previously published results. which streugtliens the rest of our analysis.," While not the main point of this paper, the variation of the amplitude of the angular correlation with apparent magnitude is in good agreement with previously published results, which strengthens the rest of our analysis."
 Furthermore. we demonstrated. for the first time from within a sinele dataset. the slight evolution in both the ampplitude of the angular correlation Duuction. aud the spatial correlation scale eneth with recdshil for z«1. as predicted by semi-analytic models of structure formation (Batichetal.1999:Ixauffinannefa£...1999).," Furthermore, we demonstrated, for the first time from within a single dataset, the slight evolution in both the amplitude of the angular correlation function, and the spatial correlation scale length with redshift for $z < 1$, as predicted by semi-analytic models of structure formation \citep{baugh99,kauffmann99}."
. These results suggestMOD low values for Ou. aud allow either fixed clustering in proper coordinates. or the precictious of linear theory.," These results suggest low values for $\Omega_0$, and allow either fixed clustering in proper coordinates, or the predictions of linear theory."
 Finally. we measured the evolution of the amplitude of the angular correlation functiou witli both redshift aud μίνιSic luminosity.," Finally, we measured the evolution of the amplitude of the angular correlation function with both redshift and intrinsic luminosity."
 The amplitude of the angular correlation functiou drops dramatically with redshift., The amplitude of the angular correlation function drops dramatically with redshift.
 Interestingly euoughi. however. we do uot see siguificant. variation in the," Interestingly enough, however, we do not see significant variation in the"
"To inspect the effect of employed mass-ratios on the temporal evolution of instabilities, we looked at the nature of the flux tubes more closely.","To inspect the effect of employed mass-ratios on the temporal evolution of instabilities, we looked at the nature of the flux tubes more closely."
" The flux tubes in the simulations with mass-ratios of my/m,=5.0 and my/m,=100.0 are illustrated in Fig.s 2 and 3,, respectively, which show the particle number density in particles per cell at three different locations perpendicular to the direction of streaming."," The flux tubes in the simulations with mass-ratios of $m_p/m_e = 5.0$ and $m_p/m_e = 100.0$ are illustrated in Fig.s \ref{9_slices_5} and \ref{9_slices_100}, respectively, which show the particle number density in particles per cell at three different locations perpendicular to the direction of streaming."
 The pictures in Fig., The pictures in Fig.
 2 are chosen such that the uppermost row shows the onset of the instability and the lowest pictures are roughly taken at the time the maximum of the instability occurs (cf., \ref{9_slices_5} are chosen such that the uppermost row shows the onset of the instability and the lowest pictures are roughly taken at the time the maximum of the instability occurs (cf.
 Fig. 1))., Fig. \ref{B_vergleich}) ).
 In Fig., In Fig.
" 3 the upper row of slices is taken at the moment the electron/positron instability peaks, the second set of pictures show the time between the two instabilities (compare with the black curve in Fig."," \ref{9_slices_100} the upper row of slices is taken at the moment the electron/positron instability peaks, the second set of pictures show the time between the two instabilities (compare with the black curve in Fig."
 1 at 8007!) and the last set shows the point in time when the proton instability reaches its peak., \ref{B_vergleich} at $80 \omega_p^{-1}$ ) and the last set shows the point in time when the proton instability reaches its peak.
" Both simulations show the archetypical behavior of filamentation instabilities: Flux tubes develop, which in turn merge until only two flux tubes survive."," Both simulations show the archetypical behavior of filamentation instabilities: Flux tubes develop, which in turn merge until only two flux tubes survive."
 But for the high mass-ratio simulations this whole process happens twice., But for the high mass-ratio simulations this whole process happens twice.
 In an early stage (which resembles the first peak of the instability in Fig. 1)), In an early stage (which resembles the first peak of the instability in Fig. \ref{B_vergleich}) )
 flux tubes arise., flux tubes arise.
" In a later stage (second peak) flux tubes of different strengths exist, one of them is more pronounced."," In a later stage (second peak) flux tubes of different strengths exist, one of them is more pronounced."
 The explanation is that during the first stage of the instability the flux tubes are carrying more of the lighter particles., The explanation is that during the first stage of the instability the flux tubes are carrying more of the lighter particles.
" The second stage is then associated with a flux tube of heavier particles which takes longer to develop, but is also able to exist for a much longer"," The second stage is then associated with a flux tube of heavier particles which takes longer to develop, but is also able to exist for a much longer"
yw observations of Hiltner 600 made (he same night with the same filters aud similar air masses.,by observations of Hiltner 600 made the same night with the same filters and similar air masses.
 [1 order to obtain a pure emission-line image of the galaxy. after sky subtraction we used tlie three wiehtest stars in the field to derive the ratio of trausimission through the on-band aud off-baux ilters.," In order to obtain a pure emission-line image of the galaxy, after sky subtraction we used the three brightest stars in the field to derive the ratio of transmission through the on-band and off-band filters."
 The oll-baud image was scaled. according to this ratio aud subtracted [rom the on-baux Image., The off-band image was scaled according to this ratio and subtracted from the on-band image.
 A larger lield of view R-bancl image of the inner portion of the NCC 1110 group was obtainec ining the Southeastern Association for Research in Astronomy (SARA) 0.9m telescope on litt Peak., A larger field of view R-band image of the inner portion of the NGC 4410 group was obtained using the Southeastern Association for Research in Astronomy (SARA) 0.9m telescope on Kitt Peak.
 These observations were made ou 1999 April 18 — 19. using a 2018 x 2018 Ανίομι/Apogee CCD.," These observations were made on 1999 April 18 $-$ 19, using a 2048 $\times$ 2048 Axiom/Apogee CCD."
 Binning 2 x 2. the pixel size is 07252 with this system and the field of view is 8199.," Binning 2 $\times$ 2, the pixel size is 52 with this system and the field of view is 9."
 The seeiug was 2.," The seeing was $\sim2""$."
 The total integration time ou the galaxy was LO minutes., The total integration time on the galaxy was 40 minutes.
 Sky flats. clarks. aud biases were also obtaiued. aud the data were reduced in a staudard way.," Sky flats, darks, and biases were also obtained, and the data were reduced in a standard way."
 In this paper. we also discuss an archival Hubble Space Telescope (HST) Wide Field Planetary Camera 2 (WEPC2) image of NGC1110A2.. obtained ou 1995 April 20.," In this paper, we also discuss an archival Hubble Space Telescope (HST) Wide Field Planetary Camera 2 (WFPC2) image of NGC, obtained on 1995 April 20."
 These data consist of a sinele 500 second exposure taken with the broadband red ΕΟΟ HST image (Ay = 59391À: AA = 1108À)., These data consist of a single 500 second exposure taken with the broadband red F606W HST image $\lambda$$_0$ = ${\rm \AA}$; $\Delta$$\lambda$ = ${\rm \AA}$ ).
 The nucleus of NGC LIOA was centered in the high resolution Planetary Camera (PC) chip of the WEPC®2. which provides 800 x 800 0700155 pixels.," The nucleus of NGC 4410A was centered in the high resolution Planetary Camera (PC) chip of the WFPC2, which provides 800 $\times$ 800 0455 pixels."
 These data were originally obtained as part of the Malkan. Corjian. Tam (1998) HST survey of active galaxies. aud have previously been presented by Tschókke et al. (," These data were originally obtained as part of the Malkan, Gorjian, Tam (1998) HST survey of active galaxies, and have previously been presented by Tschökke et al. ("
1999) aud Simith (2000).,1999) and Smith (2000).
 Optical longslit spectra of NGC £110 were obtained ou 1991 December 19 — 20 using the Double Spectrograph mounted at the Casseerain focus of the Palomar Sui Hale telescope., Optical longslit spectra of NGC 4410 were obtained on 1991 December 19 $-$ 20 using the Double Spectrograph mounted at the Cassegrain focus of the Palomar 5m Hale telescope.
 In the red channel. a 1200 line + erating blazed near 7000À. was used.," In the red channel, a 1200 line $^{-1}$ grating blazed near ${\rm \AA}$ was used."
 This provided a dispersion of QO.S1TÀ pixI. a resolution of ~ 2.54. and total wavelength coverage of 6310— 7000.," This provided a dispersion of ${\rm \AA}$ $^{-1}$, a resolution of $\sim$ ${\rm \AA}$, and total wavelength coverage of 6340$-$ ${\rm \AA}$."
 In the blue chanuel. we used a 300) liue 1 erating. which gave a clispersion of 2.152À pix1*. a resolution of -6À. and a wavelength range of 3717 — 52504.," In the blue channel, we used a 300 line $^{-1}$ grating, which gave a dispersion of ${\rm \AA}$ $^{-1}$, a resolution of $\sim$ ${\rm \AA}$, and a wavelength range of 3747 $-$ ${\rm \AA}$."
 We made observations at [ive slit positious in the NGC E110 system. aligued across tlie nucleus of NGC LHOA and various knots aud features observed in the narrow-band image.," We made observations at five slit positions in the NGC 4410 system, aligned across the nucleus of NGC 4410A and various knots and features observed in the narrow-band image."
 Slit positions are iudicated in Table 2 and are marked iu Figure 1.., Slit positions are indicated in Table \ref{Table2} and are marked in Figure \ref{fig1}.
 ludividual exposures were 15 minutes in duration., Individual exposures were 15 minutes in duration.
" We used a 2"" slit [or all observations.", We used a $''$ slit for all observations.
" The seeing was 2"".", The seeing was $''$ .
 All observations were conducted at less than 1.1 alrinasses., All observations were conducted at less than 1.1 airmasses.
We find that the host galaxies of raclio-loncd AGN are luminous ellipticals. occupying the low surlace-brightuess (ail of the Ixormendy relation for normal elliptical galaxies. and are statistically consistent will this relation.,"We find that the host galaxies of radio-loud AGN are luminous ellipticals, occupying the low surface-brightness tail of the Kormendy relation for normal elliptical galaxies, and are statistically consistent with this relation."
 Comparing the host ealaxies of low-power and radio-loud AGN. we lind general overlap. with a slight difference in median absolute Cousins R. magnitudes. —23.75 mag and —24.2 mag. respectively.," Comparing the host galaxies of low-power and high-power radio-loud AGN, we find general overlap, with a slight difference in median absolute Cousins R magnitudes, $-23.75$ mag and $-24.2$ mag, respectively."
 After correcting the (highly beamed) low-power AGN for Doppler beaming. we lind a significant positive trend between nuclear and host galaxy. huninositw. but with a very shallow slope a lactor of 1.3 in host ealaxv brightness over at least [our orders of magnitude in nuclear luminosity ruling out a close relation between host galaxy and nuclear Iuminosityv in radio-loud AGN.," After correcting the (highly beamed) low-power AGN for Doppler beaming, we find a significant positive trend between nuclear and host galaxy luminosity, but with a very shallow slope — a factor of 1.3 in host galaxy brightness over at least four orders of magnitude in nuclear luminosity — ruling out a close relation between host galaxy and nuclear luminosity in radio-loud AGN."
 We find that the central black holes of huninous radio-Ioud AGN are universally large. with median black hole mass ~10?M. [or this sanipe.," We find that the central black holes of luminous radio-loud AGN are universally large, with median black hole mass $\sim 10 \time 10^9 M_\odot$ for this sample."
" Thisis found to be the case using either the Af, Li; relation and the M, σ~ relations to derive black hole masses.", This is found to be the case using either the $M_{\bullet}$ $L_{bulge}$ relation and the $M_{\bullet}$ $\sigma_e$ relations to derive black hole masses.
 This supports the view that a high central black hole mass is an important factor in generating a powerful radio source., This supports the view that a high central black hole mass is an important factor in generating a powerful radio source.
 No correlation is lound between black hole mass aud energy output [rom (he nucleus., No correlation is found between black hole mass and energy output from the nucleus.
 Rather. the black hole masses derived span a surprisingly small range compared to the range in intrinsic power of this sample.," Rather, the black hole masses derived span a surprisingly small range compared to the range in intrinsic power of this sample."
 Eddington ratios for radio-loud AGN span more than four orders of magnitude. with LeasLbol.<2x101 in the lowest-power sources (o pk~| in the vighest.," Eddington ratios for radio-loud AGN span more than four orders of magnitude, with $\frac{L_{bol.}}{L_{Edd}} \lesssim 2\times
10^{-4}$ in the lowest-power sources to $\frac{L_{bol.}}{L_{Edd}} \sim 1$ in the highest."
 Across this range. the host galaxies buninosities are tightly constrained. all within one magnitude of brightest cluster galaxies.," Across this range, the host galaxies luminosities are tightly constrained, all within one magnitude of brightest cluster galaxies."
" Tiis. although (hie properties of the host galaxy nav have a strong influence the mass of its ceriral black hole. thev have at most a very weak influence on the mass accretion rate in raclio-οσα AGN,"," Thus, although the properties of the host galaxy may have a strong influence the mass of its central black hole, they have at most a very weak influence on the mass accretion rate in radio-loud AGN."
 We thank Aldo Treves and Laura Marascui lor very helpful discussions., We thank Aldo Treves and Laura Maraschi for very helpful discussions.
 Support for this work was provided by NASA through grant numbers GO-05933.01-94AÀ. 60-05939.01-94A. GO-06363.01-95A and GO-07893.01-96A [from the Space Telescope Science Institute. which is operated by AURA. Inc.. under NASA contract NAS5-26555.," Support for this work was provided by NASA through grant numbers GO-05938.01-94A, GO-05939.01-94A, GO-06363.01-95A and GO-07893.01-96A from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555."
0<z«0.36. using a combination of both morphological (pure de Vaucouleurs profile) ancl spectral (negative [rom principal component analvsis) criteria.,"$0<z<0.36$, using a combination of both morphological (pure de Vaucouleurs profile) and spectral (negative from principal component analysis) criteria."
 We measured observer-[rame ancl rest-lrame g and. r-band magnitudes for these galaxies by integrating over the SDSS spectra (corrected for atmospheric and Galactic absorption) weighting by the appropriate filter functions., We measured observer-frame and rest-frame $g$ and $r$ -band magnitudes for these galaxies by integrating over the SDSS spectra (corrected for atmospheric and Galactic absorption) weighting by the appropriate filter functions.
 The spectra magnitudes of these. galaxies. were then compared: with ;Whotometric (3 aresec aperture) magnitudes [rom he SDSS imaging data., The spectra magnitudes of these galaxies were then compared with photometric (3 arcsec aperture) magnitudes from the SDSS imaging data.
 There was a large scatter (~I] mag) between the two but. on. average. the spectra eave systematically redder g colours than the magnitudes. the dillerence being 0.030.04 magnitudes. at ower recdshilts.," There was a large scatter $\sim 0.1$ mag) between the two but on average, the spectra gave systematically redder $g-r$ colours than the magnitudes, the difference being 0.03–0.04 magnitudes at lower redshifts."
 Some. but not all. of this discrepancy is due to secing: he Hux in the SDSS spectra is reduced: relative to the imaging photometry by about 0.021 mag per aresec of secing in g and 0.0012 mag in r.," Some, but not all, of this discrepancy is due to seeing: the flux in the SDSS spectra is reduced relative to the imaging photometry by about 0.021 mag per arcsec of seeing in $g$ and 0.012 mag in $r$."
 As the median seeing is 1.8 arcsec this may cause Algor)—Ol mag reddening of the spectra., As the median seeing is 1.8 arcsec this may cause $\Delta (g-r)\sim 0.01$ mag reddening of the spectra.
 There may be a additional small systematic differences in the colour calibrations. consistent with the quoted uncertainties of up to 0.02 mag CXdelman-Mecarthy et al.," There may be a additional small systematic differences in the colour calibrations, consistent with the quoted uncertainties of up to 0.02 mag (Adelman-Mccarthy et al."
 2008)., 2008).
 , 2.
In the g band. the mean dillerence between giu ancl grip decreases significantly (~0.05 mag) with increasing redshift. although the scatter increases.," In the $g$ band, the mean difference between $g_{spec}$ and $g_{fib}$ decreases significantly $\sim 0.05$ mag) with increasing redshift, although the scatter increases."
 A similar trend. is seen in the r band. potentially compromising estimates of how the colours of these objects evolve.," A similar trend is seen in the $r$ band, potentially compromising estimates of how the colours of these objects evolve."
" The redshift dependence of. qagri, With redshift is much greater for galaxies with the most negative values of the spectral classification parameter.", The redshift dependence of $g_{spec}-g_{fib}$ with redshift is much greater for galaxies with the most negative values of the spectral classification parameter.
 A  0.3. such objects have low lux and high noise at the blue end of the g- and qq...Grip increases at low signal/noise.," At $z\sim 0.3$ , such objects have low flux and high noise at the blue end of the $g$ -band, and $g_{spec}-g_{fib}$ increases at low signal/noise."
 We calibrated this dependence on and signal/noise. and used LE to Ceorrect spectra-derived: magnitudes. for. these ellects.," We calibrated this dependence on and signal/noise, and used it to `correct' spectra-derived magnitudes for these effects."
 Understanding the underlying cause for these trends requires further work., Understanding the underlying cause for these trends requires further work.
 For example. a comparison of SDSS spectra with best-fitting BCOS-type models. stacking large numbers together to increase signal/noise. might help to reveal exactly where in the spectra the problem is occurring.," For example, a comparison of SDSS spectra with best-fitting BC03-type models, stacking large numbers together to increase signal/noise, might help to reveal exactly where in the spectra the problem is occurring."
 , 3.
The dillerences between observer-frame ancl rest-frame magnituces as measured from the spectra provide estimates of k-corrections in g and η., The differences between observer-frame and rest-frame magnitudes as measured from the spectra provide estimates of $k$ -corrections in $g$ and $r$.
 Phe k-corrections from the SDSS spectra of I2/80s8 were similar to those from. BC'O3 models with ages ~12 Gar. and star-formation exponentially declining with 7=1 Gyr for the most luminous galaxies and τς2 Cyr for the least luminous.," The k-corrections from the SDSS spectra of E/S0s were similar to those from BC03 models with ages $\sim 12$ Gyr, and star-formation exponentially declining with $\tau=1$ Gyr for the most luminous galaxies and $\tau=2$ Gyr for the least luminous."
 Phese SE histories and heir moderate Luminosity dependence agree with Jimenez et al. (, These SF histories and their moderate luminosity dependence agree with Jimenez et al. (
2,2007).
 4., 4.
" Rest-frame colours (gor),gp were measured directly from. he spectra. ancl also caleulated by subtracting &-corrections rom the SDSS or magnitudes."," Rest-frame colours $(g-r)_{rf}$ were measured directly from the spectra, and also calculated by subtracting $k$ -corrections from the SDSS or magnitudes."
 The first two estimates are based on fixed angular apertures (about 3 colour-arcsec): the scale associated with the latter is related to the radius. so it varies from object to object.," The first two colour estimates are based on fixed angular apertures (about 3 arcsec); the scale associated with the latter is related to the half-light radius, so it varies from object to object."
" Absolute magnitudes AZ, were calculated from the &-corrected magnitudes. and were then corrected. for evolution."," Absolute magnitudes $M_r$ were calculated from the $k$ -corrected magnitudes, and were then corrected for evolution."
 The rest-frame colour-magnitude relation. (CMIU) ancl 6 (Coli) relations were measured in a series. of recishift intervals., The rest-frame colour-magnitude relation (CMR) and $\sigma$ $\sigma$ R) relations were measured in a series of redshift intervals.
 Both are wellapproximated by power-laws that tend to shift eraclually bluewards with increasing recdshilt-, Both are well-approximated by power-laws that tend to shift gradually bluewards with increasing redshift.
 The zero-point. slope and evolution of the CMIU associated with fixed angular apertures (spectral and colours) diller from that. found. for magnitudes.," The zero-point, slope and evolution of the CMR associated with fixed angular apertures (spectral and colours) differ from that found for magnitudes."
 We found he slope steeper. and note Mel et al. (," We found the slope steeper, and note Mei et al. ("
2006) and ScodegegioME (2001)“found similar cillerences in the CALRs from ixed or from hall-lieht colours.,2006) and Scodeggio (2001) found similar differences in the CMRs from fixed aperture or from half-light colours.
 These cdilferences are a consequence of radial colour gradients., These differences are a consequence of radial colour gradients.
 Ciradients complicate interpretation of evolution of the CALR from ixecl apertures evolution of the CMIU based. on magnitudes is easier to interpret., Gradients complicate interpretation of evolution of the CMR from fixed apertures – evolution of the CMR based on magnitudes is easier to interpret.
 5., 5.
 Whereas colour gradients allect the zero-point of the CaR. he slope is much less alfected.," Whereas colour gradients affect the zero-point of the $\sigma$ R, the slope is much less affected."
" This suggests that eracdients are not positively correlated with @ but we find inications hat they are correlated with residuals in the high luminosity and low e direction [rom the £m|M,.ο) relation."," This suggests that gradients are not positively correlated with $\sigma$ – but we find indications that they are correlated with residuals in the high luminosity and low $\sigma$ direction from the $\langle\sigma|M_r,z\rangle$ relation."
 , 6.
The &-corrections obtained from fitting DCUS template spectra to the observed. igréz Uuxes (following Blanton ltoweis 2007) depend only slightly on whether one uses or magnitudes («0.01 mag at z«0.15)., The $k$ -corrections obtained from fitting BC03 template spectra to the observed $ugriz$ fluxes (following Blanton Roweis 2007) depend only slightly on whether one uses or magnitudes $< 0.01$ mag at $z < 0.15$ ).
 7., 7.
 We also caleulated the CMIt using k-corrrections derived [rom model or template spectra. rather than the SDSS spectra.," We also calculated the CMR using k-corrrections derived from model or template spectra, rather than the SDSS spectra."
 The estimate of rest-frame colour evolution is very sensitive to the assumed h-correction. and these models gave very dilferent results.," The estimate of rest-frame colour evolution is very sensitive to the assumed $k$ -correction, and these models gave very different results."
 The DCO3 Moclel 2 gave a reasonable (gr) revolution rate 0.16622. but at an uneven rate with all the evolution at z<0.15. apparently. because a model with a single SE history could. not. simultaneously. fit. the more and less luminous galaxies.," The BC03 Model 2 gave a reasonable $(g-r)_{rf}$ evolution rate $-0.1662z$, but at an uneven rate with all the evolution at $z<0.15$, apparently because a model with a single SF history could not simultaneously fit the more and less luminous galaxies."
 Phe CWW Á-correction. which is based on a non-evolving spectrum. gave a C'MI with strong evolution of 0.355897. so this did not give sell-consistent results.," The CWW $k$ -correction, which is based on a non-evolving spectrum, gave a CMR with strong evolution of $-0.3589z$, so this did not give self-consistent results."
 The &-corrections from Blanton Itowels (2007) are smaller than those based on the SDSS spectra. and so the CMS show [less evolution the CMIB. based on magnitudes showed no evolution.," The $k$ -corrections from Blanton Roweis (2007) are smaller than those based on the SDSS spectra, and so the CMRs show less evolution – the CMR based on magnitudes showed no evolution."
 This may be an artifact of the fact that the BCO3 models assume solar abuncance ratios. and thisis unrealistic.," This may be an artifact of the fact that the BC03 models assume solar abundance ratios, and this is unrealistic."
 We thank David Schlegel anc R. Sheth for interesting discussions about our work. which was supported in part by NASA grant LESA-NNGOGCGCTIOC. Funding lor the Sloan Digital Sky Survey (SDSS) has been provided. by the Alfred P. Sloan Foundation. the Participating Institutions. the National Acronautics ancl Space Administration. theNational Science Foundation. the U.S. Department of Energy. theJapanese Monbukagakusho. anc the Max. Planck Society.," We thank David Schlegel and R. Sheth for interesting discussions about our work, which was supported in part by NASA grant LTSA-NNG06GC19G. Funding for the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society."
 Phe SDSS Web. site is http://wwwosdss.ore/. “Phe SDSS is managed. by the Astrophysical Rescarch Consortium (ARC) for. the Participating Lnstitutions., The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions.
 The Participating Institutions ae The University of Chicago. Fermilab. the Institute for Advanced. Study. the Japan Participation Croup. The Johns Lopkins University. the Ixorean. Scientist Group. Los AlamosNational Laboratory. the Max-DPlanck- for Astronomy (AIPLA). the Alax-Planck-Lostitute for Astrophwsies (AIPA). New Mexico. State University. University of Pittsburgh. Universityof Portsmouth. Princeton University. the United States Naval Observatory. and the University of Washington.," The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los AlamosNational Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, Universityof Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington."
The spectra observed on the disk present the same general shape as the spectra ou the star but with a lower iuteusity evel.,The spectra observed on the disk present the same general shape as the spectra on the star but with a lower intensity level.
 Indeed. any spectrum of the disk obtained off the star CFLQQLA)) is au addition of a “noise” component and a spectrum carrving information from the disk at he pointed position.," Indeed, any spectrum of the disk obtained off the star $F_{obs}(\lambda)$ ) is an addition of a “noise” component and a spectrum carrying information from the disk at the pointed position."
 The “noise” is the spectrum of the starlight scattered by the telescope (#F(A). where F(A) is the star spectrum) plus a background level (5) due o the fact that the backerouud determined by the IST Xpelime cau be sligbitlv. miscalculated.," The “noise” is the spectrum of the starlight scattered by the telescope $a F_*(\lambda)$ , where $F_*(\lambda)$ is the star spectrum) plus a background level $b$ ) due to the fact that the background determined by the HST pipeline can be slightly miscalculated."
 The part of the spectrin due to the disk Εμ) is the starlight scattered x the dust aud the possible cussion lines due to gaseous fluorescence., The part of the spectrum due to the disk $F_{disk}$ ) is the starlight scattered by the dust and the possible emission lines due to gaseous fluorescence.
 We thus cousider that the additional noisv component (Εκ) Is a lmear combination of the stellar spectra CF.(ÀA)) obtained at the same wavelength a few orbits before: To put forward the potential presence of a component differcut from the dominant starlight scattered by the telescope. we divide the observed spectra by the stellar spectra.," We thus consider that the additional noisy component $F_{noise}$ ) is a linear combination of the stellar spectra $F_*(\lambda)$ ) obtained at the same wavelength a few orbits before: To put forward the potential presence of a component different from the dominant starlight scattered by the telescope, we divide the observed spectra by the stellar spectra."
 The presence of a disk coutribution at a wavelength A will be detected if the ratio Fuss)akfA)|5) is statistically significantly differcut frou. 1., The presence of a disk contribution at a wavelength $\lambda$ will be detected if the ratio $F_{obs}(\lambda)/(a F_*(\lambda) + b)$ is statistically significantly different from 1.
 The main problem is thus the deteruumation of « and 5. and their crrorbars within a confidence level.," The main problem is thus the determination of $a$ and $b$, and their errorbars within a confidence level."
 Asstuning that the disk spectra (dust scattered light plus eas ciuission lines) have a neglieible coutribution to the observed spectra (Fhajse(A)Z9Fijsn (A). we cau determine e aud b by a X? minimization of where uyl/oi ENd the weight. οἱ. each micasurement at A;.," Assuming that the disk spectra (dust scattered light plus gas emission lines) have a negligible contribution to the observed spectra $F_{noise}(\lambda) \gg F_{disk}(\lambda)$ ), we can determine $a$ and $b$ by a $\chi^2$ minimization of where $w_{\lambda_i}= 1/\sigma_{\lambda_i}^2$ is the weight of each measurement at $\lambda_i$."
 This procedure gives not oulv tle best deternunation of ο and b but also intervals of confidence for these constants., This procedure gives not only the best determination of $a$ and $b$ but also intervals of confidence for these constants.
 Spectra in the wwaveleneth range were obtained less than 10 ήπατος apart with the same instrament setting., Spectra in the wavelength range were obtained less than 10 minutes apart with the same instrument setting.
 The star and the disk spectra can be casily superimposed as slow iu Fie. l.., The star and the disk spectra can be easily superimposed as shown in Fig. \ref{plot_feii}.
 An excess of flux clearly appears in the blue the red part of the two strongest Hines at rest waveleugth 2371.161 aud 2382.765A., An excess of flux clearly appears in the blue the red part of the two strongest lines at rest wavelength 2374.461 and 2382.765.
" If 0 aud b are determined as described in Sect 2.2.. we get a|!=197-3 and b=(3+2).10P 1, "," If $a$ and $b$ are determined as described in Sect \ref{method}, we get $a^{-1}=197\pm 3$ and $b=(3 \pm 2)\cdot 10^{-15}$ ."
With- these parameters. a plot of the ratio of the disk to the star spectra reveals an excess endssion at 26 level (Fig. 2)).," With these parameters, a plot of the ratio of the disk to the star spectra reveals an excess emission at $\sigma$ level (Fig. \ref{ratio_feii}) )."
 The flux from the disk cau be evaluated by the difference between the two spectra (Ελ)(GPL)| by). aud is 10thore bhetween 50 aud 150 in the red part of the lines aud around πι in the blue part (Fie. 33).," The flux from the disk can be evaluated by the difference between the two spectra $F_{obs}(\lambda)-(a F_*(\lambda) + b)$ ), and is $F_{disk}\sim 10^{-14}$ between 50 and 150 in the red part of the lines and around $-$ 50 in the blue part (Fig. \ref{vel_feii}) )."
 This emission is about 1 wwide and stronger in the red part of the lines., This emission is about 1 wide and stronger in the red part of the lines.
 The detection of apparent excess enission iu the two Ines can be explained in different wavs., The detection of apparent excess emission in the two lines can be explained in different ways.
 We propose that this can be a real detection of the emission through the scattering of the starliglr by the Hous in very hieh velocity motions., We propose that this can be a real detection of the emission through the scattering of the starlight by the ions in very high velocity motions.
 This will be discussed iu detail in the next section., This will be discussed in detail in the next section.
 However other possibilities must be evaluated., However other possibilities must be evaluated.
 Fist. this feature obviously caunot be simply due to a possible nuscaleulation Guuderestimate) of b. the background correction.," First, this feature obviously cannot be simply due to a possible miscalculation (underestimate) of $b$, the background correction."
 Indeed. by underestimating ὃν we could πια false eimissiou-like features at svaveleugth where the flux is low.," Indeed, by underestimating $b$, we could find false emission-like features at wavelength where the flux is low."
 But. oue should increase the estimate of P above its lo upper limit (s+10ore- 1) to explain thedetected enission feature only by this effect.," But, one should increase the estimate of $b$ above its $\sigma$ upper limit $8\cdot 10^{-15}$ ) to explain thedetected emission feature only by this effect."
 Iu addition. the cussion is detected in both Ines. in particular in the line a 237LIGL where the level is far above the zero level. aud or which," In addition, the emission is detected in both lines, in particular in the line at 2374.461 where the level is far above the zero level, and for which"
for fa.,for $f_{att}$.
" To reduce the computation time we decided to freeze the value of faz, after checking that it did not modify the values obtained for the other output parameters of the Dust luminosities, log(L4g) between 8 and 1000 um, are computed by fitting Dale&Helou(2002) templates and are linked to the attenuated stellar population models (the stellar luminosity absorbed by the dust is re-emitted in IR)."," To reduce the computation time we decided to freeze the value of $f_{att}$, after checking that it did not modify the values obtained for the other output parameters of the Dust luminosities, $\log(L_{\rm IR})$ between 8 and 1000 $\mu$ m, are computed by fitting \citet{dale02} templates and are linked to the attenuated stellar population models (the stellar luminosity absorbed by the dust is re-emitted in IR)."
" The validity of Dale&Helou(2002) templates to measure total IR luminosities of sources detected by Herschel is confirmed by the studies of Elbazetal.(2010,2011)."," The validity of \citet{dale02} templates to measure total IR luminosities of sources detected by $Herschel$ is confirmed by the studies of \citet{elbaz10,elbaz11}."
". Non-thermal sources, not linked to the absorbed stellar population can also contribute to the dust emission."," Non-thermal sources, not linked to the absorbed stellar population can also contribute to the dust emission."
 CIGALE includes dust-enshrouded AGNs by adding two PAH-free templates from Siebenmorgenetal.(2004) as described in Buatetal.(2011)., CIGALE includes dust-enshrouded AGNs by adding two PAH-free templates from \citet{siebenmorgen04} as described in \citet{buat11}.
. These two templates differ by the amount of silicate absorption and their spectral distribution beyond 20 microns is similar to the mean template constructed by Mullaneyetal.(2011)., These two templates differ by the amount of silicate absorption and their spectral distribution beyond 20 microns is similar to the mean template constructed by \citet{mullaney11}.
". The spectrum below 20 microns is representative oftype 2 The AGN contribution to Lig is found to be lower than 1096 except for N-17, the only X-ray source of our sample with broad emission lines, and N-25 which has the highest X-ray luminosity (log(Lx/Lo)= 44.4) and exhibits a power-law spectral energy distribution."," The spectrum below 20 microns is representative oftype 2 The AGN contribution to $L_{\rm IR}$ is found to be lower than $\%$ except for N-17, the only X-ray source of our sample with broad emission lines, and N-25 which has the highest X-ray luminosity $\log(L_{\rm X}/L_{\odot}) = 44.4 $ ) and exhibits a power-law spectral energy distribution."
 For these two sources the AGN fraction is found to be larger than 50%., For these two sources the AGN fraction is found to be larger than $\%$ .
 The current version of CIGALE is unable to fit accurately these SEDs leading to minimum y? values equal to 16 and 6.4 for N-17 and N-25 respectively., The current version of CIGALE is unable to fit accurately these SEDs leading to minimum $\chi^2$ values equal to 16 and 6.4 for N-17 and N-25 respectively.
 These two sources will be discarded when the output parameters of the code will be discussed., These two sources will be discarded when the output parameters of the code will be discussed.
 The case of the other X-ray sources is discussed in section 4.2., The case of the other X-ray sources is discussed in section 4.2.
 Examples of full SED fitting are shown in Fig. 2.., Examples of full SED fitting are shown in Fig. \ref{fullSED}. .
 The figures forthe full sample are available as online material., The figures forthe full sample are available as online material.
md evolutio- iunuelv the mass assembly aud the star formation.,"nd evolution, namely the mass assembly and the star formation."
The median €GCGllIz spectral index for sources in our [uxlimited. sample is 0.39 and. as can be seen from Figure 6.. this does not change significantly: with 20€CGllz Ilux density over the range probe by our ATCA observations (σου 150mn.v).,"The median GHz spectral index for sources in our flux–limited sample is $-0.39$ and, as can be seen from Figure \ref{fig.alpha}, this does not change significantly with GHz flux density over the range probed by our ATCA observations $_{20}>150$ mJy)."
 As we will show in 855. this allows us to use the 2OGGIIz extragalactic source counts measured [rom the AVT20C survey. together with the observed. distribution⋠⋠⋠ of ⋅⋅⋅↽∣a5. to derive. the overall racio. source counts at CllIz.," As we will show in 5, this allows us to use the GHz extragalactic source counts measured from the AT20G survey, together with the observed distribution of $\alpha^{95}_{20}$, to derive the overall radio source counts at GHz."
 We note that our median GlImg spectral index of 0.39 is much flatter than the value of 0.89 measured at GCGLIz by Waldram et ((2007)., We note that our median GHz spectral index of $-0.39$ is much flatter than the value of $-0.89$ measured at GHz by Waldram et (2007).
 Phe Waldram et ((2007) sources are much fainter than those in our sample. since most of them have GCLIz flux densities below the ΑΟ survey limit of mms.," The Waldram et (2007) sources are much fainter than those in our sample, since most of them have GHz flux densities below the AT20G survey limit of mJy."
 Phe work of Waldram et ((2007) is therefore complementary to our study. aad sugeests that the 95CGCGlIz spectralindex. distribution of NP2O0G sources may steepen significantly at Lux densities below αι.ν.," The work of Waldram et (2007) is therefore complementary to our study, and suggests that the GHz spectral–index distribution of AT20G sources may steepen significantly at flux densities below mJy."
 Lor the sources in this study. we have nearsimultaneous data at 5.r δ and 20€COGllz from the APTPOG survey as well as simultaneous data (at a cillerent epoch) at 20 and 95€CGllz from our own ATCA) observations.," For the sources in this study, we have near–simultaneous data at 5, 8 and GHz from the AT20G survey as well as simultaneous data (at a different epoch) at 20 and GHz from our own ATCA observations."
 The mean, The mean
"halos with masses greater (han Mg. obtained from (he halo mass function diy,/dM(M,.2) eiven by the Press-Schechter model (72). or one of its variants. and py is the mean density of barvons.","halos with masses greater than $M_{\rm crit}$, obtained from the halo mass function $dn_h/dM(M,z)$ given by the Press-Schechter model \citep{press-schechter} or one of its variants, and $\rho_b$ is the mean density of baryons."
" One may then assign the efficiency of conversion of gas into stars e, and the critical mass M lor separate populations depending on the main coolant aud the mode of star formation."," One may then assign the efficiency of conversion of gas into stars $e_*$ and the critical mass $M_{\rm
crit}$ for separate populations depending on the main coolant and the mode of star formation."
" For example. M; corresponds to a halo virial temperature of about LO! Ix for halos that cool via atomic processes. while Z;,4100 Ix for molecular cooling."," For example, $M_{\rm crit}$ corresponds to a halo virial temperature of about $10^4$ K for halos that cool via atomic processes, while $T_{\rm crit} \simeq 100$ K for molecular cooling."
 Pop HI stars are generally assumed to form in the lower temperature. IHs-cooled halos. with a much lower efficiency than Pop I stars. which are associated with larger. Hj-cooled halos (for a more detailed discussion. see e.g. ? 2)).," Pop III stars are generally assumed to form in the lower temperature, $_2$ -cooled halos, with a much lower efficiency than Pop II stars, which are associated with larger, $_{\rm I}$ -cooled halos (for a more detailed discussion, see e.g. \citeauthor{loeb-barkana}
 \citeyear{loeb-barkana}) )."
 We hereafter refer to this as the ‘halo-collapse’ mocel., We hereafter refer to this as the `halo-collapse' model.
 Variants on simple models like (he one presented above have been used in many recent w," Variants on simple models like the one presented above have been used in many recent analytic studies of early star formation and reionization \citep[e.g.][]{cen:02,wl:02,wl:03,vts,hh:03}."
ell-developed semi-empirical approach to modeling the physics of atomic cooling. Pop II star formation and chemical enrichment. and supernova feedback. within the framework of hierarchical merging predicted by CDM models.," However, there is a well-developed semi-empirical approach to modeling the physics of atomic cooling, Pop II star formation and chemical enrichment, and supernova feedback, within the framework of hierarchical merging predicted by CDM models."
 The effect of photoionization squelchine on Pop II star formation has also been included in some semi-analvtic models (???)..," The effect of photoionization squelching on Pop II star formation has also been included in some semi-analytic models \citep{kwg:93,squelch,benson:02}."
 This approach has been used in a large number of studies of galaxy. formation at lower reclshilt 260 5 (eg.?7?7777)..," This approach has been used in a large number of studies of galaxy formation at lower redshift $z\sim
0$ –5 \citep[e.g.][]{kwg:93,cafnz:94,kauffmann:99,cole:00,sp,spf}."
 It is interesting to see how (he results based on (hese more realistic recipes compare with the simple !halo-collapse model described above. and to study the relative importance of the various processes that are expected to regulate star formation al very highredshift.," It is interesting to see how the results based on these more realistic recipes compare with the simple `halo-collapse' model described above, and to study the relative importance of the various processes that are expected to regulate star formation at very highredshift."
 llere we use the models developed in ?.SP and ?.SPE.. with photoionization squelching added: as described in ?.. using a recipe based on the numerical results of (2)..," Here we use the models developed in \citet[][SP]{sp} and \citet[][SPF]{spf}, with photoionization squelching added as described in \citet{squelch}, using a recipe based on the numerical results of \citep{gnedin:00}."
 We follow halo merger histories down to halos with temperature Ty.=104 IX. where atomic cooling becomes possible.," We follow halo merger histories down to halos with temperature $T_{\rm vir} = 10^4$ K, where atomic cooling becomes possible."
 We shall refer to these models as the merger {1ος models., We shall refer to these models as the `merger tree' models.
 We show the predicted star formation rate clensitv (SERD) for Pop II and Pop Η1 stars in Fig. 3.., We show the predicted star formation rate density (SFRD) for Pop II and Pop III stars in Fig. \ref{fig:sfrd}.
 For Pop HI stars. we have used the halo collapse model (Eqn. 1))," For Pop III stars, we have used the halo collapse model (Eqn. \ref{eqn:sfrA}) )"
 with el!=0.001 and AH—L0x1055.1AZ..," with $e^{\rm
III}_{*}=0.001$ and $M^{\rm III}_{\rm crit}=1.0 \times 10^6 \hmsun$."
 Also shown in Fig., Also shown in Fig.
 Jaa are the results [rom detailed numerical hyvdrodynamie simulations of Pop ILI star formation in a cosmological volume by ?.. for an," \ref{fig:sfrd}a a are the results from detailed numerical hydrodynamic simulations of Pop III star formation in a cosmological volume by \citet{yoshida:03}, , for an"
] thank D. Saumon for useful discussions and comments on (his manuscript.,I thank D. Saumon for useful discussions and comments on this manuscript.
 This research was supported bv the United States Department of Energy. under contract., This research was supported by the United States Department of Energy under contract W-7405-ENG-36.
If the masses of IXOI-T4b and IXNOI-S1b are in the range 0.1—0.3M... then the work we sketched above shows that there are binary. evolution models in which (heir progenitors filled their Roche lobes until the ime their envelopes were totally eroded.,"If the masses of KOI-74b and KOI-81b are in the range $0.1-0.3\, M_\odot,$ then the work we sketched above shows that there are binary evolution models in which their progenitors filled their Roche lobes until the time their envelopes were totally eroded."
 This strongly supports the hypothesis that IXOI-71 and IXOI-31 are end-states of stable mass-transler., This strongly supports the hypothesis that KOI-71 and KOI-81 are end-states of stable mass-transfer.
 We nole here. however. that.Aepler can also discover binaries in which (he mass of (he core is too large for the donor to have been filling its Roche lobe while in its current orbit.," We note here, however, that can also discover binaries in which the mass of the core is too large for the donor to have been filling its Roche lobe while in its current orbit."
 This would be a signature that the binary was a common-envelope survivor., This would be a signature that the binary was a common-envelope survivor.
 We could then use the current. values of the orbital separation and masses {ο constrain the parameters of the common envelope evolution [Equation (1)]., We could then use the current values of the orbital separation and masses to constrain the parameters of the common envelope evolution [Equation (1)].
 For IXOI-T4b. and IXOI-S1b. however. there may be reason (o suggest that (he actual Inasses areseller (han Che values associated with stable mass transfer.," For KOI-74b and KOI-81b, however, there may be reason to suggest that the actual masses are than the values associated with stable mass transfer."
 R2010 place lower limits on the masses that extend into the brown dwarf regime., R2010 place lower limits on the masses that extend into the brown dwarf regime.
 In addition. lor INOI-T4. there is only marginal overlap between R2010 aud (he stable mass (transfer model presented in the last section.," In addition, for KOI-74, there is only marginal overlap between R2010 and the stable mass transfer model presented in the last section."
 It is therefore worth seriously considering that the mass of one or both of these cores may be in the brown ciwarf regime., It is therefore worth seriously considering that the mass of one or both of these cores may be in the brown dwarf regime.
 Here we use ΟΙΤΕ as an illustrative example., Here we use KOI-74 as an illustrative example.
 We will show Chat a value of the core mass smaller (han expected [rom stable mass transler may be a signal that (here was a common envelope. but that the orbit was eccentric at the time (he primary filled its Roche lobe.," We will show that a value of the core mass smaller than expected from stable mass transfer may be a signal that there was a common envelope, but that the orbit was eccentric at the time the primary filled its Roche lobe."
 This is expected in some triple svstenis., This is expected in some triple systems.
 It therefore seems inevitable that. whatever the history of IKOI-T4 and INXOI-31. binaries in which the core mass is too low will eventually be found. and (he scenario we present below will apply.," It therefore seems inevitable that, whatever the history of KOI-74 and KOI-81, binaries in which the core mass is too low will eventually be found, and the scenario we present below will apply."
" First we note that. even if (he core mass of IKOI-T4 is small. formal solutions to the stable-mass (ransler eeuations exist. predicting 0.005AL.<M.«0.018.M. and Af,c2M. at the time of Roche-lobe filling."," First we note that, even if the core mass of KOI-74 is small, formal solutions to the stable-mass transfer equations exist, predicting $0.005\, M_\odot<M_c<0.018\, M_\odot$ and $1.2\, M_\odot<M_1<2\, M_\odot$ at the time of Roche-lobe filling."
 These solutions are not viable. however. because the equilibrium radius of a low-core-mass primary would decline as mass was donated in a steady. stable manner.," These solutions are not viable, however, because the equilibrium radius of a low-core-mass primary would decline as mass was donated in a steady, stable manner."
 The second term in Equation (1) would contribute little. ancl. although (he first term might not apply exactly throughout the evolution. the trend of smaller radius with decreasing mass woukl be followed during phase 2.," The second term in Equation (1) would contribute little, and, although the first term might not apply exactly throughout the evolution, the trend of smaller radius with decreasing mass would be followed during phase 2."
 The orbital period would have to be much smaller than 5.2 davs., The orbital period would have to be much smaller than $5.2$ days.
" If, therefore. INOI-T4b is a low-mass stellar core. the binary likely passed. through a common envelope phase."," If, therefore, KOI-74b is a low-mass stellar core, the binary likely passed through a common envelope phase."
 Using Equation (2) we find that a;>M4/7M.. Furthermore. cdenamical instability requires M4 be larger than roughly (1.3—1.5)x(2.2Al.). This predicts an initial separation so large that (he primary could not have filled its Roche lobe.," Using Equation (2) we find that $a_i > M_1/M_c.$ Furthermore, dynamical instability requires $M_1$ be larger than roughly $(1.3-1.5) \times (2.2\, M_\odot).$ This predicts an initial separation so large that the primary could not have filled its Roche lobe."
 This may indicate that the initial orbit was highly eccentric ancl that a dvnamical instabilitv. was triggered during periastron., This may indicate that the initial orbit was highly eccentric and that a dynamical instability was triggered during periastron.
 During the common envelope. the eccentricity," During the common envelope, the eccentricity"
for most targets.,for most targets.
 We study all galaxies mecting the following criteria: 1) a HERACLES imap containing a robust CO ο.—2»1 etection. 2) CALEN far UV (FUV) andSpitzer infrared ata at μα(IR). and 3) an inclination =75°.," We study all galaxies meeting the following criteria: 1) a HERACLES map containing a robust CO $J=2\rightarrow1$ detection, 2) GALEX far UV (FUV) and infrared data at $\mu$ m (IR), and 3) an inclination $\lesssim 75\degr$."
 The first condition excludes low mass galaxies without CO aneetectious., The first condition excludes low mass galaxies without CO detections.
 The second removes a few targets with poorpitzer tou data., The second removes a few targets with poor $\mu$ m data.
 The third disqualifies a haudful of dec-on galaxies., The third disqualifies a handful of edge-on galaxies.
 We are left with 30 disk galaxies. listed in Table along with distances adopted frou Walteretal.1) (2008).. LEDA. and NED.," We are left with $30$ disk galaxies, listed in Table \ref{table1} along with distances adopted from \citet{walter08}, LEDA, and NED."
" This sample is more than four times larecr than that of BOS aud spans a substantial ju mactallicities (8.36S028.93)"" aud ias follow(8.9rangeXloe(AL)E10)19.,", This sample is more than four times larger than that of B08 and spans a substantial range in metallicities $8.36\lesssim z\lesssim8.93$ and mass $8.9\lesssim {\rm log}(M_{*})\lesssim 11.0$.
 We the approach of BOs with only a few modifications., We follow the approach of B08 with only a few modifications.
 BOS compared the first seven TERACLES maps to FUV. IR. andΠα cussion to infer the relationship between the surface density of To. “yp. and the star formation rate surface deusitv. Mvp.," B08 compared the first seven HERACLES maps to FUV, IR, and$\alpha$ emission to infer the relationship between the surface density of $_2$, $\Sigma_{\rm H2}$, and the star formation rate surface density, $\Sigma_{\rm SFR}$ ."
 As in BOs. we estimate “yp from IIERACLES CO 2.5»l] cnussion.," As in B08, we estimate $\Sigma_{\rm H2}$ from HERACLES CO $J=2\rightarrow1$ emission."
" We assmue a Calactic New=οςN10? l5 correct for inclination. include heli iu our quoted surface deusities (a factor of 1.36 a difference frou DOS). aud adopt a CO line ratio I(2.Ὁτα0)=0.7 (note that BOS used a ratio of 05),"," We assume a Galactic $\xco = 2 \times 10^{20}$ , correct for inclination, include helium in our quoted surface densities (a factor of 1.36, a difference from B08), and adopt a CO line ratio $I (2-1) / I (1-0) = 0.7$ (note that B08 used a ratio of 0.8)."
 We estimate. ΜΕΝ. Guclination corrected) using a combination of FUV. eiission aud 2 tim ciission., We estimate $\Sigma_{\rm SFR}$ (inclination corrected) using a combination of FUV emission and $24\mu$ m emission.
 FUV. enission traces mainly plotospheric eiiissiou from O aud D stars. with a typical age of ~20 30 Myv. (Leithereretal.1999:Salim2007) but sensitive to populations up to NINIyY of age.," FUV emission traces mainly photospheric emission from O and B stars, with a typical age of $\sim 20$ $30$ Myr \citep{LEITHERER99,SALIM07}
 but sensitive to populations up to Myr of age."
 Infrared emission at {μι comes from dust mainly heated by vouug stars., Infrared emission at $\mu$ m comes from dust mainly heated by young stars.
 This ciission correlates closely with other signatures of recent star formation. especially Πα euission. aud so has beeu used to correct optical and UW tracers for the effects of extinction (Calzettietal.2007:I&ennicutt2007)..," This emission correlates closely with other signatures of recent star formation, especially $\alpha$ emission, and so has been used to correct optical and UV tracers for the effects of extinction \citep{CALZETTI07,KENNICUTT07}. ."
 Leroyetal.(2008) motivated this FUVIR combination. slicwing that it reproduces other estimates of “SFRX hyith 50% accuracy down to XapggzlO?AL 3 7.," \citet{LEROY08} motivated this FUV–IR combination, showing that it reproduces other estimates of $\Sigma_{\rm SFR}$ with $\sim 50\%$ accuracy down to $\Sigma_{\rm SFR}
\approx 10^{-3}$ $_\odot$ $^{-1}$ $^{-2}$."
 For 21 galaxies. we use FUW inaps from the Nearby Galaxy Survey (NCS.CaildePazetal.2007).. for five arects from the All-sky Buageiug Survey (AIS) aud for oue galaxy we use a map from the Aledimm huaegiug Survey (MIS).," For 24 galaxies, we use FUV maps from the Nearby Galaxy Survey \citep[NGS,][]{GILDEPAZ07}, for five targets from the All-sky Imaging Survey (AIS) and for one galaxy we use a map from the Medium Imaging Survey (MIS)."
 We use maps of IR emissiou at Lian frou heSpitzer Infrared Nearby Calaxies Survey (SINGS.Ieunicuttetal.2003). aud the Local Volume Legacy Survey (LVL.Daleetal.2009).," We use maps of IR emission at $\mu$ m from the Infrared Nearby Galaxies Survey \citep[SINGS,][]{KENNICUTT03} and the Local Volume Legacy Survey \citep[LVL,][]{dale09}."
. Handling of the maps ‘ollows Bos., Handling of the maps follows B08.
 We couvolye the IR and FUV iaps to the 13” (FWHAD resolution of the NMERACLES data., We convolve the IR and FUV maps to the $13\arcsec$ (FWHM) resolution of the HERACLES data.
 Civen he wide distance range of our sample. 13” resolution corresponds to plivsical scales frou 180 pc to 1.7 kpc.," Given the wide distance range of our sample, $13\arcsec$ resolution corresponds to physical scales from $180$ pc to $1.7$ kpc."
 Το avoid being influenced by plivsical resolution. we create a second set of maps at a conunon phvsical resolution of L kpc (FWIIM). appropriate to carry out a uniform analysis.," To avoid being influenced by physical resolution, we create a second set of maps at a common physical resolution of 1 kpc (FWHM), appropriate to carry out a uniform analysis."
 Five galaxies are too distant to reach 1 kpc resolution., Five galaxies are too distant to reach 1 kpc resolution.
" We include them in our ""kpc analvsis at their native resolution. L.lkkpe on average (excluding them does not chanee our couclusiouxs)."," We include them in our “kpc” analysis at their native resolution, kpc on average (excluding them does not change our conclusions)."
 The HERACLES iuaps are masked to include oulv sjenificaut cussion (Lerovoetal.2009)., The HERACLES maps are masked to include only significant emission \citep{LEROY09}.
 The exact conrpleteness of cach map du iass surface deusity depends on the inclination and. for fixed spatial resolution. the distance of the target.," The exact completeness of each map in mass surface density depends on the inclination and, for fixed spatial resolution, the distance of the target."
 A typical noise level is 25 wks per 5.2 hans + channel at 137 resolution., A typical noise level is $25$ mK per 5.2 km $^{-1}$ channel at $13\arcsec$ resolution.
 For the most cistaut. face-ou svsteiis this lutis Klaus tor 5 AL. 7 for om adopted aand line ratio.," For the most distant, face-on systems this limitis $I_{\rm CO} > 0.8$ K km $^{-1}$ or 5 $_\odot$ $^{-2}$ for our adopted and line ratio."
 Closer or more mceliued systems will be coniplete to lower Xy., Closer or more inclined systems will be complete to lower $\Sigma_{\rm H2}$.
 We suuple both sets of maps. oue at 13” and one at lkkpe resolution. using a hexagonal grid spaced by one halfvesolution clement.," We sample both sets of maps, one at $13\arcsec$ and one at kpc resolution, using a hexagonal grid spaced by one half-resolution element."
 We keep onlv saupliug points inside the D-band 257 inaguitude isophotal radius. rs. and where the HERACLES mask iuchudes cussion.," We keep only sampling points inside the $B$ -band $^{\rm
 th}$ magnitude isophotal radius, $r_{25}$, and where the HERACLES mask includes emission."
 At 13” resolution. this viclds Sopp aud Xp estimates for a total of ~27.000 points (~5.000 independent nieasurenmieuts) in 30 nearby star-forming galaxies," At $13\arcsec$ resolution, this yields $\Sigma_{\rm SFR}$ and $\Sigma_{\rm H2}$ estimates for a total of $\sim 27,000$ points $\sim 5,000$ independent measurements) in 30 nearby star-forming galaxies."
 At ] kpe resolution. this προς drops to 12.000 (~2000 independent) measurements.," At $1$ kpc resolution, this number drops to $\sim 12,000$ $\sim 2000$ independent) measurements."
 Figure d shows our data in sspace., Figure \ref{fig:combined} shows our data in space.
" The upper panels present measurenients af a common augular resolution of 13"". the lower panels show results for a conmunuon physical scale of XXkpc."," The upper panels present measurements at a common angular resolution of $13\arcsec$, the lower panels show results for a common physical scale of kpc."
 The left panels show coutours indicating the density of data with each galaxy weighted equally., The left panels show contours indicating the density of data with each galaxy weighted equally.
 The rielt panels directly show cach data point., The right panels directly show each data point.
" Dotted lines in cach plot indicate constant molecular sas depletion times. The,= Mue/Sspr. ie. fixed ratios of I-to-SER."," Dotted lines in each plot indicate constant molecular gas depletion times, $\tau_{\rm Dep}^{\rm H2} = \sightwo/\sigsfr$ , i.e., fixed ratios of $_2$ -to-SFR."
 To make the contour plots. we divide the sspace into ddex-avide cells to erid the data.," To make the contour plots, we divide the space into dex-wide cells to grid the data."
 During eridding. we assign cach data point a weight inverselv proportional to the uuuber of data points for the galaxy that it was drawn from.," During gridding, we assign each data point a weight inversely proportional to the number of data points for the galaxy that it was drawn from."
 Thisassigus the same total weielitto cach galaxy. eusurimg that a few large galaxies," Thisassigns the same total weightto each galaxy, ensuring that a few large galaxies"
The short-term variability of iis studied using the EPIC data.,The short-term variability of is studied using the EPIC data.
 The 0.4-10 keV light curve is rather constant with a low average count rate of ~ s!.., The 0.4–10 keV light curve is rather constant with a low average count rate of $\sim0.4$ .
 No flare is observed., No flare is observed.
" Considering the period and duration of outbursts derived from the long-term light curve, the expected outburst near the oobservation happens between MJD 54188 and 54206."," Considering the period and duration of outbursts derived from the long-term light curve, the expected outburst near the observation happens between MJD 54188 and 54206."
" Therefore, oobserved aat the beginning of one of its outburst (MJD 54190)."," Therefore, observed at the beginning of one of its outburst (MJD 54190)."
 We searched for the pulsation when computing the power density spectra of the EPIC light curve and of the 10 s-binned ISGRI light curve extracted during the long flare shown in Fig. 3.., We searched for the pulsation when computing the power density spectra of the EPIC light curve and of the 10 s-binned ISGRI light curve extracted during the long flare shown in Fig. \ref{isgri_fl1}.
 We used the fast computing method of the Lomb-Scargle periodogram proposed by ?.., We used the fast computing method of the Lomb-Scargle periodogram proposed by \citet{Pressal89}.
 The uncertainty of the period is computed using Eq., The uncertainty of the period is computed using Eq.
 14 in ?.., 14 in \citet{Horneal86}. .
 Both periodograms are shown in Fig., Both periodograms are shown in Fig.
 5 column)., \ref{imaperiod} ).
 The maximum power is detected at 66.09+0.07 s and 65.789+0.009 s for pn and ISGRL respectively.," The maximum power is detected at $66.09\pm0.07$ s and $65.789\pm0.009$ s for pn and ISGRI, respectively."
 The corresponding folded light curves are also shown in Fig., The corresponding folded light curves are also shown in Fig.
 5 column) with zero epochs TO of MJD 54190.391 and 52891.4., \ref{imaperiod} ) with zero epochs T0 of MJD 54190.391 and 52891.4.
" The pulse fractions, defined as P,=(Umax.Imin)/max+Tnin) Tmax and Imin being the maximum and minimum of the intensitieswith of the folded light curve, reach 22+6 and 29+11%."," The pulse fractions, defined as $P_{\mathrm{f}}=(I_{\mathrm{max}}-I_{\mathrm{min}})/(I_{\mathrm{max}}+I_{\mathrm{min}})$ with $I_{\mathrm{max}}$ and $I_{\mathrm{min}}$ being the maximum and minimum of the intensities of the folded light curve, reach $22\pm6$ and $29\pm11$."
. The pulse profiles show one broad peak for pn and a slightly narrower one for ISGRI., The pulse profiles show one broad peak for pn and a slightly narrower one for ISGRI.
" As both pulsations are similar over a period of 3.6 yr, the timing analysis confirms that aand ddetected the same source, as it is unlikely that 2 X-ray sources with the same pulsation could be located in such a small box of a few arcseconds."," As both pulsations are similar over a period of 3.6 yr, the timing analysis confirms that and detected the same source, as it is unlikely that 2 X-ray sources with the same pulsation could be located in such a small box of a few arcseconds."
" A pulsation of 132 s was also reported by ?? using the same ddata presented here, along with the ISGRI data corresponding tothe bright flare detected byINTEGRAL."," A pulsation of 132 s was also reported by \citet{Karaseval07,Karaseval08} using the same data presented here, along with the ISGRI data corresponding tothe bright flare detected by."
. No significant power appears at ~132 s in both periodograms in Fig. 5.., No significant power appears at $\sim132$ s in both periodograms in Fig. \ref{imaperiod}.
" In the pn periodogram, the closest stronger signals appear at 123 and 139 s; yet their power are twice lower than the one at 66 s, and they do not appear in the ISGRI periodogram."," In the pn periodogram, the closest stronger signals appear at 123 and 139 s; yet their power are twice lower than the one at 66 s, and they do not appear in the ISGRI periodogram."
 Folding the light curve at twice the period we derived show a double-peakprofile in both folded light curves., Folding the light curve at twice the period we derived show a double-peakprofile in both folded light curves.
" Still, both local peaks show similar shape and intensity."," Still, both local peaks show similar shape and intensity."
" Therefore, thepulsation around 66 s is likely to be the real pulsation, while the 132 s one is its first harmonic."," Therefore, thepulsation around $66$ s is likely to be the real pulsation, while the 132 s one is its first harmonic."
" ? shows that no difference is observed in the pulse profile derived with ISGRI when folding the light curve with either 66 or 132 s. On the other hand, they showa slight difference between both pulse profiles derived with EPIC/pn, but this difference is not significant within the error bars."," \citet{Karaseval08} shows that no difference is observed in the pulse profile derived with ISGRI when folding the light curve with either 66 or 132 s. On the other hand, they show a slight difference between both pulse profiles derived with EPIC/pn, but this difference is not significant within the error bars."
 The broad-band XMM-Newton-INTEGRAL XX- rayspectrumisshowninFig. 6., The broad-band $-$ X-ray spectrum is shown in Fig. \ref{imaspec}.
.Thex rayspectrumextractedwithpniscombinedwiththehard X- rayoneextractedduringthebright flareseeninIS GRI., The X-ray spectrum extracted with pn is combined with the hard X-ray one extracted during the bright flare seen in ISGRI.
"There fore, animpor bbetweenthe2observationsislarge, anditmaycorrespondtotwodif fere"," Therefore, an important constant factor must be applied, because the intensity difference of between the 2 observations is large, and it may correspond to two different states of the source."
nts ra," Still, the combined spectrum will constrain the spectral model that will fit the continuum shape of the source."
"yspectralbinsaregroupedtopossessatleast30countsperchannel, allowi statistic."," The X-ray spectral bins are grouped to possess at least 30 counts per channel, allowing use of the $\chi^{2}$ statistic."
" First, the spectrum shows a strong absorption at low energies."," First, the spectrum shows a strong absorption at low energies."
" Simple phenomenological models, such as absorbed black body (BB) or power-law (PL), fail to fit the data with X1—3.4orl.7(each106d.o.f.),"," Simple phenomenological models, such as absorbed black body (BB) or power-law (PL), fail to fit the data with $=$ 3.4 or 1.7 (each 106 d.o.f.),"
 respectively., respectively.
"DisregardingtheBBmodel, thet energycutof fto fitthedata."," Disregarding the BB model, the absorbed PL clearly needs a high-energy cutoff to fit the data."
The f itstronglyimproveswithy?—1.03(105d.o., The fit strongly improves with $=$ 1.03 (105 d.o.f.).
 keV, We also explore the possibility of a line at 6.4 keV where some excess is visible.
", Fine-(13+09)xphem? s, EWiine-52.5 eV) of X1-0.99(103d.o.f.),"," The tentative detection provides a good fit $E_{\mathrm{line}}=6.41_{-0.07}^{+0.08}$ keV, $F_{\mathrm{line}}=(1.3\pm0.9)\times10^{-5}\ \mathrm{ph}\,\unit{cm}{-2}\,\unit{s}{-1}$ , $EW_{\mathrm{line}}=52.5$ eV) of $=$ 0.99 (103 d.o.f.),"
 butthisisnotsigni ficantbecausethelinedetectionis {30, but this is not significant because the line detection is $<3\sigma$.
 The possibility of an excess at low energies in addition to the absorption was also studied., The possibility of an excess at low energies in addition to the absorption was also studied.
" However, the addition of a component at low energies is not significant as shown by the high value of the F-test probability of 0.1."," However, the addition of a component at low energies is not significant as shown by the high value of the F-test probability of 0.1."
 The best-fit parameters are listed in Table 3.., The best-fit parameters are listed in Table \ref{tab_spec}.
" The field around iis very crowded, so it possesses several counterpart candidates within the error circles of the previously reported high-energy missions."," The field around is very crowded, so it possesses several counterpart candidates within the error circles of the previously reported high-energy missions."
" In Fig. 7,,"," In Fig. \ref{imaJ}, ,"
 we show the field in the J band., we show the field in the $J$ band.
" With the higher accuracyof Swift,, 3 2MASS candidates were reported (?).."," With the higher accuracyof , 3 2MASS candidates were reported \citep{Romanoal07a}. ."
" Still, with SOFL we note that there are 11 candidates in the J band within this 6"" "," Still, with SOFI, we note that there are 11 candidates in the $J$ band within this $6\arcsec$ "
350 kk.us +.,350 km $^{-1}$.
 Of these. about half appear to be superpositions (so fje reported velocity dispersion is unrealistic}: iu liv cases. the evidence for superposition comes nof frou he ages but from the spectra (Figure D2)).," Of these, about half appear to be superpositions (so the reported velocity dispersion is unrealistic); in many cases, the evidence for superposition comes not from the images but from the spectra (Figure \ref{doubleimgspec}) )."
 These Super)ositions are rare: analytic aud \Loute-Carlo analyses in Ayo»peudix 77. sugecst that one in every three hundred objecs should have a ποσορου within one arescc., These superpositions are rare: analytic and Monte-Carlo analyses in Appendix \ref{super} suggest that one in every three hundred objects should have a neighbor within one arcsec.
 Aloreovoer. of aliguiments closer than one arcsec. not more than ten IOLCCut are expected to be from objects in different eroups.," Moreover, of alignments closer than one arcsec, not more than ten percent are expected to be from objects in different groups."
 If the superpositions we see really are in fae same halos. hen our estimates of the linc-ofsielt separations iuply aQ masses of order 5«10113AJ..," If the superpositions we see really are in the same halos, then our estimates of the line-of-sight separations imply halo masses of order $5\times 10^{14}h^{-1}M_\odot$."
 The arge-7 objects which are not obviously superpositions ropulae the tails of the scaling relations defined by the ilk of the earlv-tvpe galaxy population (quauti&ed bv Bermardi et al., The $\sigma$ objects which are not obviously superpositions populate the tails of the scaling relations defined by the bulk of the early-type galaxy population (quantified by Bernardi et al.
 2005). but they are not distant outlers YOU these relations (Figures 2. aud 5)).," 2005), but they are not distant outliers from these relations (Figures \ref{scalings} and \ref{Mg2all}) )."
 Moreover. if oulv ale ¢XE these objects turi out to be superpositions. anc tle other half are indeed single galaxies. thew he abuudauce of singes is not inconsistent with the nuuber expected w extrapolation of the observed abundance of smaller systenis (from Sheth et al.," Moreover, if only half of these objects turn out to be superpositions, and the other half are indeed single galaxies, then the abundance of singles is not inconsistent with the number expected by extrapolation of the observed abundance of smaller systems (from Sheth et al."
 2003)., 2003).
 It these laree-7 objects are indeed massive ealaxics. aud the velocity dispersions do reflect virial equilibrimm notions. hen it might be worth searching for evidence 6] eravitaional lensing around these objects: they would lave Einstein radi Lz(el[du)~2:GlAu0/2) (o£100kinsLyτή.," If these $\sigma$ objects are indeed massive galaxies, and the velocity dispersions do reflect virial equilibrium motions, then it might be worth searching for evidence of gravitational lensing around these objects: they would have Einstein radii $4\pi (\sigma/c)^2 (d_{\rm ls}/d_{\rm os})\sim 2.3\arcsec 
(d_{\rm ls}/d_{\rm os})/(1/2)$ $(\sigma/400~{\rm km~s}^{-1})^2$."
 I£they host black holes whose masses fall on the same mass-velocity dispersion relation as is seen callv. Afpy/10A.=2(0/100kans14! (Cobhardt et al.," If they host black holes whose masses fall on the same mass-velocity dispersion relation as is seen locally, $M_{\rm BH}/10^9M_\odot = 2\,(\sigma/400~{\rm km~s}^{-1})^4$ (Gebhardt et al."
 2t100: Ferrarese Merritt 2000: Tremaine et al., 2000; Ferrarese Merritt 2000; Tremaine et al.
 2002). hen the black-holes ave enorinous mdeed.," 2002), then the black-holes are enormous indeed."
 Iu this case. it wiIL be iuteresting to see if the lieht-profile slows aux evideuce of the black-hole in the ceuter (e.g. Lauer ct al.," In this case, it will be interesting to see if the light-profile shows any evidence of the black-hole in the center (e.g. Lauer et al."
 2002) πιο UST., 2002) using HST.
 Because they are large and Iuninous. thesc» objects should be relatively easy. targets.," Because they are large and luminous, these objects should be relatively easy targets."
 Therefore. it should also be possible to measure spatially resolved velocity dispersions from eround-based facilities.," Therefore, it should also be possible to measure spatially resolved velocity dispersions from ground-based facilities."
 The superpositious are interesting in their own right., The superpositions are interesting in their own right.
 The abundance of strong gravitational leuses has been usec to place Buts on the geometry of the Universe (e.g. Alithell et al., The abundance of strong gravitational lenses has been used to place limits on the geometry of the Universe (e.g. Mitchell et al.
 2001)., 2004).
 Tlowever. the observed distributious of nuage imultiplicities. separatious and flux ratios are cafπ to reconcile with single-couponcu leus models.," However, the observed distributions of image multiplicities, separations and flux ratios are difficult to reconcile with single-component lens models."
 This has led to some iuterest in the properties of leuses with iultiple compoucuts (ce... Rusin Teeimark 2001: Cohu Iochauek 2001).," This has led to some interest in the properties of lenses with multiple components (e.g., Rusin Tegmark 2001; Cohn Kochanek 2004)."
 Since carly-type galaxies are expected to be the dominaut leis population. he distribution of pair separations and velocity dispersions in our catalog of μιperpositions can be used ο incorporate realistic lens pairs mto models of binaryv-lenses.," Since early-type galaxies are expected to be the dominant lens population, the distribution of pair separations and velocity dispersions in our catalog of superpositions can be used to incorporate realistic lens pairs into models of binary-lenses."
 This is the sulject of work 1n progress., This is the subject of work in progress.
 Axd finally. in principle. the iunber aud spatial distribution of close superposi&ious contains information about the time-scale of 1iereers.," And finally, in principle, the number and spatial distribution of close superpositions contains information about the time-scale of mergers."
 Iu this regard. it is interestimg that a mmmver of the objects iu our sample appear to have slightly pecthar morphologies.," In this regard, it is interesting that a number of the objects in our sample appear to have slightly peculiar morphologies."
 If this reflects a recent merecr. then it is interesting to recall that none of the spectra in our sale show strong eniussion lines.," If this reflects a recent merger, then it is interesting to recall that none of the spectra in our sample show strong emission lines."
 Therefore. it may be that these objects are the low redshift analogs of the red iuteracting galaxies seeu iu the GOODS survey (Somerville et al.," Therefore, it may be that these objects are the low redshift analogs of the red interacting galaxies seen in the GOODS survey (Somerville et al."
 2003)., 2003).
 Or perhaps they are fossil eroups of the sort diseussed by. Vikhliuiu (1999) aud Jones et al. (, Or perhaps they are fossil groups of the sort discussed by Vikhlinin (1999) and Jones et al. (
2003).,2003).
 Follow-up obscrvaticous of these objects is ongoing., Follow-up observations of these objects is ongoing.
 We thank Iarl Gebhardt for cucouragement., We thank Karl Gebhardt for encouragement.
" Funding for the «‘reation aud. istribution of the SDSS Archive has been prewided by the Alfred P. Sloan Foundation. the Participating Istitutions. the National Aeronautics and Space Administration. the Ntional Science Foundation. the U.S, Departinen of Encrev. the Japanese Monbukagakusho. aud the Mas Plauck Societv."," Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society."
 The SDSS Woeb site is http:/Awww.esdss.ore| The SDSS is maweed by the Astrophysical Research Cousortinm (ARC) for the Participating Iustitutious., The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions.
" The Participating Iustitiions are The University of Chicago. Fermilab. the Iustiute for Advanced Study. the Japan Participation Group. The Johus Hopkius University. the Korean Scieutist Croup. Los Alamos National Laboratory. the Max-Plauck-Iusitute for Astronomy (AIPIA). the Max-Plauck-Iustitute for Astrophysics (AIPA). New Mexico State Universitv. University of Pittsburgh. Princeton University. the United States Naval Observatory, aud the University of Washington."," The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington."
these values suggest that the median galaxy is an Lzc1.2L. early-type galaxy at redshift z0.11.,these values suggest that the median galaxy is an $L\approx 1.2 L_*$ early-type galaxy at redshift $z\approx 0.11$.
 Currently we have redshifts for only nine of the 123 galaxies: four in the CDF-S from COMBO-17 (Wolf et 22005). two in the 11030+05 field from the SDSS 2000). and three in the 11255401 field from the SDSS.," Currently we have redshifts for only nine of the 123 galaxies: four in the CDF-S from COMBO-17 (Wolf et 2005), two in the 1030+05 field from the SDSS 2000), and three in the 1255+01 field from the SDSS."
 The mean redshift of these nine objects (zj=0.13 with a spread of 0.02. consistent with the expectations from our color selection.," The mean redshift of these nine objects $\langle z \rangle = 0.13$ with a spread of 0.02, consistent with the expectations from our color selection."
 As a further test on the selection we obtained photometric and spectroscopic data in ten randomly selected 3°« fields from the SDSS.," As a further test on the selection we obtained photometric and spectroscopic data in ten randomly selected $3^{\circ}
\times 3^{\circ}$ fields from the SDSS."
" Galaxies were selected in the g—r rplaneinthesamemannerasinourstudy. usingtheF ukugitaetal, (1995 wmagesootiallod so cgaulvaresuakushBan R/imitstoSDSSrandg-rlimits."," Galaxies were selected in the $g-r$ $r$ plane in the same manner as in our study, using the Fukugita et (1995) transformations to convert our $R$ and $B-R$ limits to SDSS $r$ and $g-r$ limits."
T hemedianredshi ftis0.098. with90 galaxiesatz>0.05.," The median redshift is 0.098, with galaxies at $z>0.05$."
Therms field—to—fieldvariationofthemed , The rms field-to-field variation of the median is only 0.008.
In the following we will adopt z20.1 as the median redshift: our conclusions change very little 1f we were to use. δ.σ. 2=0.08 or z=0.13 instead.," In the following we will adopt $z=0.1$ as the median redshift; our conclusions change very little if we were to use, e.g., $z=0.08$ or $z=0.13$ instead."
 For z=0.1 our observed R-band limit corresponds to Mj~—21. and the median galaxy has Mp~—22.," For $z\approx 0.1$ our observed $R$ -band limit corresponds to $M_R \sim
-21$, and the median galaxy has $M_R \sim -22$."
" All galaxies were assigned a morphological type by visually inspecting their summed images (1.e.. the ""BVR"" images for MUSYC galaxies and the ""BRI"" images for NDWFS objects)."," All galaxies were assigned a morphological type by visually inspecting their summed images (i.e., the “BVR” images for MUSYC galaxies and the “BRI” images for NDWFS objects)."
 The images span a large range in surface brightness levels. going from the nearly saturated central regions to very low surface brightness features up to > SOkkpe away from the center.," The images span a large range in surface brightness levels, going from the nearly saturated central regions to very low surface brightness features up to $>50$ kpc away from the center."
 As the relevant dynamic brightness range is >107 each galaxy was displayed at four different. contrast. levels simultaneously., As the relevant dynamic brightness range is $\gtrsim 10^4$ each galaxy was displayed at four different contrast levels simultaneously.
 The morphological types are necessarily broad., The morphological types are necessarily broad.
 Although the S/N ratio is very high the spatial resolution is quite poor: the typical seeing is 171. which corresponds to 3kkpe at z=0.1.," Although the S/N ratio is very high the spatial resolution is quite poor: the typical seeing is $1\farcs 1$, which corresponds to kpc at $z=0.1$."
 Therefore. we only have 2—3 resolution elements within the half-light radii of many galaxies (see. e.g.. Jérrgensen.Franx. 1995).," Therefore, we only have $2-3$ resolution elements within the half-light radii of many galaxies (see, e.g., rgensen, 1995)."
 The assigned types are spiral (S). indicating the presence of spiral arms and/or star forming regions im a disk: SO. indicating an early-type galaxy with an unambiguous disk component: and E/SO. indicating a bulge-dominated early-type galaxy.," The assigned types are spiral (S), indicating the presence of spiral arms and/or star forming regions in a disk; S0, indicating an early-type galaxy with an unambiguous disk component; and E/S0, indicating a bulge-dominated early-type galaxy."
 We cannot securely separate elliptical galaxies from bulge-dominated or face-on SO galaxies., We cannot securely separate elliptical galaxies from bulge-dominated or face-on S0 galaxies.
 Contrary to the usual definition the E/SO class therefore encompasses ellipticals. bulge-dominated SOs. E/SOs. and SO/Es.," Contrary to the usual definition the E/S0 class therefore encompasses ellipticals, bulge-dominated S0s, E/S0s, and S0/Es."
 Morphological classifications are listed in Table |. and in the Appendix.," Morphological classifications are listed in Table 1, and images of all 126 galaxies are shown in the Appendix."
 As expected. the sample is dominated by early-type galaxies: of ianison 10 as SOs (r.e.. xb.o@pects.disk-dominated early-type galaxies). and 86 early-type galaxies).," As expected, the sample is dominated by early-type galaxies: of 126 objects, 10 as S0s (i.e., disk-dominated early-type galaxies), and 86 early-type galaxies)."
 Most of the spiral galaxies have large red bulges and faint blue arms., Most of the spiral galaxies have large red bulges and faint blue arms.
 Based on their morphologies at surface brightness levels p<25 aaresec we infer that virtually all galaxies in our sample are red because of their evolved stellar populations. and not because of dust (as is well known from many previous studies of bright red galaxies 1n the local Universe: see. e.g.. Sandage Visvanathan 1978. Strateva et 22001).," Based on their morphologies at surface brightness levels $\mu \lesssim 25$ $^2$ we infer that virtually all galaxies in our sample are red because of their evolved stellar populations, and not because of dust (as is well known from many previous studies of bright red galaxies in the local Universe; see, e.g., Sandage Visvanathan 1978, Strateva et 2001)."
 Tidal features were first identified by visual inspection of the full sample of 126 galaxies: a quantitative analysis of disturbances in the restricted sample of 86 bulge-dominated early-type galaxies follows in refquant.sec.., Tidal features were first identified by visual inspection of the full sample of 126 galaxies; a quantitative analysis of disturbances in the restricted sample of 86 bulge-dominated early-type galaxies follows in \\ref{quant.sec}.
 The flag describing tidal features can have one of four values: 0 for no tidal features. | for weak features. 2 for strong features. and 3 for an ongoing interaction with another galaxy.," The flag describing tidal features can have one of four values: 0 for no tidal features, 1 for weak features, 2 for strong features, and 3 for an ongoing interaction with another galaxy."
 Galaxies in the 727 class are generally highly deformed, Galaxies in the “2” class are generally highly deformed
At the redshifts z21.7 considered here. all stellar populations will be voung. and therefore galaxy morphology based shortcuts applicable at lower reclshilt. (hat ellipticals never host core-collapse SNe. cannot be used.,"At the redshifts $z>1.7$ considered here, all stellar populations will be young, and therefore galaxy morphology based shortcuts applicable at lower redshift, that ellipticals never host core-collapse SNe, cannot be used."
 With the spatial resolution 11 kpe at := 3) and multicolor information from SNAP it may be possible to sulliciently constrain the stellar population age at the (projected) location of à SN to partly discriminate some core-collapse SNe from SNe Ia. The critical assumption here is (hat most core-collapse SNe will be produced in regions dominated by a single starburst. and (hat the light of such a starburst will have high surface brightness and thus dominate over any underlviug older population.," With the spatial resolution 1 kpc at $z=3$ ) and multicolor information from SNAP it may be possible to sufficiently constrain the stellar population age at the (projected) location of a SN to partly discriminate some core-collapse SNe from SNe Ia. The critical assumption here is that most core-collapse SNe will be produced in regions dominated by a single starburst, and that the light of such a starburst will have high surface brightness and thus dominate over any underlying older population."
 In this case multicolor photometry covering the restframe UV can constrain the starburst age and therelore the lowest mass of (he stars completing their evolution., In this case multicolor photometry covering the restframe UV can constrain the starburst age and therefore the lowest mass of the stars completing their evolution.
 Taking 8M. as the dividing line between core-collapse ancl thermonuclear supernovae Renzini 1983).. evidence of à starburst vounger than 50 Myr (Schalleretal.1993) at the location of à SN would strongly suggest that the SN is a core-collapse SN.," Taking $8~M_\odot$ as the dividing line between core-collapse and thermonuclear supernovae \citep{iben83}, evidence of a starburst younger than 50 Myr \citep{schaller92,schaerer93} at the location of a SN would strongly suggest that the SN is a core-collapse SN."
 Protracted starbursts. low-level star lormation. aud projection effects will complicate this technique.," Protracted starbursts, low-level star formation, and projection effects will complicate this technique."
 Absence of detectable star formation anvwhere near à SN would suggest a SN Iu. but it will be difficult to rule-out. low-level star Formation aud hence a core-collapse origin.," Absence of detectable star formation anywhere near a SN would suggest a SN Ia, but it will be difficult to rule-out low-level star formation and hence a core-collapse origin."
 Again. SNAP spectroscopic follow-up of SNe hosts at lower redshift will help calibrate this technique.," Again, SNAP spectroscopic follow-up of SNe hosts at lower redshift will help calibrate this technique."
 Detection of the shock breakout [rom core-collapse SNe would provide a completely new and independent means of discriminating SN tvpes., Detection of the shock breakout from core-collapse SNe would provide a completely new and independent means of discriminating SN types.
 As discussed in relsec:corecoll.. predictions of luminosity and Gimescale. and hence detectability. are cuite uncertain.," As discussed in \\ref{sec:corecoll}, predictions of luminosity and timescale, and hence detectability, are quite uncertain."
 It is encouraging in this respect that shock breakout has been detected at restframe optical wavelengths in low redshift Tvpe II (SN 1987À. Menziesetal.(19837):Lammy (1983))). Hb (SN 1993J. Lewisetal.(1994):Richmond (1994))). and Ib/c (SN 1999ex. SUilvingerοἱal. (2002))) SNe with timescales and luminosities that SNAP could detect out to high redshift.," It is encouraging in this respect that shock breakout has been detected at restframe optical wavelengths in low redshift Type II (SN 1987A, \citet{menzies87,hamuy88}) ), IIb (SN 1993J, \citet{lewis94,richmond94}) ), and Ib/c (SN 1999ex, \citet{stritzinger}) ) SNe with timescales and luminosities that SNAP could detect out to high redshift."
 SNAP will sample the restframe UV of high-redshift SNe. where the hot shock breakout will be brighter. however. the fastest events may be missed due to SNAP's 1-2 clav rest{rame cadence.," SNAP will sample the restframe UV of high-redshift SNe, where the hot shock breakout will be brighter, however, the fastest events may be missed due to SNAP's 1-2 day restframe cadence."
 It is tempting to exploit the fact that core-collapse SNe are generally fainter al peak than SNe Ia to obtain the (vpe., It is tempting to exploit the fact that core-collapse SNe are generally fainter at peak than SNe Ia to obtain the type.
 ILowever. the Iuminosity. functions do overlap (Richardson 2006).. and gravitational lensing (see the next section). extinction. and recshilt errors can further blur this distinction.," However, the luminosity functions do overlap \citep{richardson02,richardson06}, and gravitational lensing (see the next section), extinction, and redshift errors can further blur this distinction."
 Using Iuminosity as (he sole (wpe discriminant would surely bias any cosmological measurement by modilving the statistical distribution of true 5Ne Ia and inviting interlopers (lomeier2005)., Using luminosity as the sole type discriminant would surely bias any cosmological measurement by modifying the statistical distribution of true SNe Ia and inviting interlopers \citep{homeier05}.
. Luminosity still may prove useful as a weak prior in concert with other (vpe discriminants., Luminosity still may prove useful as a weak prior in concert with other type discriminants.
 Without the need (o trigger spectroscopic followup. one can wait for the full light curve to tvpe the supernova.," Without the need to trigger spectroscopic followup, one can wait for the full light curve to type the supernova."
 The magnitude might. however. be used to feed the supernova to JWST or TAIT: Chis poses no danger as that," The magnitude might, however, be used to feed the supernova to JWST or TMT; this poses no danger as that"
equivalently the 2D function shown in Fig. 7)),equivalently the 2D function shown in Fig. \ref{PB}) )
 by a piece- constant function., by a piece-wise constant function.
 The maximum error due to such an approximation ean be estimated using the following equation: For a required RMS noise in the image of 77. the peak error due to the piece-wise constant approximation should be 3-5 times smaller than 7.," The maximum error due to such an approximation can be estimated using the following equation: For a required RMS noise in the image of $\eta$, the peak error due to the piece-wise constant approximation should be 3–5 times smaller than $\eta$."
 The minimum PA increment such that the RMS norse in the image ts not limited by the piece-wise constant approximation would be given by For the I4GHz. VLA C-array test data. arem=0.0003 deg'.," The minimum PA increment such that the RMS noise in the image is not limited by the piece-wise constant approximation would be given by For the 1.4GHz, VLA C-array test data, $\left.\frac{\partial{PB}}{\partial\psi}\right|_{max}
\approx~0.0003~deg^{-1}$ ."
 For a PA increment of 10°. peak imasresiduals in Stokes-I and -V would be about 1 mJy and 5 mJy respectively.," For a PA increment of $10^\circ$, peak residuals in Stokes-I and -V would be about 1 mJy and 5 mJy respectively."
 With the expected thermal sensitivity of 0.1 mJy/beam for the 1.4 GHz test data we used. PA increments of 1° were required.," With the expected thermal sensitivity of $0.1$ mJy/beam for the 1.4 GHz test data we used, PA increments of $1^\circ$ were required."
 The PA increment for higher sensitivity telescopes like the EVLA or SKA such that imaging is not limited by the above approximation will be much smaller., The PA increment for higher sensitivity telescopes like the EVLA or SKA such that imaging is not limited by the above approximation will be much smaller.
 This requirement however can be significantly relaxed by approximating the error function by a piecewise linear approximation (interpolation of the functions computed at larger PA increments)., This requirement however can be significantly relaxed by approximating the error function by a piecewise linear approximation (interpolation of the functions computed at larger PA increments).
 Furthermore. since Image interpolation itself can be expensive. caching of pre-computed aperture functions at appropriate PA increments will be necessary.," Furthermore, since image interpolation itself can be expensive, caching of pre-computed aperture functions at appropriate PA increments will be necessary."
 Note that the gridding cost is relatively insensitive to the number of convolution functions used., Note that the gridding cost is relatively insensitive to the number of convolution functions used.
 A hybrid approach of FFT based transforms plus analytical computations for the strongest sources will probably deliver optimal performance., A hybrid approach of FFT based transforms plus analytical computations for the strongest sources will probably deliver optimal performance.
 Some residual deconvolution errors are still left around the second strongest source in Fig. 5.., Some residual deconvolution errors are still left around the second strongest source in Fig. \ref{IC2233_STOKES_I}.
 The pattern in the residual image (not shown) suggests that these errors are due to image pixelation (??)..," The pattern in the residual image (not shown) suggests that these errors are due to image pixelation \citep{Pixelation_Errors, Cotton_Uson_2007}."
 More sophisticated parametrization of the sky. independent of the image pixel size (e.g. as is done in scale sensitive deconvolution algorithms like the Asp-Clean (?) or MS-Clean) along with the imaging algorithm described here to correct for DD gains should give better results.," More sophisticated parametrization of the sky, independent of the image pixel size (e.g. as is done in scale sensitive deconvolution algorithms like the Asp-Clean \citep{Asp_Clean} or MS-Clean) along with the imaging algorithm described here to correct for DD gains should give better results."
 It 1s also possible that the residual errors are due to pointing errors during the observation., It is also possible that the residual errors are due to pointing errors during the observation.
 We are investigating this possibility and hope to report on it in due course., We are investigating this possibility and hope to report on it in due course.
 The algorithm described here corrects for DD gains without loosing the efficiency advantage of the FFT algorithm., The algorithm described here corrects for DD gains without loosing the efficiency advantage of the FFT algorithm.
 Our algorithm scales well in run-time efficiency and implementation complexity. for large. data volume. complex field as well as for arrays where antenna elements cannot be assumed to be identical.," Our algorithm scales well in run-time efficiency and implementation complexity for large data volume, complex field as well as for arrays where antenna elements cannot be assumed to be identical."
" Various variants of the ""Peeling"" algorithm can also. be used to correct for direction-dependent gains.", Various variants of the “Peeling” algorithm can also be used to correct for direction-dependent gains.
 In this approach antenna based gains are determined in the direction of each compact source., In this approach antenna based gains are determined in the direction of each compact source.
 These gains are then used to subtract the contribution of compact sources from the observed data using a Direct Fourier Transform (DFT) and the residual visibilities are Imaged again., These gains are then used to subtract the contribution of compact sources from the observed data using a Direct Fourier Transform (DFT) and the residual visibilities are imaged again.
 While this is useful in removing the artifacts due to strong compact sources. since the gains are determined independently for each direction in the sky. as the image complexity increases. too many degrees of freedom (DoF) might be added to the problem.," While this is useful in removing the artifacts due to strong compact sources, since the gains are determined independently for each direction in the sky, as the image complexity increases, too many degrees of freedom (DoF) might be added to the problem."
 For crowded fields (arge number of compact sources). this leads to a proliferation of DoFs and potentially to the problem of over-fitting (the extreme case being when each pixel in the image has an associated independent gain which gives the best-fit result).," For crowded fields (large number of compact sources), this leads to a proliferation of DoFs and potentially to the problem of over-fitting (the extreme case being when each pixel in the image has an associated independent gain which gives the best-fit result)."
 Since DFTs have to be used to compute residuals. the computing load ts also significantly higher than the corresponding one for FFT-based computation of residuals.," Since DFTs have to be used to compute residuals, the computing load is also significantly higher than the corresponding one for FFT-based computation of residuals."
 For complex fields containing extended emission. this approach quickly becomes numerically un-viable because of the large number of DoFs included as well as the high computing and I/O loads involved.," For complex fields containing extended emission, this approach quickly becomes numerically un-viable because of the large number of DoFs included as well as the high computing and I/O loads involved."
 Therefore. while variants of the Peeling algorithm could have given better results for the particular 1.4 GHz VLA data that we have used in this paper. we did not resort to Peeling based algorithms.," Therefore, while variants of the Peeling algorithm could have given better results for the particular 1.4 GHz VLA data that we have used in this paper, we did not resort to Peeling based algorithms."
 However since the goal here ts to demonstrate the effectiveness of the algorithm in correcting for otherwise difficult to correct DD gains. we used this relatively simple field for our tests so that the advantages and limitations of our algorithm are brought to the fore.," However since the goal here is to demonstrate the effectiveness of the algorithm in correcting for otherwise difficult to correct DD gains, we used this relatively simple field for our tests so that the advantages and limitations of our algorithm are brought to the fore."
 Of course. using a direct Fourier transform (DFT) for predicting model visibilities rather than using the FFT algorithm will give the most accurate results.," Of course, using a direct Fourier transform (DFT) for predicting model visibilities rather than using the FFT algorithm will give the most accurate results."
 While such a brute-force approach might be useful for simple fields. as mentioned above. the computing cost for even such simple fields becomes prohibitive for data with more than a few frequency channels. even when assuming that the various antenna elements are identical.," While such a brute-force approach might be useful for simple fields, as mentioned above, the computing cost for even such simple fields becomes prohibitive for data with more than a few frequency channels, even when assuming that the various antenna elements are identical."
 For cases where this assumption breaks down. as it does even for the simple case of random antenna pointing errors. computing costs are impractically high.," For cases where this assumption breaks down, as it does even for the simple case of random antenna pointing errors, computing costs are impractically high."
 Furthermore. for full-beam. full-Stokes imaging. which requires use of at least the diagonal terms of the Mueller matrix (Eq. 4))," Furthermore, for full-beam, full-Stokes imaging, which requires use of at least the diagonal terms of the Mueller matrix (Eq. \ref{MUELLER}) )"
 if not the full matrix. it is unclear if a brute-force DFT approach will work.," if not the full matrix, it is unclear if a brute-force DFT approach will work."
 Antenna pointing errors. azimuthally asymmetric aperture illuminations. wide bandwidths and deconvolution errors due to the use of discrete pixels for the sky representation all leave residuals that limit the full-beam imaging dynamic range to 10—10°.," Antenna pointing errors, azimuthally asymmetric aperture illuminations, wide bandwidths and deconvolution errors due to the use of discrete pixels for the sky representation all leave residuals that limit the full-beam imaging dynamic range to $10^4-10^5$."
 Therefore. apart from correcting for the direction dependent effects. for the highest imaging dynamic range. scale-sensitive decomposition of the sky might also be necessary (?)..," Therefore, apart from correcting for the direction dependent effects, for the highest imaging dynamic range, scale-sensitive decomposition of the sky might also be necessary \citep{Asp_Clean}. ."
 Thealgorithm described here can be combined efficiently with scale-sensitive deconvolution and has the, Thealgorithm described here can be combined efficiently with scale-sensitive deconvolution and has the
This is clearly a very approximate number.,This is clearly a very approximate number.
 Lt assumes that we know both the number of systems. produced. by the CE2 formation channel and the fraction of those systems which have short enough periods to merge within à IIubble time., It assumes that we know both the number of systems produced by the CE2 formation channel and the fraction of those systems which have short enough periods to merge within a Hubble time.
 Uncertainties in the CE2 channel include the treatment of common-envyelope evolution itself: the extent to which the first mass transfer. phase is non-conservative and the criterion for clvnanically unstable mass transfer.," Uncertainties in the CE2 channel include the treatment of common-envelope evolution itself, the extent to which the first mass transfer phase is non-conservative and the criterion for dynamically unstable mass transfer."
 lHlowever. our estimate for the relative numbers of Le- sdOs and sdB stars seems to be a reasonable match o the observations.," However, our estimate for the relative numbers of He-rich sdOs and sdB stars seems to be a reasonable match to the observations."
" We are not aware of samples that can be compared: precisely. but Strocer et. ((2007) list 33 He-rich. sdO stars: in à companion paper. Lisker οἱ ((2005) state that over 200 sdD stars have been ""analysed or atmospheric parameters’."," We are not aware of samples that can be compared precisely, but Stroeer et (2007) list 33 He-rich sdO stars; in a companion paper, Lisker et (2005) state that over 200 sdB stars have been `analysed for atmospheric parameters'."
" Heber (2008) increases that number to ""several hundred! κα stars.", Heber (2008) increases that number to `several hundred' sdB stars.
 Phe Palomar-Creen survey (Green. Schmidt Lichert 1986) found ~ 1 He-sdO or every + There seems to be Littl doubt. that He-WD| mergers (Salo Jellery 2000). and. Le-\WD|post-sdD. mergers. (this work) both happen.," The Palomar-Green survey (Green, Schmidt Liebert 1986) found $\sim$ 1 He-sdO for every 4 There seems to be little doubt that He-WD+He-WD mergers (Saio Jeffery 2000) and He-WD+post-sdB mergers (this work) both happen."
 The potential dillerence between the outcomes of those events is worth examining., The potential difference between the outcomes of those events is worth examining.
 Han ct (2002. 2003) and Lan (2008) have argued that double Lle-WD mergers can explain single sclB stars. whilst here we argue that He-WD|post-sdB mergers can produce. ον) stars.," Han et (2002, 2003) and Han (2008) have argued that double He-WD mergers can explain single sdB stars, whilst here we argue that He-WD+post-sdB mergers can produce He-sdO stars."
 The dillerence between the atmospheres of sc and sd stars should be able to account for this., The difference between the atmospheres of sdB and sdO stars should be able to account for this.
 Groth. Ixudritzki lleber (1985) examined the occurence of convection zones," Groth, Kudritzki Heber (1985) examined the occurence of convection zones"
Similarly V5~VvLEe of inverse Compton scatteringo between cosmic rav e aud various backeroundo radiations are also in the rough range (2.00V..20CGeV) where E is the οποίον of cose ray e.,"Similarly $\sqrt{s}\sim\sqrt{4E\epsilon}$ of inverse Compton scattering between cosmic ray $e^\pm$ and various background radiations are also in the rough range $(2.0{\rm eV},~20{\rm GeV})$ where $E$ is the energy of cosmic ray $e^\pm$."
 Wo plot Fig.7 to describe the variation of the [.M[? of inverse Compton scattering with variable Vs., We plot Fig.7 to describe the variation of the $\overline{|{\cal M}|^2}$ of inverse Compton scattering with variable $\sqrt{s}$.
" The .M|? of the inverse Compton scattering versus 0 in the cased, —d,=1.1. Ay=A»1.0 and Age= L.OTeV with different. s."," The $\overline{|{\cal M}|^2}$ of the inverse Compton scattering versus $\theta$ in the case $d_{\rm t}=d_{\rm s}=1.1$, $\lambda_0=\lambda_2=1.0$ and $\Lambda_{\cal U}=1.0$ TeV with different $\sqrt{s}$."
 Similar to the case of cosinic ray. s of the inverse Compton scattering of a cosmic rav et is also small compared to those in the photon.colliders. which results iu the impact of uuparticle plysics on cosude rav 67 is almost ueglieible as Fig.7 indicates.," Similar to the case of cosmic ray photon, $s$ of the inverse Compton scattering of a cosmic ray $e^\pm$ is also small compared to those in the colliders, which results in the impact of unparticle physics on cosmic ray $e^\pm$ is almost negligible as Fig.7 indicates."
" Now let us turn to the hot topic. observed cosmic rav 6+ excess about the energv. 100€/0V. where cosi ray e mainly interacts with optical background radiation of energy ον), We can obtain figures simular to that at the bottom right corner in Fie.7. so. the same conchision cau be drawn for cosmic ray 67 excess: the influcuee of uuparticle plivsics on cosmic ray 6h excess can nearly be neelected."," Now let us turn to the hot topic, observed cosmic ray $e^\pm$ excess about the energy $100$ GeV, where cosmic ray $e^\pm$ mainly interacts with optical background radiation of energy $\sim$ eV. We can obtain figures similar to that at the bottom right corner in Fig.7, so, the same conclusion can be drawn for cosmic ray $e^\pm$ excess: the influence of unparticle physics on cosmic ray $e^\pm$ excess can nearly be neglected."
 Iu fact. as have been pointed out in papers 10.0].. the low energy experiments will never be able to observe ," In fact, as have been pointed out in papers \cite{higgs, scale}, the low energy experiments will never be able to observe unparticle physics."
The ~ΠΟ between scalar muparticle operator aud SM Hiees boson will cause iiparticlethe plivsies.breaking of couplingconformal svuuuetry of uuparticle sector at some scale Ay. thus. the experimental probes of the conformal hidden sector must probe cucreies m the conformal window MagozVESAg.," The coupling $\sim H^2O_{\cal U}$ between scalar unparticle operator and SM Higgs boson will cause the breaking of conformal symmetry of unparticle sector at some scale $\Lambda_{\not\!{\cal
U}}$, thus, the experimental probes of the conformal hidden sector must probe energies in the conformal window $\Lambda_{\not\!{\cal
U}}< \sqrt{s}_{\rm exp}<\Lambda_{\cal U}$."
 Tu general. Avy has the scale 2 106eV. aud below this scale the muparticle sector becomes a traditional particle sector.," In general, $\Lambda_{\not\!{\cal U}}$ has the scale $\gtrsim10$ GeV, and below this scale the unparticle sector becomes a traditional particle sector."
 Coniparably. the typical cnerey s=(~)¥LEe of interaction between a cosnuc ταν photon (« *) and a backeround photon is in the scope (2.0eV. 20GeV).," Comparably, the typical energy $\sqrt{s}=(\sim)\sqrt{4E\epsilon}$ of interaction between a cosmic ray photon $e^{\pm}$ ) and a background photon is in the scope $(2.0{\rm eV},~ 20{\rm GeV})$ ."
 The coming photon (e*) couples uuparticle operators if aud only if it satisfies where e=Tj =216GcV is the vacuum expectation value (VEV) of Higes boson |0}., The incoming photon $e^{\pm}$ ) couples unparticle operators if and only if it satisfies where $v=\langle H\rangle=$ 246GeV is the vacuum expectation value (VEV) of Higgs boson \cite{higgs}.
. Deviating frou the kinematic conditious (18)) for unparticle exchange. cosmic ray photon (e+) decouples rapidly from unparticle sector. which makes wuparticle plivsies inaccessible for most cosmic rav events.," Deviating from the kinematic conditions \ref{condition}) ) for unparticle exchange, cosmic ray photon $e^{\pm}$ ) decouples rapidly from unparticle sector, which makes unparticle physics inaccessible for most cosmic ray events."
 Iu the particular case of observed cosmic rav oT excess. Vsπο~ 10°eV is far below the characteristic scale Ayez LOGeYV. thus. unparticle plivsics should be irrelevant to the issue.," In the particular case of observed cosmic ray $e^\pm$ excess, $\sqrt{s}\sim\sqrt{4E\epsilon}\sim10^6$ eV is far below the characteristic scale $\Lambda_{\not\!\cal U}\gtrsim10$ GeV, thus, unparticle physics should be irrelevant to the issue."
 The conclusions drawn here more precisely qualify the above negative results obtained from Fig.6 aud Fie.7., The conclusions drawn here more precisely qualify the above negative results obtained from Fig.6 and Fig.7.
 We compute the amplitudes of PP aud ES for diphotou interaction aud the amplitudeof inverse, We compute the amplitudes of PP and ES for diphoton interaction and the amplitudeof inverse
extra-mixing process in this star.,extra-mixing process in this star.
 Data on the discovery and period of V16 have been summarized by Lloyd-Evans (1982))., Data on the discovery and period of V16 have been summarized by Lloyd-Evans \cite{LE83}) ).
 In the same paper it is shown that V16 has a high probability for cluster membership according to radial velocity data., In the same paper it is shown that V16 has a high probability for cluster membership according to radial velocity data.
 The most recent detailed study has been published by Szekely et al. (2007)., The most recent detailed study has been published by Szekely et al. \cite{Szekely07}) ).
 Beside V16 they detected four stars which they classified as long period variables. two of them are probably sources in the background.," Beside V16 they detected four stars which they classified as long period variables, two of them are probably sources in the background."
 For one star. V17. they give a period of approximately 69 d. The K-magnitude places the star on the RGB of NGC 362.," For one star, V17, they give a period of approximately 69 d. The $K$ -magnitude places the star on the RGB of NGC 362."
 As Szekely et al., As Szekely et al.
 note. their fourth LPV νου is likely a cluster member according to the star's metallicity.," note, their fourth LPV V36 is likely a cluster member according to the star's metallicity."
 V2 is not found in their list of variables., V2 is not found in their list of variables.
 After the discovery of the red variable V1 in NGC 2808 in the 1960s. Clement Hazen (1989)) reported the finding of a second long period variable. ΝΤ. and presented first data on the light changes of these two stars.," After the discovery of the red variable V1 in NGC 2808 in the 1960s, Clement Hazen \cite{CH89}) ) reported the finding of a second long period variable, V11, and presented first data on the light changes of these two stars."
 The variability of V1 has been confirmed by Corwin et al. (2004))., The variability of V1 has been confirmed by Corwin et al. \cite{corwin04}) ).
 For none of the LPVs could a period be derived., For none of the LPVs could a period be derived.
 The two clusters were monitored as part of a larger program searching for long period variables in. Galactic. globular clusters., The two clusters were monitored as part of a larger program searching for long period variables in Galactic globular clusters.
 Results for 47 Tue (Lebzelter Wood 2005)) and NGC 1846 (Lebzelter Wood 2007)) have been published as the first papers from this monitoring program., Results for 47 Tuc (Lebzelter Wood \cite{LW05}) ) and NGC 1846 (Lebzelter Wood \cite{LW07}) ) have been published as the first papers from this monitoring program.
 The observations of NGC 2808 and NCG 362 were obtained and analysed the same way., The observations of NGC 2808 and NCG 362 were obtained and analysed the same way.
 Thus we will give here only a brief summary anc refer to Lebzelter Wood (2005)) for details., Thus we will give here only a brief summary and refer to Lebzelter Wood \cite{LW05}) ) for details.
 The time series were obtained in two parts., The time series were obtained in two parts.
 The first part was observed at Mount Stromlo using the 50inch telescope anc the camera of the MACHO experiment (Alcock et al. 1992))., The first part was observed at Mount Stromlo using the 50inch telescope and the camera of the MACHO experiment (Alcock et al. \cite{Macho92}) ).
 The MACHO camera obtained two images in two broad banc filters at the same time., The MACHO camera obtained two images in two broad band filters at the same time.
 These passbands did not corresponc to standard filters but the blue one was similar to Johnsor V., These passbands did not correspond to standard filters but the blue one was similar to Johnson $V$.
 Observations started in May 2002. but came to an abrupt stop after a few months when Mount Stromlo observatory was destroyed by a bush fire.," Observations started in May 2002, but came to an abrupt stop after a few months when Mount Stromlo observatory was destroyed by a bush fire."
 We continued our monitoring program in late 2003 at CTIO's 1.3m telescope operated by the SMARTS consortium., We continued our monitoring program in late 2003 at CTIO's 1.3m telescope operated by the SMARTS consortium.
 The instrument ANDICAM was used for two monitoring runs in service mode from October 2003 to January 2004 and from March 2005 to July 2005 (only NGC 2808). respectively.," The instrument ANDICAM was used for two monitoring runs in service mode from October 2003 to January 2004 and from March 2005 to July 2005 (only NGC 2808), respectively."
 Monitoring was done in Johnson V and Jc., Monitoring was done in Johnson $V$ and $I_C$.
 The V and the {ο data sets were analyzed separately., The $V$ and the $I_C$ data sets were analyzed separately.
 To detect variable stars and to derive light curves we applied an image subtraction technique using the ISIS 2.1 code developed by Alard (2000))., To detect variable stars and to derive light curves we applied an image subtraction technique using the ISIS 2.1 code developed by Alard \cite{Alard00}) ).
 Stellar fluxes on the reference frames were measured using the PSF fitting software written by Ch., Stellar fluxes on the reference frames were measured using the PSF fitting software written by Ch.
 Alard for the DENIS project (see Schuller et al. 2003))., Alard for the DENIS project (see Schuller et al. \cite{Schuller03}) ).
 A typical photometric accuracy derived from 2 images obtained in the same night is 0702 in V., A typical photometric accuracy derived from 2 images obtained in the same night is $\fm$ 02 in $V$.
 For both clusters we observed two fields with ANDICAM. each having a field of view (FOV) of 6x6 aremin.," For both clusters we observed two fields with ANDICAM, each having a field of view (FOV) of 6x6 arcmin."
 The central coordinates of the two fields had an offset of approximately 3 areminutes. re. the two fields were overlapping by almost was considerably larger (even though we used only one segment out of 4). but no long period variables beyond the FOV covered by the ANDICAM images could be detected.," The central coordinates of the two fields had an offset of approximately 3 arcminutes, i.e. the two fields were overlapping by almost was considerably larger (even though we used only one segment out of 4), but no long period variables beyond the FOV covered by the ANDICAM images could be detected."
 For NGC 362. Rosenberg et al. (2000))," For NGC 362, Rosenberg et al. \cite{rosenberg00}) )"
 give a core radius of 0.17 aremin and a concentration parameter (tyjgai/feore) of 1.94., give a core radius of 0.17 arcmin and a concentration parameter $_{tidal}$ $_{core}$ ) of 1.94.
 For NGC 2808 corresponding values of 0.26 aremin and 1.77 are listed., For NGC 2808 corresponding values of 0.26 arcmin and 1.77 are listed.
 Accordingly. the tidal radius of both clusters is approximately 15 aremin. and our observations. which have been centered at the cluster centre. extend to only 20 to tidal radius.," Accordingly, the tidal radius of both clusters is approximately 15 arcmin, and our observations, which have been centered at the cluster centre, extend to only 20 to tidal radius."
 Since the stars of interest are relatively bright. they are individually uncrowded and we expect the giant branch sample of detected stars to be complete.," Since the stars of interest are relatively bright, they are individually uncrowded and we expect the giant branch sample of detected stars to be complete."
 In this region. the ratio of the cluster to the field star populations should be high.," In this region, the ratio of the cluster to the field star populations should be high."
 To estimate the expected contamination by field stars in the direction of the two clusters we used the TRILEGAL model (Girardi et al. 2005)), To estimate the expected contamination by field stars in the direction of the two clusters we used the TRILEGAL model (Girardi et al. \cite{trilegal}) )
 via its webinterface!., via its web.
. Standard settings were applied including a halo contribution., Standard settings were applied including a halo contribution.
 Within a field of 0.02 deg (the size of the two ANDICAM fields in each cluster) around the cluster centres the TRILEGAL output did not include any field stars that would by chance fall onto the upper giant branch in à V vs. V—7 colour-magnitude diagram., Within a field of 0.02 $^{2}$ (the size of the two ANDICAM fields in each cluster) around the cluster centres the TRILEGAL output did not include any field stars that would by chance fall onto the upper giant branch in a $V$ vs. $V-I$ colour-magnitude diagram.
 Among the variable stars detected. we selected the long period variables based on the brightness (V.«14.5 for NGC 362. and V«15 for NGC 2808). timescale of the variation (exceeding 30 days) and a total light amplitude in V of at least 0.1 mag.," Among the variable stars detected, we selected the long period variables based on the brightness $V<14.5$ for NGC 362, and $V<15$ for NGC 2808), timescale of the variation (exceeding 30 days) and a total light amplitude in $V$ of at least 0.1 mag."
 Period search was done using Period98 (Sperl 1998)). a code which can compute a discrete Fourier transformation in combination with à least-squares fitting of multiple frequencies on the data.," Period search was done using Period98 (Sperl \cite{Sperl98}) ), a code which can compute a discrete Fourier transformation in combination with a least-squares fitting of multiple frequencies on the data."
 A maximum of two periods was allowed for each star., A maximum of two periods was allowed for each star.
 The period search. was done independently on the light curve segments from each of the several monitoring runs and then refined using the combined light curves., The period search was done independently on the light curve segments from each of the several monitoring runs and then refined using the combined light curves.
 Stars with periods close to or exceeding the length of one series of observations Were analysed only on the basis of the combined light curve., Stars with periods close to or exceeding the length of one series of observations were analysed only on the basis of the combined light curve.
 We note that for the typical periods of tens of days found for the variables. the light curves are well sampled so that aliasing should not be a significant problem.," We note that for the typical periods of tens of days found for the variables, the light curves are well sampled so that aliasing should not be a significant problem."
 Due to the semi-regular nature of the variability in. this kind of star. any periodicity found represents only a snapshot of a possibly more complex light curve. and some non-detected periodicities on much longer time scales may exist as well.," Due to the semi-regular nature of the variability in this kind of star, any periodicity found represents only a snapshot of a possibly more complex light curve, and some non-detected periodicities on much longer time scales may exist as well."
 The ANDICAM instrument offers the possibility to get near-infrared images at the same time as the optical image., The ANDICAM instrument offers the possibility to get near-infrared images at the same time as the optical image.
 During the time span between October 2003 and January 2004 we obtained 12 epochs of K-band data for NGC 2808 and 10 epochs for NGC 362. respectively.," During the time span between October 2003 and January 2004 we obtained 12 epochs of $K$ -band data for NGC 2808 and 10 epochs for NGC 362, respectively."
 However. the field-of-view is significantly smaller in the infrared than in the optical. and the infrared (IR) field is a little bit off center.," However, the field-of-view is significantly smaller in the infrared than in the optical, and the infrared (IR) field is a little bit off center."
 Therefore only some of the variables identified in the optical could also be, Therefore only some of the variables identified in the optical could also be
to calibration uncertainties and/or unrelated ionized absorption lines in the spectra.,to calibration uncertainties and/or unrelated ionized absorption lines in the spectra.
 The black hole sources were fit with a continuum consisting of a disk blackbody and a power-law., The black hole sources were fit with a continuum consisting of a disk blackbody and a power-law.
 The neutron star spectra were all fit with a continuum consisting of a simple blackbody function and a power-law., The neutron star spectra were all fit with a continuum consisting of a simple blackbody function and a power-law.
 To represent the evolution of absorption with luminosity. the luminosity in each observation was calculated for a given distance.," To represent the evolution of absorption with luminosity, the luminosity in each observation was calculated for a given distance."
 Errors on the luminosity were then calculated using the 1o errors on the continuum flux., Errors on the luminosity were then calculated using the $1\sigma$ errors on the continuum flux.
 The distances assumed in order to calculate lummosity values are listed in Table 1., The distances assumed in order to calculate luminosity values are listed in Table 1.
 Some of the spectra modeled in this paper have not been analyzed previously., Some of the spectra modeled in this paper have not been analyzed previously.
 All fourChandra observations of XTE J1817—330 were made in the high/soft state., All four observations of XTE $-$ 330 were made in the high/soft state.
 This is evident from inner disk color temperatures that range between kT=0.48 keV and 0.94 keV. and power-law indices that range between [=2.4 and 4.0.," This is evident from inner disk color temperatures that range between $=$ 0.48 keV and 0.94 keV, and power-law indices that range between $\Gamma=2.4$ and 4.0."
 The evolution of the bright phase of the outburst of XTE J1817—330 is detailed in Rykoff et (02007). and comparisons to that work again indicates that the observations were all made in high/soft states.," The evolution of the bright phase of the outburst of XTE $-$ 330 is detailed in Rykoff et (2007), and comparisons to that work again indicates that the observations were all made in high/soft states."
 Similarly. spectral results have not been reported based on fits to the second and third observations of GX 339-4 that are considered in this work (obsids 4569 and 4570).," Similarly, spectral results have not been reported based on fits to the second and third observations of GX $-$ 4 that are considered in this work (obsids 4569 and 4570)."
" Here again. the flux was strongly dominated by the aceretion disk. with inner disk color temperatures of AT=0.68 keV and 0.81 keV. Finally. the third observation of 4U 1820-30 (obsid 7032) has not been published previously. but analysis as per Cackett et (020080. 2009) suggests that the source was observed in the ""banana branch”."," Here again, the flux was strongly dominated by the accretion disk, with inner disk color temperatures of $kT = 0.68$ keV and 0.81 keV. Finally, the third observation of 4U $-$ 30 (obsid 7032) has not been published previously, but analysis as per Cackett et (2008b, 2009) suggests that the source was observed in the “banana branch”."
 We find that neutral absorption ts remarkably constant with source luminosity. and consistent across. different spectral states.," We find that neutral absorption is remarkably constant with source luminosity, and consistent across different spectral states."
 Figure 1 shows the Ne K edge in the high/soft and low/hard state spectra of Cygnus X-I., Figure 1 shows the Ne K edge in the high/soft and low/hard state spectra of Cygnus X-1.
 The jump in the continuum at the Ne K edge is consistent., The jump in the continuum at the Ne K edge is consistent.
 Figure 2 plots the column density measured in individual absorption edges versus luminosity for the sources in our sample., Figure 2 plots the column density measured in individual absorption edges versus luminosity for the sources in our sample.
 For the black hole sources. the column density in a given edge is constant with luminosity within lo errors.," For the black hole sources, the column density in a given edge is constant with luminosity within $1\sigma$ errors."
 The case is much the same with the neutron star X-ray binaries., The case is much the same with the neutron star X-ray binaries.
 The column density measured in the Ne K edge of 4U 1820-30 is marginally different at the Io level in two observations. but both are consistent with a third observation.," The column density measured in the Ne K edge of 4U $-$ 30 is marginally different at the $1\sigma$ level in two observations, but both are consistent with a third observation."
 All three columns agree at the confidence level., All three columns agree at the confidence level.
 The same holds true for two observations of Cygnus X-2., The same holds true for two observations of Cygnus X-2.
 The Ne column densities that we have measured agree with values reported by Juett. Schulz. Chakrabarty (2004) for 4U 1820-30. Cygnus X-2. and GX 339—4.," The Ne column densities that we have measured agree with values reported by Juett, Schulz, Chakrabarty (2004) for 4U $-$ 30, Cygnus X-2, and GX $-$ 4."
 The Ne column density that we measured in Cygnus X-2 also agrees with a detailed analysis made by Yao et (02009)., The Ne column density that we measured in Cygnus X-2 also agrees with a detailed analysis made by Yao et (2009).
 Our value of the Ne column density agrees with that measured in Cygnus X-1 by Hanke et ((2009) though our values of the O and Fe columns differ by factor of approximately two., Our value of the Ne column density agrees with that measured in Cygnus X-1 by Hanke et (2009) though our values of the O and Fe columns differ by factor of approximately two.
" These disparities can likely the result of different continuum modeling procedures and implementations of ""tbnew"".", These disparities can likely the result of different continuum modeling procedures and implementations of “tbnew”.
 To better understand the evolution of the low energy spectrum. of X-ray binaries. we made fits to individual photoelectric absorption edges in high resolution X-ray spectra of selected sources.," To better understand the evolution of the low energy spectrum of X-ray binaries, we made fits to individual photoelectric absorption edges in high resolution X-ray spectra of selected sources."
 The column density measured in individual edges is not observed to vary across different spectral states. nor over a broad range in luminosity (see Table | and Figure 2).," The column density measured in individual edges is not observed to vary across different spectral states, nor over a broad range in luminosity (see Table 1 and Figure 2)."
 This suggests that gas from X-ray binaries 15 not typically an important source of the neutral absorption observed in the spectra of these systems., This suggests that gas from X-ray binaries is not typically an important source of the neutral absorption observed in the spectra of these systems.
 Rather. neutral absorption must be dominated by the ISM.," Rather, neutral absorption must be dominated by the ISM."
 A similar conclusion was reached by Juett. Schulz. Chakrabarty (2004) based on upper limits on the velocity dispersion of the ISM às measured through absorption lines.," A similar conclusion was reached by Juett, Schulz, Chakrabarty (2004) based on upper limits on the velocity dispersion of the ISM as measured through absorption lines."
 Evolution in the low energy spectrum of typical X-ray binaries. then. is best attributed to evolution in the source continuum.," Evolution in the low energy spectrum of typical X-ray binaries, then, is best attributed to evolution in the source continuum."
 Neutral absorption in. X-ray spectra is often fit by a single model that parameterizes the accumulated absorption. from individual edges às an equivalent neutral hydrogen columi density., Neutral absorption in X-ray spectra is often fit by a single model that parameterizes the accumulated absorption from individual edges as an equivalent neutral hydrogen column density.
 Values obtained from high resolution spectra are likely to give the best measure of a true equivalent total columr density., Values obtained from high resolution spectra are likely to give the best measure of a true equivalent total column density.
 In practice. instrumental problems such as internal scattering. carbon build-up from optical blocking filters. anc eam drift could prevent the adoption of a gratings-derivec value for the neutral column.," In practice, instrumental problems such as internal scattering, carbon build-up from optical blocking filters, and gain drift could prevent the adoption of a gratings-derived value for the neutral column."
 In such cases. our results suggest that a single value of the equivalent neutral hydrogen columr density should be used to fit multiple spectra from monitoring observations of a given source with a given detector.," In such cases, our results suggest that a single value of the equivalent neutral hydrogen column density should be used to fit multiple spectra from monitoring observations of a given source with a given detector."
 The outflows that are observed in. X-ray binaries are highly ionized — dominated by He-like and H-like charge states (see. e.g.. Lee et 22002. Miller et 22004. Miller et 22006b. Schulz et 22008).," The outflows that are observed in X-ray binaries are highly ionized – dominated by He-like and H-like charge states (see, e.g., Lee et 2002, Miller et 2004, Miller et 2006b, Schulz et 2008)."
 An especially dense wind was observed in GRO J1655—40. and even in that case the ionized columns observed are insufficient to create strong absorption edges that could be mistaken for additional neutral absorption (Miller et 22006c. 2008).," An especially dense wind was observed in GRO $-$ 40, and even in that case the ionized columns observed are insufficient to create strong absorption edges that could be mistaken for additional neutral absorption (Miller et 2006c, 2008)."
 Moreover. in sources such as H 1743-322. GRO J1655—40. and GRS 19154105. a paradigm is emerging wherein ionized winds are active in soft. disk-dominated states. but absent in spectrally hard states like those that typically hold when sources accrete at a low fraction of their Eddington limit (Miller et 220060. 2006c. Miller et 22008. Neilsen Lee 2009).," Moreover, in sources such as H $-$ 322, GRO $-$ 40, and GRS $+$ 105, a paradigm is emerging wherein ionized winds are active in soft, disk-dominated states, but absent in spectrally hard states like those that typically hold when sources accrete at a low fraction of their Eddington limit (Miller et 2006b, 2006c, Miller et 2008, Neilsen Lee 2009)."
 In Figure 2. it is clear that any variation m ionized winds across states does not affect the column density measured in neutral edges.," In Figure 2, it is clear that any variation in ionized winds across states does not affect the column density measured in neutral edges."
 Our results are based on spectra which only reach down to approximately 0.01Lijj., Our results are based on spectra which only reach down to approximately $0.01~{\rm L}_{\rm Edd.}$.
 Sensitive high-resolution X-ray spectra that would permit strong constraints on absorption variability have not yet been obtained from sources at lower luminosity., Sensitive high-resolution X-ray spectra that would permit strong constraints on absorption variability have not yet been obtained from sources at lower luminosity.
. However. theoretical arguments again point to ionized outflows that would contribute little to a neutral column.," However, theoretical arguments again point to ionized outflows that would contribute little to a neutral column."
 Winds from advection-dominated aceretion flows are expected to be extremely hot (since advective flows are very hot). and line spectra should be dominated by He-like and H- charge states (e.g. Narayan Raymond 1999).," Winds from advection-dominated accretion flows are expected to be extremely hot (since advective flows are very hot), and line spectra should be dominated by He-like and H-like charge states (e.g. Narayan Raymond 1999)."
 Recent observations of the stellar-mass black hole V404 Cyg. which aceretes at about 107Εμ. are able to rule-out the winds predicted by some advective models (Bradley et 22007).," Recent observations of the stellar-mass black hole V404 Cyg, which accretes at about $10^{-5}~ {\rm L}_{\rm Edd.}$, are able to rule-out the winds predicted by some advective models (Bradley et 2007)."
 This further suggests that ionized outflows are not likely to contribute significantly to line-of-sight absorption. even. as sources approach quiescence.," This further suggests that ionized outflows are not likely to contribute significantly to line-of-sight absorption, even as sources approach quiescence."
 There are at least two classes of sources where our results may not hold in all circumstances., There are at least two classes of sources where our results may not hold in all circumstances.
 Neutron star X-ray binaries known as “dippers” are viewed at high inclinations. and material in the outer disk can block emission from the central engine (see. e.g.. Diaz Trigo et 22006).," Neutron star X-ray binaries known as “dippers” are viewed at high inclinations, and material in the outer disk can block emission from the central engine (see, e.g., Diaz Trigo et 2006)."
 Within such flux dips. the observed neutral absorption column may vary due to the changing geometry within the binary.," Within such flux dips, the observed neutral absorption column may vary due to the changing geometry within the binary."
 Similarly. winds from massive stars are known to be clumpy and to sometimes cause flux dips: some of these dips may also cause variations in the observed equivalent neutral hydrogen column density (e.g. Balucinska-Church et 22000).," Similarly, winds from massive stars are known to be clumpy and to sometimes cause flux dips; some of these dips may also cause variations in the observed equivalent neutral hydrogen column density (e.g. Balucinska-Church et 2000)."
" We thank Joern Wilms for creating the ""tbnew"" model used", We thank Joern Wilms for creating the “tbnew” model used
function ofA.,function of$R$.
 Shown on a logarithmic scale. the behaviour of the peak signal clearly appears to be a power law in ή). be. meus=07.," Shown on a logarithmic scale, the behaviour of the peak signal clearly appears to be a power law in $R$ , i.e. $m_{peak}=aR^n$."
 From the plots shown. it is apparent that e and ài are strongly dependent on the mass and only weakly dependent on the polynomial order. /.," From the plots shown, it is apparent that $a$ and $n$ are strongly dependent on the mass and only weakly dependent on the polynomial order, $l$."
 Here again. the zero-signal radius appears to follow a power law behaviour. with fy=bAU.," Here again, the zero-signal radius appears to follow a power law behaviour, with $R_0=bR^p$."
 Table 2. shows the fit. parameters for the combinations shown in the figure., Table \ref{tab:nfw_r} shows the fit parameters for the combinations shown in the figure.
 The figure shows a degeneracy in values of Ry between the reconstructions withf=10.Λίο=1075 TAL. and those with FALL.," The figure shows a degeneracy in values of $R_0$ between the reconstructions with $l=10,\ M_{200}=10^{15}h^{-1}\,$ $_{\odot}$ and those with $_{\odot}$."
 Dhis is to be expected: for a fixed mass. concentration parameter and aperture size. increasing f will decrease Ay as the filter will be narrower in. width.," This is to be expected: for a fixed mass, concentration parameter and aperture size, increasing $l$ will decrease $R_0$ as the filter will be narrower in width."
 On the other hand. for a fixed. concentration parameter. increasing the mass increases the scale radius 6. which will have the effect of increasing Ay if all aperture parameters remain fixed.," On the other hand, for a fixed concentration parameter, increasing the mass increases the scale radius $\theta_s$, which will have the effect of increasing $R_0$ if all aperture parameters remain fixed."
 We now consider the behaviour of the peak signal anc zero-signal contour as a function of at fixed mass and. /?., We now consider the behaviour of the peak signal and zero-signal contour as a function of $l$ at fixed mass and $R$.
" Figure 5 shows this behaviour for various/ values of Mog, and HB. with eagain fixed at 3."," Figure \ref{fg:nfw_l} shows this behaviour for various values of $M_{200}$ and $R$ , with $c$again fixed at 3."
" Again. this behaviour seems well fit by a power law in / with variable index: Le. my=el"" "," Again, this behaviour seems well fit by a power law in $l$ with variable index; i.e. $m_{peak}=al^n$ "
"Ἱ115 kin (the physical size of the extraction aperture in the skv). we fud ος<91077 3, ","14480 km (the physical size of the extraction aperture in the sky), we find $Q_{\rm CN} < 9\times10^{23}$ $^{-1}$."
"Taking average ratios of species in previously observed: comets oelQex/Qoul2.5: Qou/Qu,o=90£)) CATIearnctal. 1995).. we estimate a water production rate of Quo«1? L"," Taking average ratios of species in previously observed comets $\log [{Q_{\rm CN}}/{Q_{\rm OH}}]=-2.5$; ${Q_{\rm OH}}/{Q_{\rm H_{2}O}} = 90$ ) \citep{ahe95}, we estimate a water production rate of $Q_{\rm H_{2}O} < 10^{27}$ $^{-1}$."
 Iowever. given the uncertaiuties involved iu assunuüug ratios of comet species measured at much closer helioceutric distances remain uuchaueed for an object in the main asteroid belt. we regard this estimate to be precise. at best. to an order of magnitude.," However, given the uncertainties involved in assuming ratios of comet species measured at much closer heliocentric distances remain unchanged for an object in the main asteroid belt, we regard this estimate to be precise, at best, to an order of magnitude."
 To gain a more complete understanding of the cizetustances surrounding Scheilas unusual outburst. we also consider various aspects of the objects dynamical nature.," To gain a more complete understanding of the circumstances surrounding Scheila's unusual outburst, we also consider various aspects of the object's dynamical nature."
" Specifically, we consider its likely origin aud whether it belongs to an asteroid family."," Specifically, we consider its likely origin and whether it belongs to an asteroid family."
 To address the first issue. an effort motivated by the possibility that cometary objects in the asteroid belt nay nof necessarily originate where they are currently seen (chP/2008RL(Carradd):Jewittcfaf2009).. we perform nunuerical simulations to assess Scheila’s dynamical stability.," To address the first issue, an effort motivated by the possibility that cometary objects in the asteroid belt may not necessarily originate where they are currently seen \citep[cf.\ P/2008 R1 (Garradd);][]{jew09}, we perform numerical simulations to assess Scheila's dynamical stability."
" We eeuerate two sets of 100 test particles with Caussian distributions im orbital clement space. ceutered on Scheilas JPL-tabulated osculating orbital clemeuts. where the two sets are characterize: by ao values equalto 1« aud 1004 the JPL-tabulatec ""uncertainties for cach orbital clement (Fig."," We generate two sets of 100 test particles with Gaussian distributions in orbital element space, centered on Scheila's JPL-tabulated osculating orbital elements, where the two sets are characterized by $\sigma$ values equalto $\times$ and $\times$ the JPL-tabulated uncertainties for each orbital element (Fig."
 Saa)., \ref{scheila_sims}a a).
 We then use the N-body inteeration package. Mercury (Chambers 1999).. to iuteerate the orbit of cach test particle forwiux in time for LOO My.," We then use the N-body integration package, Mercury \citep{cha99}, to integrate the orbit of each test particle forward in time for 100 Myr."
 Iu three runs using different randomly generated sets of test particles. no objects escape from the asterok belt. indicating that Scheila is dynamically stable over this time period. aud is likely not a recent arrival frou elsewhere in the main belt or the outer solar svsteiu.," In three runs using different randomly generated sets of test particles, no objects escape from the asteroid belt, indicating that Scheila is dynamically stable over this time period, and is likely not a recent arrival from elsewhere in the main belt or the outer solar system."
 We note that despite the 100-fold difference iu their initial dispersions. objects frou both the 1-0 aud σ sets of test particles diverge to occupy similar regions of orbital clement space (Fig.," We note that despite the 100-fold difference in their initial dispersions, objects from both the $\sigma$ and $\sigma$ sets of test particles diverge to occupy similar regions of orbital element space (Fig."
 8Sbb)., \ref{scheila_sims}b b).
 This divergence occurs quickly (within LO years) and then remains approximately constant for the 100 Alyy test period (Fig., This divergence occurs quickly (within $^4$ years) and then remains approximately constant for the 100 Myr test period (Fig.
 Sec). with all objects remaining roughly confined to 2.919<aCAU)«2.936. 0.06<e«0.28. aud 11.57<(m d8.57.," \ref{scheila_sims}c c), with all objects remaining roughly confined to $2.919<a~{\rm (AU)} <2.936$, $0.06<e<0.28$, and $11.5\degr<i<18.5\degr$ ."
 Objects as larec as Scheila in the main asteroid belt are often simply assumed to be dynamically stable. of course. but the example of the Centaur (2060) Chiron shows that it is possible for similarly large objects to occupy dynamically unstable orbits (e.g...1993).," Objects as large as Scheila in the main asteroid belt are often simply assumed to be dynamically stable, of course, but the example of the Centaur (2060) Chiron shows that it is possible for similarly large objects to occupy dynamically unstable orbits \citep[{\it e.g.},."
 As such. given Sclieila uuusual comet- outburst. it is uscful to have explicits coufirmation (provided by our simulations) that the object is in fact dynamically stable. and is therefore uulikelv to be a receutlv-arrived iuterloper from elsewhere in the solar πλΜΟΙ.," As such, given Scheila's unusual comet-like outburst, it is useful to have explicit confirmation (provided by our simulations) that the object is in fact dynamically stable, and is therefore unlikely to be a recently-arrived interloper from elsewhere in the solar system."
 Next. given the sugecstion that AMIBCs τσ be prefercutially found among members of voune asteroid familics due to thei imereased likelihood of haviug fresh near-surface ice compared to wndistupted asteroids (sich2009).. we perform a hierarchical clustering analysis (Zappalactal.1990.1991) on proper elements for ~135.000 asteroids from the AstDys website (http://linilton.diiiwniprit/astdyvs/:Ituezevic&ΔΠ-lami2003) to search for asteroids dynamically related o Scheila.," Next, given the suggestion that MBCs might be preferentially found among members of young asteroid families due to their increased likelihood of having fresh near-surface ice compared to undisrupted asteroids \citep{hsi09b}, we perform a hierarchical clustering analysis \citep{zap90,zap94}
 on proper elements for $\sim$ 135,000 asteroids from the AstDys website \citep[http://hamilton.dm.unipi.it/astdys/;][]{kne03b} to search for asteroids dynamically related to Scheila."
" We find ouly six asteroids within a cutoff value of de""=120 1n 1. where commonly recognized zunudies have teus to thousauds of ανασα related nembers. usually within wich smaller cutoff values; as VAtown by Nesvoru*ef«L(2005).. despite the fact that ier analysis was performed when far fewer asteroids were known compared to the present day."," We find only six asteroids within a cutoff value of $\delta v'=120$ m $^{-1}$, where commonly recognized families have tens to thousands of dynamically related members, usually within much smaller cutoff values, as shown by \citet{nes05}, despite the fact that their analysis was performed when far fewer asteroids were known compared to the present day."
 Such a small imber of related asteroids indicates that Scheila Likely oes not belong to a family., Such a small number of related asteroids indicates that Scheila likely does not belong to a family.
 This conclusion is consistent with Scheilas size: objects ~100 kin in diameter are predicted to have collisional destruction timescales longer than the age of the solar system (Fariuellaefaf1998:Bottkeetαἱ.2005).," This conclusion is consistent with Scheila's size: objects $\sim100$ km in diameter are predicted to have collisional destruction timescales longer than the age of the solar system \citep{far98,bot05}."
. Thus. anv such body. observed today is likely to have a prinordial origin.," Thus, any such body observed today is likely to have a primordial origin."
 The Vesta family. however. shows that even extremely large asteroids can be associated with families. specifically if those familics were produced by large but uou-catastroplic cratering impacts (Diuzel&Xu1993:Thomascfαἱ. 1997).," The Vesta family, however, shows that even extremely large asteroids can be associated with families, specifically if those families were produced by large but non-catastrophic cratering impacts \citep{bin93,tho97}."
. While such events will leave pareut asteroids mostly intact. they would still excavate large amounts of surface material.," While such events will leave parent asteroids mostly intact, they would still excavate large amounts of surface material."
 If a parent asteroid happeus to contain ice reservoirs preserved deep beneath its surface. by removing much (if not all) of the smrface material previously insulating that ice against sublimation by solar heating. large cratering iupacts could render that body far more susceptible to subsequent activating impacts by sinaller asteroids. such as those hypothesized to have triggered activity in other MBCs (sich&Jewitt2006).," If a parent asteroid happens to contain ice reservoirs preserved deep beneath its surface, by removing much (if not all) of the surface material previously insulating that ice against sublimation by solar heating, large cratering impacts could render that body far more susceptible to subsequent activating impacts by smaller asteroids, such as those hypothesized to have triggered activity in other MBCs \citep{hsi06}."
". The insignificant number of asteroids found to be dvnamically related to Scheila lucicates. however. that not only is Scheila uulikelv. to be a receuth-produced fragment of a larger asteroid. it is also unlikely to have expericuced a laree (fragmoent-producing) but non-catastrophlic cratering impact in the recent past. and so we conclude that its likelihood. of having recently exposed preserved icy maternal frou its deep interior(οι, several kin or more below its surface) is low."," The insignificant number of asteroids found to be dynamically related to Scheila indicates, however, that not only is Scheila unlikely to be a recently-produced fragment of a larger asteroid, it is also unlikely to have experienced a large (fragment-producing) but non-catastrophic cratering impact in the recent past, and so we conclude that its likelihood of having recently exposed preserved icy material from its deep interior, several km or more below its surface) is low."
 Yane&Usieh(2011) found that Scheila’s ucar-infrared spectrum (from 0.8 to LO pau) exhibits a consistent red slope. has no apparent absorption features. and ecuerally resembles spectra of D-type asteroids.," \citet{yan11} found that Scheila's near-infrared spectrum (from 0.8 to 4.0 $\mu$ m) exhibits a consistent red slope, has no apparent absorption features, and generally resembles spectra of D-type asteroids."
 Using an intimate mixing model incorporating water icc. amorphous carbon. and monaich pyroxcue. they were able to reproduce Scheila’s spectrum except for a clearly visible water absorption feature that is present m the svuthetic spectrmm but not the observed. spectrua.," Using an intimate mixing model incorporating water ice, amorphous carbon, and iron-rich pyroxene, they were able to reproduce Scheila's spectrum except for a clearly visible water absorption feature that is present in the synthetic spectrum but not the observed spectrum."
 Despite the absence of uuiuubiguous evidence of water ice in these observations. given the signal-to-noise ratio of the data. Yang&IIeh(2011). concluded. that the presence of water ice on Scheila’s surface could not be excluded toa level of a few perceut.," Despite the absence of unambiguous evidence of water ice in these observations, given the signal-to-noise ratio of the data, \citet{yan11} concluded that the presence of water ice on Scheila's surface could not be excluded toa level of a few percent."
 They further noted that the similarity between Scheila aud D-type asteroids. which in turu have been noted for them similarities to classical cometary nuclei from the outer solar svsteni (Fitzsiumuousctal. 1991).. suggests that Scheila could contain preserved ice deep within its interior (e.y... 1990).," They further noted that the similarity between Scheila and D-type asteroids, which in turn have been noted for their similarities to classical cometary nuclei from the outer solar system \citep{fit94}, , suggests that Scheila could contain preserved ice deep within its interior \citep[{\it e.g.}, ."
 For comparison. two other AIBCs. 133P/Elst-Pizarro and L76P/LINEAR. have been identified as B-type or F-type asteroids," For comparison, two other MBCs, 133P/Elst-Pizarro and 176P/LINEAR, have been identified as B-type or F-type asteroids"
Our understanding ο “the chwarl spheroidal companions of the Milky Way las aclvanced significantly over the last few vears.,Our understanding of the dwarf spheroidal companions of the Milky Way has advanced significantly over the last few years.
 Studies of the internal cdvnamies of stars measuring velocity. clispersions. lave reveaed the presence of varying but alwavs signijcant amounts o⋅ dark matter (e.g. Mateo et al.," Studies of the internal dynamics of stars measuring velocity dispersions, have revealed the presence of varying but always significant amounts of dark matter (e.g. Mateo et al."
 1993. “Tania vet al.," 1993, Tamura et al."
 2001). strengthening the classification of these systems as galaxies.," 2001), strengthening the classification of these systems as galaxies."
 The structure of the dark haloes associated with hese galaxies ap»ears LO be well represented bv a constant density region. over the extent across which measurements exist.," The structure of the dark haloes associated with these galaxies appears to be well represented by a constant density region, over the extent across which measurements exist."
 High quality imagine of the stellar populations has permitted the construction of LL diagrams or many of these galaxies. which in turn has stimulate he development of new statistical analysis techniques aine a recovering the star formation histories of the image systems e.g. Aparicio CGallart. (1995). ‘Volstoy Saha 9963. Mighell (1997). Llernandez et al. (," High quality imaging of the stellar populations has permitted the construction of HR diagrams for many of these galaxies, which in turn has stimulated the development of new statistical analysis techniques aimed at recovering the star formation histories of the imaged systems e.g. Aparicio Gallart (1995), Tolstoy Saha (1996), Mighell (1997), Hernandez et al. ("
1999).,1999).
 These las ave vielded. valuable constraints on the temporal structure ο ‘the star formation hisories in the local dSph population., These last have yielded valuable constraints on the temporal structure of the star formation histories in the local dSph population.
 tesults> have shown there to be a wide range of cdilleren μαar formation histories [rere., Results have shown there to be a wide range of different star formation histories here.
 Some systems being consisten =μαith à single burst of acivity in the remote past. but many showing clear signs of extended or repeated: periods of star formation activity.," Some systems being consistent with a single burst of activity in the remote past, but many showing clear signs of extended or repeated periods of star formation activity."
 Phe dominance of «warf galaxies in cluster Luminosity, The dominance of dwarf galaxies in cluster luminosity
 Phe dominance of «warf galaxies in cluster Luminosity., The dominance of dwarf galaxies in cluster luminosity
(1993).. Zhekov&AIvasnikov (2000))).,", \citet{zhe00}) )."
 However the source of heat into the cold side οἱ the interface will continuously. evaporate material (here and potentially induce interface instabilities ancl mass mixing (Stone&Zweibel(2009))) that could tangle the magnetic Ποια., However the source of heat into the cold side of the interface will continuously evaporate material there and potentially induce interface instabilities and mass mixing \citet{sto09}) ) that could tangle the magnetic field.
" Understanding the thermal conduction and its dependence on magnetic structure is important for determining the thermal properties of the plasma on either side of the interlace,", Understanding the thermal conduction and its dependence on magnetic structure is important for determining the thermal properties of the plasma on either side of the interface.
 A second example is the unexpected slow mass deposition rate of the cooling flows in some galaxy cores which might be inhibited by a restricted thermal conduction (Rosner& (1989).. Balbus&Revnolds (2008).. Mikellidesetal. (2011))).," A second example is the unexpected slow mass deposition rate of the cooling flows in some galaxy cores which might be inhibited by a restricted thermal conduction \citet{ros89}, \citet{bal08}, \citet{mik11}) )."
 In the intracluster medium (ICM). the (angled magnetic field can potentially produce a strongly. anistropic thermal conductivity that may sienilicantlv influence temperature and density proliles (Chandran&Maron(2004):: Maronetal. (2004): Naravan&Medvedev (2001)... elal. (2011))).," In the intracluster medium (ICM), the tangled magnetic field can potentially produce a strongly anistropic thermal conductivity that may significantly influence temperature and density profiles \citet{cha04}; \citet{mar04}; \citet{nar01}, \citet{mik11}) )."
 For the ISM and ICM. it is usually valid to assume that the electrons are totally inhibited from moving across field lines (λοςοτίetal (2011))). as the electron mean free path is much greater (han the electron evroracius.," For the ISM and ICM, it is usually valid to assume that the electrons are totally inhibited from moving across field lines \citet{mcc11}) ), as the electron mean free path is much greater than the electron gyroradius."
 The magnetic Ποια structure therefore plavs a Κον role in controlling the rate of thermal conduction since electrons can move freely onlv along the field lines., The magnetic field structure therefore plays a key role in controlling the rate of thermal conduction since electrons can move freely only along the field lines.
 The result is a strong thermal conductivity parallel to the field lines and a weak conductivity across the field lines., The result is a strong thermal conductivity parallel to the field lines and a weak conductivity across the field lines.
 The quantitative subtleties of how a complicated magnetic field structure. affects thermal conduction for raises the open question of whether Chere is a simple measure of field (angling that allows a practical but reasonably accurate correction to (he isotropic conduction coefficient for arbitrarily (anelecl fields., The quantitative subtleties of how a complicated magnetic field structure affects thermal conduction for raises the open question of whether there is a simple measure of field tangling that allows a practical but reasonably accurate correction to the isotropic conduction coefficient for arbitrarily tangled fields.
 In this context. two classes of problenis can be distinguished.," In this context, two classes of problems can be distinguished."
 The first is the conduction in a medium for which forced velocity [Iows drive turbulence. which in turn tangles the field into a statistically steady state turbulent," The first is the conduction in a medium for which forced velocity flows drive turbulence, which in turn tangles the field into a statistically steady state turbulent"
The authors would like to thank Rene’ Walterbos for providing the filter set. for ihe APO observations and the staff at APO and IXNPNO [or their expert assistance at the telescopes.,The authors would like to thank Rene' Walterbos for providing the filter set for the APO observations and the staff at APO and KPNO for their expert assistance at the telescopes.
 We would also like to thank the referee lor useful comments (hat improved the presentation of the paper., We would also like to thank the referee for useful comments that improved the presentation of the paper.
"hypothesis can be excluded at a level, given the empirical constraints showing the Milky Way potential to be spherical 2006).","hypothesis can be excluded at a level, given the empirical constraints showing the Milky Way potential to be spherical ."
". Multiple arguments have been put (Fellhauerforward to explain the disk-of-satellites problem, primarily based on CDM simulation models."," Multiple arguments have been put forward to explain the disk-of-satellites problem, primarily based on CDM simulation models."
" argue that the observed distribution of the Milky (2005)Way satellites is indeed consistent with being CDM subhalos, assuming that the satellites follow the distribution of the dark matter within the Milky Way halo."," argue that the observed distribution of the Milky Way satellites is indeed consistent with being CDM subhalos, assuming that the satellites follow the distribution of the dark matter within the Milky Way halo."
" used a semi-analytic model to identify luminous satellites(2005) and showed that an isotropic distribution is not the correct null-hypothesis; rather, the host halos are mildly triaxial (tending to be more prolate than oblate)."," used a semi-analytic model to identify luminous satellites and showed that an isotropic distribution is not the correct null-hypothesis; rather, the host halos are mildly triaxial (tending to be more prolate than oblate)."
" Following similar lines to (2005),, they found that the distribution of the Galactic satellite system is in fact consistent with being CDM substructure, albeit with a low probability."," Following similar lines to , they found that the distribution of the Galactic satellite system is in fact consistent with being CDM substructure, albeit with a low probability."
" However, this disk-of-satellites is much less extended than nearby dwarf galaxy associations, and such an association falling into the Galaxy is unlikely to have produced the satellites 2009)."," However, this disk-of-satellites is much less extended than nearby dwarf galaxy associations, and such an association falling into the Galaxy is unlikely to have produced the disk-of-satellites ."
". The second (Metzmore specific problem is that, if simple accretion were the only mechanism for Galactic growth, then the spheroidal dwarf galaxy Leo I has an improbably high radial velocity."," The second more specific problem is that, if simple accretion were the only mechanism for Galactic growth, then the spheroidal dwarf galaxy Leo I has an improbably high radial velocity."
 finds the systemic velocity of Leo I to be 287.0(1998)41.9 km s-! for any subsample of the set of 33 red giants in the Leo I dwarf spheroidal galaxy for which they obtained radial velocities from spectra taken using the HIRES echelle spectrograph on the Keck telescope., finds the systemic velocity of Leo I to be $287.0\pm1.9$ km $^{-1}$ for any subsample of the set of 33 red giants in the Leo I dwarf spheroidal galaxy for which they obtained radial velocities from spectra taken using the HIRES echelle spectrograph on the Keck telescope.
 This suggests that Milky Way satellites as a whole need to be considered in the wider context of the whole Local Group., This suggests that Milky Way satellites as a whole need to be considered in the wider context of the whole Local Group.
" Due to this exceptional velocity, Leo I has an anomalously large effect compared to other satellites on estimates of the mass of the Milky Way."," Due to this exceptional velocity, Leo I has an anomalously large effect compared to other satellites on estimates of the mass of the Milky Way."
 use Bayes’ theorem and the assumption of isotropic orbits for the satellites of our Galaxy to estimate a median probable mass of ~2.5x1012 Mo., use Bayes' theorem and the assumption of isotropic orbits for the satellites of our Galaxy to estimate a median probable mass of $\sim$$2.5\times10^{12}$ $_\odot$.
" Interestingly, however, the exclusion of Leo I would lower this estimate to ~1.8x1013 Mo."," Interestingly, however, the exclusion of Leo I would lower this estimate to $\sim$$1.8\times10^{12}$ $_\odot$."
" Their result implies that Leo I may not be gravitationally bound to the Milky Way (in order to agree with other estimates of the Milky Way mass derived by and others, see Table 1))."," Their result implies that Leo I may not be gravitationally bound to the Milky Way (in order to agree with other estimates of the Milky Way mass derived by and others, see Table \ref{Tab:LMCSMCorb}) )."
" In this paper we postulate an additional mechanism to explain the asymmetric dwarf galaxy distribution and the unusually high radial velocity of Leo I. We conjecture that some of the dwarf galaxies may have ‘piggybacked’ in with the LMC-SMC binary pair, but had their bound orbits disrupted by interactions with the central Galactic potential."," In this paper we postulate an additional mechanism to explain the asymmetric dwarf galaxy distribution and the unusually high radial velocity of Leo I. We conjecture that some of the dwarf galaxies may have `piggybacked' in with the LMC-SMC binary pair, but had their bound orbits disrupted by interactions with the central Galactic potential."
" Dwarfs bound to the LMC initially will be closer than most dwarf galaxy associations, and the subsequent interactions may have resulted in a 3-body interaction that ejected Leo I and thus could reproduce its current high velocity while still explaining the narrow spacing of the disk-of-satellites association."," Dwarfs bound to the LMC initially will be closer than most dwarf galaxy associations, and the subsequent interactions may have resulted in a 3-body interaction that ejected Leo I and thus could reproduce its current high velocity while still explaining the narrow spacing of the disk-of-satellites association."
 To test this hypothesis we first explore the past orbits of the LMC-SMC under the effect of a central Galactic potential pair in accordance with the latest measurements of their proper motions., To test this hypothesis we first explore the past orbits of the LMC-SMC under the effect of a central Galactic potential pair in accordance with the latest measurements of their proper motions.
" Numerically solving Newton's equations backwards in time, we proceed to find their position in phase space at apogalacticon."," Numerically solving Newton's equations backwards in time, we proceed to find their position in phase space at apogalacticon."
" We then model the infall of this configuration as an N-body system containing the LMC and SMC as well as multiple dwarf galaxies (hereafter, all references to dwarfs and dwarf-dwarf interactions exclude the LMC and SMC) in bound orbits around the LMC."," We then model the infall of this configuration as an -body system containing the LMC and SMC as well as multiple dwarf galaxies (hereafter, all references to dwarfs and dwarf-dwarf interactions exclude the LMC and SMC) in bound orbits around the LMC."
" We evolve our system forwards in time and see whether it can reproduce the anomalies in the Local Group discussed above, and if so what was the state of the dwarfs when bound to the Magellanic system."," We evolve our system forwards in time and see whether it can reproduce the anomalies in the Local Group discussed above, and if so what was the state of the dwarfs when bound to the Magellanic system."
 'The orbits of the LMC and SMC will have evolved over time as they interact gravitationally between each other and with the Galaxy over many gigayears., The orbits of the LMC and SMC will have evolved over time as they interact gravitationally between each other and with the Galaxy over many gigayears.
 Assuming minimal perturbation of the orbits of the LMC and SMC; the orbits of dwarfs that accompanied the Magellanic system can be calculated from a previous apogalacticon to the present day and into the future., Assuming minimal perturbation of the orbits of the LMC and SMC; the orbits of dwarfs that accompanied the Magellanic system can be calculated from a previous apogalacticon to the present day and into the future.
" This is achieved by running a Monte Carlo suite of these multi-system models with varying initial conditions of the LMC and SMC (based upon the observed initial parameters, see refssec:LMCorb))."," This is achieved by running a Monte Carlo suite of these multi-system models with varying initial conditions of the LMC and SMC (based upon the observed initial parameters, see \\ref{ssec:LMCorb}) )."
 The LMC/SMC orbits are calculated within a fixed Galactic potential and with gravitational interactions between the LMC and SMC refssec:Pot)) backwards in time for 3.5 Gyr and calculating the position of either the last or second last apogalacticon of the LMC., The LMC/SMC orbits are calculated within a fixed Galactic potential and with gravitational interactions between the LMC and SMC \\ref{ssec:Pot}) ) backwards in time for $3.5$ Gyr and calculating the position of either the last or second last apogalacticon of the LMC.
" At this apogalacticon a number of dwarfs are inserted in a bound orbit of the LMC (see refssec:DwarfIC)) and then traced forward in time to the present day and to +0.5 Gyr in the future, interacting with other dwarfs, the LMC/SMC system and the Galaxy."," At this apogalacticon a number of dwarfs are inserted in a bound orbit of the LMC (see \\ref{ssec:DwarfIC}) ) and then traced forward in time to the present day and to $+0.5$ Gyr in the future, interacting with other dwarfs, the LMC/SMC system and the Galaxy."
" 'The orbit of Corbthe LMC and SMC will be affected by their current positions, velocities and by their masses."," The orbit of the LMC and SMC will be affected by their current positions, velocities and by their masses."
 'The position and velocities used here for the LMC and SMC are given in Table 1.., The position and velocities used here for the LMC and SMC are given in Table \ref{Tab:LMCSMCorb}. .
" Particular note should be taken of most recent measurements of the proper motions of the LMC and SMC by which give a relative velocity between the clouds at the (2006),,current epoch of 105+42 km s~!."," Particular note should be taken of most recent measurements of the proper motions of the LMC and SMC by, which give a relative velocity between the clouds at the current epoch of $105\pm42$ km $^{-1}$."
 These values imply that the LMC tangential velocity is approximately 100 km s! higher than previously thought2006)., These values imply that the LMC tangential velocity is approximately $100$ km $^{-1}$ higher than previously thought.
". Given the low uncertainty in (Kallivayalilposition, we assume that the LMC and SMC are at fixed locations given"," Given the low uncertainty in position, we assume that the LMC and SMC are at fixed locations given"
and Notice that the second term on the right hand side of cach of the equations 11. and 12. is the same normalization factor.,and Notice that the second term on the right hand side of each of the equations \ref{eqn:rate1} and \ref{eqn:lumf} is the same normalization factor.
 We have a set of non-linear equations with as many equations as variables., We have a set of non-linear equations with as many equations as variables.
 We solve numerically these non linear equations using successive iterations until convergence., We solve numerically these non linear equations using successive iterations until convergence.
 A-priori it 1s not clear whether © and 7/2 are uniquely determined and whether there is a solution at all., A-priori it is not clear whether $\phi$ and $R$ are uniquely determined and whether there is a solution at all.
 However. we find good convergence.," However, we find good convergence."
 We have examined a large set (107) of initial guesses where each component was randomly drawn from a uniform distribution., We have examined a large set $10^8$ ) of initial guesses where each component was randomly drawn from a uniform distribution.
" We found a rapid convergence to a unique solution for all initial guesses, all reaching the requested accuracy of 10."" with less than 25 iterations."," We found a rapid convergence to a unique solution for all initial guesses, all reaching the requested accuracy of $10^{-6}$ with less than 25 iterations."
 We thus conclude that the existence of other stable solutions is very unlikely., We thus conclude that the existence of other stable solutions is very unlikely.
 We approximate the error as the value for which M deviate by -1 from it's maximum: (i.c. the likelihood is smaller by a factor €)., We approximate the error as the value for which M deviate by -1 from it's maximum: (i.e. the likelihood is smaller by a factor $e$ ).
 This reflects an lo error for a normal-distribution., This reflects an $1\sigma$ error for a normal-distribution.
" The two solutions, i.c. the positive one and the negative one, give an upper and a lower bounds on the error respectively."," The two solutions, i.e. the positive one and the negative one, give an upper and a lower bounds on the error respectively."
" For small deviations we can approximate the error using the second derivatives of M: To estimate the uncertainty induced by the specific bins choice, we preform all the analysis for a 1/2 unit redshitt and Logy)(L) binning and repeat for a 1/3 unit binning (where all bins widths are 1/3 unit, except the last two redshift bins which we cannot change because they contain too few data points)."," For small deviations we can approximate the error using the second derivatives of M: To estimate the uncertainty induced by the specific bins choice, we preform all the analysis for a 1/2 unit redshift and $Log_{10}(L)$ binning and repeat for a 1/3 unit binning (where all bins widths are 1/3 unit, except the last two redshift bins which we cannot change because they contain too few data points)."
" In the following, unless otherwise stated, we use the 1/2 unit binning for all further analysis."," In the following, unless otherwise stated, we use the 1/2 unit binning for all further analysis."
" Clearly, the results with different binning are slightly different, but they are all within each other’s error range."," Clearly, the results with different binning are slightly different, but they are all within each other's error range."
 When we include the uncertainty induced by the binning the error ranges become only slightly wider., When we include the uncertainty induced by the binning the error ranges become only slightly wider.
We develop the analvlic theory in 822 and derive (he conditions needed Lor protoplanets to accrete collision fragments and grow to masses of ~ 1 iin |2 Myr.,We develop the analytic theory in 2 and derive the conditions needed for protoplanets to accrete collision fragments and grow to masses of $\sim$ 1 in 1–2 Myr.
 We confirm these estimates in 833. with detailed numerical caleulations., We confirm these estimates in 3 with detailed numerical calculations.
 We conclude with a brief discussion in 844., We conclude with a brief discussion in 4.
 The crucial element of our model is the interaction of collision Iragments with the gaseous disk., The crucial element of our model is the interaction of collision fragments with the gaseous disk.
" Fragments larger than the ‘stopping radius’ r,© 0.52 m a( 510 AU (Weidenschilling 2004).. orbit with the growing protoplanets. independently of the gas."," Fragments larger than the `stopping radius' $r_s \approx$ 0.5–2 m at 5–10 AU \citep{wei77,raf04}, orbit with the growing protoplanets, independently of the gas."
 Destructive collisions among these fragments fuel the collisional eascade., Destructive collisions among these fragments fuel the collisional cascade.
 Ilowever. the gas entrains particles with radii rSr.," However, the gas entrains particles with radii $r \lesssim r_s$."
 These fragments orbit with the gas: thus. their velocity dispersions are small and independent of massive protoplanets.," These fragments orbit with the gas; thus, their velocity dispersions are small and independent of massive protoplanets."
 By (rapping small collision fragments. the gas halts the collisional cascade.," By trapping small collision fragments, the gas halts the collisional cascade."
 The gas also allows protoplanets to accrete the debris., The gas also allows protoplanets to accrete the debris.
 When (he collisional cascade begins. (he mass in leltover planetesimals is ~ 110.," When the collisional cascade begins, the mass in leftover planetesimals is $\sim$ 1–10."
. The cascade grinds all of this mass into small fragments which are trapped by the gas., The cascade grinds all of this mass into small fragments which are trapped by the gas.
 Most of the trapped Iragments fall through the eas into the midplane of the disk. where erowing protoplanets accrete (hem.," Most of the trapped fragments fall through the gas into the midplane of the disk, where growing protoplanets accrete them."
 Protoplanets that accrete ~ 0.11 bbefore the gas dissipates (~3.10Myr:Harüinannetal.1998:Haisch.Lada.&Lada:lxennedy&Kenvon2009) become gas giants.," Protoplanets that accrete $\sim$ 0.1–1 before the gas dissipates \citep[$\sim$ 3--10~Myr;][]{hart98,hai01,kenn09} become gas giants."
 Thus. our model vields gas giant cores if (1) the collisional cascade produces Iragments fast enough. (ii) the fragments quickly settle to (he midplane. and (ii) the largest protoplanets rapidly accrete the fragments.," Thus, our model yields gas giant cores if (i) the collisional cascade produces fragments fast enough, (ii) the fragments quickly settle to the midplane, and (iii) the largest protoplanets rapidly accrete the fragments."
 To examine whether (his physical model leads (o cores with masses of ~ 1M... we consider the growth of planets in a disk of gas and iev objects around a star will massAL.," To examine whether this physical model leads to cores with masses of $\sim$ 1, we consider the growth of planets in a disk of gas and icy objects around a star with mass."
". Material at a distance @ [from the central star orbits with angular frequency. Q and has surface densities X. (solids) and. X, (gas).", Material at a distance $a$ from the central star orbits with angular frequency $\Omega$ and has surface densities $\Sigma_s$ (solids) and $\Sigma_g$ (gas).
" We adopt a solid-to-gas ratio of 1:100. and My4=Montyd372 U7.where Soy4 = i2.5 g. E at 5 AU- and c, is. a scale factor."," We adopt a solid-to-gas ratio of 1:100 and $\Sigma_s = \Sigma_{s,0} ~ x_m ~ a^{-3/2}$, where $\Sigma_{s,0}$ = 2.5 g $^{-2}$ at 5 AU and $x_m$ is a scale factor."
. Forming icy protoplanets is the first step in our model., Forming icy protoplanets is the first step in our model.
 In an ensemble of 1 km planetesimads. collisional growth vields a few 1000 km objects ‘oligarchs’ that contain an ever-increasing fraction of the mass in solids (Ida&Makino1993:Wetherill 2003).," In an ensemble of 1 km planetesimals, collisional growth yields a few 1000 km objects – `oligarchs' – that contain an ever-increasing fraction of the mass in solids \citep{ida93,wet93,raf03}."
. From numerical simulations of planet growth at 30.150 AU. the timescale to produce an oligarch around a solar-(wpe star is (INDOS)," From numerical simulations of planet growth at 30–150 AU, the timescale to produce an oligarch around a solar-type star is (KB08)"
"ionization parameter (number of ionizing photons per hydrogen atom at the illuminated face of the slab) for a fixed total hvdrogen column of 5 x 10?"" 7. which corresponds to a reddening of E(B— V) = 0.10 (Shull van Steenberg 1985).","ionization parameter (number of ionizing photons per hydrogen atom at the illuminated face of the slab) for a fixed total hydrogen column of 5 x $^{20}$ $^{-2}$, which corresponds to a reddening of $-$ V) $=$ 0.10 (Shull van Steenberg 1985)."
 We asssumed solar abunclances (see Grevesse Anders 1989). and a depletion of the carbon onto grains.," We asssumed solar abundances (see Grevesse Anders 1989), and a depletion of the carbon onto grains."
 We find that for ionization parameters U < 3.0. the column density of C IV will be > LOM 7. which is (he approximate detection limit for current. high-resolution STIS spectra (Ixraemer et al.," We find that for ionization parameters U $<$ 3.0, the column density of C IV will be $>$ $^{13}$ $^{-2}$, which is the approximate detection limit for current high-resolution STIS spectra (Kraemer et al."
 2001)., 2001).
 The labeled Sevfert 1 galaxies in Figure 2 ave particularly interesting., The labeled Seyfert 1 galaxies in Figure 2 are particularly interesting.
 All show evidence for reddenimg. and in addition. saturated C IV and NV absorption lines near the svstemic velocities of their host galaxies.," All show evidence for reddening, and in addition, saturated C IV and N V absorption lines near the systemic velocities of their host galaxies."
 As we have shown. these are the signatures of clusty Inkewarm absorbers in NGC 3227 and Akn 564. and we expect that future high-resolution spectra and modeling of the absorbers in WPVS 007 ancl MCG 88-11-11: will show that the columns of UV absorbing gas are sufficient to provide the observed reddenines.," As we have shown, these are the signatures of dusty lukewarm absorbers in NGC 3227 and Akn 564, and we expect that future high-resolution spectra and modeling of the absorbers in WPVS 007 and MCG 8-11-11 will show that the columns of UV absorbing gas are sufficient to provide the observed reddenings."
 Furthermore. we predict that the other heavily reddened. inclined Sevfert galaxies (NGC! 931. IC 43329A. NGC 5506. and MCG -6-30-15 in partüeular) will show dusty hikewarm absorbers.," Furthermore, we predict that the other heavily reddened, inclined Seyfert galaxies (NGC 931, IC 4329A, NGC 5506, and MCG -6-30-15 in particular) will show dusty lukewarm absorbers."
 We conclude that there are at least two types of UV absorbers in Sevlert 1 galaxies: dusty lukewarm absorbers in (he plane of the host galaxy. ancl absorbers intrinsic to the nucleus., We conclude that there are at least two types of UV absorbers in Seyfert 1 galaxies: dusty lukewarm absorbers in the plane of the host galaxy and absorbers intrinsic to the nucleus.
 The first (wpe is a natural consequence of viewing the nucleus through a host galaxy al a large inclination angle., The first type is a natural consequence of viewing the nucleus through a host galaxy at a large inclination angle.
 It can be identified through saturated UV absorption lines (typically CC IV and N V) near the systemic velocity in à Sevíert galaxy that shows evidence lor reddening ol its nonstellar continuum and emission lines. including those [rom the NLR.," It can be identified through saturated UV absorption lines (typically C IV and N V) near the systemic velocity in a Seyfert galaxy that shows evidence for reddening of its nonstellar continuum and emission lines, including those from the NLR."
 Given the morphological ancl kinematic evidence that the extended narrow-line region (ENLIR) in a sevlert galaxy is ionized gas in the galactie disk (Unger et al., Given the morphological and kinematic evidence that the extended narrow-line region (ENLR) in a Seyfert galaxy is ionized gas in the galactic disk (Unger et al.
 1987). we suggest that the clusty lukewarm absorber is a hiehlv ionized component of the ENLB seen in absorption.," 1987), we suggest that the dusty lukewarm absorber is a highly ionized component of the ENLR seen in absorption."
 The other (wpe of absorber (i.e.. intrinsic to the nucleus) can be identilied through absorplion-line variability. high outflow velocities. and/or covering factors that are less (han one.," The other type of absorber (i.e., intrinsic to the nucleus) can be identified through absorption-line variability, high outflow velocities, and/or covering factors that are less than one."
 Thus. it is possible in many cases (o use (his information to separate the two types of absorbers. permitng more focused studies of either phenomenon.," Thus, it is possible in many cases to use this information to separate the two types of absorbers, permitting more focused studies of either phenomenon."
 We note that it max nol always be possible to identify the origin of a particular absorber: for example. a saturated absorber with lowradial velocity. a covering [actor of one. and no evidence for variability does not automatically fall into the clusty lukewarm absorber class (1.6.. in the host galaxy).," We note that it may not always be possible to identify the origin of a particular absorber; for example, a saturated absorber with low velocity, a covering factor of one, and no evidence for variability does not automatically fall into the dusty lukewarm absorber class (i.e., in the host galaxy)."
 llowever. we suggest (hat evidence [or reddening by a column sufficient (ο produce the absorption lines. plus evidence for covering of the NLR. does place it in (his class.," However, we suggest that evidence for reddening by a column sufficient to produce the absorption lines, plus evidence for covering of the NLR, does place it in this class."
Dunlop Peacock 1993: opticallyselected quasars Maloney Petrosian 1999: X-rav sources — Bovle 11993)) Gts the observations rather well.,Dunlop Peacock \nocite{dun93}; optically–selected quasars – Maloney Petrosian \nocite{mal99}; X-ray sources – Boyle \nocite{boy93}) ) fits the observations rather well.
 Deep radio imaging of the z=0.83 cluster 08 has revealed a population of cluster radio sources., Deep radio imaging of the $z=0.83$ cluster $-$ 03 has revealed a population of cluster radio sources.
 Eight radio sources are associatecdl with galaxies that are alreacly spectroscopically confirmed cluster members., Eight radio sources are associated with galaxies that are already spectroscopically confirmed cluster members.
 This corresponds to approximately of carlytype confirmed cluster galaxies with Alp<20.5 within MMpe. of the cluster centre having rest.[rame Ciz luminosity above 23.4 !., This corresponds to approximately of early–type confirmed cluster galaxies with $M_R < -20.5$ within Mpc of the cluster centre having rest–frame GHz luminosity above 23.1 $^{-1}$.
 The cluster radio sources fall into two distinct categories., The cluster radio sources fall into two distinct categories.
 4 sources are hosted by isolated galaxies which have a range of morphologies from ellipticals to Se ealaxies: the radio emission appears to be associated with a starburst in at least one case. and CIN activity in (wo.," 4 sources are hosted by isolated galaxies which have a range of morphologies from ellipticals to Sc galaxies; the radio emission appears to be associated with a starburst in at least one case, and AGN activity in two."
 The other four cluster radio sources are associated with close pairs of galaxies. possibly interacting. although not all bound. systems.," The other four cluster radio sources are associated with close pairs of galaxies, possibly interacting, although not all bound systems."
 7 of the S galaxies comprising these ours are of tvpe S0/a or earlier. ancl the radio emission rom these galaxy pairs is almost certainly nuclear in origin.," 7 of the 8 galaxies comprising these pairs are of type S0/a or earlier, and the radio emission from these galaxy pairs is almost certainly nuclear in origin."
 This o=75% proportion of AGN in the cluster is in contrast o the field. where ~50.604 of radio sources at this lux density level are associated: with starburst galaxies.," This $\gta
75$ proportion of AGN in the cluster is in contrast to the field, where $\sim 50-60$ of radio sources at this flux density level are associated with starburst galaxies."
 Considering the isolated cluster radio galaxies alone. these are consistent with the field distribution and may essentially. x an extension of it. with the radio sources associated with galaxy pairs being a new AGN population. driven by earlyvpe galaxy interactions. and thus fairly. unique to high redshift cluster environmoents.," Considering the isolated cluster radio galaxies alone, these are consistent with the field distribution and may essentially be an extension of it, with the radio sources associated with galaxy pairs being a new AGN population, driven by early--type galaxy interactions, and thus fairly unique to high redshift cluster environments."
 03 is à cluster which contains a hich woportion of ongoing mergers., $-$ 03 is a cluster which contains a high proportion of on–going mergers.
 However. although up o of the confirmed. cluster. radio sources appear o be interaction driven. none are associated with the confirmed. merger events. anc the upper limit to the mean radio luminosity of these merger events is of order 1072 comparable to that of MS2.," However, although up to of the confirmed cluster radio sources appear to be interaction driven, none are associated with the confirmed merger events, and the upper limit to the mean radio luminosity of these merger events is of order $10^{22}$ $^{-1}$, comparable to that of M82."
 Lt appears that galaxy.galaxy interactions may be more ellicient than direct mergers at inducing radio emission., It appears that galaxy–galaxy interactions may be more efficient than direct mergers at inducing radio emission.
 Although the sample of confirmed cluster radio sources is small (S). the cluster radio luminosity function. shows a hint of bimodality. mirroring that observed. in the low redshift cluster Abell 2125. with a possible increase in the break luminosity with recdshilt.," Although the sample of confirmed cluster radio sources is small (8), the cluster radio luminosity function shows a hint of bimodality, mirroring that observed in the low redshift cluster Abell 2125, with a possible increase in the break luminosity with redshift."
 Clearly to investigate these issues further. spectroscopic redshilts for the remainder of the radio sources in the sample will be required. together with deep radio surveys of a larger sample of distant. clusters to improve the statistics and confirm the results suggested here.," Clearly to investigate these issues further, spectroscopic redshifts for the remainder of the radio sources in the sample will be required, together with deep radio surveys of a larger sample of distant clusters to improve the statistics and confirm the results suggested here."
 The National Badio Astronomy Observatory is operated by Associated: Universities Inc... under co-operative agreement with the National Science. Foundation.," The National Radio Astronomy Observatory is operated by Associated Universities Inc., under co-operative agreement with the National Science Foundation."
 PNB would. like to thank the Roval Society for generous financial support through its University Research Fellowship scheme., PNB would like to thank the Royal Society for generous financial support through its University Research Fellowship scheme.
 PGvD acknowledges support by NASA through Hubble Fellowship erant. LLP-O1126.01-99A awarded by the Space Telescope, PGvD acknowledges support by NASA through Hubble Fellowship grant HF-01126.01-99A awarded by the Space Telescope
"with a A7 III-IV spectral type (?),, Te=7925 K, L=87Lo (?),, and Ay=0.49 mag.","with a A7 III-IV spectral type \citep{tjin89}, , $_{\rm{eff}}$ =7925 K, L=87$_{\odot}$ \citep{vanboekel05}, and $_{\rm{v}}$ =0.49 mag."
 Photometric and spectroscopic variability was observed in the optical (?) and UV (?) and interpreted as evidence of accreting gas in a boundary layer in a highly inclined disk., Photometric and spectroscopic variability was observed in the optical \citep{perez92} and UV \citep{perez93} and interpreted as evidence of accreting gas in a boundary layer in a highly inclined disk.
" ? detected a magnetic field, which was found to be variable, with a strength varying between -75 G and +166 G, possibly related to the spectroscopic variations."," \cite{hubrig07} detected a magnetic field, which was found to be variable, with a strength varying between -75 G and +166 G, possibly related to the spectroscopic variations."
" Its spectral energy distribution (SED) presents strong near and mid-infrared (MIR) excesses (?),, as well as a weak emission at millimetric wavelengths (?).."," Its spectral energy distribution (SED) presents strong near and mid-infrared (MIR) excesses \citep{hillenbrand92}, as well as a weak emission at millimetric wavelengths \citep{henning94}."
" This indicates that a circumstellar disk is present, which is probably of low mass (0.006Mo;3)."," This indicates that a circumstellar disk is present, which is probably of low mass \citep[0.006~M$_{\odot}$."
" ? found no indication of a nebulosity at radii largerthan 70 AU, which was later confirmed by MIR spatially resolved observations (?).."," \citet{grady05} found no indication of a nebulosity at radii largerthan 70 AU, which was later confirmed by MIR spatially resolved observations \citep{preibisch06}."
" The MIDI/VLTI measurements indicated an angular extent of the MIR emission smaller than that of other HAeBes, and were consistent with an inclined disk (1—58?,, PA~115°)), truncated at an outer radius of 2.5 AU."," The MIDI/VLTI measurements indicated an angular extent of the MIR emission smaller than that of other HAeBes, and were consistent with an inclined disk $\sim$, $\sim$ ), truncated at an outer radius of 2.5 AU."
 The authors speculated that the low mass and the small outer radius of the disk are probably caused by mechanisms of dynamic clearing by a close binary., The authors speculated that the low mass and the small outer radius of the disk are probably caused by mechanisms of dynamic clearing by a close binary.
" In addition, ? measured an intrinsic linear polarization, due to scattering of the stellar light off circumstellar material along PA~137°,, in agreement with the PA of the disk measured by ?.."," In addition, \citet{rodrigues09} measured an intrinsic linear polarization, due to scattering of the stellar light off circumstellar material along $\sim$, in agreement with the PA of the disk measured by \citet{preibisch06}."
" Very little is known about the structure and morphology of the circumstellar disk in the first AU, as no spatially resolved observations have so far been published on the NIR emission."," Very little is known about the structure and morphology of the circumstellar disk in the first AU, as no spatially resolved observations have so far been published on the NIR emission."
" Here, we present the first observational study of the circumstellar disk around at the sub-AU scale using the AMBER/VLTI."," Here, we present the first observational study of the circumstellar disk around at the sub-AU scale using the AMBER/VLTI."
" We gathered a large number of measurements in the H and K bands from 2008 to 2010, and present here the first reconstructed images of 5999,, as well as a qualitative model to account for the interferometric measurements."," We gathered a large number of measurements in the $H$ and $K$ bands from 2008 to 2010, and present here the first reconstructed images of , as well as a qualitative model to account for the interferometric measurements."
 The article is organized as follow., The article is organized as follow.
 Sect., Sect.
" 2 describes the observations, the data processing and the image reconstruction method."," \ref{sec:datared} describes the observations, the data processing and the image reconstruction method."
 Sect., Sect.
" 3 presents the reconstructed images obtained in the H and K bands, and Sect."," \ref{sec:image} presents the reconstructed images obtained in the $H$ and $K$ bands, and Sect."
 4 provides a temptative disk model., \ref{sec:model} provides a temptative disk model.
" In Sect. 5,,"," In Sect. \ref{sec:discussion},"
 we discuss our results and conclude., we discuss our results and conclude.
" We observed between February 2008 and June 2010, during fourteen nights."," We observed between February 2008 and June 2010, during fourteen nights."
" We used the near-infrared instrument AMBER, located at the Very Large Telescope Interferometer (VLTI;?)."," We used the near-infrared instrument AMBER, located at the Very Large Telescope Interferometer \citep[VLTI;][]{vlti1}."
" AMBER enables the simultaneous combination of three beams in the H (1.69-1.73 µπι)) and K bands um)), with a spectral resolution up to ~12 000 (?).."," AMBER enables the simultaneous combination of three beams in the $H$ (1.69-1.73 ) and $K$ bands (2.0-2.4 ), with a spectral resolution up to $\sim$ 12 000 \citep{petrov07}."
" In the following, we present measurements obtained with the low spectral resolution mode (4/Δ ~35)."," In the following, we present measurements obtained with the low spectral resolution mode $\lambda$ $\Delta \lambda
\sim$ 35)."
 The data were obtained within programs of Guaranteed Time., The data were obtained within programs of Guaranteed Time.
" We performed these observations using therelocatable 1.8 m auxiliary telescopes (ATs) in seven different configurations, sampling a large range of baseline position angles and providing an excellent coverage."," We performed these observations using therelocatable 1.8 m auxiliary telescopes (ATs) in seven different configurations, sampling a large range of baseline position angles and providing an excellent coverage."
 The longest baseline is «128 m corresponding to a maximum angular resolution B/A of 1.3 mas., The longest baseline is $\sim$ 128 m corresponding to a maximum angular resolution $B/\lambda$ of 1.3 mas.
 A summary of the observations presented in this paper is given in Table Al.., A summary of the observations presented in this paper is given in Table \ref{tab:obs}.
" Each measurement for was encircled by observations of a calibrator targets (HD136014, HD123004, HD145921, HD137730) to measure the instrumental transfer function and correct for instrumental effects."," Each measurement for was encircled by observations of a calibrator targets (HD136014, HD123004, HD145921, HD137730) to measure the instrumental transfer function and correct for instrumental effects."
 About of the observations were performed using the fringe-tracker FINITO (?).., About of the observations were performed using the fringe-tracker FINITO\citep{lebouquin08}. .
" The data reduction was performed following standard procedures described in ? and ?,, usingthe package, release 2.99, and the interface provided by the Jean- Mariotti footnotetexthttp://www.jmmc.fr."," The data reduction was performed following standard procedures described in \citet{tatulli07} and \citet{chelli09}, , usingthe package, release 2.99, and the interface provided by the Jean-Marie Mariotti ."
" Raw spectral visibilities, differential phases, and closure phases were extracted for"," Raw spectral visibilities, differential phases, and closure phases were extracted for"
does not correlate with projected distance from the brightest aud most massive galaxy.,does not correlate with projected distance from the brightest and most massive galaxy.
 Instead. they attribute the bursts in star formation to accretion along the flament.," Instead, they attribute the bursts in star formation to accretion along the filament."
 However. it is well known that NGC 672 and IC 1727 are undergoing a strong interaction (Combesetal.1980:SohnDovidee 1996)..," However, it is well known that NGC 672 and IC 1727 are undergoing a strong interaction \citep{com80, soh96}. ."
 Table 6. lists galaxy properties., Table \ref{n672tab} lists galaxy properties.
 The NGC 15 eroup contains 3 large. low surface brightness galaxies (NGC 15. NGC 21. NGC 59) and ds located at a distance of approximately 6 AIpe (Fougueetal.1992).," The NGC 45 group contains 3 large, low surface brightness galaxies (NGC 45, NGC 24, NGC 59) and is located at a distance of approximately 6 Mpc \citep{fou92}."
.. NGC 15 has a kinematical twist iu the major axis but NGC 2[ is dnematically regular (Cheminetal.2006).," NGC 45 has a kinematical twist in the major axis, but NGC 24 is kinematically regular \citep{che06}."
. Towever. NGC 2t has star forming reelous scattered across the eutire disk (Rossa&Doettiiar 2003).," However, NGC 24 has star forming regions scattered across the entire disk \citep{ros03}."
.. NCC 59 is the urd ealaxy in the eroup. and it appears to be normal and unudisturbed.," NGC 59 is the third galaxy in the group, and it appears to be normal and undisturbed."
 Table 7 lists ooOalaxy properties., Table \ref{n45tab} lists galaxy properties.
 Measuring the probability of a recent galaxy interaction or merger i an observational dataset has been a goal for decades: common methods eniplov pair couuts (Zepf&Ίνου1989:Carlbere 2006).. morphological classification techniques (1.6.. concentration. ο. ando clumpiness (Abrahametal.1996:seliceetal.2003). or the Cami coefficient. (Lotzetal. 2001))). or star formation (Saucersetal.1988:Itnapen&James 2009).," Measuring the probability of a recent galaxy interaction or merger in an observational dataset has been a goal for decades; common methods employ pair counts \citep{zep89, carl94, pat97, lef00, pat02, con03, bell06, berrier06}, morphological classification techniques (i.e., concentration, asymmetry, and clumpiness \citep{abraham96,con03} or the Gini coefficient \citep{lotz04}) ), or star formation \citep{sand88,kna09}."
. None of these are iron-clad mereer indicators phenomena that are solnetimes dnduced by interactions are not a guuantee of interactions., None of these are iron-clad merger indicators– phenomena that are sometimes induced by interactions are not a guarantee of interactions.
 Furthermore. it is uot clear how mach weight to eive each possible indicator.," Furthermore, it is not clear how much weight to give each possible indicator."
 With these caveats. we used a combination of these parameters as a euide to rank the level of interactions In a ealaxy group.," With these caveats, we used a combination of these parameters as a guide to rank the level of interactions in a galaxy group."
 Tere we describe how we compiled merger characteristics mto an “interaction index”.," Here we describe how we compiled merger characteristics into an “interaction index""."
 We use this as a rough guide to quautifviug galaxy interactions., We use this as a rough guide to quantifying galaxy interactions.
 A kev svinptom of galaxy interaction is found in the galaxy morphology., A key symptom of galaxy interaction is found in the galaxy morphology.
 Various morphological features πας be induced by galaxy interactions., Various morphological features may be induced by galaxy interactions.
 Although spiral. barred. auc elliptical galaxies cau all be related to interactions. the most reliable uorphological indication of recent interactions are idal bridges. tails. aud shells.," Although spiral, barred, and elliptical galaxies can all be related to interactions, the most reliable morphological indication of recent interactions are tidal bridges, tails, and shells."
 Secondly. strong ceutral star formation is à kev cature of recent or ongoiug luteractions.," Secondly, strong central star formation is a key feature of recent or ongoing interactions."
 Mix interacting systems show iudications of starburst activity such as high levels «of Πα cuaission anc Hel iufrared πιουντν (eto. Sendersotal.(1988):huapen&Jamies(2009))).," Many interacting systems show indications of starburst activity such as high levels of $\alpha$ emission and high infrared luminosity (e.g., \citet{sand88,kna09}) )."
 ILIowever. rot all interacting svstenis srow enhanced star-ormiues activity.," However, not all interacting systems show enhanced star-forming activity."
 The effect oorbital parameters and internal structure of the salaxies play an nuportant part im the doetais of gas dymauies cading to star formation (sec. e.gOO. Coxetal.(2008):\Ghos&IIeruquist (1996)}).," The effect of orbital parameters and internal structure of the galaxies play an important part in the details of gas dynamics leading to star formation (see, e.g., \citet{cox08,mh96}) )."
 The detailed relationship between galaxy iiteractious aud star rmatioun is not well understood., The detailed relationship between galaxy interactions and star formation is not well understood.
" Ilowever. iu general it is found that the star formation rate (SER) is increased in micreine spiral galaxies (ο,ος, I&enuicutt&Ivecl(1981):Νοαetal.(1985):etal.(2010b)))."," However, in general it is found that the star formation rate (SFR) is increased in merging spiral galaxies (e.g., \citet{kenn84, keel85, bus86, hum90, darg10}) )."
 Ticrefore. we use the relative star formation rates in our observed sample as an indicator of ongoing galaxy interactions.," Therefore, we use the relative star formation rates in our observed sample as an indicator of ongoing galaxy interactions."
" Finally, ACN activity may be triggered bv ealaxy iuteractious."," Finally, AGN activity may be triggered by galaxy interactions."
 This is because a huge amount of eas must be funucled to the uuclear regions to fuel the ACNS activity., This is because a huge amount of gas must be funneled to the nuclear regions to fuel the AGN's activity.
 There are various physical mechanisius by which gas loses angular luonuentulnui al falls to the ceuter of a galaxy. includiug eravitational torques. viscous torques. and bydrodvuamical torques or shocks.," There are various physical mechanisms by which gas loses angular momentum and falls to the center of a galaxy, including gravitational torques, viscous torques, and hydrodynamical torques or shocks."
 Galaxy interactions aud mergers provide efficient mechiauisuis for fuuneliug Omeas to the nucleus of a Ooealaxy (Milios&Ileruquist 1996)., Galaxy interactions and mergers provide efficient mechanisms for funneling gas to the nucleus of a galaxy \citep{mh96}.
. There ave links between ealaxv iuteractious and the onset of nuclear activity in galaxies in both obscrvatious (Sanders aud simulations (Springeletal.2005)., There are links between galaxy interactions and the onset of nuclear activity in galaxies in both observations \citep{sand88} and simulations \citep{spri05}.
 Mauy active galaxies show sigus ofiuteraction aud moreer such as disturbed morphology. particularly in III (ποetal.2008).," Many active galaxies show signs of interaction and merger such as disturbed morphology, particularly in HI \citep{kuo08}."
. Sevfert nuclei are found prefercutially ina interacting galaxies (IlXeunicutt&IKecl1981:LaurikainenSalo 1995).," Seyfert nuclei are found preferentially in interacting galaxies \citep{kenn84, lau95}."
. The strongest links between interactions and ACN are found iu the svstems with the highest luninosity (Bahealletal.1997)., The strongest links between interactions and AGN are found in the systems with the highest luminosity \citep{bah97}.
. Using these three factors. we calculate auOinteraction iudexO. described below.," Using these three factors, we calculate anÒinteraction indexÓ, described below."
 The iudex includes only those galaxies witlin + 1 Mpc of the most massive galaxy in each eroup., The index includes only those galaxies within $\pm$ 1 Mpc of the most massive galaxy in each group.
 For galaxies with no distance measurement. the distance of the," For galaxies with no distance measurement, the distance of the"
compared. pixel by pixel.,"compared, pixel by pixel."
 If either the scatter or the mean pixel value exceeded adopted thresholds (about Jena level). that pixel was flagecd as “bad”.," If either the scatter or the mean pixel value exceeded adopted thresholds (about 3-sigma level), that pixel was flagged as “bad""."
 This process was repeated for all exposure times and a combined list of pixels generated of those pixels which appeared at least once on any of the individual “bad” pixel lists.," This process was repeated for all exposure times and a combined list of pixels generated of those pixels which appeared at least once on any of the individual “bad"" pixel lists."
 A total of 13.091 such pixels was identified. which is less than 0.1 of all pixels on the detector.," A total of 13,094 such pixels was identified, which is less than 0.1 of all pixels on the detector."
 The average background intensity (rou bias and dark current) of raw CCD frames taken with our Us camera is very nonnuiforiu over the field., The average background intensity (from bias and dark current) of raw CCD frames taken with our 4k camera is very nonuniform over the field.
 Towever. the pattern is verv simular frou exposure to exposure. while the amplitude of the vattern depends on many things. like exposure ime. ambient temperature aud vac pressure.," However, the pattern is very similar from exposure to exposure, while the amplitude of the pattern depends on many things, like exposure time, ambient temperature and vacuum pressure."
 The mean difference in backeround ADU between he left aud right side of the CCD frame scrves as a parameter to quantify the amplitude of this vackeround pattern., The mean difference in background ADU between the left and right side of the CCD frame serves as a parameter to quantify the amplitude of this background pattern.
 The re-processing of the pixel data was split up iuto batches of about 10.000 consecutive CCD jyenues taken over a narrow rauge of epochs.," The re-processing of the pixel data was split up into batches of about 10,000 consecutive CCD frames taken over a narrow range of epochs."
 A 211 of appropriate master darks for cach standard exposure time was selected., A pair of appropriate master darks for each standard exposure time was selected.
 Each pair spaus a range iu backeround differences (left to right. see above) that is as large as possible with the restriction of being taken close to the epoch of the frames under investigation.," Each pair spans a range in background differences (left to right, see above) that is as large as possible with the restriction of being taken close to the epoch of the frames under investigation."
 The raw data processing then involved a determination of the mean backeround differcuce (left to right) of each individual frame., The raw data processing then involved a determination of the mean background difference (left to right) of each individual frame.
 This value was used in a linear interpolation between the 2 master darks selected for that set of data aud the exposure time of the object frame., This value was used in a linear interpolation between the 2 master darks selected for that set of data and the exposure time of the object frame.
 The pixel-by-pixel interpolated dark was then subtracted frou the object frame., The pixel-by-pixel interpolated dark was then subtracted from the object frame.
 This method of dark subtraction was new for τςΑΟ and resulted in a significant inuprovemoeut in backeround flatucss and lower noise. which leads to a deeper and more uniform limiting magnitude than before.," This method of dark subtraction was new for UCAC3 and resulted in a significant improvement in background flatness and lower noise, which leads to a deeper and more uniform limiting magnitude than before."
 For UCAC2 a more or less random nick of a dark near the tarect properties was selected: without interpolation., For UCAC2 a more or less random pick of a dark near the target properties was selected without interpolation.
 As with previous releases. no additional bias frames were needed.," As with previous releases, no additional bias frames were needed."
 Due to the small size of the field utilized by the CCD. as compared to the optical design of the astroeraph. there is no vignetting from the optical svstem expected.," Due to the small size of the field utilized by the CCD, as compared to the optical design of the astrograph, there is no vignetting from the optical system expected."
 Initial tests also revealed ouly siunall pixel-to-pixel seusitivitv variations., Initial tests also revealed only small pixel-to-pixel sensitivity variations.
 The window on the camera serves as the oulv filter iu a sealed system without moving parts., The window on the camera serves as the only filter in a sealed system without moving parts.
 Thus for the UCACT aud UCAC? releases no flats were applied at all to the survey data. alineg at astrometric results without the goal of precise photometry.," Thus for the UCAC1 and UCAC2 releases no flats were applied at all to the survey data, aiming at astrometric results without the goal of precise photometry."
 Ilowever. a set of about 25 dome flats were taken every few months with an exposure time of 5 s aud light intensity set to give about 30 to full well capacity illunination.," However, a set of about 25 dome flats were taken every few months with an exposure time of 5 s and light intensity set to give about 30 to full well capacity illumination."
 These data were reduced aud applied for the UCAC3 release., These data were reduced and applied for the UCAC3 release.
 The appropriate combined dark frame was subtracted from each individual fat exposure. and all flats of a given epoch were combined excluding extreme low aud high counts. similarly to the darks processing described above.," The appropriate combined dark frame was subtracted from each individual flat exposure, and all flats of a given epoch were combined excluding extreme low and high counts, similarly to the darks processing described above."
 The flats were sealed to 1000 ADU iean intensity (iuteeer) representius ai factor of 1.0 for the science frames data processing to follow., The flats were scaled to 1000 ADU mean intensity (integer) representing a factor of 1.0 for the science frames data processing to follow.
 For some epochs the flat data were split iuto 2 groups of hieh/low average illunination to check ou interna consistency., For some epochs the flat data were split into 2 groups of high/low average illumination to check on internal consistency.
 A total of 28 combined master flats was thus obtained spanning the cutive duration of the UCAC observing., A total of 28 combined master flats was thus obtained spanning the entire duration of the UCAC observing.
 The pixelto-pixel scusitivity variations are small., The pixel-to-pixel sensitivity variations are small.
 Taking 1/25 of the cutive CCD area a a time. sorting all the pixels of a given master fla and cutting the low aud hig[um of the pixels. the resulting standard deviation for pixel-to-pixel variation is only on the order of 0.1 to of the nean pixel count.," Taking 1/25 of the entire CCD area at a time, sorting all the pixels of a given master flat and cutting the low and high of the pixels, the resulting standard deviation for pixel-to-pixel variation is only on the order of 0.4 to of the mean pixel count."
 This fact explains why excellent astrometric results (center fit precision close to L/100 xel) were obtained in UCAC2 even without applying aux flats., This fact explains why excellent astrometric results (center fit precision close to 1/100 pixel) were obtained in UCAC2 even without applying any flats.
 Larec-scale scusitivity variations over the CCD frame area were found to be or less., Large-scale sensitivity variations over the CCD frame area were found to be or less.
 Comparing different master flats of ditfereut epochs. variations of about or less are found. except for the set taken around night numbers 2000 to 2150 (truncated Julian Dates). where significant deviations due to a shutter fülure problem are found in the corners of CCD frames.," Comparing different master flats of different epochs, variations of about or less are found, except for the set taken around night numbers 2000 to 2150 (truncated Julian Dates), where significant deviations due to a shutter failure problem are found in the corners of CCD frames."
 Based on these results a single master fat file close to the epoch of cach object. frame was, Based on these results a single master flat file close to the epoch of each object frame was
The DDeep Survey/Spectrometer (DS/S) telescope wilh Lexan/Borou filler was used for most of the pointed observations in the Guest Observer pliase of the mission. from. 1993 January through 2001 January.,"The Deep Survey/Spectrometer (DS/S) telescope with Lexan/Boron filter was used for most of the pointed observations in the Guest Observer phase of the mission, from 1993 January through 2001 January."
 A description of the instruments on and their performance can be found in Sirketal.(1997)., A description of the instruments on and their performance can be found in \cite{svf97}.
. Although the DS Lexan band is sensitive in the range G7173A. photons are detected from extragalactic sources only at the short wavelength end because of the steep increase in interstellar absorption as a function of wavelength.," Although the DS Lexan band is sensitive in the range 67–178, photons are detected from extragalactic sources only at the short wavelength end because of the steep increase in interstellar absorption as a function of wavelength."
 For example Halpern.Martin.&Marshall(1996). show the effective energy distribution of detected photons in the DS for a range of power-law source spectra.," For example \cite{hmm96}
 show the effective energy distribution of detected photons in the DS for a range of power-law source spectra."
 Since nearly all of the detected flix is in the range 70.LOO ((0.120.15 keV). we refer to this band. according to convention. as soft. N-ravs.," Since nearly all of the detected flux is in the range 70–100 (0.12–0.18 keV), we refer to this band, according to convention, as soft X-rays."
 lt may not be well known that the DDeep Survey imager (DS) made more long X-ray observations of Sevlert galaxies (han any other X-ray. satellite., It may not be well known that the Deep Survey imager (DS) made more long X-ray observations of Seyfert galaxies than any other X-ray satellite.
 nmnmade 23 nearly continuous observations. interrupted only by Earth occultation. of 14 sevlert &alaxies and QSOs.," made 23 nearly continuous observations, interrupted only by Earth occultation, of 14 Seyfert galaxies and QSOs."
 The duration of these pointines ranged from 3 (to 33 davs., The duration of these pointings ranged from 3 to 33 days.
 In total. they account for some 231 days of elapsed time.," In total, they account for some 231 days of elapsed time."
 A log of the observations presented here is given in Table 1.. (, A log of the observations presented here is given in Table \ref{tbl1}. (
We do not include in (his paper many shorter oobservations of additional Sevfert. galaxies that were detected in the DS.),We do not include in this paper many shorter observations of additional Seyfert galaxies that were detected in the DS.)
 These do not represent a complete or unbiased sample of Sevlert galaxies in any sense., These do not represent a complete or unbiased sample of Seyfert galaxies in any sense.
 Most were chosen mainlv on (the basis of their detectabilitv withECVE.. à rare prospect whose chances are improved by selecting targets having small Galactic aud intrinsic absorbing column densities.," Most were chosen mainly on the basis of their detectability with, a rare prospect whose chances are improved by selecting targets having small Galactic and intrinsic absorbing column densities."
 Also. famous Narrow-line Sevlert 1 Galaxies (NLSIs) are heavily represented. (NGC 4051. Alrk 478. Ton S180. RE J10344396) because they are bright. soft X-ray sources wilh steep X-ray spectra (Leighlv|1999h).," Also, famous Narrow-line Seyfert 1 Galaxies (NLS1s) are heavily represented (NGC 4051, Mrk 478, Ton S180, RE J1034+396) because they are bright, soft X-ray sources with steep X-ray spectra \citep{l99b}."
. Many of these data sets have been published. at least in part. bv the authors listed in the notes to Table 1..," Many of these data sets have been published, at least in part, by the authors listed in the notes to Table \ref{tbl1}."
 Few of these papers. however. were concerned wilh power-spectrum analvsis or evidence for periodicitv.," Few of these papers, however, were concerned with power-spectrum analysis or evidence for periodicity."
 Several papers presented spectra of the Sevlerts from ihe sshort-waveleneth spectrometer. a heroic effort (hal. unfortunately. vielded results that only a mother could love.," Several papers presented spectra of the Seyferts from the short-wavelength spectrometer, a heroic effort that, unfortunately, yielded results that only a mother could love."
 ILowever. the corresponding long Ds lisht curves. which are of a quality ranging Irom mediocre to excellent. deserve a separate and comprehensive analysis.," However, the corresponding long DS light curves, which are of a quality ranging from mediocre to excellent, deserve a separate and comprehensive analysis."
 For this paper. we simply extracted a light curve [rom the DS imager using a circle whose radius was chosen to include at least of the source counts. and a surrounding annulus [or backeround subtraction.," For this paper, we simply extracted a light curve from the DS imager using a circle whose radius was chosen to include at least of the source counts, and a surrounding annulus for background subtraction."
 Correction [actors for dead-time and Primbsching (variable loss of, Correction factors for dead-time and Primbsching (variable loss of
where we assumed a clecaving magnetic field in the PWN [pi].,where we assumed a decaying magnetic field in the PWN ].
 This parametrization for B is justified as follows., This parametrization for $B$ is justified as follows.
 After 10 to 20kkvr. the PWN field strength is already. of the order of 5 iG as observed by HIZSS from a number of PWN and alter 100 kkvr we expect that the ISM pressure will ranclomize the PWN field structure. leading to relatively fast diffusive escape of eliarged particles [rom the nebula.," After 10 to kyr, the PWN field strength is already of the order of $5\,\mu$ G as observed by HESS from a number of PWN \citep[see e.g.][]{2008arXiv0803.2104D}
 and after $\sim 100$ kyr we expect that the ISM pressure will randomize the PWN field structure, leading to relatively fast diffusive escape of charged particles from the nebula."
 Although the actual age for breakup is difficult to estimate. we assume to a first order a number of less than kkvr.," Although the actual age for breakup is difficult to estimate, we assume to a first order a number of less than kyr."
 GLAST observations of a limiting age lor mature PWN mav shed more light on this epoch of breakup (deJager2003) , GLAST observations of a limiting age for mature PWN may shed more light on this epoch of breakup \citep{2008arXiv0803.2104D} .
eq., Eq.
 21 can be solved using (he Green's function formalism., \ref{pwnevo} can be solved using the Green's function formalism.
 |je particle spectrum al lime Tis given by )dlo. where O is the Heaviside step function ancl Our model predicts sequal iunbers of positrons and electrons to be accelerated. by pulsars. (hus Eq.," The particle spectrum at time $T$ is given by )dt_0, where $\Theta$ is the Heaviside step function and Our model predicts $\approx$ equal numbers of positrons and electrons to be accelerated by pulsars, thus Eq."
 27. also describes (he source function for CR electrons., \ref{geminga:spec} also describes the source function for CR electrons.
]xeywords: Celestial Mechauies: Planetary Dynamics: Planetary Rines: Saturn. rings Corresponding Author: Matthew Space Sciences Cornell Ithaca NY inmbecdianCastro.cornell.edu,"Keywords: Celestial Mechanics; Planetary Dynamics; Planetary Rings; Saturn, rings Corresponding Author: Matthew Space Sciences Cornell Ithaca NY mmhedmanastro.cornell.edu"
WWoe first present an order-ofiiacnitude calculation which leads to the correct power-law solution for the radius of the PWN.,We first present an order-of-magnitude calculation which leads to the correct power-law solution for the radius of the PWN.
 The assumption of 3ubsonic expansion nuples approximate pressure equilibrium between the wind material and the stellar ejecta at the edee the PWN., The assumption of subsonic expansion implies approximate pressure equilibrium between the wind material and the stellar ejecta at the edge the PWN.
 Iu the interior of the SNR the pressure scales as Ras., In the interior of the SNR the pressure scales as ^3.
 Ou the other hand. the pressure iu the interior of the PWN scales as Rowen’?. withLy the mechanical huuinosity driving the wind.," On the other hand, the pressure in the interior of the PWN scales as ^3, with$L_{0}$ the mechanical luminosity driving the wind."
 Pressure equilibrimn at the coutact discontinüty at Rowen plies the following relation for the radius of the PWN as a function of time: οE16) with the constantof proportionality C to be determiued below.,"	 Pressure equilibrium at the contact discontinuity at $R_{\rm pwn}$ implies the following relation for the radius of the PWN as a function of time: (t) =, with the constantof proportionality $\bar{C}$ to be determined below."
 A qnore detailed derivation uses the first law of thermodynamics. assunine once again aconstant cucrey input Ly iuto the PWN by the pulsar-cdriven wind: dtt ΠΠy.," A more detailed derivation uses the first law of thermodynamics, assuming once again aconstant energy input $L_{0}$ into the PWN by the pulsar-driven wind: t -."
" ere £u, is the thermal οποιον of the PWN. 73 its internal pressure. and Yi, its vole."," Here $E_{\rm th}$ is the thermal energy of the PWN, $P_{\rm i}$ its internal pressure, and ${\cal V}_{\rm pwn}$ its volume."
 This vields the following equation describing the energv balance of a slowly expaucding PWN: or equivalentlyFRUTTItrail S Lo | Hus?MARTE ( )(," This yields the following equation describing the energy balance of a slowly expanding PWN: ) 	= L_0- ^2 ( ), or equivalently ) 	= L_0 + ^3 ( )."
19) This equation has a power-law solution for hf) provided the internal pressure P(t) in the SNR behaves as a power-law im time so that the relation can be satisfied., This equation has a power-law solution for $R_{\rm pwn}(t)$ provided the internal pressure $P_{\rm i}(t)$ in the SNR behaves as a power-law in time so that the relation ^3 ( ) 	 = can be satisfied.
 For a Sedov SNR. expaudiug into a uniform ISM one las Roxt&? and oue finds: D(is)o where D-_ J.," For a Sedov SNR expanding into a uniform ISM one has $P_{\rm i} \propto t^{-6/5}$ and one finds: }(t)= D, where 	D = )."
" P,udEsSRoy we cau use the ceutral pressure frou the Sedov solution with 5,44=5/3 for the interior pressure in the SNR which coufines the PWN (e.g. Shu. 1992): Pu) (Get"," 	 If $R_{\rm pwn} \ll R_{\rm snr}$ we can use the central pressure from the Sedov solution with $\gamma_{\rm ism} =5/3$ for the interior pressure in the SNR which confines the PWN (e.g. Shu, 1992): (t) ( ) ."
 We fiud the same result for fhgG) as in the order- calculation (Equ. 16)).," We find the same result for $R_{\rm pwn}(t)$ as in the order-of-magnitude calculation (Eqn. \ref{pwnexp}) ),"
 deteruiuniung the, determining the
The error in the measurement of each spectral bin ts thus or For each experimental configuration (EC*) we simulated 3000 measurements. using equation 6.. and adding an error term extracted from a Gaussian distribution with zero average and standard deviation derived from equations 11. and 17..,"The error in the measurement of each spectral bin is thus or For each experimental configuration (EC*) we simulated 3000 measurements, using equation \ref{theory}, and adding an error term extracted from a Gaussian distribution with zero average and standard deviation derived from equations \ref{noise_phot} and \ref{noise_spec}."
 Typical simulated spectral measurements are reported in figure 2.., Typical simulated spectral measurements are reported in figure \ref{fig2}.
 We fitted each simulated measurement using equation 6.., We fitted each simulated measurement using equation \ref{theory}.
 In table | we report the averages of the best-fit parameters with their standard deviation., In table \ref{tab1} we report the averages of the best-fit parameters with their standard deviation.
 While giving a general idea of the relative efficiency of the different configurations. the results reported in table | can be misleading in the details. since the distributions of the best-fit parameters are not Gaussian (nor symmetrical). and there are significant correlations between the parameters.," While giving a general idea of the relative efficiency of the different configurations, the results reported in table \ref{tab1}
 can be misleading in the details, since the distributions of the best-fit parameters are not Gaussian (nor symmetrical), and there are significant correlations between the parameters."
 This is evident from the joint likelihood contours plotted 1n figures 3.. 5.. 6.. 7.. 9.. 10. 11.," This is evident from the joint likelihood contours plotted in figures \ref{fig3a}, \ref{fig3b}, \ref{fig4}, \ref{fig5}, \ref{fig6}, \ref{fig7}, \ref{fig8}."
" For ECO (4-band ground-based photometer). where only four independent data-sets are available for each measurement. we tried to fit either three parameters (τι. T. AZ) or four parameters τι. T,. AZy and ATcoag ). addingc a fictitious data point with zero brightness at zero frequency."," For EC0 (4-band ground-based photometer), where only four independent data-sets are available for each measurement, we tried to fit either three parameters $\tau_t$, $T$, $\Delta I_d$ ) or four parameters $\tau_t$, $T_e$, $\Delta I_d$ and $\Delta
T_{CMB}$ ), adding a fictitious data point with zero brightness at zero frequency."
"y. The results are dominated by the degeneracy between 7, and r,. evident from equations | and 2:: without relativistic corrections. the thermal SZ depends on the product of electron density and electron temperature."," The results are dominated by the degeneracy between $T_e$ and $\tau_t$, evident from equations \ref{sz} and \ref{yy}: without relativistic corrections, the thermal SZ depends on the product of electron density and electron temperature."
" For this reason a decrease of. say. a factor 2 of r, is almost perfectly compensated for by an increase of a factor 2 of Τ.."," For this reason a decrease of, say, a factor 2 of $\tau_t$ is almost perfectly compensated for by an increase of a factor 2 of $T_e$."
 The only way to break the degeneracy tis through the relativistic corrections. which. however. are very small: their effect is negligible with respect to the typical uncertainties of ground-based measurements.," The only way to break the degeneracy is through the relativistic corrections, which, however, are very small: their effect is negligible with respect to the typical uncertainties of ground-based measurements."
 For this reason we had to use a prior on Το. assuming that the information is obtained through independent X-ray measurements of the specific brightness of the cluster along the same line of sight.," For this reason we had to use a prior on $T_e$, assuming that the information is obtained through independent X-ray measurements of the specific brightness of the cluster along the same line of sight."
 We tried a very weak prior. with a Gaussian distribution centred on the true value and a standard deviation of 8 keV: otherwise the best fit would converge to non-physical values for 7.," We tried a very weak prior, with a Gaussian distribution centred on the true value and a standard deviation of 8 keV: otherwise the best fit would converge to non-physical values for $T_e$."
 The bias ts only mitigated by the introduction of this prior., The bias is only mitigated by the introduction of this prior.
 In the 3-parameter case the best fits converge on values of the parameters that are not very close (in units of their standard deviation) to the input values. and the typical y is high. confirming that the effect of the measurement error is negligible with respect to the effect of the parameter degeneracies and to the necessity of neglecting the non-thermal component in the fit.," In the 3-parameter case the best fits converge on values of the parameters that are not very close (in units of their standard deviation) to the input values, and the typical $\chi^2$ is high, confirming that the effect of the measurement error is negligible with respect to the effect of the parameter degeneracies and to the necessity of neglecting the non-thermal component in the fit."
 In figure 3 we plot the joint likelihood contours for couples of parameters in the 3-parameter fits., In figure \ref{fig3a} we plot the joint likelihood contours for couples of parameters in the 3-parameter fits.
 The comparison with figure 5. shows that part but not all of the bias depends on, The comparison with figure \ref{fig3b} shows that part but not all of the bias depends on
μ,].
πα μμ μμ μμ μμ μας form where gq coustraius the EDoF of the fit (0«q<JN). can easily be accommodated in this formulation.," 
 
 An additional linear inequality or equality constraint of the form where $q$ constrains the EDoF of the fit $0 < q \le N$ ), can easily be accommodated in this formulation."
 This reformulation of the monotone risk minimization problem makes it possible to use standard minimization methods (???) ancl computational tools (?22) for convex quadratic umininization problems subject to linear constraints aud simple bounds.," This reformulation of the monotone risk minimization problem makes it possible to use standard minimization methods \citep{PD1978,Powell1985,GI1983} and computational tools \citep{Schittkowski2007,Vanderbei1999}
 for convex quadratic minimization problems subject to linear constraints and simple bounds."
 To motivate the discussion iu this section. consider the full-freecdom monotone fit to the WALAP data sets obtained as above (greeu curves in effis:fitsl. and £D). Byfil.," To motivate the discussion in this section, consider the full-freedom monotone fit to the WMAP data sets obtained as above (green curves in \\ref{fig:fits1} and \ref{fig:fits2}) )."
 we mean the fit that minimizes risk over the eutire inonotone-adimissible region 'effigzmonotoue)) without auy restriction on the EDoF of the fit.," By, we mean the fit that minimizes risk over the entire monotone-admissible region \\ref{fig:monotone}) ) without any restriction on the EDoF of the fit."
 This fit turus out to be quite wigely especially at the high-/ eud because of the high nolse variance liere., This fit turns out to be quite wiggly especially at the $l$ end because of the high noise variance here.
 Such wigelinessMD implies sresence of bieh-frequency components in the fit. which in turi implies a large number of EDoF in he fit.," Such wiggliness implies presence of high-frequency components in the fit, which in turn implies a large number of EDoF in the fit."
 Without cosmological pre-couditioniug (i.e.. from a completely aguostic aud data-driven perspeclive) aud when viewed iu relation to the data. it is clear that this fit is not at all unreasouable. eiven the high noise levels at the high-/ end.," Without cosmological pre-conditioning (i.e., from a completely agnostic and data-driven perspective) and when viewed in relation to the data, it is clear that this fit is not at all unreasonable, given the high noise levels at the $l$ end."
 However. all cosinological models suggest far smoother shapes for the angular© power spectrum.," However, all cosmological models suggest far smoother shapes for the angular power spectrum."
 Iu the contest of the present methodology.a one candidate for a smoother fit is the NSS fit (ie.. one that has the minimal risk over the set of CV+1) NSS Tits).," In the context of the present methodology, one candidate for a smoother fit is the NSS fit (i.e., one that has the minimal risk over the set of $(N+1)$ NSS fits)."
 Iudeed. this possibility has been exploited. e.g.. in (?)..," Indeed, this possibility has been exploited, e.g., in \citep{GMN+2004}."
 However. the NSS fit (see the blue curve in aud. L)) may also turn out to be somewhat unsatisfactory with respect to cosmological expectatious (and. some times. also with respect to trends reflected in the full-Creedour monotone it).," However, the NSS fit (see the blue curve in \\ref{fig:fits1} and \ref{fig:fits2}) ) may also turn out to be somewhat unsatisfactory with respect to cosmological expectations (and, some times, also with respect to trends reflected in the full-freedom monotone fit)."
 This is primarily because of the limited freedom available in the NSS class., This is primarily because of the limited freedom available in the NSS class.
 Notice again tliat he NSS fit is not entirely unreasonable (rom an agnostic viewpoiut., Notice again that the NSS fit is not entirely unreasonable from an agnostic viewpoint.
 The inouotoue set. ou the other παπα. offers the possibility of haruessing local miuima in the ‘isk function that are constrained to lie in appropriate “smoother” subsets of the full ruonotone set.," The monotone set, on the other hand, offers the possibility of harnessing local minima in the risk function that are constrained to lie in appropriate “smoother"" subsets of the full monotone set."
 This may be achieved in two distinct ways that may be combined for greater effect: In practice. such smoother restrictecd-freedoim monotone fit cau be obtained by gradually," This may be achieved in two distinct ways that may be combined for greater effect: In practice, such smoother restricted-freedom monotone fit can be obtained by gradually"
"where r, characterizes the radius of the shape function. /(r). through the integral of its square.","where $r_*$ characterizes the radius of the shape function, $f(r)$, through the integral of its square."
 The parameter is defined (0 match the root-mean-squared radius of a Gaussian V.rape., The parameter is defined to match the root-mean-squared radius of a Gaussian shape.
" The uncorrectedshape function. 4.1)). vields. r,= V2d. whose introduction into (4.1)) τοις the variance of the vertical field αἱ a height d. above a distribution of point charges. ((2.1))."," The uncorrectedshape function, \ref{eq:shape}) ), yields, $r_*=\sqrt{2}d$ , whose introduction into \ref{eq:sig_subpole}) ) returns the variance of the vertical field at a height $d$ above a distribution of point charges, \ref{eq:sig_mpole}) )."
 The MTE-corrected shape function is notably narrower (solid line in relfig:shape)). under (he anticipation that it is broadened by the point spread. function to produce the broader observed shape (dashed) with its larger radius r..," The MTF-corrected shape function is notably narrower (solid line in \\ref{fig:shape}) ), under the anticipation that it is broadened by the point spread function to produce the broader observed shape (dashed) with its larger radius $r_*$ ."
 The kurtosis of the composite lield given bv expression (4.1)) is where the dimensionless coefficient \ depends only on the shape of the individual elements. f(r).," The kurtosis of the composite field given by expression \ref{eq:composite}) ) is K_p =, = r_*^2)^3 d^2x, where the dimensionless coefficient $\chi$ depends only on the shape of the individual elements, $f(r)$."
 It is unity lor a perfectly flat. function and greater as the shape becomes more peaked., It is unity for a perfectly flat function and greater as the shape becomes more peaked.
" For charges submerged αἱ a depth d. the value 4=32/5 can be inferred by comparison between expressions (2.1)) and (4.11) and use of the relation r,=2dV2:."," For charges submerged at a depth $d$, the value $\chi=32/5$ can be inferred by comparison between expressions \ref{eq:kurt_mpole}) ) and \ref{eq:kurt_subpole}) ) and use of the relation $r_*=\sqrt{2}d=\sqrt{2}z$."
" The dimensionless ratio. $=(Ve), depends only on the distribution of element amplitudes. aid not on their size or shape."," The dimensionless ratio, $\xi=\avg{\phi^4}/\avg{\phi^2}^2$, depends only on the distribution of element amplitudes, and not on their size or shape."
 Flux amplitudes distributed uniformly or exponentially will be characterized by €=9/5 or £=6 respectively., Flux amplitudes distributed uniformly or exponentially will be characterized by $\xi=9/5$ or $\xi=6$ respectively.
 Parnell (2002) found. that fhixes of each polarity were distributed with a hybricl between an exponential aud power-law known as a Weibull distribution., Parnell (2002) \nocite{Parnell2002} found that fluxes of each polarity were distributed with a hybrid between an exponential and power-law known as a Weibull distribution.
 The particular Weibull distributions reported are characterized bv values of£ between 22 and 30., The particular Weibull distributions reported are characterized by values of $\xi$ between $22$ and $30$.
 These are larger (han lor purely exponential distribution since broader wings lead to more common occurrence of large fluxes., These are larger than for purely exponential distribution since broader wings lead to more common occurrence of large fluxes.
 The variance of Gaussian. white noise. o7. adds (to expression (4.1)) to give the total variance in a magnelogram. og=T;«07.," The variance of Gaussian white noise, $\sigma_n^2$, adds to expression \ref{eq:sig_subpole}) ) to give the total variance in a magnetogram, $\sigma_0^2=\sigma_p^2+\sigma_n^2$."
 The Gaussian noise has zero kurtosis. so its addition will decrease (he kurtosis of the composite. ((4.1)). bv the [actor aj) aj.," The Gaussian noise has zero kurtosis, so its addition will decrease the kurtosis of the composite, \ref{eq:kurt_subpole}) ), by the factor $\sigma_p^4/\sigma_0^4$ ."
 Theareal clensityof flux elements follows directly. [rom the, Theareal densityof flux elements follows directly from the
As an observation progresses. NRÀO staff mouitor the arrays health. maintain an observing log. aud eusure that science data are being archived.,"As an observation progresses, NRAO staff monitor the array's health, maintain an observing log, and ensure that science data are being archived."
 At the couclusion of au observation the observing log is e-mailed to the astronomer., At the conclusion of an observation the observing log is e-mailed to the astronomer.
 This log includes a link to the Archive Access Tool (AAT). an on-line search tool that the astronomer can use to locate and download the archived data.," This log includes a link to the Archive Access Tool (AAT), an on-line search tool that the astronomer can use to locate and download the archived data."
 Those data are proprictary to the proposals authors for a period of 12 mouths., Those data are proprietary to the proposal's authors for a period of 12 months.
 Tt is clear that the data post-processing needs of the EVLA will fav exceed those of the VLA., It is clear that the data post-processing needs of the EVLA will far exceed those of the VLA.
 The salieut features of the EVLA that will drive the post-processing software development are the capabilities to produce data covering: G) a large instantancous bandwidth (at the lowest three frequency bauds the ligh-trequency end is twice the frequency of the low cud). aud (i) a large nunuber of spectral channels (usuallv flexibly arranged in non-contiguous uniltiple spectral windows of varving width aud frequency resolution).," The salient features of the EVLA that will drive the post-processing software development are the capabilities to produce data covering: (i) a large instantaneous bandwidth (at the lowest three frequency bands the high-frequency end is twice the frequency of the low end), and (ii) a large number of spectral channels (usually flexibly arranged in non-contiguous multiple spectral windows of varying width and frequency resolution)."
 These two features result in high data rates ο 5 AIB/s) as a matter of course. with the WIDAR correlelator capable of producing much higher rates (up to 350 GDB/s!).," These two features result in high data rates $>$ 5 MB/s) as a matter of course, with the WIDAR correlelator capable of producing much higher rates (up to 350 GB/s!),"
 and also therefore with the prospect of dealing with large (7 1 TB) datasets., and also therefore with the prospect of dealing with large $>$ 1 TB) datasets.
 Therefore. calibration aud imagine of the data from the EVLA will present. problems that mist 0 solved by a combination of a scalable post-processing xickage. algorithmic miprovenieuts. aud processing aud I/O speed gains.," Therefore, calibration and imaging of the data from the EVLA will present problems that must be solved by a combination of a scalable post-processing package, algorithmic improvements, and processing and I/O speed gains."
 A lavee fraction of data collected bv the EVLA wiLB © taken in one of a umber of standard observing nodes. for example. low frequeney ουπα. high yequency continua. EHI (neutral hwdroseu) spectral ine. or polarization.," A large fraction of data collected by the EVLA will be taken in one of a number of standard observing modes, for example, low frequency continuum, high frequency continuum, HI (neutral hydrogen) spectral line, or polarization."
 Caven the considerable expericuce in reducing data taken iu similar kinds of modes with he VLA. it is reasonable to assunue that reduction of this type of data can be mostly automated.," Given the considerable experience in reducing data taken in similar kinds of modes with the VLA, it is reasonable to assume that reduction of this type of data can be mostly automated."
 The )ost-processiug package (see below]. when combined with some information collected frou the astrouomer im he observation preparation stage (in the Observation Preparation Tool - for instance what a particular source is ncant to actually be used for iu the post-processing). daring actual observing. aud with some heuristics (rules for what to do given certain situations) should be sufficient to complete such automatic reductions.," The post-processing package (see below), when combined with some information collected from the astronomer in the observation preparation stage (in the Observation Preparation Tool - for instance what a particular source is meant to actually be used for in the post-processing), during actual observing, and with some heuristics (rules for what to do given certain situations) should be sufficient to complete such automatic reductions."
 While we are not currently providing an automated reduction pipeline for EVLA data. we plan to do so in the near future.," While we are not currently providing an automated reduction pipeline for EVLA data, we plan to do so in the near future."
 When this occurs all data taken in auv of the standard modes on the EVLA will be processed with this pipeline. and the results (niünulv so-called “reference inage cubes”) made available via the science data archive. subject to proprietary constraiuts.," When this occurs, all data taken in any of the standard modes on the EVLA will be processed with this pipeline, and the results (mainly so-called “reference image cubes”) made available via the science data archive, subject to proprietary constraints."
 While these reference nuage cubes may be sufficicut to give the investigators (and others) an idea of data quality and crude source characteristics. there is some conceru that it will be extremely difficult to ever provide completely reliable automatic pipcline products as afried data product from the EVLA.," While these reference image cubes may be sufficient to give the investigators (and others) an idea of data quality and crude source characteristics, there is some concern that it will be extremely difficult to ever provide completely reliable automatic pipeline products as a data product from the EVLA."
 For that. some Inman -intervention. either by NRAO staff. or the astronomers themselves. may be needed.," For that, some human intervention, either by NRAO staff, or the astronomers themselves, may be needed."
 This is an active area of oewestigation within the observatory., This is an active area of investigation within the observatory.
 For all data which cannot be reliablv reduced via a pipeline. or for astronomers who wish to modifv or extend what is done within the pipeline. there must be a yost-processing software package capable of performing all steps necessary to turn the measured visibilitics mto final image cubes.," For all data which cannot be reliably reduced via a pipeline, or for astronomers who wish to modify or extend what is done within the pipeline, there must be a post-processing software package capable of performing all steps necessary to turn the measured visibilities into final image cubes."
 For the VLA. several packages have οσα used for data editing aud calibration over the vears. but for uearly the entire lifetime of the VLA. AIPS (Creiseu(2003))) has been the primary software oickage for data processing.," For the VLA, several packages have been used for data editing and calibration over the years, but for nearly the entire lifetime of the VLA, AIPS \cite{grei03}) ) has been the primary software package for data processing."
 There are problems with AIPS. however. that prevent its coutinued loue-term use for EVLA data post-processing.," There are problems with AIPS, however, that prevent its continued long-term use for EVLA data post-processing."
 The post-processing wackage of choice for the EVLA project is CASA (Common Astronomical Software Applications. see. e.g.. ALeMwulliuetαἱ.(2007))). because of its scalability. ability o be parallelized. scriptabilitv. expertise within NRAO. and conuuonalitv with ALALA.," The post-processing package of choice for the EVLA project is CASA (Common Astronomical Software Applications, see, e.g., \cite{McMul07}) ), because of its scalability, ability to be parallelized, scriptability, expertise within NRAO, and commonality with ALMA."
 Not evervthiug that is weeded for EVLA data reduction (aud certainly mot for robust pipeline-reduction) is currently available within CASA. however. so there is a program of implementation of iuissine pieces within the package.," Not everything that is needed for EVLA data reduction (and certainly not for robust pipeline-reduction) is currently available within CASA, however, so there is a program of implementation of missing pieces within the package."
 Iu addition. a vigorous program of algorithm development within NRAO is ongoing. to address items that are not only rot Huplemented within CASA. but have no eenerally accepted algorithmic solution at all.," In addition, a vigorous program of algorithm development within NRAO is ongoing, to address items that are not only not implemented within CASA, but have no generally accepted algorithmic solution at all."
 Notably. automatic dageine of suspect data. wide-field wide-baudwidth full volarization nuaegiug. ΠΕΙ detection and excision. aud ionospheric corrections are all areas of active research. and will be implemented within CASA as soon as xossible after accepted aleorithius are developed.," Notably, automatic flagging of suspect data, wide-field wide-bandwidth full polarization imaging, RFI detection and excision, and ionospheric corrections are all areas of active research, and will be implemented within CASA as soon as possible after accepted algorithms are developed."
 Maux of these areas of research are of course not unique o the EVLA. so developments at other observatories and telescopes are closely. watched so that we can take advantage when appropriate.," Many of these areas of research are of course not unique to the EVLA, so developments at other observatories and telescopes are closely watched so that we can take advantage when appropriate."
 Finally. in order to support the scale of computing that is needed for both pipeline aud lLauds-on post-processing of EVLA data. we ave planning to provide a mid-sized computing cluster (10's of nodes) for both the automatic xpelime reduction of standard mode observations. aud ‘or somewhat more interactive reduction by astrononiers.," Finally, in order to support the scale of computing that is needed for both pipeline and hands-on post-processing of EVLA data, we are planning to provide a mid-sized computing cluster (10's of nodes) for both the automatic pipeline reduction of standard mode observations, and for somewhat more interactive reduction by astronomers."
 We believe this. along with inuprovenieuts in the speed of the CASA code itself. is sufficient to support the reeds of the astronomical cominuuitv.," We believe this, along with improvements in the speed of the CASA code itself, is sufficient to support the needs of the astronomical community."
 We assume that uost access to the cluster will be either bv the NRAO-controlled automatic reduction pipeline. or bw batch jobs submitted by remote users.," We assume that most access to the cluster will be either by the NRAO-controlled automatic reduction pipeline, or by batch jobs submitted by remote users."
 We are connuuitted to relmaiine flexible iu this plan. however. as this will be a lew cra for post-processing of interferometer data. and we must be able to react to new developiicuts. pressure rou the community. and other realities as we eo forward.," We are committed to remaining flexible in this plan, however, as this will be a new era for post-processing of interferometer data, and we must be able to react to new developments, pressure from the community, and other realities as we go forward."
 The EVLA is a major expausion to the highly flexible and productive VLA., The EVLA is a major expansion to the highly flexible and productive VLA.
 By expanding the bandwidth to S CdIz/polarization. adding receivers to provide full frequency coverage from 1 to 50 GITz. aud implementing a now correlator with superb spectral resolution aud flexibility. the EVLA will provide orders of magnitude inrovennieut iu scientific capability over the ΝΤΑ capabilities that will ensure that the EVLA will be the premicr seueralopurpose cniewave imaging radio telescope for at least the next decade. serving the world user comunity for investigations into. aud nuderstanding of. celestial racio trausieuts. the evolution," By expanding the bandwidth to 8 GHz/polarization, adding receivers to provide full frequency coverage from 1 to 50 GHz, and implementing a new correlator with superb spectral resolution and flexibility, the EVLA will provide orders of magnitude improvement in scientific capability over the VLA -- capabilities that will ensure that the EVLA will be the premier general-purpose cm-wave imaging radio telescope for at least the next decade, serving the world user community for investigations into, and understanding of, celestial radio transients, the evolution"
following matter distribution 2008).,following matter distribution .
. At present. the volume filling fraction of relatively strong (210 nG) magnetic fields. ie. filaments aud clusters. highly depends on models and methods (see Figure 9 of (2011))).," At present, the volume filling fraction of relatively strong $\gtrsim 10$ nG) magnetic fields, i.e., filaments and clusters, highly depends on models and methods (see Figure 9 of )."
 Also. the spectrum of the maguetic fields is crucial for the propagation of UIIECTRs. though it is not certain.," Also, the spectrum of the magnetic fields is crucial for the propagation of UHECRs, though it is not certain."
 An observational constraint of the magnetic strength of EGAIFs in filamentary structures is oulv ο μα and there is no direct. observationalX duplication ou the direction aud coherent leneth of the maguetie fields., An observational constraint of the magnetic strength of EGMFs in filamentary structures is only $\lesssim 0.1 \mu$ G and there is no direct observational implication on the direction and coherent length of the magnetic fields.
 While a turbulent naenetic field with the Nolmogorey spectrum with Be=10 nC is simply adopted im this work. several mnerical simulations have indicated the existence of arge-scale fields in filamentary structures2005).," While a turbulent magnetic field with the Kolmogorov spectrum with $B_{\rm f} = 10$ nG is simply adopted in this work, several numerical simulations have indicated the existence of large-scale fields in filamentary structures."
. Such a coherent component deflects the rajectories of UMECRs amore efiicicutly aud makes onegcr time-delay compared to a turbulent componeut., Such a coherent component deflects the trajectories of UHECRs more efficiently and makes longer time-delay compared to a turbulent component.
 Tu this case the time spread of a UITECR burst is snaller hau the time-delay because particles similarly propagate due to the large-scale componcut., In this case the time spread of a UHECR burst is smaller than the time-delay because particles similarly propagate due to the large-scale component.
 The complex web of ECMES implies that structured ECGMEs on the way from sources to the Milkv Way outside ECGAIFs eiibedadiug the sources could also play a siguificaut role in the total deflection and time sperad of UIIECTs. but these do not affect our coustraiuts derived in the previous section in the scope of our ECATF models.," The complex web of EGMFs implies that structured EGMFs on the way from sources to the Milky Way outside EGMFs embedding the sources could also play a significant role in the total deflection and time sperad of UHECRs, but these do not affect our constraints derived in the previous section in the scope of our EGMF models."
 Possible effects of such EGAIFs are making additional deflection and time spread of UITECRs., Possible effects of such EGMFs are making additional deflection and time spread of UHECRs.
 As long as the additional deflection is small chough. the time spread by the ECOMES crubedding the sources provides couscrvative constraints.," As long as the additional deflection is small enough, the time spread by the EGMFs embedding the sources provides conservative constraints."
 Di order to see the effects; we beein frou evaluating the probability that UNECRs cucounter a magnetic structure on the wav to the Earth during propagation. which can be calculated from the nuuber density. iy. aud cross-sectional area. zl. of thestructure x. The number density. 4zA/V. where ὃν is the volume of the structiwe x. is pgz3«10.7? P aud new10.9 P; respectivelv.," In order to see the effects, we begin from evaluating the probability that UHECRs encounter a magnetic structure on the way to the Earth during propagation, which can be calculated from the number density, $n_{\rm x}$ , and cross-sectional area, $A_{\rm x}$, of thestructure x. The number density, $n_{\rm x} \approx f_{\rm x} / V_{\rm x}$, where $V_{\rm x}$ is the volume of the structure x, is $n_{\rm f} \approx 3 \times 10^{-5}$ $^{-3}$ and $n_{\rm c} \approx 10^{-6}$ $^{-3}$, respectively."
" The cross-sectioual areas are dym27425=100 Mpc? aud A.mo633=OF Mp. so the encounter probability is 0.21 and 2«10.7? for 75 AIpe propagation iu the cases of filaments and clusters, respectively,"," The cross-sectional areas are $A_{\rm f} \approx 2^2 \times 25 = 100$ $^2$ and $A_{\rm c} \approx \pi \times 3^2 = 9 \pi$ $^2$, so the encounter probability is 0.24 and $2 \times 10^{-3}$ for 75 Mpc propagation in the cases of filaments and clusters, respectively."
" Thus. whereas it is unlikely for UIIECTs to encounter clusters during their propagation. ""Cue of UITECRs penetrate into a filamentary structure ouce."," Thus, whereas it is unlikely for UHECRs to encounter clusters during their propagation, some of UHECRs penetrate into a filamentary structure once."
 But their typical deviation angle of protous with enereies above 1079 eV is still smaller than the considere value of c=57 (see Figure 5)). so that such interveniug EGAIFs do not affect our conservative results.," But their typical deviation angle of protons with energies above $10^{20}$ eV is still smaller than the considered value of $\psi = 5^{\circ}$ (see Figure \ref{fig:def200}) ), so that such intervening EGMFs do not affect our conservative results."
" Stronger constraints on p, and Eb frou additional time spreac can be expected especially if UMECRs must pass the local mmaguetized structure. as discussed. afterwards."," Stronger constraints on $\rho_s$ and $\tilde{\mathcal{E}}_{\rm CR}^{\rm iso}$ from additional time spread can be expected especially if UHECRs must pass the local magnetized structure, as discussed afterwards."
 One iuieht expect the situation where effects of structured ECAIFs are even more prominent., One might expect the situation where effects of structured EGMFs are even more prominent.
 We cole musperceive the positions of UITECT. sources from their arrival directions if VIECRs propagate selectively aloug the maguetic web structure and/or are strongly scatteres off bv the structured. ECAIFs2010)., We could misperceive the positions of UHECR sources from their arrival directions if UHECRs propagate selectively along the magnetic web structure and/or are strongly scattered off by the structured EGMFs.
. When such effects are large in the Universe. talking larger values of c will be more realistic.," When such effects are large in the Universe, taking larger values of $\psi$ will be more realistic."
 Also. as recently sugeested. the structured ECGMES may increase the probability that we observe UITECTs from transicnt sources thanks to significant tine spread longer than the intrinsic burst duration of the sources2011).," Also, as recently suggested, the structured EGMFs may increase the probability that we observe UHECRs from transient sources thanks to significant time spread longer than the intrinsic burst duration of the sources."
. The Milkv Wavy is thought to be located in a deuse region in local Universe., The Milky Way is thought to be located in a dense region in local Universe.
 Although maguetic fields iu the local structure i9 highlv uncertain. it could be another unavoidable ECGME for UITECTS arriving at the Earth.," Although magnetic fields in the local structure is highly uncertain, it could be another unavoidable EGMF for UHECRs arriving at the Earth."
 À coustrained simulation has shown that the Milkv Wav belongs to a filamentary structure adjacent to the local Superchister2003)., A constrained simulation has shown that the Milky Way belongs to a filamentary structure adjacent to the local Supercluster.
. Asstuuing our filament model for the local maguetic structure. this ECME is dominant in Τμ1). im the case where sources are located in filamentary structures because the time profile spread should be estimated as cgE) instead of τε).," Assuming our filament model for the local magnetic structure, this EGMF is dominant in $\tau_{\rm min}(E)$ in the case where sources are located in filamentary structures because the time profile spread should be estimated as $\sigma_{\rm f}(E)$ instead of $\tau_{\rm f}(E)$ ."
 Figure 7 shows possible constraints on py ale Eh πι the case where the local filament is included., Figure \ref{fig:einput2} shows possible constraints on $\rho_s$ and $\tilde{\mathcal{E}}_{\rm CR}^{\rm iso}$ in the case where the local filament is included.
 Conservative constraiuts bv the GMPE. which is diseussed im(2009).. is also shown.," Conservative constraints by the GMF, which is discussed in, is also shown."
 For a filamentary structure between a source and the local enviromment discussed above. the time profile spread can also be couscrvatively estimated by o¢(£). and therefore the same constraints as the case of the local filament are applied even if CHECRs pass several filamentary structures.," For a filamentary structure between a source and the local environment discussed above, the time profile spread can also be conservatively estimated by $\sigma_{\rm f}(E)$, and therefore the same constraints as the case of the local filament are applied even if UHECRs pass several filamentary structures."
 Iu the cases that sources are enibedded in clusters of galaxies. constraints are unchanged because the time spread of CHECRs by ECGCMEs iu the clusters of galaxies is much larger.," In the cases that sources are embedded in clusters of galaxies, constraints are unchanged because the time spread of UHECRs by EGMFs in the clusters of galaxies is much larger."
 The discussions iu Section L. where oulv EGAIFs surrounding the sources are considered. provide conservative constraints.," The discussions in Section \ref{results}, where only EGMFs surrounding the sources are considered, provide conservative constraints."
 If the volume flliug fraction of structured EGAIFs aud the nature of local magnetic euvironnienuts are understood. we would be able to obtain better constraints.," If the volume filling fraction of structured EGMFs and the nature of local magnetic environments are understood, we would be able to obtain better constraints."
 As seen above. it is obviously crucial το reduce the uncertainty of the ECAIFs both theoretically aud observationally iu future to understand the propertics of trausient. UTIEC'R. sources.," As seen above, it is obviously crucial to reduce the uncertainty of the EGMFs both theoretically and observationally in future to understand the properties of transient UHECR sources."
 Iu order to get better knowledgeSA on the EGAIFs. Faraday rotation surveys bv future experiments such as Square Kilometer are usoful.," In order to get better knowledge on the EGMFs, Faraday rotation surveys by future experiments such as Square Kilometer are useful."
 Detection of TeV svuchrotrou pair echo/halo cluission produced by UIIE sanuua-ray bursts‘fares also nav allow us to probe structured ECGAIFs with 2 lou2011).. Future πουΊσα) simulations ou structured ECAIFs can also give us more insielit iuto consequences to transient UITECR source population., Detection of TeV synchrotron pair echo/halo emission produced by UHE gamma-ray bursts/flares also may allow us to probe structured EGMFs with $\gtrsim 10$ nG. Future numerical simulations on structured EGMFs can also give us more insight into consequences to transient UHECR source population.
 Throughout this paper we have focused on protons., Throughout this paper we have focused on protons.
 Lveu though heavy nuclei are cousidered. the discussions in this paper are iun principle applicable.," Even though heavy nuclei are considered, the discussions in this paper are in principle applicable."
 A basic difference between protons and heavy nuclei is electric charge. ie. nuclei suffer from deflectious Z times as arge as protons aud the time spread roughly Z? times as large as protons.," A basic difference between protons and heavy nuclei is electric charge, i.e., nuclei suffer from deflections $Z$ times as large as protons and the time spread roughly $Z^2$ times as large as protons."
" If structured ECGMES ouly in the vicinity of CHECR sources affect the propagation of miclei. the discussions are valid because the deviation scale. c. reflects not the deflection angles of nuclei iu the uaenetic structures but a viewing anele of the structures,"," If structured EGMFs only in the vicinity of UHECR sources affect the propagation of nuclei, the discussions are valid because the deviation scale, $\psi$, reflects not the deflection angles of nuclei in the magnetic structures but a viewing angle of the structures."
 However. the CAIF aud. a maenetico field in the Local," However, the GMF and a magnetic field in the Local"
This contrasts with optical counts which fatten only at very faint limits (οσα ~O40 for 1—22.24 llattening to a=0.28 beyond Vo=24 (Smail 1995b)).,This contrasts with optical counts which flatten only at very faint limits (e.g $\alpha\simeq 0.40$ for $V=22-24$ flattening to $\alpha=0.28$ beyond $V=24$ (Smail 1995b)).
 Moreover. recd-infrared colours (e.g. Z/—A ) are more sensitive to recishift than to spectral class in the redshift range of interest.," Moreover, red-infrared colours (e.g. $I-K$ ) are more sensitive to redshift than to spectral class in the redshift range of interest."
 The opposite is true for sav. D{ (see Fig. 1)).," The opposite is true for say, $B-I$ (see Fig. \ref{fig-colz}) )."
 This leads to a much cleaner and efficient. method. of eliminating likely cluster members: we retain both the Lat slope and sullicient numbers required. for measurement of the depletion effect., This leads to a much cleaner and efficient method of eliminating likely cluster members: we retain both the flat slope and sufficient numbers required for measurement of the depletion effect.
 The major drawback of measuring depletion signals in the near-infrared until now has been the absence of panoramic infrared. detectors capable of surveving large areas of sky rapidly to the required. depth., The major drawback of measuring depletion signals in the near-infrared until now has been the absence of panoramic infrared detectors capable of surveying large areas of sky rapidly to the required depth.
 With the commissioning of the Cambridge Infrared Survey Instrument (CIHAUSI. Beckett 1998). this becomes a practicality.," With the commissioning of the Cambridge Infrared Survey Instrument (CIRSI, Beckett 1998), this becomes a practicality."
 A number of factors enter when considering the merits of undertaking depletion studies at near-infrared wavelengths., A number of factors enter when considering the merits of undertaking depletion studies at near-infrared wavelengths.
 Foremost. we can expect the counts to [atten considerably at. cosmoloegicallv-significant depths. for any passband Iongward of Tym. Whereas classical number-count studies have been almost exclusively undertaken in the A- or A7- (c.g. Moustakas 1997 obtain a=0.23 for 15«A23: Gardner 1993 obtain a=0.26 lor A> IS). recent counts at Jf (Yan 1998) show little change in slope. with a=0.31x0.02 for 20«df24.5.," Foremost, we can expect the counts to flatten considerably at cosmologically-significant depths for any passband longward of $\mu$ m. Whereas classical number-count studies have been almost exclusively undertaken in the $K$ - or $K'$ -band (e.g. Moustakas 1997 obtain $\alpha=0.23$ for $18<K<23$; Gardner 1993 obtain $\alpha=0.26$ for $K>18$ ), recent counts at $H$ (Yan 1998) show little change in slope, with $\alpha=0.31\pm 0.02$ for $20<H<24.5$."
 Our lensing study will be undertaken using the Z/-band filter., Our lensing study will be undertaken using the $H$ -band filter.
 Secondly. in terms of colour-selection. the degeneracy between redshift ancl spectral class. likewise. iniproves dramaticallv when infrared magnitudes are ασ. particularly when account is taken of likely photometric errors.," Secondly, in terms of colour-selection, the degeneracy between redshift and spectral class likewise improves dramatically when infrared magnitudes are added, particularly when account is taken of likely photometric errors."
 Fig., Fig.
 1 illustrates a typical measurement of the {di and Bf colour of a cluster earlv-type sequence at intermediate redshift., \ref{fig-colz} illustrates a typical measurement of the $I-H$ and $B-I$ colour of a cluster early-type sequence at intermediate redshift.
 For the optical-optical colour we see that the single measurement is not. enough to. break he cegeneracy between colour ancl redshift: an object uer than the cluster sequence may be a low recshilt elliptical or a late-tvpe galaxy at any redshift., For the optical-optical colour we see that the single measurement is not enough to break the degeneracy between colour and redshift: an object bluer than the cluster sequence may be a low redshift elliptical or a late-type galaxy at any redshift.
 But) when he optical-infrared colour is considered. the sensitivity to spectral type is greatly. reduced. and we see that the blucr and. redder galaxies map more cleanly onto foreground and ickeround. populations.," But when the optical-infrared colour is considered, the sensitivity to spectral type is greatly reduced, and we see that the bluer and redder galaxies map more cleanly onto foreground and background populations."
 One can therefore select more red objects with redshifts greater than that of the cluster., One can therefore select more red objects with redshifts greater than that of the cluster.
 This accurate and. ellicient cüscrimination between the two »opulations is of ereat importance for our depletion study. which depends both on having a Hat number count. slope and a sullicient. surface number censity of background galaxies.," This accurate and efficient discrimination between the two populations is of great importance for our depletion study, which depends both on having a flat number count slope and a sufficient surface number density of background galaxies."
 Our principal goal is to explore the depletion expected in Abell 2219 in the context. of earlier. studies. of this cluster., Our principal goal is to explore the depletion expected in Abell 2219 in the context of earlier studies of this cluster.
 This is an X-rav luminous (Allen 1992) cluster Iving at a redshift of 0.22. with an N-ray temperature of Tx=11.5 keV and showing no evidence of a cooling Iow (Allen Fabian. 1998).," This is an X-ray luminous (Allen 1992) cluster lying at a redshift of 0.22, with an X-ray temperature of $T_X=11.8$ keV and showing no evidence of a cooling flow (Allen Fabian 1998)."
 The distribution of the X-ray gas is elliptical ancl misaligned. with the cD galaxy on small scales., The distribution of the X-ray gas is elliptical and misaligned with the cD galaxy on small scales.
 Smail (1995a) report. two systems of giant ares with undetermined redshifts: a red! are (possible two merging images of a single background source) ancl a blue? are consisting of three separate segments., Smail (1995a) report two systems of giant arcs with undetermined redshifts: a `red' arc (possible two merging images of a single background source) and a `blue' arc consisting of three separate segments.
 The red arc is shorter and brighter. and is prominent in our Z/-band image (Fig. 6)).," The red arc is shorter and brighter, and is prominent in our $H$ -band image (Fig. \ref{fig-arczoom}) )."
 The Cambridge Infrared Survey Instrument (CIRSL Beckett 1998) is à wide-ield. infrared. imager consisting of a mosaic of four Rockwell Llawaii LgC'd'Te detectors.," The Cambridge Infrared Survey Instrument (CIRSI, Beckett 1998) is a wide-field infrared imager consisting of a mosaic of four Rockwell Hawaii HgCdTe detectors."
 Each detector is separated. by a gap of approximately one detector width so that. multiple pointings can be easily arranged to produce a larger contiguouslv-imaged field., Each detector is separated by a gap of approximately one detector width so that multiple pointings can be easily arranged to produce a larger contiguously-imaged field.
 ‘Table 1 summarizes the observations that form the basis of this paper., Table 1 summarizes the observations that form the basis of this paper.
 The d/-banck CIRSL observations of were mace at the prime focus of the +.2-m William LHerschel Telescope (LUE): this olfers a plate scale ofL, The $H$ -band CIRSI observations of were made at the prime focus of the 4.2-m William Herschel Telescope (WHT); this offers a plate scale of.
o Each CLRSE detector has a field of view of so the mosaic of four detectors gives an instantaneous total field of view of Ll.11 arcmin., Each CIRSI detector has a field of view of so the mosaic of four detectors gives an instantaneous total field of view of $11\times 11$ arcmin.
 The cluster. was observed. on the nights 1 to 4 July 1999 using a field configuration chosen to optimally overlap with existing B- and f-band LEVY CCD data of plate scale, The cluster was observed on the nights 1 to 4 July 1999 using a field configuration chosen to optimally overlap with existing $B$ - and $I$ -band EEV CCD data of plate scale
data to constrain possible radio power models and by producing mock radio sky maps that can be directly compared to observations.,data to constrain possible radio power models and by producing mock radio sky maps that can be directly compared to observations.
" From our analysis we have determined that the slope and normalization of the P;4Gg;—My and P4—L, relations are potentially key probes of the various models of CR generation.", From our analysis we have determined that the slope and normalization of the $\pmvir$ and $P_{1.4} - L_x$ relations are potentially key probes of the various models of CR generation.
 They also allow us to place limits on the average cluster magnetic field strength and the scaling of magnetic fields with cluster mass., They also allow us to place limits on the average cluster magnetic field strength and the scaling of magnetic fields with cluster mass.
 With the uncertainties from only 131 observed radio halos we can significantly constrain the scaling of radio power with cluster mass and turbulent pressure., With the uncertainties from only $131$ observed radio halos we can significantly constrain the scaling of radio power with cluster mass and turbulent pressure.
 With the 131 objects of our high-resolution sample we are able to clearly separate some models with strong statistical significance., With the $131$ objects of our high-resolution sample we are able to clearly separate some models with strong statistical significance.
 The evolution with redshift of these relations also allows us to potentially distinguish various models., The evolution with redshift of these relations also allows us to potentially distinguish various models.
" Future low-frequency missions, which will surveys large portions of the sky, may then"," Future low-frequency missions, which will surveys large portions of the sky, may then"
6680.6780A.,6680–6780.
.. We cross correlated all the T. CrD spectra in order to determine the velocity shift relative to a standard star., We cross correlated all the T CrB spectra in order to determine the velocity shift relative to a standard star.
 The spectra. were then Doppler shifted ancl summed (see Figure 1)., The spectra were then Doppler shifted and summed (see Figure 1).
 For this analvsis we use model atmospheres with a setup similar to the “NextGen” model grid of Hauschildt. et al (1998)., For this analysis we use model atmospheres with a setup similar to the “NextGen” model grid of Hauschildt et al (1998).
 Our models are spherically symmetric LEE models calculated with the general stellar atmosphere codePHOENIX., Our models are spherically symmetric LTE models calculated with the general stellar atmosphere code.
 We use a direct opacity sampling method to include line blanketing of both atoms anc molecules., We use a direct opacity sampling method to include line blanketing of both atoms and molecules.
 “Phe equation of state includes more than 500 species (atoms. ions and molecules).," The equation of state includes more than 500 species (atoms, ions and molecules)."
 For the relatively high effective. temperatures considered here. the cllects of dust condensation. and opacities are negligible.," For the relatively high effective temperatures considered here, the effects of dust condensation and opacities are negligible."
 The radiative transfer. equation is solved. using an operator splitting method., The radiative transfer equation is solved using an operator splitting method.
 Details of the calculational methods are given in the above reference., Details of the calculational methods are given in the above reference.
 We used. solar abundance. models. in the effective temperature range 3000μις3600 with 2.5<3.5 as starting point.," We used solar abundance models in the effective temperature range $3000
\leq T_{\rm eff} \leq 3600\,$ with $2.5 \leq \log(g) \leq 3.5$ as starting point."
" For the best fitting model. log(g)=2.5 and Tig= 320014x. we calculated. a set. ol svnthetic spectra with lithium abundances 0.0<log),¢(Li)3.31."," For the best fitting model, $\log(g) = 2.5$ and $T_{\rm
eff}=3200\,$ K, we calculated a set of synthetic spectra with lithium abundances $0.0 \leq
\log_{10}\epsilon(\rm Li)\leq 3.31$."
 Here. c(Li) is the number of lithium nuclei for cach 1057 hvdrogen nuclei.," Here, $\epsilon(\rm Li)$ is the number of lithium nuclei for each $10^{12}$ hydrogen nuclei."
" logy,«(Li)=1.16 is the abundance. of lithium in the solar atmosphere and log),(Li)=3.31 is the meteoritic lithium abundance.", $\log_{10}\epsilon(\rm Li)=1.16$ is the abundance of lithium in the solar atmosphere and $\log_{10}\epsilon(\rm Li)=3.31$ is the meteoritic lithium abundance.
 The spectra were calculate with the same code and general setup (including spherica svmmetrv) that was used to calculate the mocdels in. the model atmosphere. however. the spectral resolution was se to about 130.000.," The spectra were calculated with the same code and general setup (including spherical symmetry) that was used to calculate the models in the model atmosphere, however, the spectral resolution was set to about 130,000."
 “Phe sets of svnthetie spectra were then compared to the observations to find the model with the bes fitting lithium line to estimate the abundance of lithium., The sets of synthetic spectra were then compared to the observations to find the model with the best fitting lithium line to estimate the abundance of lithium.
 For the comparison. the synthetic spectra were convolved with a rotational profile of 15 km/s to account for the rotationa broadening of the star (xenvon Garcia 1986). ancl the observed spectrum: was converted to vacuum wavelengths.," For the comparison, the synthetic spectra were convolved with a rotational profile of $15\,$ km/s to account for the rotational broadening of the star (Kenyon Garcia 1986) and the observed spectrum was converted to vacuum wavelengths."
 In acidition. a global bluc-shift of 31 km/s was applied to the synthetic spectra to match observed and computed [eatures.," In addition, a global blue-shift of $31\,$ km/s was applied to the synthetic spectra to match observed and computed features."
 We have also caleulated: spectra for. effective. temperature and gravities close to the best fitting mocel to establish the error in the estimated lithium abundance., We have also calculated spectra for effective temperature and gravities close to the best fitting model to establish the error in the estimated lithium abundance.
 For the purpose of the analysis presented here. we used a fixed miero-turbulent velocity €= 2km/s. In all cases. the quality of the fits was established manually by. inspection of the plots comparing the synthetic spectra to the data.," For the purpose of the analysis presented here, we used a fixed micro-turbulent velocity $\xi=2\,$ km/s. In all cases, the quality of the fits was established manually by inspection of the plots comparing the synthetic spectra to the data."
 The Li rresonance line is well known to be verv sensitive to Tr., The Li resonance line is well known to be very sensitive to $_{\rm eff}$.
 Thus we tried. dillerent temperatures between 3000 Ix. and 3600 IX in our abundance analvsis.," Thus we tried different temperatures between 3000 K, and 3600 K in our abundance analysis."
 We also tried three different values for the &ravitv: log $2.5. log g—3.0 and log g—3.5.," We also tried three different values for the gravity; $\log$ g=2.5, $\log$ g=3.0 and $\log$ g=3.5."
 The best fitting model for T. CrB. £r=3200 hk. log(g)= 2.5] showed the Li abundance to be between 0.5 and 0.7.," The best fitting model for T CrB $T_{\rm eff}=3200\,$ K, $\log(g)=2.5$ ] showed the Li abundance to be between 0.5 and 0.7."
i We estimate uncertainies of 2001Ix and ~0.5 in Tr and |log(g) respectively., We estimate uncertainies of $\sim$ 200K and $\sim$ 0.5 in $T_{\rm eff}$ and $\log(g)$ respectively.
 As shown in Figure Lowe obtained a good representation of the spectrum without changing the abundances of the other elements (AL Ca. Fe. S1) present in the svnthesised spectral region.," As shown in Figure 1 we obtained a good representation of the spectrum without changing the abundances of the other elements (Al, Ca, Fe, Si) present in the synthesised spectral region."
 Note that the Fe; {line is included in the svnthetic spectrum., Note that the $\sc i$ line is included in the synthetic spectrum.
 A similar analysis for the standard star LID 151203 shows that its Li abundance is at least θ dex below that of T ο. As one can see from Figure 1 the Li line is not well matched. suggesting that there may. be a line nussing from the svnthetic spectrum. accounting for the nussing absorption.," A similar analysis for the standard star HD 151203 shows that its Li abundance is at least 0.4 dex below that of T CrB. As one can see from Figure 1 the Li line is not well matched, suggesting that there may be a line missing from the synthetic spectrum, accounting for the missing absorption."
 However. this could. well be that. the CN line data. which is included in the model. not being very accurate.," However, this could well be that the CN line data, which is included in the model, not being very accurate."
 Normal stars reach sullicicnthy high temperatures to destroy lithium in their interiors., Normal stars reach sufficiently high temperatures to destroy lithium in their interiors.
 As a result. if there is significant convection of material to the surface. from. regions hot enough to destroy. lithium. its abundance will decline with age.," As a result, if there is significant convection of material to the surface from regions hot enough to destroy lithium, its abundance will decline with age."
 This effect is seen for cool stars. whilst the surfaces of hotter stars. within which convection does not. occur. retain what is thought to be their initial lithium abundance.," This effect is seen for cool stars, whilst the surfaces of hotter stars, within which convection does not occur, retain what is thought to be their initial lithium abundance."
 Although b-stars break this monotonic relationship. it is possible to sav that main-sequence stars of 1 ΛΙ. do not show significant depletion (Balachancran 1988)," Although F-stars break this monotonic relationship, it is possible to say that main-sequence stars of $>$ $M_{\odot}$ do not show significant depletion (Balachandran 1988)."
 Once the stars leave the main sequence. the surface abundance of the hotter stars depends crucially on the onset of convection.," Once the stars leave the main sequence, the surface abundance of the hotter stars depends crucially on the onset of convection."
 This vields a possible explanation of the lithium we have detected., This yields a possible explanation of the lithium we have detected.
 The secondary star in T CrD was probably initially ereater than 1.53... and although the star has become a elant. convection or dredge-up may not vet have begun.," The secondary star in T CrB was probably initially greater than $M_{\odot}$, and although the star has become a giant, convection or dredge-up may not yet have begun."
 Just such an explanation is used for the few normal giants which have almost solar abundance lithium. although most giants are. às one would expect. lithium poor (Brown et al 1989).," Just such an explanation is used for the few normal giants which have almost solar abundance lithium, although most giants are, as one would expect, lithium poor (Brown et al 1989)."
 Another explanation. of the lithium. abundance may be provided by comparison with other late-type giants., Another explanation of the lithium abundance may be provided by comparison with other late-type giants.
 Pallavicini. ltandich and Ciampapa (1992) show that coronally active Ix-giants have relatively strong lithium lines.," Pallavicini, Randich and Giampapa (1992) show that coronally active K-giants have relatively strong lithium lines."
 Although sunspots also show strong lithium. starspots alone cannot be the cause of the enhanced lithium line (Pallavicini et al 1993). and it is thought to reflect a truc abundance anomaly.," Although sunspots also show strong lithium, starspots alone cannot be the cause of the enhanced lithium line (Pallavicini et al 1993), and it is thought to reflect a true abundance anomaly."
 Phe reason for this is unclear. but ideas relate o a lack of dilferential rotation as a function of radius. would fit in with the observation that tidal locking can also inhibit lithium cepletion.," The reason for this is unclear, but ideas related to a lack of differential rotation as a function of radius, would fit in with the observation that tidal locking can also inhibit lithium depletion."
 Llowever. it should be noted tha here is observational evidence for this is very limited.," However, it should be noted that there is observational evidence for this is very limited."
 Both mechanisms should be present in T CrB. helping to explain he high lithium abundance. although it should be note hat the latest Esspectral type studied by Pallavicini et a (1992) was Ix. not. M. A final mechanism which may enhance the surface abundance is material placed. there by the nova explosion.," Both mechanisms should be present in T CrB, helping to explain the high lithium abundance, although it should be noted that the latest spectral type studied by Pallavicini et al (1992) was K, not M. A final mechanism which may enhance the surface abundance is material placed there by the nova explosion."
 Unfortunately the production. of. lithium in. novae is controversial. with estimates for the abundance in the ejecta varving from solar (Bollin et al.," Unfortunately the production of lithium in novae is controversial, with estimates for the abundance in the ejecta varying from solar (Boffin et al."
 1993) to several hundred times solar (Starrfield et al LOTS)., 1993) to several hundred times solar (Starrfield et al 1978).
 The observations may of, The observations may of
there is unresolved ancl apparently extended X-ray emission in (he central region of M 31 (TrinchierianclFabbiano1991)..,there is unresolved and apparently extended X-ray emission in the central region of M 31 \citep{M31_Trinchieri}.
 The phenomenon was later confinmed with ROSAT. aud it has become generally believed that the emission is contributed not only by faint discrete sources but also by diffuse hot plasmas (Priminietal.1993:Supper1997:IrwinandBregman1999:DorozdinPrieclhorsky 2000).," The phenomenon was later confirmed with ${\it ROSAT}$, and it has become generally believed that the emission is contributed not only by faint discrete sources but also by diffuse hot plasmas \citep{M31_Primini,M31_Supper,M31_West,M31_Irwin,M31_diffuse_Borozdin}."
. In addition to these soft X-ray imagine studies. detailed wide-band X-ray spectral studies of M 31 have been enabled with the Ginga satellite: Makishimaetal.(19500) showed that (he integrated spectrum of the whole galaxy in (he hard 220 keV enerey band cannot be represented by a power-law or a bremsstrahilung model. but can be reproduced successfully by a physical model developed for Galactic hieh-Iuminosity. low-mass X-ray binaries (hereafter LAINBs).," In addition to these soft X-ray imaging studies, detailed wide-band X-ray spectral studies of M 31 have been enabled with the ${\it Ginga}$ satellite; \citet{M31_Makishima} showed that the integrated spectrum of the whole galaxy in the hard 2–20 keV energy band cannot be represented by a power-law or a bremsstrahlung model, but can be reproduced successfully by a physical model developed for Galactic high-luminosity low-mass X-ray binaries (hereafter LMXBs)."
 This model consists ofa disk black-body (DBB) aud a black-body (BB) component. which represent emission from an opticall-thick accretion disk and a central neutron star. respectively (Mitsiidaetal.1984:Makishima19892;Asai2000) we hereafter refer to (this model as (he LAINB moclel.," This model consists of a disk black-body (DBB) and a black-body (BB) component, which represent emission from an optically-thick accretion disk and a central neutron star, respectively \citep{LMXB_Mitsuda,LMXB_Makishima,LMXB_Asai}; we hereafter refer to this model as the LMXB model."
 This result confirms that bright LAINBs are dominant above the 2 keV energy range. with the 220 keV [uminositv integrated over the whole M 31 reaching ~5x107 eres /!.," This result confirms that bright LMXBs are dominant above the 2 keV energy range, with the 2–20 keV luminosity integrated over the whole M 31 reaching $\sim 5 \times 10^{39}$ erg $^{-1}$."
 Based on these Ginga resulis. Takahashietal.(2001).. hereafter Paper 1. analvzed ihe 0.610 keV ASCA spectra integrated. over the central 12’ (2.4 kpe) radius region of AL 31.," Based on these ${\it Ginga}$ results, \citet{Takahashi}, hereafter Paper 1, analyzed the 0.6–10 keV ${\it ASCA}$ spectra integrated over the central $'$ (2.4 kpc) radius region of M 31."
 This study revealed a clear spectral excess below  1 keV when the Ginga spectral model mentioned above is extrapolated into the soft energv band., This study revealed a clear spectral excess below $\sim$ 1 keV when the ${\it Ginga}$ spectral model mentioned above is extrapolated into the soft energy band.
 This excess has been represented successfully with emission [rom two opticallv-thin thermal plasmas. of which the temperatures are ~ 0.9 keV and ~ 0.3 keV. These components are spatially extended a least over (he central 2.4 kpc radius. reinforcing (he inference from (he Γη and ROSAT images (hat some form of apparently diffuse hot plasma is distributed in the central region of M 31.," This excess has been represented successfully with emission from two optically-thin thermal plasmas, of which the temperatures are $\sim$ 0.9 keV and $\sim$ 0.3 keV. These components are spatially extended at least over the central 2.4 kpc radius, reinforcing the inference from the ${\it Einstein}$ and ${\it ROSAT}$ images that some form of apparently diffuse hot plasma is distributed in the central region of M 31."
" The spectral soft excess discovered with ,15C51 is also confirmed with PeppoS.1.X (Trinchierietal.1999)..", The spectral soft excess discovered with ${\it ASCA}$ is also confirmed with ${\it BeppoSAX}$ \citep{M31_diffuse_Trinchieri}.
 However. these results have been subject to a possibility that some fraction. if not all. of these thermal soft. X-rays are associated. with [aint discrete sources rather (han emitted by truly diffuse large-scale plasmas.," However, these results have been subject to a possibility that some fraction, if not all, of these thermal soft X-rays are associated with faint discrete sources rather than emitted by truly diffuse large-scale plasmas."
 With the advent of the Chandra aad VALAL-Neiwlon satellites. it has become possible to study the extended X-ray enission after excluding point sources down (o limiting Iuminosities of ~10? erg 5," With the advent of the ${\it Chandra}$ and ${\it XMM}$ ${\it Newton}$ satellites, it has become possible to study the extended X-ray emission after excluding point sources down to limiting luminosities of $\sim 10^{36}$ erg $^{-1}$."
 Shirevοἱal.(2001.hereafterSEAOL) actually conducted. such an analysis on the VA/A/-New/on spectra integrated over a central 5' region of M 31. first by excluding bright point sources using (he X-rav. image. and (hen modeling the contribution from unresolved [aint discrete sources by scaling the average spectrum of the bright sources.," \citet[hereafter SEA01]{M31_diffuse_Shirey}
 actually conducted such an analysis on the ${\it XMM}$ ${\it Newton}$ spectra integrated over a central $\arcmin$ region of M 31, first by excluding bright point sources using the X-ray image, and then modeling the contribution from unresolved faint discrete sources by scaling the average spectrum of the bright sources."
 Thev found only one optücallv-thin thermal plasma. of which the temperature is  0.35 keV. This result was apparently reconfirmed by Chandra ," They found only one optically-thin thermal plasma, of which the temperature is $\sim$ 0.35 keV. This result was apparently reconfirmed by ${\it Chandra}$ "
and is expelled from the dark matter halo.,and is expelled from the dark matter halo.
" The more the distance increases, the more the cloud is stretched, and there is always enough time for metals to be mixed in the primordial gas to levels consistent with our previous runs."," The more the distance increases, the more the cloud is stretched, and there is always enough time for metals to be mixed in the primordial gas to levels consistent with our previous runs."
" Finally, at the larget R, values, the cluster evolution is radically different than in the other models."," 	 	Finally, at the larget $R_s$ values, the cluster evolution is radically different than in the other models."
 The cloud is stretched as before but the resulting cluster does not leave the halo., The cloud is stretched as before but the resulting cluster does not leave the halo.
" The abundance of metals in the shock at this distance is already low, much lower than even the final cluster metallicities in many of our other runs, and while some metals are mixed into the cluster, it is very deficient compared to our other models."," The abundance of metals in the shock at this distance is already low, much lower than even the final cluster metallicities in many of our other runs, and while some metals are mixed into the cluster, it is very deficient compared to our other models."
 Figure 11 shows the evolved state for each of these models., 	 	Figure \ref{distance} shows the evolved state for each of these models.
 The panels are the same as Figure 5.., The panels are the same as Figure \ref{energy}.
 The closest halo to the galaxy is transformed into a single cluster with a total mass of 7.0x109Mo., The closest halo to the galaxy is transformed into a single cluster with a total mass of $7.0 \times 10^{5}M_\odot$.
 The intermediate distance halos form large clusters with masses of zz3.0x10?M and several other smaller clusters with velocities and positions consistent of being free from the dark matter halo., The intermediate distance halos form large clusters with masses of $\approx 3.0 \times 10^{5} M_\odot$ and several other smaller clusters with velocities and positions consistent of being free from the dark matter halo.
" Finally, the farthest halo forms two dense clusters, however the largest cluster is found at the center of the dark matter halo, and only the smaller cluster is free of the halo potential at 5 kpc from its center."," Finally, the farthest halo forms two dense clusters, however the largest cluster is found at the center of the dark matter halo, and only the smaller cluster is free of the halo potential at 5 kpc from its center."
 This suggests that there is a preferred distance from the outflow at which enriched clusters form most efficiently., 	 	This suggests that there is a preferred distance from the outflow at which enriched clusters form most efficiently.
 Too close to the outflow and the minihalo is crushed before it is enriched and too far from the outflow and the minihalo in neither enriched nor ejected from its dark matter halo., Too close to the outflow and the minihalo is crushed before it is enriched and too far from the outflow and the minihalo in neither enriched nor ejected from its dark matter halo.
 Therefore it seems that between ~3 and 7 (physical) kpc is a preferable distance from a typical starburst for the formation of compact stellar clusters., Therefore it seems that between $\approx 3$ and 7 (physical) kpc is a preferable distance from a typical starburst for the formation of compact stellar clusters.
 The observed distribution of halo globular cluster positions shows a drop-off beyond a galactocentric distance of 40 kpc (Dauphole 1996)., The observed distribution of halo globular cluster positions shows a drop-off beyond a galactocentric distance of 40 kpc (Dauphole 1996).
" After evolving these clusters, the typical distance from the galaxy is between 15-30 kpc, which agrees nicely with the observed distances."," After evolving these clusters, the typical distance from the galaxy is between 15-30 kpc, which agrees nicely with the observed distances."
 Next we explored the effect of net rotation on the evolution of the minihalo., 	 	Next we explored the effect of net rotation on the evolution of the minihalo.
" In this case, the gas was given an initial velocity according to where α is a constant, v. is the virial velocity of the cloud, R, is the virial radius, x and y are the positions within Πο, and ¢ is the rotation angle."," In this case, the gas was given an initial velocity according to where $\alpha$ is a constant, $v_c$ is the virial velocity of the cloud, $R_c$ is the virial radius, $x$ and $y$ are the positions within $R_c$, and $\phi$ is the rotation angle."
" Here, a is set at 0.05 and we vary ¢ between 0 and 90 degrees so that the halo rotates around the z-axis and x-axis respectively."," Here, $\alpha$ is set at 0.05 and we vary $\phi$ between 0 and 90 degrees so that the halo rotates around the $z$ -axis and $x$ -axis respectively."
" For this value of α we can calculate the spin parameter of our halos using the form from Bullock (2001b), N= where UgJ is the angular momentum of the halo with mass M,;, contained in a sphere of radius Ri, and has a circular velocity of νι."," For this value of $\alpha$ we can calculate the spin parameter of our halos using the form from Bullock (2001b), = where J is the angular momentum of the halo with mass $_{\rm vir}$ contained in a sphere of radius $_{\rm vir}$ and has a circular velocity of $_{\rm vir}$ ."
" For the halos studied this gives a spin parameter of λ'=0.023, which is within 1 σ of the mean value of Aj, — 0.035."," For the halos studied this gives a spin parameter of $\lambda' = 0.023$, which is within 1 $\sigma$ of the mean value of $\lambda_0'$ = 0.035."
 Figure 12 compares the simulations at the final time., Figure \ref{smerge} compares the simulations at the final time.
 It is obvious that neither the spin direction nor the magnitude of the spin changes the final distribution., It is obvious that neither the spin direction nor the magnitude of the spin changes the final distribution.
" In all cases the cloud is stretched into a ribbon along the x-axis, the primordial gas is enriched to nearly constant value near 1072? Zo, and the cluster is cooled to a few hundred degrees K. The reason for this insensitivity to A' is a result of the shock itself."," In all cases the cloud is stretched into a ribbon along the $x$ -axis, the primordial gas is enriched to nearly constant value near $^{-2.0}$ $_{\odot},$ and the cluster is cooled to a few hundred degrees K. The reason for this insensitivity to $\lambda'$ is a result of the shock itself."
" As the shock advances toward the halo it begins to develop vorticity, defined as @=VxV, which evolves as 28zaVpxVp, where v is the velocity, p is the density, and p is the pressure."," As the shock advances toward the halo it begins to develop vorticity, defined as $\vec{\omega} \equiv \vec{\triangledown} \times \vec{v},$ which evolves as $\frac{D\vec{\omega}}{Dt} \approx \frac{1}{\rho^2} \vec{\triangledown} \rho \times \vec{\triangledown} p $, where $v$ is the velocity, $\rho$ is the density, and $p$ is the pressure."
" Physically, this baroclinic source term is a measure of the generation of vorticity due to the mismatch between the gradients of pressure and density (Glasner 1997)."," Physically, this baroclinic source term is a measure of the generation of vorticity due to the mismatch between the gradients of pressure and density (Glasner 1997)."
" Since the shock is not aligned with the density gradient of the halo, this term is large throughout the simulation and vorticity begins to grow rapidly."," Since the shock is not aligned with the density gradient of the halo, this term is large throughout the simulation and vorticity begins to grow rapidly."
 Figure 13. shows the z-component of vorticity as the shock heads toward the halo., Figure \ref{vort} shows the $z$ -component of vorticity as the shock heads toward the halo.
 By the time they meet the magnitude of the vorticity is much greater than the spin of the halo., By the time they meet the magnitude of the vorticity is much greater than the spin of the halo.
" In fact, the vorticity would be much greaterthan the spin of the halo even if we had chosen an a of 1.0."," In fact, the vorticity would be much greaterthan the spin of the halo even if we had chosen an $\alpha$ of 1.0."
supported. by a Marie-C'urie-Fellowship of the European Commission.,supported by a Marie-Curie-Fellowship of the European Commission.
 This paper is based on observations mace with the VLT and on data obtained from the LIST data archive., This paper is based on observations made with the VLT and on data obtained from the HST data archive.
"the sealing (1+2)°°="""""" measured by Le Floch et al. (2005))",the scaling $(1+z)^{3.9\pm0.7}$ measured by Le Floc'h et al. \cite{lefloch05}) )
 to zo| for ym-selected galaxies.," to $z\sim 1$ for $\,\mu$ m-selected galaxies."
 One of the key goals of H-ATLAS will be to understand the nature of the evolution detected in this letter., One of the key goals of H-ATLAS will be to understand the nature of the evolution detected in this letter.
 In turn. we aim to improve our understanding of the evolutionary link between high redshift and local submm systems.," In turn, we aim to improve our understanding of the evolutionary link between high redshift and local submm systems."
 This letter has only considered sources selected at jm. merely one of the five wavebands on offer from H-ATLAS.," This letter has only considered sources selected at $\,\mu$ m, merely one of the five wavebands on offer from H-ATLAS."
 Furthermore. the ddeg of survey data analysed in this work represent only of the final. proposed H-ATLAS survey area.," Furthermore, the $^2$ of survey data analysed in this work represent only of the final, proposed H-ATLAS survey area."
 A repeat of the analysis presented here with the final survey data. would therefore result in the quoted uncertainties falling by at least a factor of five.," A repeat of the analysis presented here with the final survey data, would therefore result in the quoted uncertainties falling by at least a factor of five."
 In light of these considerations. it is clear that our results offer only a small glimpse of the anticipated wealth of science that H-ATLAS has to offer.," In light of these considerations, it is clear that our results offer only a small glimpse of the anticipated wealth of science that H-ATLAS has to offer."
been lacking.,been lacking.
 In order to address this. the PLaN-D working was formed to co-ordinate the investigative elfort.," In order to address this, the PLaN-B working was formed to co-ordinate the investigative effort."
 Spatio-kinematic modelling is an important tool in the testing of theoretical models. providing 3-D. morphologies and orientations. as well as the velocity field of the outflows and their kinematical ages. all of which must be replicated theoretically.," Spatio-kinematic modelling is an important tool in the testing of theoretical models, providing 3-D morphologies and orientations as well as the velocity field of the outflows and their kinematical ages, all of which must be replicated theoretically."
 Actelitionally. for those PNe with well constrained. binary systems. one can compare the parameters of the central binarics to those of their host nebulae. in particular the theoretical prediction. that the nebular symmetry axis will lie perpendicular to the orbital plane of the binary system (?)..," Additionally, for those PNe with well constrained binary systems, one can compare the parameters of the central binaries to those of their host nebulae, in particular the theoretical prediction that the nebular symmetry axis will lie perpendicular to the orbital plane of the binary system \citep{nordhaus06}."
" Sp 1 (a=I15""51""AL. 8—5173123"". J2000). discovered ον νι was described as “nearly perfectly circular in appearance by ο (7. see Fig. 1))."," Sp 1 $\alpha=15^{h}51^{m} 41^{s}$, $\delta=-51\degr 31' 23''$, J2000), discovered by \citet{shapley36}, was described as “nearly perfectly circular” in appearance by \citeauthor{bond90} \citeyear{bond90}, see Fig. \ref{Sp1_image}) )."
 This apparent morphology is somewhat at. odes with presence. of a binary central star. discovered. spectroscopically by ο and confirmed. photometrically by 2.. which would be expected to produce an aspherical nebula.," This apparent morphology is somewhat at odds with presence of a binary central star, discovered spectroscopically by \citet{mendez88} and confirmed photometrically by \citet{bond90}, which would be expected to produce an aspherical nebula."
 However. this can be reconciled. by the hypothesis that Sp 1 is actually an axisvmmetrie nebula viewed almost. pole-on. making Sp 1 morphologically akin to other PNe with known close-binary central stars (A 63: 7: A 41: ?: NOGC6337: ?: LaIr 4: ?)).," However, this can be reconciled by the hypothesis that Sp 1 is actually an axisymmetric nebula viewed almost pole-on, making Sp 1 morphologically akin to other PNe with known close-binary central stars (A 63: \citealp{mitchell07b}; A 41: \citealp{jones10b}; NGC6337: \citealp{garcia-diaz09}; HaTr 4: \citealp{tyndall11b}) )."
" This interpretation is supported. by the low amplitude of the photometric variations of the central star ancl the absence of an eclipse"" (?)..", This interpretation is “ supported by the low amplitude of the photometric variations of the central star and the absence of an eclipse” \citep{bond90}.
 Recent work by ? and LHillwig et al. (, Recent work by \citet{bodman11} and Hillwig et al. (
in preparation) photometrically confirms the 2.9 day period of ?.. and indicates that the binary. plane does indeed lic very close to the plane of the sky (10°27207 2).,"in preparation) photometrically confirms the 2.9 day period of \citealt{bond90}, and indicates that the binary plane does indeed lie very close to the plane of the sky $10\degr\geq i \geq 20\degr$ )."
 Indeed. it has been proposed that many rine-like PNe may be bipolars with svmmetry axes inclined to the plane of the skv: this suggestion is supported by kinematical stuclics ol several rine-like PNe. all of which are found to be bipolar. e.g. the Ring Nebula (2).. Lolr 5 (2).. the Helix Nebula (?).. SBW 1(?) and SuWt 2(?)..," Indeed, it has been proposed that many ring-like PNe may be bipolars with symmetry axes inclined to the plane of the sky; this suggestion is supported by kinematical studies of several ring-like PNe, all of which are found to be bipolar, e.g. the Ring Nebula \citep{bryce94}, LoTr 5 \citep{graham04}, the Helix Nebula \citep{meaburn05b}, SBW 1 \citep{smith07} and SuWt 2 \citep{jones10a}."
 Despite the importance of Sp 1 as a test of current understanding of how close-binaries alleet the morphological evolution of PNe. until now. there have been no kinematical observations of the nebula in order to constrain its three dimensional structure.," Despite the importance of Sp 1 as a test of current understanding of how close-binaries affect the morphological evolution of PNe, until now, there have been no kinematical observations of the nebula in order to constrain its three dimensional structure."
 Detailed imagery ancl hieh-resolution longslit spectroscopy are thus presented. in order to determine the true. morphology of Sp 1., Detailed imagery and high-resolution longslit spectroscopy are thus presented in order to determine the true morphology of Sp 1.
 The nebula morphology and orientation are then compared to that of the central binary in order to ascertain their relationship and test current theories of binarv-induced PN shaping., The nebula morphology and orientation are then compared to that of the central binary in order to ascertain their relationship and test current theories of binary-induced PN shaping.
 Deep narrow-band aand imagery of Sp I was obtained using the ESO (european Southern Observatory) Multi-Mocde Instrument. (EEMMLE: ?7)) on the 3.6-m ESO New Technology Telescope (NTE). and is shown in Fig. 1..," Deep narrow-band and imagery of Sp 1 was obtained using the ESO (European Southern Observatory) Multi-Mode Instrument (EMMI; \citealp{dekker86}) ) on the 3.6-m ESO New Technology Telescope (NTT), and is shown in Fig. \ref{Sp1_image}."
 Phe 1200-5 image (Pig. L((, The 1200-s image (Fig. \ref{Sp1_image}( (
a)) was taken on 1995 April 22 with a seeing of aand shows the nebula as a dilfuse ring in the plane of the sky. upon which. bright filaments are superimposed.,"a)) was taken on 1995 April 22 with a seeing of and shows the nebula as a diffuse ring in the plane of the sky, upon which, bright filaments are superimposed."
 The filaments give the appearance of two bright. narrow rings.," The filaments give the appearance of two bright, narrow rings."
 It is not clear whether they are two concentric rings or two rings that are olfset in the east-west direction., It is not clear whether they are two concentric rings or two rings that are offset in the east-west direction.
 The filaments appear to intersect in the south of the nebula. but there is no obvious counterpart in the north. whieh would be expected if they are two ollset rings.," The filaments appear to intersect in the south of the nebula, but there is no obvious counterpart in the north, which would be expected if they are two offset rings."
 Both rings are brighter in the west of the nebula than the east., Both rings are brighter in the west of the nebula than the east.
 Diffuse material is present in the innermost region of the nebula and à very faint outer “halo” is visible surrounding the bright nebular shell., Diffuse material is present in the innermost region of the nebula and a very faint outer “halo” is visible surrounding the bright nebular shell.
 The 900-5 image (Eig. I((, The 900-s image (Fig. \ref{Sp1_image}( (
"b)). taken on 2005 March. 03 with a seeing of0.9""... shows the same bright ring-like filaments. however. the diffuse material visible close to the central star appears brighter in tthan inA.","b)), taken on 2005 March 03 with a seeing of, shows the same bright ring-like filaments, however, the diffuse material visible close to the central star appears brighter in than in."
. The limage is also shown atA low-contrast in Fie., The image is also shown at low-contrast in Fig.
 lee to reveal. for the first time. à prominent bowshock to the west of Sp 1.," \ref{Sp1_image}c c to reveal, for the first time, a prominent bowshock to the west of Sp 1."
 The origin of this bowshock is cliscussecl in Section 3.2.., The origin of this bowshock is discussed in Section \ref{sec:ISM}.
 Spatially resolved. longslit emission-line spectra of Sp 1 were been obtained with IZMMIE on the NT.," Spatially resolved, longslit emission-line spectra of Sp 1 were been obtained with EMMI on the NTT."
 Observations took place in 2005 March. 2-4 using the red arm of the spectrograph which employs two MET/LL. CCDs. cach of 2048 4096 15 pm pixels (= pper pixel).. in a mosaic.," Observations took place in 2005 March 2-4 using the red arm of the spectrograph which employs two MIT/LL CCDs, each of 2048 $\times$ 4096 15 $\mu$ m pixels $\equiv$ per pixel), in a mosaic."
 There is a gap of 47 pixels (=7.82” ) between the two CCD chips which can be seen in the observed spectra., There is a gap of 47 pixels $\equiv 7.82\arcsec$ ) between the two CCD chips which can be seen in the observed spectra.
 IMMLE was used in single order echelle moce. with erating #110 and a narrow-band [filter 596) to isolate the ST! echelle order containing the aand cemission lines.," EMMI was used in single order echelle mode, with grating 10 and a narrow-band filter 596) to isolate the $87^{\rm{th}}$ echelle order containing the and emission lines."
 Binning of was used giving spatial and spectral scales of pper pixel and pper pixel. respectively.," Binning of was used giving spatial and spectral scales of per pixel and per pixel, respectively."
 Phe slit had a length of and width +))., The slit had a length of and width ).
 All integrations were of 1800. s duration and the seeing never exceeded., All integrations were of 1800 s duration and the seeing never exceeded.
 Data reduction was performed using software., Data reduction was performed using software.
 The spectra. were bias-correeted and cleaned of cosmic ravs., The spectra were bias-corrected and cleaned of cosmic rays.
 The spectra were then wavelength calibrated. against a long exposure Thr emission lamp. taken at the start of cach night.," The spectra were then wavelength calibrated against a long exposure ThAr emission lamp, taken at the start of each night."
 The calibration was confirmed. using short Ne emission lamp exposures throughout the night. and by checking the wavelengths of skvlines visible in the exposure.," The calibration was confirmed using short Ne emission lamp exposures throughout the night, and by checking the wavelengths of skylines visible in the exposure."
 Finally the data were rescaled to a linear velocity scale (relative to the rest wavelength of ttaken to be 6562.81. A)) ancl corrected. for. LHeliocentric velocity., Finally the data were rescaled to a linear velocity scale (relative to the rest wavelength of taken to be $6562.81$ ) and corrected for Heliocentric velocity.
 Five slit positions were obtained with the slit orientated east-west across Sp 1 (numbered 1 to 5) and [four slit positions with the slit positioned in a north-south direction (number 6 to 9)., Five slit positions were obtained with the slit orientated east-west across Sp 1 (numbered 1 to 5) and four slit positions with the slit positioned in a north-south direction (number 6 to 9).
 The slit positions are shown on the image of Sp 1 in Fig. 1a, The slit positions are shown on the image of Sp 1 in Fig. \ref{Sp1_image}( (
) (Note that the full extent of the slits is not shown).,a) (Note that the full extent of the slits is not shown).
 The fully reduced. position-velocity, The fully reduced position-velocity
emission suggesting the OH emission arises from lower density material than towards IRAS 20126+4104 (Cragg et al.2002).,emission suggesting the OH emission arises from lower density material than towards IRAS $20126+4104$ (Cragg et al.2002).
" We have used MERLIN to study the immediate vicinity of IRAS 20126+4104 at high angular resolution and have shown that the 1665 MHz OH. aand mmasers towards this source all originate within ~0.5"" (850 AU) of the central source."," We have used MERLIN to study the immediate vicinity of IRAS $20126+4104$ at high angular resolution and have shown that the 1665 MHz OH, and masers towards this source all originate within $\sim0.5''$ (850 AU) of the central source."
 The OH masers have an elongated distribution. tracing part of a disk of material around the source which is orthogonal to the axis of the jet from the soure.," The OH masers have an elongated distribution, tracing part of a disk of material around the source which is orthogonal to the axis of the jet from the soure."
 We could identify one Zeeman pair of OH masers which indicates a magnetic field of strength ~11 mG in this disk., We could identify one Zeeman pair of OH masers which indicates a magnetic field of strength $\sim$ 11 mG in this disk.
 The velocity structure of the OH masers ts consistent with Keplerian motion around a central source of «10M..., The velocity structure of the OH masers is consistent with Keplerian motion around a central source of $\stackrel{<}{\sim}$ 10.
 The methanol masers are intermingled with the north-western part of the OH maser distribution and are at velocities intermediate between the north-western OH masers and those to the south-east., The methanol masers are intermingled with the north-western part of the OH maser distribution and are at velocities intermediate between the north-western OH masers and those to the south-east.
 Our observations confirm the close association of OH and methanol masers., Our observations confirm the close association of OH and methanol masers.
 We suggest that the high methanol (and OH) column densities necessary for the maser emission may result from the release of mantles from the dust grains in the surface layers of the circumstellar disk as the disk material has been heated by the central young star or as the stellar wind has shocked the disk material., We suggest that the high methanol (and OH) column densities necessary for the maser emission may result from the release of mantles from the dust grains in the surface layers of the circumstellar disk as the disk material has been heated by the central young star or as the stellar wind has shocked the disk material.
 The mmasers have significantly varied since they were last observed at high angular resolution., The masers have significantly varied since they were last observed at high angular resolution.
 We detect only one of the three clusters previously seen., We detect only one of the three clusters previously seen.
 Although the mmasers detected are close to the location central source. as was seen in the previous observation. the maser spots have a considerably different spatial and kinematic structure to those previously measured.," Although the masers detected are close to the location central source, as was seen in the previous observation, the maser spots have a considerably different spatial and kinematic structure to those previously measured."
 In particular the detailed model proposed by MCR for the mmasers arising at the survey an outflow cavity fails to acount for the velocities and locations of the current spots., In particular the detailed model proposed by MCR for the masers arising at the survey an outflow cavity fails to acount for the velocities and locations of the current spots.
 These observations show that. at least for this source. the three common types of maser associated with young high mass stars probe different components of the circumstellar environment allowing a coherent view of the circumstellar regions to be constructed.," These observations show that, at least for this source, the three common types of maser associated with young high mass stars probe different components of the circumstellar environment allowing a coherent view of the circumstellar regions to be constructed."
" The OH masers provide a measurement of the magnetic field in the circumstellar disk within ~ SOOAU of a young high mass star,", The OH masers provide a measurement of the magnetic field in the circumstellar disk within $\sim500$ AU of a young high mass star.
 We thank Peter Hofner for providing us with the 3.6cm map. and Riccardo Cesaroni. Malcolm. Gray and Anita Richards for useful communication.," We thank Peter Hofner for providing us with the 3.6cm map, and Riccardo Cesaroni, Malcolm Gray and Anita Richards for useful communication."
 MERLIN ts a national facility operated by the University of Manchester at Jodrell Bank Observatory on behalf of PPARC., MERLIN is a national facility operated by the University of Manchester at Jodrell Bank Observatory on behalf of PPARC.
was discovered. with the (EENOSAT. ?)) in 1985.,"was discovered with the (EXOSAT, \citealt{pawhgi1985}) ) in 1985."
 Soon after the discovery. the detection. of type I Nay. bursts. from. the source (2). marked it as à Galactic low-mass X-ray binary (LAINDB) where a neutron star (INS) is accreting matter from a low-mass companion star.," Soon after the discovery, the detection of type I X-ray bursts from the source \citep{gohapa1986} marked it as a Galactic low-mass X-ray binary (LMXB) where a neutron star (NS) is accreting matter from a low-mass companion star."
 Many LMXNDs are known to be transient. alternating periods of quiescence at a relatively low X-ray. luminosity (7107 tin a 05-10 keV. range) with month to vear-long bright X-ray outbursts (107 1075 19).," Many LMXBs are known to be transient, alternating periods of quiescence at a relatively low X-ray luminosity $\sim$ $^{32}$ in a 0.5-10 keV range) with month to year-long bright X-ray outbursts $^{36}-$ $^{38}$ )."
 has been continuously in outburst for the 24 vears since its discovery: tens of vears-long X-ray outbursts have been observed from a number of LAINBs. e.g. WS 1731-260 (2).. GRS | 105 and 4U 348 (sce ? or a review).," has been continuously in outburst for the 24 years since its discovery: tens of years-long X-ray outbursts have been observed from a number of LMXBs, e.g. KS 1731-260 \citep{2001ApJ...560L.159W}, GRS $+$ 105 and 4U $-$ 338 (see \citealt{2006ARA&A..44...49R} for a review)."
 During outbiusts mass aceretion proceeds at a high rate forming an extended. aceretion disc around je accreting compact object., During outbursts mass accretion proceeds at a high rate forming an extended accretion disc around the accreting compact object.
 X-rays are emitted from the innermost regions. whereas the optical originates further out in the disk.," X-rays are emitted from the innermost regions, whereas the optical originates further out in the disk."
 In. LAIXDs the cise dominates the optical Dux uring outbursts. outshining he low-mass companion star.," In LMXBs the disc dominates the optical flux during outbursts, outshining the low-mass companion star."
 The latter can become visibk' during quiescence. when the ise is less bright.," The latter can become visible during quiescence, when the disc is less bright."
 A few LAINBs are. known wiere the NS is detected. as a pulsar (2). but for the majoritv of them the companion star is the onlv viable source of infmation regarding the svsteni dynamics., A few LMXBs are known where the NS is detected as a pulsar \citep{2005AIPC..797...71C} but for the majority of them the companion star is the only viable source of information regarding the system dynamics.
 Optical spectroscoov of the companion star can be used to measure the orital parameters and.under," Optical spectroscopy of the companion star can be used to measure the orbital parameters and,under"
launching power of the jets. The first term describes the rest energy. of the accreting matter on to the BIE and the second. term. describes the energy transfer from the rotating DII to the disc inside the ergosphere.,"launching power of the jets, The first term describes the rest energy of the accreting matter on to the BH and the second term describes the energy transfer from the rotating BH to the disc inside the ergosphere."
" £, and £4, are the specific energy. of the gas particle (eq. 13))", $E^{\dagger}_{\mathrm{sl}}$ and $E^{\dagger}_{\mathrm{ms}}$ are the specific energy of the gas particle (Eq. \ref{eq:spenergy}) )
 evaluated at the stationary limit. surface and at the innermost stable orbit. respectively.," evaluated at the stationary limit surface and at the innermost stable orbit, respectively."
 Using Eq. (143)).," Using Eq. \ref{eq:li}) ),"
 we obtain the launching power of the Jets as where the angular velocities of the BII and the accretion disc. respectively. are To caleulate the launching power of the jets. we need to evaluate both Wy and αμdi).," we obtain the launching power of the jets as where the angular velocities of the BH and the accretion disc, respectively, are To calculate the launching power of the jets, we need to evaluate both $\Psi_{\mathrm{D}}$ and $( -dR_{\mathrm{H}}/dr)$."
 First. we write the maenetic [ux that threads the accretion disc surface. where By is the poloidal component of the magnetic field that threads the disc.," First, we write the magnetic flux that threads the accretion disc surface, where $B_{\mathrm{D}}$ is the poloidal component of the magnetic field that threads the disc."
 The surface area between two equatorial surfaces in a Ixerr space-time can be calculated from where the determinant of the surface metric is This result. follows from Eqs. (1). (22).," The surface area between two equatorial surfaces in a Kerr space-time can be calculated from where the determinant of the surface metric is This result follows from Eqs. \ref{eq:metric2}) ), \ref{eq:coeff1}) ),"
 and (3))., and \ref{eq:coeff2}) ).
 With these. the surface area in Eq. (21))," With these, the surface area in Eq. \ref{eq:arie}) )"
 reads The poloidal component of the magnetic field. that threads the DII horizon By and the poloidal component of the magnetic field. at the inner edge of the accretion disc Bola.) can be of the same order (e.g..2) and related by On the other hand. the poloidal component of the magnetic ficld that threads the accretion disc surface scales as rU. where 0«n3 (2)..," reads The poloidal component of the magnetic field that threads the BH horizon $B_{\mathrm{H}}$ and the poloidal component of the magnetic field at the inner edge of the accretion disc $B_{\mathrm{D}}(r_{\mathrm{ms}})$ can be of the same order \cite[e.g.,][]{livio} and related by On the other hand, the poloidal component of the magnetic field that threads the accretion disc surface scales as $B_{\mathrm{D}}\propto r^{-n}$ , where $0 < n < 3$ \citep{bland76}."
" Consequently. Since the DII horizon behaves. in some aspects. like a rotating conducting surface (c.g..22?7).. it can be thought ol as being a ""battery driving currents around a circuit."," Consequently, Since the BH horizon behaves, in some aspects, like a rotating conducting surface \cite[e.g.,][]{carter73,damour,znajek78,membrane}, it can be thought of as being a `battery' driving currents around a circuit."
 The energy for this comes from the BIL rotation (2).., The energy for this comes from the BH rotation \citep{znajek78}.
 Phe internal resistance of the battery in the horizon. Le. the resistance between two magnetic surfaces that thread the horizon.is where Ry=4trfe377 ohm. df is the horizon distance between two magnetic surfaces (see Fig. 1)).," The internal resistance of the battery in the horizon, i.e., the resistance between two magnetic surfaces that thread the horizon,is where $R_{\mathrm{H}}=4\pi/c =377$ ohm, $dl$ is the horizon distance between two magnetic surfaces (see Fig. \ref{fig:jetBlack}) ),"
 22rg is the evlindrical circumference ator =rg and rg—rella:)77]χαο=rargs ds. the radius.of⋅ the DII horizon⊀ (?)..EN, $2\pi r_{\mathrm{H}}$ is the cylindrical circumference at $r=r_{\mathrm{H}}$ and $r_{\mathrm{H}}=r_{\mathrm{g}}[1+(1-a_*^2)^{1/2}] = r_{\mathrm{g}} r_{\mathrm{H*}}$ is the radiusof the BH horizon \citep{membrane}.
 The voltage dillerence. generated by the DII. has a maximum magnitude of 1—OyWy. where Wy=Byely is the magnetic Dux threading the BII and ely=Szrarg is the surface area of the DII.," The voltage difference generated by the BH has a maximum magnitude of $V = \Omega_{\mathrm{H}} \Psi_{\mathrm{H}}$, where $\Psi_{\mathrm{H}} = B_{\mathrm{H}}A_{\mathrm{H}}$ is the magnetic flux threading the BH and $A_{\mathrm{H}} = 8\pi r_{\mathrm{g}}r_{\mathrm{H}}$ is the surface area of the BH."
 Assuming that the magnetic field is carried into the BLL by the accreted disc gas. we set the BIL potential crop to the energy of the gas particles carried into the BIL. the latter being the particle specific energy at the innermost stable orbit.," Assuming that the magnetic field is carried into the BH by the accreted disc gas, we set the BH potential drop to the energy of the gas particles carried into the BH, the latter being the particle specific energy at the innermost stable orbit."
" Suppose that during a first epoch. the DII accretes at a rate approximately equal to the Edelington ""This supposition provides i=μμ..."," Suppose that during a first epoch, the BH accretes at a rate approximately equal to the Eddington This supposition provides $V^2 = {\dot{M}}_{\mathrm{acc}}E^{\dagger}_{\mathrm{ms}}c^2$."
 Therefore. the maximum value of the magnetic [field that threads the BI horizon is where dsjay0.9082 is the DIL limiting spin in the case of a racliatively ellicient accretion disc (?).. and the corresponding particle specific energy at. the innermost stable orbit is ζω=0.6759.," Therefore, the maximum value of the magnetic field that threads the BH horizon is where $a_{\mathrm{*,lim}} = 0.9982 $ is the BH limiting spin in the case of a radiatively efficient accretion disc \citep{t74}, and the corresponding particle specific energy at the innermost stable orbit is $E^{\dagger}_{\mathrm{ms,lim}}= 0.6759$."
 Although this limit of the DII spin may. beμι even closer to its maximum value (s~l. it produces a negligible variation in the maximum value of the BIL magnetic field.," Although this limit of the BH spin may be even closer to its maximum value $a_* \sim 1$, it produces a negligible variation in the maximum value of the BH magnetic field."
 Using the expression of the eravitational radius. the maximum value of the magnetic field that threads the BLE horizon (leq. 27))," Using the expression of the gravitational radius, the maximum value of the magnetic field that threads the BH horizon (Eq. \ref{eq:magn}) )"
 becomes Or This result is similar to the calculation performed. bv. 2.. , becomes or This result is similar to the calculation performed by \citet{znajek78}. [
See also ?.],See also \citet{lovelace}. .]
 The only difference is that we set the BL »otential drop to the specific energy of the particles at the innermost stable orbit. whereas ? makes use of the fac hat the Eddington luminosity sets an upper bound on the radiation pressure (as the dise is racatively cllicicnt). anc hus M~ Lect.," The only difference is that we set the BH potential drop to the specific energy of the particles at the innermost stable orbit, whereas \citet{znajek78} makes use of the fact that the Eddington luminosity sets an upper bound on the radiation pressure (as the disc is radiatively efficient), and thus $V^2 \sim L_{\mathrm{Edd}}$ ."
 The continuum of the magnetic field within a narrow strip between two magnetic surfaces. which connect the BL ο the disc inside the ergosphere. dWy=di (e.g. 7).. gives," The continuum of the magnetic field within a narrow strip between two magnetic surfaces, which connect the BH to the disc inside the ergosphere, $d\Psi_{\mathrm{H}}=d\Psi_{\mathrm{D}}$ \cite[e.g.,][]{wang}, gives"
(his image is mapped back onto the individual input exposures ancl subtiracted. residuals of approximately peak are found under the stellar image.,"this image is mapped back onto the individual input exposures and subtracted, residuals of approximately peak are found under the stellar image."
 These small but measureable errors are most likely caused by temporal variations in the PSF produced by the change in (he insolation of the telescope as it orbits the earth., These small but measureable errors are most likely caused by temporal variations in the PSF produced by the change in the insolation of the telescope as it orbits the earth.
 ILere. the residuals on the bright star were not improved by going bevond a few iterations.," Here, the residuals on the bright star were not improved by going beyond a few iterations."
 As noted in the discussion of the method. iDrizzle will converge exactly in the absence of noise.," As noted in the discussion of the method, iDrizzle will converge exactly in the absence of noise."
 In the presence of noise. however. successive iterations eventually lose their ability {ο improve (he image as (he power in (he statistical noise overwhelms any systematic errors caused by the [ailure to converge to the correct underlving band-limited function.," In the presence of noise, however, successive iterations eventually lose their ability to improve the image as the power in the statistical noise overwhelms any systematic errors caused by the failure to converge to the correct underlying band-limited function."
 For example. (he noise in the combined image tested in left-hand side of Figure 10 is dominated bv the Poisson noise of the bright stars in (he original exposures.," For example, the noise in the combined image tested in left-hand side of Figure \ref{UDF} is dominated by the Poisson noise of the bright stars in the original exposures."
" This statistical noise limits (he convergence of the method. and prevents (he complete removal of (he faint ""ringing seen surrounding the centers of the (subtracted) point sources."," This statistical noise limits the convergence of the method, and prevents the complete removal of the faint “ringing” seen surrounding the centers of the (subtracted) point sources."
 This is because two pixels from two different images may lie verv close (o one another on the sky. but have very clifferent noise values.," This is because two pixels from two different images may lie very close to one another on the sky, but have very different noise values."
 Thus. the noise breaks (he assumption that the data is truly baid-dIimited. ancl (he effect of (his is most apparent in the Poisson noise of brisht point sources.," Thus, the noise breaks the assumption that the data is truly band-limited, and the effect of this is most apparent in the Poisson noise of bright point sources."
 However. the ringing in the image is only ~1x10.! of peak and is limited to a radius a few times the full-width at hall-maximun (FWIIM) of the PSF.," However, the ringing in the image is only $\sim 1 \times 10^{-4}$ of peak and is limited to a radius a few times the full-width at half-maximum (FWHM) of the PSF."
 Without the subtraction of the original point source. (he ringing is not visible.," Without the subtraction of the original point source, the ringing is not visible."
 The test shown on the left-hand side of Figure I0. was conducted using twelve simulated ACS images [rom UST with random sub-pixel dithers., The test shown on the left-hand side of Figure \ref{UDF} was conducted using twelve simulated ACS images from HST with random sub-pixel dithers.
 Good subtractions were seen with ihe ACS PSF and sampling with as few as eight random positions., Good subtractions were seen with the ACS PSF and sampling with as few as eight random positions.
 When the same test was repeated with simulated WEPC? images. which are widersamplec (o a far greater degree. a minimum of twelve random positions was required belore one saw good convergence.," When the same test was repeated with simulated WFPC2 images, which are undersampled to a far greater degree, a minimum of twelve random positions was required before one saw good convergence."
 At (he sanie lime. eightορ placed dithers eave excellent results using WEDPC? sampling.," At the same time, eight placed dithers gave excellent results using WFPC2 sampling."
 The ability of iDrizzle to accurately reproduce the PSF will depend on the ratio of the EWIIM ol the PSF to the size of the detector pixels. the number of samples that are available. ancl the pattern of those samples.," The ability of iDrizzle to accurately reproduce the PSF will depend on the ratio of the FWHM of the PSF to the size of the detector pixels, the number of samples that are available, and the pattern of those samples."
 Additionally. because the removal of the svstematice or pattern errors can be limited by the statistical noise power. deeper integrations will not only improve (he statistical errors. (hey will also generally improve (he svstematic fidelity of the images.," Additionally, because the removal of the systematic or pattern errors can be limited by the statistical noise power, deeper integrations will not only improve the statistical errors, they will also generally improve the systematic fidelity of the images."
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by additional galaxies whose dark matter haloes are sphericallv-svmuimetric.,by additional galaxies whose dark matter haloes are spherically-symmetric.
 This second. set. of Monte. Carlo. simulations is constructed as follows., This second set of Monte Carlo simulations is constructed as follows.
 An elliptical lens of fixed mass axis ratio. f. is placed at the origin of the coordinate system.," An elliptical lens of fixed mass axis ratio, $f$, is placed at the origin of the coordinate system."
 Llere fois the axis ratio of the projected dark matter halo., Here $f$ is the axis ratio of the projected dark matter halo.
 The elliptical lens is assigned a random position angle and a redshift. σι crawn from the redshift. distribution adopted for the D'ECH0 objects with apparent. magnitudes IS<figx20.," The elliptical lens is assigned a random position angle and a redshift, $z_{el}$, drawn from the redshift distribution adopted for the BTC40 objects with apparent magnitudes $18 \le I_{AB} \le 20$."
 The elliptical lens is assigned an intrinsic. Iuminous galaxy shape drawn from equation (7) above. and the intrinsic position angle of the luminous lens galaxy is taken to be the position angle of its dark matter halo.," The elliptical lens is assigned an intrinsic, luminous galaxy shape drawn from equation (7) above, and the intrinsic position angle of the luminous lens galaxy is taken to be the position angle of its dark matter halo."
 A source galaxy is placed. randomly along the horizontal axis ofthe coordinate svstem. such that it lies within a distance ol £30” of the elliptical lens.," A source galaxy is placed randomly along the horizontal axis of the coordinate system, such that it lies within a distance of $\pm 30''$ of the elliptical lens."
" Phe source galaxy is assigned a fixed redshift. 2,= 0.6."," The source galaxy is assigned a fixed redshift, $z_s = 0.6$ ."
" Next. a circle of radius 60"". centred on the elliptical lens. is populated with additional galaxy lenses whose haloes are taken to be singular isothermal spheres (SUS)."," Next, a circle of radius $60''$, centred on the elliptical lens, is populated with additional galaxy lenses whose haloes are taken to be singular isothermal spheres (SIS)."
 The number density of the SIS lenses is matched to the observed number density of galaxies with apparent magnitudes 18xLie20 in the D'TCHO data. and they are assigned random locations within the field.," The number density of the SIS lenses is matched to the observed number density of galaxies with apparent magnitudes $18 \le I_{AB} \le 20$ in the BTC40 data, and they are assigned random locations within the field."
 Lach SIS lens is assigned a redshift. based upon its apparent magnitude. again drawn from our adopted probability. distribution.," Each SIS lens is assigned a redshift based upon its apparent magnitude, again drawn from our adopted probability distribution."
 The elliptical lens is assigned a velocity dispersion. a. and truncation radius. ary.," The elliptical lens is assigned a velocity dispersion, $\sigma_v$, and truncation radius, $x_t$."
 bor simplicity. the SIS. lenses are assigned a velocity dispersion. equal to the velocity dispersion that is assigned. to the elliptical lens.," For simplicity, the SIS lenses are assigned a velocity dispersion equal to the velocity dispersion that is assigned to the elliptical lens."
 Having assigned positions. redshifts. and gravitational potentials to all of the lenses. then. the net shear experienced. by the source is computed as the sum of the individual shears due to all lenses (elliptical and SIS) with redshifts z;«0.6.," Having assigned positions, redshifts, and gravitational potentials to all of the lenses, then, the net shear experienced by the source is computed as the sum of the individual shears due to all lenses (elliptical and SIS) with redshifts $z_l < 0.6$."
 In addition. the final image shape of the lens galaxy residing within the elliptical dark matter halo is computed using the net shear due to all foreground. SIS lenses (1.0... SIS lenses with 2p<n4).," In addition, the final image shape of the lens galaxy residing within the elliptical dark matter halo is computed using the net shear due to all foreground SIS lenses (i.e., SIS lenses with $z_l < z_{el}$ )."
" The above procedure is repeated: 20 million times for a fixed axis ratio. f. of the halo of the elliptical lens. fixed values of o, and ο and. fixed. source redshift. ος=0.6."," The above procedure is repeated 20 million times for a fixed axis ratio, $f$, of the halo of the elliptical lens, fixed values of $\sigma_v$ and $x_t$, and fixed source redshift, $z_s = 0.6$."
 For each new Monte Carlo realisation. a new intrinsic position angle and a new intrinsic image shape for the Iuminous galaxy within the elliptical lens halo are generated.," For each new Monte Carlo realisation, a new intrinsic position angle and a new intrinsic image shape for the luminous galaxy within the elliptical lens halo are generated."
 That is. with cach new realisation we randomly “spin” the elliptical lens and we assign its luminous galaxy a new intrinsic ellipticitv.," That is, with each new realisation we randomly “spin” the elliptical lens and we assign its luminous galaxy a new intrinsic ellipticity."
 In addition. the elliptical lens is assigned a new redshift in each new realisation.," In addition, the elliptical lens is assigned a new redshift in each new realisation."
 Thus. alter many realisations. the redshifts of the elliptical lenses will span the entire range of redshift space that was adopted for D'TCHO ealaxics with ISxfig20.," Thus, after many realisations, the redshifts of the elliptical lenses will span the entire range of redshift space that was adopted for BTC40 galaxies with $18 \le I_{AB} \le 20$."
" For cach new Monte. Carlo realisation a new location for the source along the horizontal axis is generated. and a new suite of SIS lenses is laid down (including new redshifts and new locations within the 60"" circle)."," For each new Monte Carlo realisation a new location for the source along the horizontal axis is generated, and a new suite of SIS lenses is laid down (including new redshifts and new locations within the $60''$ circle)."
 After the source at ος=0.6 ancl the elliptical lens at the origin have been lensed by all foreground galaxics. the net shear for both the source and the luminous galaxy within the elliptical halo are computed in cach individual Monte Carlo realisation.," After the source at $z_s = 0.6$ and the elliptical lens at the origin have been lensed by all foreground galaxies, the net shear for both the source and the luminous galaxy within the elliptical halo are computed in each individual Monte Carlo realisation."
 The mean tangential shear for the sources. and .isthen computed by taking the elliptical lenses as the centres for the caleulation.," The mean tangential shear for the sources, $\gamma^+$ and $\gamma^-$, is then computed by taking the elliptical lenses as the centres for the calculation."
 Shown in Figures 13-15 is the function ~(8)/(A). obtained by computing the mean tangential shear for sources located within £45° of the svmmetry axes of the elliptical lens.," Shown in Figures 13-15 is the function $\gamma^+ (\theta) / \gamma^-(\theta)$, obtained by computing the mean tangential shear for sources located within $\pm 45^\circ$ of the symmetry axes of the elliptical lens."
 Results from a range of halo parameters (c.=100 km 150 km 200 kn sec.t: = κρο 1005.! kpe. 200& kpe) are shown in the different panels.," Results from a range of halo parameters $\sigma_v = 100$ km $^{-1}$, 150 km $^{-1}$, 200 km $^{-1}$; $x_t = 50~h^{-1}$ kpc, $100~h^{-1}$ kpc, $200~h^{-1}$ kpc) are shown in the different panels."
 Figure I:3 shows results for central elliptical lenses in which the ellipticitv of the dark matter halo is Chie=0.1 (corresponding to a projected. mass axis ratio f= 0.82)., Figure 13 shows results for central elliptical lenses in which the ellipticity of the dark matter halo is $\epsilon_{\rm halo} = 0.1$ (corresponding to a projected mass axis ratio $f = 0.82$ ).
 Figure 14 shows results for central elliptical lenses in which the ellipticitv of the dark matter halo is Guide=0.3 (corresponding to a projected mass axis ratio of f= 0.54)., Figure 14 shows results for central elliptical lenses in which the ellipticity of the dark matter halo is $\epsilon_{\rm halo} = 0.3$ (corresponding to a projected mass axis ratio of $f = 0.54$ ).
 Figure 15 shows results for central elliptical lenses in which the ellipticitv of the dark matter halo is cua=0.5 (corresponding to a projected mass axis ratio of f=0.3wx 3)., Figure 15 shows results for central elliptical lenses in which the ellipticity of the dark matter halo is $\epsilon_{\rm halo} = 0.5$ (corresponding to a projected mass axis ratio of $f = 0.33$ ).
 The circles in Figures 13-15 show 5.(0)/5.(8) for the case that the source galaxies are lensed solely by the central elliptical lens., The circles in Figures 13-15 show $\gamma^+ (\theta) / \gamma^- (\theta)$ for the case that the source galaxies are lensed solely by the central elliptical lens.
 “Phe svnumetry axes used for the calculation are the intrinsic svinmetry axes of the central elliptical lens., The symmetry axes used for the calculation are the intrinsic symmetry axes of the central elliptical lens.
 In other words. the circles show the simplest expected result: all source galaxies are lensed by only one foreground galaxy. the lens has a non-spherical dark matter halo. and the svinmetry axes of the lens galaxy. are its intrinsic svmnmietry axes.," In other words, the circles show the simplest expected result: all source galaxies are lensed by only one foreground galaxy, the lens has a non-spherical dark matter halo, and the symmetry axes of the lens galaxy are its intrinsic symmetry axes."
 The crosses in Figures 13-15 show 5(0)(8)for the case that the source galaxies. are [ensed. by both the central elliptical lens. as well as all foreground: SIS lenses.," The crosses in Figures 13-15 show $\gamma^+ (\theta) / 
\gamma^- (\theta)$for the case that the source galaxies are lensed by both the central elliptical lens, as well as all foreground SIS lenses."
 ο svmmetry axes used for the calculation are the intrinsic, The symmetry axes used for the calculation are the intrinsic
ealaxies can rauge from z = Oto at least z — 0.558. however. from Bell(2002cd.TableL.cols2.5.8). most appear to be less than zi = 0.005.,"galaxies can range from z = 0 to at least z = 0.558, however, from \citet[Table 4, cols 2,5,8]{bel02d}, most appear to be less than $_{\rm i}$ = 0.005."
 Can some of these imtrinsic components be present iu the FP cluster velocities?, Can some of these intrinsic components be present in the FP cluster velocities?
 If so. their presence would likely prevent the determination of an accurate Hubble constant.," If so, their presence would likely prevent the determination of an accurate Hubble constant."
" Tf it is assumned aj) that galaxy distances are accurately kuown. b) that all peculiar. velocities ue to local density fluctuations can be accurately accounted for. aud ο) that the observed redshifts are entirely Doppler-releed aud due to the Wabble How. (i.c. no intrinsic components present) then. if IL, = 72. all galaxies should fall along the solid ine in the Tubble pk in Fie."," If it is assumed a) that galaxy distances are accurately known, b) that all peculiar velocities due to local density fluctuations can be accurately accounted for, and c) that the observed redshifts are entirely Doppler-related and due to the Hubble flow, (i.e. no intrinsic components present) then, if $_{\rm o}$ = 72, all galaxies should fall along the solid line in the Hubble plot in Fig."
 1., 4.
 Tf there are oeitrinisic components present m some galaxies witli he discrete values fouud by Tifft(1997) to be the uost conmuuon. aud defined here by equ Bl for Α΄ = 1. with in <8. then these sources will fall ou he appropriate dashed lines in Fig.," If there are intrinsic components present in some galaxies with the discrete values found by \citet{tif97} to be the most common, and defined here by eqn B1 for $N$ = 1, with $m <$ 8, then these sources will fall on the appropriate dashed lines in Fig."
 l., 4.
 To avoid confusion. lines for siall mtriusic redshifts (i> T) have not been included im Fie.," To avoid confusion, lines for small intrinsic redshifts $m >$ 7) have not been included in Fig."
 1., 4.
 Iu order to test for the presence of discrete redshifts we superimposed the discrete redshift erid in Fie., In order to test for the presence of discrete redshifts we superimposed the discrete redshift grid in Fig.
 L| onto he FP data in the IIubble ot in Fig.l., 4 onto the FP data in the Hubble plot in Fig.1.
 The result is shown in Fig., The result is shown in Fig.
" 5 where 1ο 21ο μι grid lines (dashed lines) assume I, =Tlhus + Mpc+ aud zp = 0.62."," 5 where the $_{\rm iG}$ [1,m] grid lines (dashed lines) assume $_{\rm o}$ = 71 km $^{-1}$ $^{-1}$ and $_{f}$ = 0.62."
" The z;-value letermines the separation between grid es while 1e value of IL, determines the slope.", The $_{f}$ -value determines the separation between grid lines while the value of $_{\rm o}$ determines the slope.
 It is clear iu Fie., It is clear in Fig.
 5 that nine of the cleven FP clusters fall along 1ο dashed lines defined by the ιο 110} discrete redshifts with m = 3.L5.and 7.," 5 that nine of the eleven FP clusters fall along the dashed lines defined by the $_{\rm iG}$ $m$ ] discrete redshifts with $m$ = 3,4,5,and 7."
 Although two of ιο clusters (Abell 8753 and Abell 539) do not fall rear dashed lines. they do fall on the two dotted ines included in the figure.," Although two of the clusters (Abell S753 and Abell 539) do not fall near dashed lines, they do fall on the two dotted lines included in the figure."
 These Ines represeut j6 z;a[2.6| μη discrete redshifts.," These lines represent the $_{\rm iG}$ [2,6] and $_{\rm iG}$ [2,7] discrete redshifts."
 It is rerefore asstuned that these two clusters are NV = 2 sources while the remaining niue are No = l sources., It is therefore assumed that these two clusters are $N$ = 2 sources while the remaining nine are $N$ = 1 sources.
 Fig., Fig.
 5 has siguificauce for both the nodel proposed by Tiftt(1996.2002). aud for the scenario proposed earlier (Bell2002) (see section 6 below).," 5 has significance for both the model proposed by \citet{tif96,tif02} and for the scenario proposed earlier \citep{bel02b} (see section 6 below)."
 In Fig., In Fig.
 2 we plotted the RAIS deviation in, 2 we plotted the RMS deviation in
use of the SIMIAD database. operated at CDS. Strasbourg. France.,"use of the SIMBAD database, operated at CDS, Strasbourg, France."
test simulations we found that varying mj by a few per cent causes a negligible dillerence to the results.,test simulations we found that varying $m_1$ by a few per cent causes a negligible difference to the results.
 Secondary masses are drawn from a [lat mass ratio distribution with the constraint that if the companion mass is « ML. or the total mass of the binary. misc< 2MM. it is resclected. thereby. removing the possibility of creating VLMDs in the stellar domain.," Secondary masses are drawn from a flat mass ratio distribution with the constraint that if the companion mass is $<$ $_\odot$ or the total mass of the binary, $m_{\rm tot} < $ $_\odot$ it is reselected, thereby removing the possibility of creating VLMBs in the stellar domain."
 Note that. this method does not produce the input LME. exactly due to the way that secondaries are chosen.," Note that this method does not produce the input IMF, exactly due to the way that secondaries are chosen."
 In accordance with the observations of ? and ?.. the periods of stellar binary svstemis are drawn from a logiu- normal distribution of the form where logy2=4S. toye=28 and P is in days.," In accordance with the observations of \citet{Duquennoy91} and \citet{Fischer92}, the periods of stellar binary systems are drawn from a $_{10}$ -normal distribution of the form where $\overline{{\rm log_{10}}P} = 4.8$, $\sigma_{{\rm log_{10}}P} = 2.3$ and $P$ is in days."
 The periods are then converted to semi-major axes., The periods are then converted to semi-major axes.
 Eecentricities of stellar binaries are drawn from a thermal eccentricity cistribution (72?) of the form nares with small periods but laree eccentricities would expect to undergo the tidal circularisation shown in the sample of CG-dwarfs in 2..," Eccentricities of stellar binaries are drawn from a thermal eccentricity distribution \citep{Heggie75,Kroupa95a,Kroupa08} of the form Binaries with small periods but large eccentricities would expect to undergo the tidal circularisation shown in the sample of G-dwarfs in \citet{Duquennoy91}. ."
 We account. for this by resclecting the eccentricity iit exceeds the following period-dependent value eiua: with logig2 inαντι.," We account for this by reselecting the eccentricity if it exceeds the following period-dependent value $e_{\rm tid}$: with ${\rm log_{10}}\,P$ in."
 This ensures that the eccentricityperiod distribution matches the observations of 7.., This ensures that the eccentricity–period distribution matches the observations of \citet{Duquennoy91}. .
 In three sets of simulations. we use the VELMDA data (?) to randomly choose binaries and use their masses and semi-major axes as initial values for substellar binaries in the cluster.," In three sets of simulations, we use the VLMBA data \citep[]{Burgasser07} to randomly choose binaries and use their masses and semi-major axes as initial values for substellar binaries in the cluster."
" We run simulations with semi-major axes drawn from the ο fit to the VLAIB separation distribution. with Gaussian parameters of logye=0.66. where e is the semi-major axis in au (0.66 corresponds to 4.Gaau). and variance Toya= Os and also the fit by 2.. which accounts [or he outlving binaries in the VLAIB separation distribution ον adopting the same logyo-normal peak but increasing the variance (οσα=0.66. 0,444,= 0.85)."," We run simulations with semi-major axes drawn from the \citet{Thies07} fit to the VLMB separation distribution, with Gaussian parameters of $\overline{{\rm log_{10}}\,a} = 0.66$, where $a$ is the semi-major axis in au (0.66 corresponds to au), and variance $\sigma_{{\rm
 log_{10}}\,a} = 0.4$ ; and also the fit by \citet{Basri06}, which accounts for the outlying binaries in the VLMB separation distribution by adopting the same $_{\rm 10}$ -normal peak but increasing the variance $\overline{{\rm log_{10}}\,a} = 0.66$, $\sigma_{{\rm log_{10}}\,a} = 0.85$ )."
 For completeness. we run simulations in which the sub-stellar. binaries have he same separation distribution as the stellar. binaries (logigP?— S. σι=2.3: P in days).," For completeness, we run simulations in which the sub-stellar binaries have the same separation distribution as the stellar binaries $\overline{{\rm
 log_{10}}\,P} = 4.8$ , $\sigma_{{\rm log_{10}}\,P} = 2.3$; $P$ in days)."
 In cach case. we adopt an initial VLAIB fraction: either V5 (elthestellarbinariesinfield7).. 0.25 (toaccount ?2).. or 0.15 (the 7. fit o the observations)," In each case, we adopt an initial VLMB fraction; either 0.5 \citep[c.f.\,\,the stellar binaries in the field][]{Duquennoy91}, 0.25 \citep[to account for potentially undiscovered VLMBs,][]{Basri06}, or 0.15 (the \citet{Thies07} fit to the observations)."
" In the simulations that choose separations from the various logy-normal clüstributions. the masses of the sub-stellar binary components are chosen by randomly assigning the primary a mass in the range MM.<m,x OAOGAMAL.."," In the simulations that choose separations from the various $_{\rm
 10}$ -normal distributions, the masses of the sub-stellar binary components are chosen by randomly assigning the primary a mass in the range $_\odot < m_p \leq$ $_\odot$ ."
 We then adopt a tat mass ratio (q) istribution to choose the mass of the secondary component L.OlMM.<i. ον, We then adopt a flat mass ratio $q$ ) distribution to choose the mass of the secondary component $_\odot \leq m_s < m_p$ ).
 This mass range allows a clirect comparison between the VLAIBA ancl the simulations., This mass range allows a direct comparison between the VLMBA and the simulations.
 We find that reducing the upper limit of the VLMD primaries to MM. has a negligible ellect on the results., We find that reducing the upper limit of the VLMB primaries to $_\odot$ has a negligible effect on the results.
 The eccentricities are drawn from a thermal eccentricity istribution and then tically circularised (I5qns., The eccentricities are drawn from a thermal eccentricity distribution and then tidally circularised (Eqns.
 6 and 7))., \ref{ecc_therm}~ and \ref{ecc_tidal}) ).
 A summary of the cillerent mass. semi-major axes ancl eccentricity cistributions used to create the substellar binaries is given in Table 2..," A summary of the different mass, semi-major axes and eccentricity distributions used to create the substellar binaries is given in Table \ref{BDBDtable}."
 v combining the primary and secondary masses. of the stellar and VLAIBs with their semi-major axes and eccentricities. the relative. velocity and radial. components of the stars/very low-mass objects in each system are determined.," By combining the primary and secondary masses of the stellar and VLMBs with their semi-major axes and eccentricities, the relative velocity and radial components of the stars/very low-mass objects in each system are determined."
 These are then placed at the centre of mass ancl centre of velocity for cach system in the Plummer sphere., These are then placed at the centre of mass and centre of velocity for each system in the Plummer sphere.
 Simulationsare run using the integrator in Starlab(e.g.27.andreferencestherein) and evolved forMMwr.," Simulationsare run using the integrator in Starlab\citep[e.g.][and references therein]{Zwart99,Zwart01} and evolved forMyr."
 We do notinclude stellar evolution in the simulations., We do notinclude stellar evolution in the simulations.
 We use the nearest-neighbour algorithm described hy ? (anclindependentlyverifiedby2). to determine whether a star/very low-massobject is in a bound binary system., We use the nearest-neighbour algorithm described by \citet{Parker09} \citep[and independently verified by][]{Kouwenhoven10} to determine whether a star/very low-massobject is in a bound binary system.
preventing the estimation of model parameters being influenced by the collective over- or underestimation of error bars.,preventing the estimation of model parameters being influenced by the collective over- or underestimation of error bars.
 It was pointed out by ?. that planets orbiting the lens star can reveal heir existence by causing significant deviations to microlensing ight curves., It was pointed out by \citet{MP91} that planets orbiting the lens star can reveal their existence by causing significant deviations to microlensing light curves.
" They also found that the probability to detect a planet becomes resonant if the angular separation from its host star is comparable to the angular Einstein radius 8p. which reflects the ""uet that the detection of planets is aided by the tidal field. of heir host star."," They also found that the probability to detect a planet becomes resonant if the angular separation from its host star is comparable to the angular Einstein radius $\theta_\rmn{E}$, which reflects the fact that the detection of planets is aided by the tidal field of their host star."
 However. us pointed out in the Appendix. for a given event. in particular for larger impact parameters. the detection orobability of smaller planets ean actually drop to zero for angular separations close to 8p rather than reaching a maximum.," However, as pointed out in the Appendix, for a given event, in particular for larger impact parameters, the detection probability of smaller planets can actually drop to zero for angular separations close to $\theta_\rmn{E}$ rather than reaching a maximum."
 In such case. only slightly wider or closer separations can be probed.," In such case, only slightly wider or closer separations can be probed."
" It is a lucky coincidence that the gravitational radius of stars and distances within the Milky Way combine in such a way that the angular Einstein radius converts to a projected separation Jj,6p.~2AU for AJ=0.3AM.. the typicalmass of the lens stars. assuming Ds~8.5kpe and D,~6.5Kpe."," It is a lucky coincidence that the gravitational radius of stars and distances within the Milky Way combine in such a way that the angular Einstein radius converts to a projected separation $D_\rmn{L}\,\theta_\rmn{E} \sim 2~\mbox{AU}$ for $M = 0.3~M_\odot$, the typicalmass of the lens stars, assuming $D_\rmn{S} \sim 8.5~\mbox{kpc}$ and $D_\rmn{L} \sim 6.5~\mbox{kpc}$."
 ?. quantitied the prospects for detecting planets from mierolensing signatures by finding that Jupiter-mass planets distributed uniformly within angular separations 0.6Ge5dO1.66p. comprising the so-calledzone. have a probability of 15 per cent of being detected among microlensing events with peak magnifications ely&1.34. corresponding to the source entering the Einstein ring (of angular radius 6Η} of the lens star. ie. vyx1.," \citet{GL92} quantified the prospects for detecting planets from microlensing signatures by finding that Jupiter-mass planets distributed uniformly within angular separations $0.6~\theta_\rmn{E} \leq d\,\theta_\rmn{E} \leq 1.6~\theta_\rmn{E}$, comprising the so-called, have a probability of 15 per cent of being detected among microlensing events with peak magnifications $A_0 \geq 1.34$, corresponding to the source entering the Einstein ring (of angular radius $\theta_\rmn{E}$ ) of the lens star, i.e. $u_0 \leq 1$."
 As shown by ?.. this probability increases significantly if one restricts the attention to events with larger peak magnifications. where about 8O per cent is reached for ο10.," As shown by \citet{GS:HME}, this probability increases significantly if one restricts the attention to events with larger peak magnifications, where about 80 per cent is reached for $A_0 \geq 10$."
 Since the area subtended on the sky by angular source positions that correspond to a significant deviation decreases towards smaller planet masses. both a shorter duration of the planetary signal and a smaller probability to observe it result.," Since the area subtended on the sky by angular source positions that correspond to a significant deviation decreases towards smaller planet masses, both a shorter duration of the planetary signal and a smaller probability to observe it result."
 In contrast. the signal amplitude is only limited by the finite angular size of the source. where significant signal reductions start arising once it becomes comparable or larger than the size of the region for which a point source provides a significant deviation.," In contrast, the signal amplitude is only limited by the finite angular size of the source, where significant signal reductions start arising once it becomes comparable or larger than the size of the region for which a point source provides a significant deviation."
 However. ? estimated that Earth-mass planets still have a 1—2 per cent chance of providing a signal in excess of a few per cent.," However, \citet{BenRhie} estimated that Earth-mass planets still have a 1–2 per cent chance of providing a signal in excess of a few per cent."
 Planets around the lens star affect the light curve only by means of two dimensionless parameters. namely the planet-to-star mass ratio q and the separation parameter d. where «θε is the instantaneous angular separation of the planets from its host star tthe lens star).," Planets around the lens star affect the light curve only by means of two dimensionless parameters, namely the planet-to-star mass ratio $q$ and the separation parameter $d$, where $d\,\theta_\rmn{E}$ is the instantaneous angular separation of the planets from its host star the lens star)."
 With typical relative proper motions between lens and source stars of i15µας. microlensing events on Galactic bulge stars are usually observable for about a month or two. whereas planetary deviations last between a few hours and a few days. depending on the mass of the planet.," With typical relative proper motions between lens and source stars of $\mu \sim 15~\umu\mbox{as}\,\mbox{d}^{-1}$, microlensing events on Galactic bulge stars are usually observable for about a month or two, whereas planetary deviations last between a few hours and a few days, depending on the mass of the planet."
 In contrast to other indirect techniques. microlensing therefore obtains a snapshot measurement of the planet rather than having to wait for it to complete its orbit.," In contrast to other indirect techniques, microlensing therefore obtains a snapshot measurement of the planet rather than having to wait for it to complete its orbit."
 This gives microlensing the unique capability of probing planets in wide orbits whose periods otherwise easily exceed the life-time of a project or its investigator., This gives microlensing the unique capability of probing planets in wide orbits whose periods otherwise easily exceed the life-time of a project or its investigator.
 With many events on offer from the OGLE and MOA surveys and only limited resources available for follow-up observations. one needs to make a choice which of these to monitor and how frequently to sample each event.," With many events on offer from the OGLE and MOA surveys and only limited resources available for follow-up observations, one needs to make a choice which of these to monitor and how frequently to sample each event."
 With the goal to maximize the number of detections of planetary deviations. a prioritization algorithm that spreads the available observing time over the potential targets has been devised by ?.. which forms a central engine of the RoboNet observing strategy.," With the goal to maximize the number of detections of planetary deviations, a prioritization algorithm that spreads the available observing time over the potential targets has been devised by \citet{Horne:priority}, which forms a central engine of the RoboNet observing strategy."
 Any such strategy must be based on observables. model parameters arising from the collected data. or any other data statistics.," Any such strategy must be based on observables, model parameters arising from the collected data, or any other data statistics."
 As ?— pointed out. each data point carries a detection zone with it. composed of the angular positions for which a planet would have caused a detectable deviation.," As \citet{Horne:priority} pointed out, each data point carries a detection zone with it, composed of the angular positions for which a planet would have caused a detectable deviation."
 Unless tinite-source effects begin diminishing the detectability of planets (2).. detection zones grow with the current magnification.," Unless finite-source effects begin diminishing the detectability of planets \citep{Han:priority}, detection zones grow with the current magnification."
 Moreover. the same photometric accuracy can be achieved with smaller exposure times for brighter targets.," Moreover, the same photometric accuracy can be achieved with smaller exposure times for brighter targets."
 An efficient prioritization algorithm therefore needs to be based on both the current magnification and brightness along with the time when the last observation was carried out. where taking into account the latter avoids obtaining redundant information.," An efficient prioritization algorithm therefore needs to be based on both the current magnification and brightness along with the time when the last observation was carried out, where taking into account the latter avoids obtaining redundant information."
 Such a prioritization of events however does not consider how well an observed deviation allows to constrain its nature of origin and it also assumes that the model parameters of the ordinary light curve are known exactly., Such a prioritization of events however does not consider how well an observed deviation allows to constrain its nature of origin and it also assumes that the model parameters of the ordinary light curve are known exactly.
 If the effect on the microlensing light curve is dominated by a single planet. the lens system can be fairly approximated as a binary system consisting of the star and this planet.," If the effect on the microlensing light curve is dominated by a single planet, the lens system can be fairly approximated as a binary system consisting of the star and this planet."
 Gravitational lensing by a binary point-mass lens has been studied in great detail for equal masses by 2?) and later generalized for arbitrary mass ratios by ?.., Gravitational lensing by a binary point-mass lens has been studied in great detail for equal masses by \citet{SchneiWei:twomass} and later generalized for arbitrary mass ratios by \citet{Erdl}.
 On the other hand. ?. have discussed lensing by bodies of different mass scales.," On the other hand, \citet{CR} have discussed lensing by bodies of different mass scales."
 While their target of interest was the brightness variation of individual images of QSOs that are gravitationally lensed by an intervening galaxy. a very similar situation. arises for planets orbiting a lens star.," While their target of interest was the brightness variation of individual images of QSOs that are gravitationally lensed by an intervening galaxy, a very similar situation arises for planets orbiting a lens star."
 Similarly. to individual stars in the galaxy splitting an image due to lensing by the galaxy as a whole into miero-lensing'. a planet can further split one of the two images due to lensing by its host star if it roughly coincides in angular position with that image.," Similarly to individual stars in the galaxy splitting an image due to lensing by the galaxy as a whole into 'micro-lensing', a planet can further split one of the two images due to lensing by its host star if it roughly coincides in angular position with that image."
 ? has further investigated the transition towards extreme mass ratios and shown yow the case described by ?.. the so-called lens. is approached.," \citet{Do99:CR} has further investigated the transition towards extreme mass ratios and shown how the case described by \citet{CR}, the so-called lens, is approached."
 The derived expansions into series have later been used by ? for discussing the case of multiple planets., The derived expansions into series have later been used by \citet{Bozza} for discussing the case of multiple planets.
 Binary enses in general and planetary systems in particular create a system of extended caustics. consisting of the angular positions or which a point-like source star would be infinitely magnified.," Binary lenses in general and planetary systems in particular create a system of extended caustics, consisting of the angular positions for which a point-like source star would be infinitely magnified."
 While sufficiently small sources passing the caustics can provide quite spectacular signals. planets are more likely to already reveal heir existence on entering a much larger region surrounding these.," While sufficiently small sources passing the caustics can provide quite spectacular signals, planets are more likely to already reveal their existence on entering a much larger region surrounding these."
 For less massive planets. there are usually two separate regions or positions of the source star that lead to detectable planetary signals. which are related to two types of caustics.," For less massive planets, there are usually two separate regions for positions of the source star that lead to detectable planetary signals, which are related to two types of caustics."
 Only if the angular separation. of the planet from its host star is in a close vicinity to the angular Einstein radius 8e. where the corresponding range is broader for more massive planets. a single caustic results and these regions merge.," Only if the angular separation of the planet from its host star is in a close vicinity to the angular Einstein radius $\theta_\rmn{E}$, where the corresponding range is broader for more massive planets, a single caustic results and these regions merge."
 Otherwise. there are one or two Which are locaed around positions for which bending of its light due to the grav‘itational field of the lens star causes he source to have image at the position of the planet. and a which can be found near the lens star (22)...," Otherwise, there are one or two which are located around positions for which bending of its light due to the gravitational field of the lens star causes the source to have image at the position of the planet, and a which can be found near the lens star \citep{GS:HME,Do99:CR}."
 As ? demonstrated. the planeary caustics associated with different jxanets are almost always separated and any kind of interference between these is quite unlikely.," As \citet{Bozza} demonstrated, the planetary caustics associated with different planets are almost always separated and any kind of interference between these is quite unlikely."
 In contrast. ?.» pointed out that the central caustic is always afected by the combined action of all planets.," In contrast, \citet{GNS} pointed out that the central caustic is always affected by the combined action of all planets."
 However. it is likey. although not guaranteed. that there is a hierarchical order among the effects of different planets. so that a linear superposition is a fair approximation 990 (22). ," However, it is likely, although not guaranteed, that there is a hierarchical order among the effects of different planets, so that a linear superposition is a fair approximation \citep{Ratt:high,Han:central}. ."
While the absence of any deviations near the peak of extreme vighly-magnified ordinary events that are related to the source xotentially approaching the central caustic poses strict limits on the, While the absence of any deviations near the peak of extreme highly-magnified ordinary events that are related to the source potentially approaching the central caustic poses strict limits on the
 , 
black line divides the [ragmenting anc non-[ragmoenting simulations and has been included by eve as a fit to where the boundary lies.,black line divides the fragmenting and non-fragmenting simulations and has been included by eye as a fit to where the boundary lies.
" For 250.000. 2 million and 16 million particles. the critical value of the cooling timescale in units of the orbital timescale. toa,725.6. 10 ancl 18. respectively. since these have been identified as cases."," For 250,000, 2 million and 16 million particles, the critical value of the cooling timescale in units of the orbital timescale, $\beta_{\rm crit} \approx 5.6$, 10 and 18, respectively, since these have been identified as cases."
 For the clises simulated. with 31.250 particles. L assume that the critical value is between the fragmenting case of 3=3.0 and the non-fragmenting case of 3=3.5 and thus take Jeg&3.25.," For the discs simulated with 31,250 particles, I assume that the critical value is between the fragmenting case of $\beta = 3.0$ and the non-fragmenting case of $\beta = 3.5$ and thus take $\beta_{\rm crit} \approx 3.25$."
 H can clearly be seen that with the cata that is available. the dividing line between the fragmenting and non fragmenting cases increases linearly. with linear resolution and therefore a convergence has not been reached.," It can clearly be seen that with the data that is available, the dividing line between the fragmenting and non fragmenting cases increases linearly with linear resolution and therefore a convergence has not been reached."
 Figure 3 also shows how the trend may continue if convergence does not take place at even higher resolution., Figure \ref{fig:res_beta} also shows how the trend may continue if convergence does not take place at even higher resolution.
 To date. it has been widely accepted that a single critical value of the gravitational stress determines if a cise will fragment.," To date, it has been widely accepted that a single critical value of the gravitational stress determines if a disc will fragment."
 However. a thorough convergence test has not been carried out.," However, a thorough convergence test has not been carried out."
 The dependence of fragmentation on resolution presented in this letter shows that convergence has clearly not taken place., The dependence of fragmentation on resolution presented in this letter shows that convergence has clearly not taken place.
 Vhis therefore calls into question many of the previous results on the fragmentation boundary (c.g.2???77). as well as any results that have taken the critical value of the gravitational stress to be a single value of oca720.06 (or a similarly high value of acy). ancl based conclusions on these (c.g. 7?7?7)).," This therefore calls into question many of the previous results on the fragmentation boundary \citep[e.g.][]{Gammie_betacool,Rice_Gammie_confirm,Rice_beta_condition,Alexander_ecc_discs,Cossins_opacity_beta,Meru_Bate_fragmentation}, as well as any results that have taken the critical value of the gravitational stress to be a single value of $\alpha_{\rm GI} \approx 0.06$ (or a similarly high value of $\alpha_{\rm GI}$ ), and based conclusions on these (e.g. \citealp{Clarke2009_analytical,Rafikov_SI,Nero_Bjorkman_GI_analysis,Kratter_runts}) )."
 Lt is possible that results that are to each other may still stand., It is possible that results that are to each other may still stand.
 For example. ? clearly showed that a still equation of state requires a faster cooling for fragmentation o occur.," For example, \cite{Rice_beta_condition} clearly showed that a stiff equation of state requires a faster cooling for fragmentation to occur."
 Similarly. ? presented. physical arguments for why he cooling that is required for fragmentation may vary for dilferent surface mass densities ancl star masses.," Similarly, \cite{Meru_Bate_fragmentation} presented physical arguments for why the cooling that is required for fragmentation may vary for different surface mass densities and star masses."
 However. until convergence is demonstrated. all such results must be reateck with caution.," However, until convergence is demonstrated, all such results must be treated with caution."
 If convergence can be obtained at. higher resolution. hese results imply that gai can. be much higher than oweviouslv thought.," If convergence can be obtained at higher resolution, these results imply that $\betacrit$ can be much higher than previously thought."
 In. light of the new results presented wre. we caution against using cooling timescale or eravitational stress arguments to deduce whether certain danetarv svstems may or may not have formed. by gravitational instability.," In light of the new results presented here, we caution against using cooling timescale or gravitational stress arguments to deduce whether certain planetary systems may or may not have formed by gravitational instability."
 ο produced. an analytical model or the structure of a eravitationally unstable clise which is subject to realistic cooling., \cite{Clarke2009_analytical} produced an analytical model for the structure of a gravitationally unstable disc which is subject to realistic cooling.
 She showed that for optically hick cises that are sulliciently low in temperature that they are dominated by ice grains. for a disc with interstellar opacities ancl surrounding a 1M. star. where /2 is the radius being considered.," She showed that for optically thick discs that are sufficiently low in temperature that they are dominated by ice grains, for a disc with interstellar opacities and surrounding a $1 \Msolar$ star, where $R$ is the radius being considered."
 This relationship shows that for a maximum value of the eravitational stress. a critical radius. Bey. can be found outside of which fragmentation can occur (for a disc with a shallow surface mass censity profile).," This relationship shows that for a maximum value of the gravitational stress, a critical radius, $R_{\rm crit}$, can be found outside of which fragmentation can occur (for a disc with a shallow surface mass density profile)."
 For example. if Ανν&O.O7. then. RaicGS au.," For example, if $\alpha_{\rm GI,max} \approx 0.07$, then, $R_{\rm crit} \approx 68$ au."
 The critical radius also scales as AMI (as described by 2)) and also depends on the metallicity anc grain sizes in the disc (as shown by τὸ)., The critical radius also scales as $M_{\star}^{1/3}$ (as described by \citealp{Clarke2009_analytical}) ) and also depends on the metallicity and grain sizes in the disc (as shown by \citealp{Meru_Bate_opacity}) ).
 One might then use this to compare to observational data and conclude whether à svstem may or may not have formed via gravitational instability., One might then use this to compare to observational data and conclude whether a system may or may not have formed via gravitational instability.
" ‘Table 2.. however. shows the equivalent value of AGaus that ids associated with the value of tos, identified for each resolution considered. in this letter. as well as the critical racius outside of which fragmentation may take place according to 7. lor central star masses of 1M. and 1.5M."," Table \ref{tab:Rcrit_res}, however, shows the equivalent value of $\alpha_{\rm GI,max}$ that is associated with the value of $\beta_{\rm crit}$ identified for each resolution considered in this letter, as well as the critical radius outside of which fragmentation may take place according to \cite{Clarke2009_analytical} for central star masses of $1 \Msolar$ and $1.5 \Msolar$."
- It can be seen that the critical. radius. of fragmentation identified for a disc with 16 million particles is smaller than the value identified for a disc with 250.000 by =20%.," It can be seen that the critical radius of fragmentation identified for a disc with 16 million particles is smaller than the value identified for a disc with 250,000 by $> 20 \%$."
 This can have profound. consequences on the interpretation of observational results., This can have profound consequences on the interpretation of observational results.
 Table 2. shows that while the value of AGlauas from simulations using 250.000 particlesmay cause one to conclude that the outer planet around the 1.5M. A star. Lt 8799 (2).. may be cdillicult to form hy gravitational instability (since its projected separation according to 2. is =68 au). the results using 16 million particles suggest that this planet could have formed by eravitational instability.," Table \ref{tab:Rcrit_res} shows that while the value of $\alpha_{\rm GI,max}$ from simulations using 250,000 particlesmay cause one to conclude that the outer planet around the $1.5 \Msolar$ A star, HR 8799 \citep{HR8799_metallicity}, may be difficult to form by gravitational instability (since its projected separation according to \citealp{HR8799} is $\approx 68$ au), the results using 16 million particles suggest that this planet could have formed by gravitational instability."
 Finally. with the results as they stand. it is possible mt convergence will never be obtained. regardless of the resolution.," Finally, with the results as they stand, it is possible that convergence will never be obtained regardless of the resolution."
 Ε this is the case. it suggests that the problem may be ill posed.," If this is the case, it suggests that the problem may be ill posed."
 La other words. it may. not. be. possible [or a disc to settle into an equilibrium. where there is a balance between heating from gravitational instabilities and a imposed. cooling timescale.," In other words, it may not be possible for a disc to settle into an equilibrium where there is a balance between heating from gravitational instabilities and a imposed cooling timescale."
 We notice that once our simulations have developed significant density structure, We notice that once our simulations have developed significant density structure
 (Veilletοἱal.2002:Nollet (Pravecetal.2002) Jewill(2004))). Ostroetal.(2002)))," \citep{veillet02,noll02,osip03,noll04a,noll04b,stans05,stephens05}
 \citep{pravec02} \citet{jewitt91,nalin}) \citet{ast3})"
 (Veilletοἱal.2002:Nollet (Pravecetal.2002) Jewill(2004))). Ostroetal.(2002))).," \citep{veillet02,noll02,osip03,noll04a,noll04b,stans05,stephens05}
 \citep{pravec02} \citet{jewitt91,nalin}) \citet{ast3})"
Observations and interpretations of red- and/or blueshifted emission lines from cosmic objects are crucial to understand the physical processes at work there.,Observations and interpretations of red- and/or blueshifted emission lines from cosmic objects are crucial to understand the physical processes at work there.
" The net redshift in the solar transition region (TR) emission lines has been known since the Skylab era (e.g.,Doscheketal.,1976,andreferences therein).."," The net redshift in the solar transition region (TR) emission lines has been known since the Skylab era \citep[e.g.,][and references therein]{Doschek76}."
" Redshifts have also been recorded in stellar spectra (Ayresetal.,1983;Wood 1996).."," Redshifts have also been recorded in stellar spectra \citep{Ayres83,Wood96}. ."
" More recently, Brekkeetal.(1997) and Chaeetal.(1998) independently verified this result, analysing high spectral resolution observations from the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) instrument on SoHO (Wilhelmetal.1995)."," More recently, \citet{Brekke97} and \citet{Chae98} independently verified this result, analysing high spectral resolution observations from the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) instrument on $SoHO$ \citep{Wilhelm95}."
 Both these groups found similar results for the quantitative dependence of the net redshift on line formation temperature in the range from 10* K to 10° K. The reported peak downflow of 6 to 8 km/s at a temperature of around 10? K is four times higher than the detection limit of the instrument., Both these groups found similar results for the quantitative dependence of the net redshift on line formation temperature in the range from $^4$ K to $^6$ K. The reported peak downflow of 6 to 8 km/s at a temperature of around $^5$ K is four times higher than the detection limit of the instrument.
" However, both groups adopted incorrect literature values for the rest wavelengths for the and emission."," However, both groups adopted incorrect literature values for the rest wavelengths for the and emission."
 Dammaschetal.(1999) and Peter&Judge(1999) have established more realistic rest wavelength values for these species and have demonstrated the disappearance of the net redshift in coronal emission lines.," \citet{Dammasch99}
 and \citet{Peter99} have established more realistic rest wavelength values for these species and have demonstrated the disappearance of the net redshift in coronal emission lines."
" To our knowledge, a satisfactory physical explanation of the net redshift has not yet been found."," To our knowledge, a satisfactory physical explanation of the net redshift has not yet been found."
" Peter(2006) has recently reported the first full-Sun VUV emission line profile, showing enhanced emission in the wings."," \citet{Peter06} has recently reported the first full-Sun VUV emission line profile, showing enhanced emission in the wings."
 We present a new method to investigate and explain the TR redshift using the network contrast., We present a new method to investigate and explain the TR redshift using the network contrast.
" A spectrally resolved contrast curve has been included in the SUMER disk atlas of Curdtetal.(2001,hereafterreferredtoasSDA)..", A spectrally resolved contrast curve has been included in the SUMER disk atlas of \citet[hereafter referred to as SDA]{Curdt01}.
" Here, the network contrast — defined as the radiance ratio of pixels in the bright network and pixels in the cell interior — has values of about 3 in the continua, and rises to values of 6 to 8 in TR emission lines."," Here, the network contrast – defined as the radiance ratio of pixels in the bright network and pixels in the cell interior – has values of about 3 in the continua, and rises to values of 6 to 8 in TR emission lines."
 A similar result was reported by Reeves(1976).., A similar result was reported by \citet{Reeves}.
" In coronal lines such as and the contrast is below the background value, a finding which is equivalent to the result of Doschek(2006), who reported a low correlation between the emission of the TR and corona."," In coronal lines such as and the contrast is below the background value, a finding which is equivalent to the result of \citet{Doschek06}, who reported a low correlation between the emission of the TR and corona."
" An enlarged cutout of the SDA quiet-Sun profile — dominated by the strongNevm,,Sv,, and emission lines around 785 — is displayed in Fig.l."," An enlarged cutout of the SDA quiet-Sun profile -- dominated by the strong, and emission lines around 785 – is displayed in Fig.1."
" It is also obvious, although not explicitly mentioned in the SDA, that the network profiles are redshifted compared to the emission lines themselves."," It is also obvious, although not explicitly mentioned in the SDA, that the network profiles are redshifted compared to the emission lines themselves."
 Our goal is to give a physical explanation for this offset., Our goal is to give a physical explanation for this offset.
" In this paper, we extend the earlier work of Reeves(1976) and the work reported in the SDA by a comprehensive investigation of the contrast employing a much larger data set."," In this paper, we extend the earlier work of \citet{Reeves} and the work reported in the SDA by a comprehensive investigation of the contrast employing a much larger data set."
 We show that our result is a direct consequence of the redshift-to-brightness relationship and can be reconstructed by a simple model using multi-component contributions to the line profile., We show that our result is a direct consequence of the redshift-to-brightness relationship and can be reconstructed by a simple model using multi-component contributions to the line profile.
 A full discussion of the implications for loop models is beyond the scope of this work., A full discussion of the implications for loop models is beyond the scope of this work.
" We only present here some salient features, and a detailed study taking account of atmospheric models will be covered in a separate paper."," We only present here some salient features, and a detailed study taking account of atmospheric models will be covered in a separate paper."
" In contrast to the earlier work of Brekkeetal.(1997) and Chaeetal.(1998),, our new indirect method is unique in several ways, namely (1) it does not require an accurate wavelength calibration, (i) it is independent ofan exact knowledge of the rest wavelength,"," In contrast to the earlier work of \citet{Brekke97} and \citet{Chae98}, our new indirect method is unique in several ways, namely (i) it does not require an accurate wavelength calibration, (ii) it is independent ofan exact knowledge of the rest wavelength,"
the table notes.,the table notes.
" Spectral line data and partition functions have been taken from The Cologne Database for Molecular Spectroscopy (?), with supplementary data from the JPLdatabase*."," Spectral line data and partition functions have been taken from The Cologne Database for Molecular Spectroscopy \citep{mul01}, with supplementary data from the JPL."
. Partition functions for the different nuclear spin configurations of c-C43H; and CH3OH were calculated by direct summation over the relevant energy levels., Partition functions for the different nuclear spin configurations of $c$ $_3$ $_2$ and $_3$ OH were calculated by direct summation over the relevant energy levels.
" The beam-filling factor was assumed to be unity for all emission, which is justified based on the spatial extent of the emission maps."," The beam-filling factor was assumed to be unity for all emission, which is justified based on the spatial extent of the emission maps."
" However, structure on size scales less than the size of the Mopra beam is likely given the presence of the compact protostellar core."," However, structure on size scales less than the size of the Mopra beam is likely given the presence of the compact protostellar core."
 This may introduce additional uncertainties into the derived column densities and temperatures., This may introduce additional uncertainties into the derived column densities and temperatures.
" Rotational diagrams (see,e.g.?) were used for those species for which at least two transitions from significantly different upper-state energies were observed."," Rotational diagrams \citep[see, \eg][]{cum86} were used for those species for which at least two transitions from significantly different upper-state energies were observed."
 The rotational diagrams containing at least three transitions each are shown in Figure 5.., The rotational diagrams containing at least three transitions each are shown in Figure \ref{fig:rotdiags}.
" Where possible, in order to better constrain the temperatures and column densities, our data were supplemented with data from the SEST observations of ?.."," Where possible, in order to better constrain the temperatures and column densities, our data were supplemented with data from the SEST observations of \citet{kon00}."
" Derived rotational excitation temperatures 7,,, are relatively low (<10 K), so it was necessary to account for the cosmic microwave background (CMB) radiation by including a factor [1—GO»)JTot)! in the column density calculations, where J,(T) is the Planck radiation law and Tj,=2.73 K is the CMB temperature."," Derived rotational excitation temperatures $T_{rot}$ are relatively low $\lesssim10$ K), so it was necessary to account for the cosmic microwave background (CMB) radiation by including a factor $[1-(J_{\nu}(T_{bg})/J_{\nu}(T_{rot})]^{-1}$ in the column density calculations, where $J_{\nu}(T)$ is the Planck radiation law and $T_{bg}=2.73$ K is the CMB temperature."
" For HC3N, C4H, ortho-c-C3H» and CCS, the peak opacities (τν) are significant for one or more lines, so for these species the points on the rotational diagram were corrected using the factor tau,where //(1-e-»τν was derived from the opacity equation e) The correction factors were determined iteratively, with initial values (c9) calculated at temperatures of T9(HC3N)- K, Τοro(Ο/Η)=43 K, 0. T?,(ortho-c-C3H2)=7.7 K and T°(CCS)5.8 K, which were derived from the"," For $_3$ N, $_4$ H, $c$ $_3$ $_2$ and CCS, the peak opacities $\tau_\nu$ ) are significant for one or more lines, so for these species the points on the rotational diagram were corrected using the factor where $\tau_\nu$ was derived from the opacity equation ) The correction factors were determined iteratively, with initial values $c_\nu^0$ ) calculated at temperatures of $T_{rot}^0({\rm HC_3N})=7.6$ K, $T_{rot}^0({\rm C_4H})=4.3$ K, $T_{rot}^0({\rm ortho}$ $c$ ${\rm C_3H_2})=7.7$ K and $T_{rot}^0({\rm CCS})=5.8$ K, which were derived from the"
Fig.,Fig.
" 3. (bottom) displavs (f.ijj) (CZ.X,) for values of Z in the range [0.1—2]."," \ref{fig3} (bottom) displays $\left<f_{\star,ff}\right>$ $Z^{'},\Sigma_{g}$ ) for values of $Z^{'}$ in the range $0.1-2$ ]."
" As in IXMT09. we also assume that there is a critical value of X, below which clumps are pressurized by their internal stellar feedback. and for the sake of comparison. we adopt the same value of Moos4=85 M. »7 such that X,4=X,,,; where X,4<X,,,4; and X,4ος= when M,mNae "," As in KMT09, we also assume that there is a critical value of $\Sigma_{g}$ below which clumps are pressurized by their internal stellar feedback, and for the sake of comparison, we adopt the same value of $\Sigma_{g,crit}=85$ $_{\odot}$ $^{-2}$ such that $\Sigma_{cl}=\Sigma_{g,crit}$ where $\Sigma_{g} < \Sigma_{g,crit}$ and $\Sigma_{cl}=\Sigma_{GMC}=\Sigma_{g}$ when $\Sigma_{g} \geq \Sigma_{g,crit}$."
1n Eq., In Eq.
 6 (55) can be approximated by the free-fall time of the clump with the characteristic mass bppMona)—SM᾿Moss Avr where Minas—Motorf107 M...," \ref{eq6} $\left<t_{ff}\right>$ can be approximated by the free-fall time of the clump with the characteristic mass $t_{ff} (M_{char})=8 \Sigma_{cl}^{' -3/4} M_{char,6}^{1/4}$ Myr where $M_{char,6}=M_{char}/10^{6}$ $_{\odot}$."
" We also adopt the same /j, as in IKMTO9 which is given by Eq. 2..", We also adopt the same $f_{H_{2}}$ as in KMT09 which is given by Eq. \ref{eq2}.
 With the above elements. the star formation law ean be re-written as: where Nye isin M. ! 7. Ma is given by Eq. 4..," With the above elements, the star formation law can be re-written as: where $\Sigma_{SFR}$ is in $_{\odot}$ $^{-1}$ $^{-2}$, $M_{char}$ is given by Eq. \ref{eq4},"
" and (f,55) by Eqs."," and $\left<f_{\star,ff}\right>$ by Eqs."
 7 anc..., \ref{eq7} and \ref{eq8}.
 Fig., Fig.
 (lop panel) displays the results obtained using Eq., \ref{fig4} (top panel) displays the results obtained using Eq.
" 9 lor X, values starting [rom low gas surface densities up to the starburst regime.", \ref{eq9} for $\Sigma_{g}$ values starting from low gas surface densities up to the starburst regime.
 The results are calculated for the metallicity values of Z=[0.1.0.3.0.5.1.2]. and use a value of e=5 (the structure of the results is displaved in Tab.," The results are calculated for the metallicity values of $Z^{'}=[0.1,0.3,0.5,1,2]$, and use a value of $c=5$ (the structure of the results is displayed in Tab."
 D. and the full set of results is available in (he electronic version of the paper)., \ref{tab1} and the full set of results is available in the electronic version of the paper).
 The results are compared to the sub-kpe data of Bigiel et al. (, The results are compared to the sub-kpc data of Bigiel et al. (
2008) and to the normal and starburst galaxies results of Kennicutt (1998) ancl also to the KAITO9 results (Fig. 4..,"2008) and to the normal and starburst galaxies results of Kennicutt (1998) and also to the KMT09 results (Fig. \ref{fig4},"
 bottom panel)., bottom panel).
 Our models fits remarkably well the observational resulis over the entire range of surface densities., Our models fits remarkably well the observational results over the entire range of surface densities.
" Furthermore. the segregation by metallicity extends bevond the low surface density regime up to the starburst regime where a segregation in metallicity of ~0.3 dex is observed (dependence is Z ""?). in contrast to the IKMT09 models which do not contain a metallicity dependence in the intermediate to high surface density regimes."," Furthermore, the segregation by metallicity extends beyond the low surface density regime up to the starburst regime where a segregation in metallicity of $\sim 0.3$ dex is observed (dependence is $Z^{',-0.3}$ ), in contrast to the KMT09 models which do not contain a metallicity dependence in the intermediate to high surface density regimes."
 Furthermore the solar metallicity curve in our model overlaps with a signilicant fraction of the sub-regions in the data of Digiel et al. (, Furthermore the solar metallicity curve in our model overlaps with a significant fraction of the sub-regions in the data of Bigiel et al. (
2003.2010) in contrast to the INKMTO09 model.,"2008,2010) in contrast to the KMT09 model."
" The values of the slopes in the high (X,>85 M. 7) and intermediate (10 M, ?&N\X,«85 M. 7 ) surface density regimes are [1.75.1.74.174.174.1.74] and [1.20.0.97.0.93.0.90.0.85] for Z —[0.1.0.3.0.5.1.2]. respectivelv."," The values of the slopes in the high $\Sigma_{g} > 85$ $_{\odot}$ $^{-2}$ ) and intermediate $10$ $_{\odot}$ $^{-2} < \Sigma_{g} < 85$ $_{\odot}$ $^{-2}$ ) surface density regimes are [1.75,1.74,1.74,1.74,1.74] and [1.20,0.97,0.93,0.90,0.88] for $Z^{'}$ =[0.1,0.3,0.5,1,2], respectively."
" The slope of the X,—“sip relation increases to ~5.65 ab low surface densities (X,<1 M. 7).", The slope of the $\Sigma_{g}-\Sigma_{SFR}$ relation increases to $\sim 5.65$ at low surface densities $\Sigma_{g} < 1$ $_{\odot}$ $^{-2}$ ).
 A few additional factors may enhance the, A few additional factors may enhance the
"After the type I seesaw we get The bilinear DIC!D,, relevant for Mj. transforms under this svnmetry as We introduce a scalar SU(2) triplet A written in 2x matrix notation as which remains invariant under Z4.",After the type I seesaw we get The bilinear $D_{L_j}^T C^{-1}D_{L_k}$ relevant for $M_L$ transforms under this symmetry as We introduce a scalar SU(2) triplet $\Delta$ written in $2\times2$ matrix notation as which remains invariant under $Z_3$.
" The vacuum expectation value (VEV) of Llges (riplet is where I""),=war", The vacuum expectation value (VEV) of Higgs triplet is where $\langle H^0 \rangle_0=\frac{v_t}{\sqrt{2}}$.
 This induced VEV in the scalar potential is suppressed bv the high mass of the scalar triplet |1H.17].," This induced VEV in the scalar potential is suppressed by the high mass of the scalar triplet \cite{14, 17}."
. Thus. the type HH seesaw contribution is given by which is the class sly of FGM {1} two zero," Thus, the type II seesaw contribution is given by The effective neutrino mass matrix $M_{\nu}$ after type (I+II) seesaw mechanism becomes which is the class $A_1$ of FGM \cite{1} two zero"
While radial velocity planet searches tend to exclude binaries from their target lists. transit searches do. not apply «prior? selection criteria against binaries.,"While radial velocity planet searches tend to exclude binaries from their target lists, transit searches do not apply $a\,priori$ selection criteria against binaries."
 Transiting planets are routinely searched among all stars. and then subjected to follow-up photometric and spectroscopic analysis.," Transiting planets are routinely searched among all stars, and then subjected to follow-up photometric and spectroscopic analysis."
 Photometric analysis aims mainly at ruling out grazing eclipsing binary stellar systems which manifest themselves by means of markedly V-shaped eclipses. the presence of secondary eclipses. color changes during the eclipses and light modulations with the same periodicity of the transiting object.," Photometric analysis aims mainly at ruling out grazing eclipsing binary stellar systems which manifest themselves by means of markedly V-shaped eclipses, the presence of secondary eclipses, color changes during the eclipses and light modulations with the same periodicity of the transiting object."
 Spectroscopic analysis is then used to further rule-out giant stars primaries and the more complicated scenarios involving hierarchical triple systems with an eclipsing binary. stellar system. and blends with background eclipsing binaries (Brown 2003).," Spectroscopic analysis is then used to further rule-out giant stars primaries and the more complicated scenarios involving hierarchical triple systems with an eclipsing binary stellar system, and blends with background eclipsing binaries (Brown 2003)."
 However. these follow-up analysis do not eliminate planets in binary stellar systems.," However, these follow-up analysis do not eliminate planets in binary stellar systems."
 Several transiting planets are already known members of binaries (ο. g. Daemgen et al., Several transiting planets are already known members of binaries (e. g. Daemgen et al.
 2009). and others have suspected close companions as indicated by the presence of radial velocity and transit timing variations (Winn et al.," 2009), and others have suspected close companions as indicated by the presence of radial velocity and transit timing variations (Winn et al."
 2010; Maxted et al., 2010; Maxted et al.
 2010: Queloz et al., 2010; Queloz et al.
 2010: Rabus et al., 2010; Rabus et al.
 2009)., 2009).
 Moreover for transiting planets we have a firm constraint on the planetary orbital inclination (which is close to 90°)., Moreover for transiting planets we have a firm constraint on the planetary orbital inclination (which is close to $90^{\circ}$ ).
 The Rossiter-McLaughlit effect (Rossiter 1924: McLaughlin 1924) can be used to probe the sky-projected angle 8 between the stellar rotation axis anc the planet's orbital axis., The Rossiter-McLaughlin effect (Rossiter 1924; McLaughlin 1924) can be used to probe the sky-projected angle $\beta$ between the stellar rotation axis and the planet's orbital axis.
 By transforming the projected angle5 into the the real spin-orbit angle w using a statistical approach and the entire sample of planets with Rossiter-MceLaughli measurements. Triaud et al. (," By transforming the projected angle $\beta$ into the the real spin-orbit angle $\psi$ using a statistical approach and the entire sample of planets with Rossiter-McLaughlin measurements, Triaud et al. ("
2010) derived that most transiting planets have misaligned orbits (80% with £j> 22°). ane that the histogram of projected obliquities closely reproduces the theoretical distribution of w using Kozai cycles and tidal friction (Fabrycky Tremaine 2007).,"2010) derived that most transiting planets have misaligned orbits $\%$ with $\psi>22^{\circ}$ ), and that the histogram of projected obliquities closely reproduces the theoretical distribution of $\psi$ using Kozai cycles and tidal friction (Fabrycky Tremaine 2007)."
 Since type I and II migration are not able to explain the present observations. the indication is that the Kozai mechanism is the major responsible of the formation of hot-jupiter planets.," Since type I and II migration are not able to explain the present observations, the indication is that the Kozai mechanism is the major responsible of the formation of hot-jupiter planets."
 In this case. we should expect that most hot-jupiter planets have stellar companions.," In this case, we should expect that most hot-jupiter planets have stellar companions."
 The discovery of close stellar companions to transiting planets systems ts then of primary importance. since 1t would constitute a strong proof in favor of the Kozay cycles and tidal friction mechanism.," The discovery of close stellar companions to transiting planets systems is then of primary importance, since it would constitute a strong proof in favor of the Kozay cycles and tidal friction mechanism."
 Transiting planets host stars then constitute an interesting sample of objects where to look for additional distant companions., Transiting planets host stars then constitute an interesting sample of objects where to look for additional distant companions.
 The presence of a stellar companion around these stars can be inferred at least by means of four independent and complementary techniques: transit timing variations. radial velocity drifts. direct imaging and IR excess.," The presence of a stellar companion around these stars can be inferred at least by means of four independent and complementary techniques: transit timing variations, radial velocity drifts, direct imaging and IR excess."
 Deriving the expected frequency of transiting planet host stars in binary stellar systems detectable by each one of the above mentioned techniques is then important. since comparing the results of the observations with the predictions we can better understand which influence close binary systems have on planet formation and evolution.," Deriving the expected $frequency$ of transiting planet host stars in binary stellar systems $detectable$ by each one of the above mentioned techniques is then important, since comparing the results of the observations with the predictions we can better understand which influence close binary systems have on planet formation and evolution."
 If. for example. the existence of hot-jupiters is connected to the presence of close-by stellar companions. we should expect to derive a higher binary frequency around stars hosting these planets. with respect to the frequency of binaries observed m the solar neighborhood.," If, for example, the existence of hot-jupiters is connected to the presence of close-by stellar companions, we should expect to derive a higher binary frequency around stars hosting these planets, with respect to the frequency of binaries observed in the solar neighborhood."
 If. on the contrary. the presence of close-by stellar companions strongly prevents the existence of planets. we should expect a lower frequency.," If, on the contrary, the presence of close-by stellar companions strongly prevents the existence of planets, we should expect a lower frequency."
 In this paper we focus our attention on transit timing variations (TTVs) induced by stellar binarity., In this paper we focus our attention on transit timing variations (TTVs) induced by stellar binarity.
 Future contributes will account for the other techniques., Future contributes will account for the other techniques.
" In particular here we derive the expected frequency of transitingplanets in binary systems detectable by TTVs,", In particular here we derive the expected $frequency$ of transitingplanets in binary systems $detectable$ by TTVs.
 We define the detectionfrequency(fue) as the fraction of transiting planets expected to show detectable TTVs induced by stellar binarity over some fixed timescales. when the only source of TTVs under consideration is the light travel time effect in binary systems.," We define the $detection\,frequency\,(f_{det})$ as the fraction of $transiting$ planets expected to show $detectable$ TTVs induced by stellar binarity over some fixed timescales, when the only source of TTVs under consideration is the light travel time effect in binary systems."
 The presence of an additional stellar companion around a transiting planet-host star. should induce TTVs even if we neglect perturbing effects. because of the variable distance of the host star with respect to the observer in the course of its orbital revolution around the barycenter of the binary stellar system.," The presence of an additional stellar companion around a transiting planet-host star, should induce TTVs even if we neglect perturbing effects, because of the variable distance of the host star with respect to the observer in the course of its orbital revolution around the barycenter of the binary stellar system."
 This motion induces TTVs affecting the observed period of the transiting object. and consequently the ephemerides of the transits (e.g. Irwin 1959).," This motion induces TTVs affecting the observed period of the transiting object, and consequently the ephemerides of the transits (e.g. Irwin 1959)."
 Transit timing allows detenction of close stellar companions around more distant planet-host stars than direct Imaging., Transit timing allows detenction of close stellar companions around more distant planet-host stars than direct imaging.
 Accurate transit timing measurements are achievable also for planets discovered around faint and distant planet-hosts. by means of a careful choice of the telescope and the detector (e. g. Adams et al.," Accurate transit timing measurements are achievable also for planets discovered around faint and distant planet-hosts, by means of a careful choice of the telescope and the detector (e. g. Adams et al."
 2010)., 2010).
 On the contrary. the distance of the planet-host constitutes a limit for direct imaging detection of stellar companions.," On the contrary, the distance of the planet-host constitutes a limit for direct imaging detection of stellar companions."
 Using VLT/NACO. and targeting solar type close-by stars (~10 pe). a companion with a mass of 0.08M. (then just at the limit of the brown dwarf regime) can be detected at the 3—c limit at a projected separation of 0.3 aresec (e.g. Schnupp et al.," Using VLT/NACO, and targeting solar type close-by stars $\sim10$ pc), a companion with a mass of $\rm 0.08\,M_{\odot}$ (then just at the limit of the brown dwarf regime) can be detected at the $-\sigma$ limit at a projected separation of 0.3 arcsec (e.g. Schnupp et al."
 2010: Eggenberger et al., 2010; Eggenberger et al.
 2007). which corresponds to AU.," 2007), which corresponds to $\,$ AU."
 If. however. the star is located at à distance >333 pe. direct Imaging can probe only separations >100 AU.," If, however, the star is located at a distance $>333$ pc, direct imaging can probe only separations $>100$ AU."
 Then transit timing allows us to probe stellar multiplicity at critical separations <100 AU (as demonstrated in this work) around nore distant samples of transiting planet host-stars with respect to what can be done by direct imaging. giving the opportunity to probe stellar multiplicity around targets located in different regions of the Galaxy.," Then transit timing allows us to probe stellar multiplicity at critical separations $<100$ AU (as demonstrated in this work) around more distant samples of transiting planet host-stars with respect to what can be done by direct imaging, giving the opportunity to probe stellar multiplicity around targets located in different regions of the Galaxy."
 Moreover. while direct imaging is more efficient in detecting companions in face-on orbits. transit timing (and Doppler spectroscopy) is more efficient in the case of edge-on systems.," Moreover, while direct imaging is more efficient in detecting companions in face-on orbits, transit timing (and Doppler spectroscopy) is more efficient in the case of edge-on systems."
 This paper is organized as follows: in Sect. 2..," This paper is organized as follows: in Sect. \ref{s:bin},"
 we review the known propertiesof binary stellar systems in the solar neighborhood: in Sect. 3..," we review the known propertiesof binary stellar systems in the solar neighborhood; in Sect. \ref{s:travel_time},"
 we discuss the light travel time effect of transiting planets in binaries: in Sect 4.. we describe the Monte Carlo simulations we did to constrain the frequency of transiting planet-host stars presenting detectable transit timing variations induced by binarity over some fixed timescales: in Sect. 5.. ," we discuss the light travel time effect of transiting planets in binaries; in Sect \ref{s:simulations}, we describe the Monte Carlo simulations we did to constrain the frequency of transiting planet-host stars presenting detectable transit timing variations induced by binarity over some fixed timescales; in Sect. \ref{s:results}, ,"
we discuss the results of our analysis: in Sect. 6..," we discuss the results of our analysis; in Sect. \ref{s:conclusions}, ,"
 we summarize and conclude., we summarize and conclude.
right). right).“a5.,"), ),."
 This equation can be approached following a method similar to that in Β10., This equation can be approached following a method similar to that in B10.
 This ts slightly complicated by the extra integration across Φ., This is slightly complicated by the extra integration across $\phib$.
 Note. though.that é appears only in combination with sin(d).," Note, though,that $\phib$ appears only in combination with $\sin(\phi)$ ."
 The cases ὁ=0. ὁ€(0.7) and @=7 are then distinct from one-another and can be considered separately.," The cases $\phi=0$, $\phi\in(0,\pi)$ and $\phi=\pi$ are then distinct from one-another and can be considered separately."
 This corresponds to a separation into the bulk. the colinear plane and line. and the squeezed plane and degenerate line.," This corresponds to a separation into the bulk, the colinear plane and line, and the squeezed plane and degenerate line."
 The integral (11)) is better cast as an integration across αν instead of 4., The integral \ref{BStep1}) ) is better cast as an integration across $\alpha_p$ instead of $\phib$.
 To do so it is useful to findan expression for sind., To do so it is useful to findan expression for$\sin\phib$ .
" Writing cosà in terms of a, Pegives sing=+.4/d7Ásind—(wv,iaycosó)/d,sind.", Writing $\cos\phib$ in terms of $\alpha_p$ gives $\sin\phib=\pm\sqrt{\alphaks^2\sin^2\phi-(\alpha_p-\alpha_k\cos\phi)^2}/\alphaks\sin\phi$.
 Then when @€[O.7). sind> Oand while 9επ.27). sind<0.," Then when $\phib\in[0,\pi)$, $\sin\phib>0$ and while $\phib\in[\pi,2\pi)$, $\sin\phib<0$."
 Consider first the case where ὁ€ [0.π).," Consider first the case where $\phib\in[0,\pi)$ ."
" Holding o;constant. de,/dó=—NEsin*&(a,agcosór. and so where μμνος and sinphi."," Holding $\alpha_k$constant, $d\alpha_p/d\phib=-\sqrt{\alphaks^2\sin^2\phi-(\alpha_p-\alpha_k\cos\phi)^2}$ and so where )^2 and , ."
. Nowset z=[p+ al.transforming the integral to," Nowset $z=\left|\mathbf{p+a}\right|^2$ ,transforming the integral to"
continued fallback of material when the explosion is too müld Ileger 2001).,continued fallback of material when the explosion is too mild \citep{macfadyen01}.
. DATSE «did detect a few bursts longer than 1000 s. with its standard trigger. instead of a f[uence trigger.," BATSE did detect a few bursts longer than $1000$ s, with its standard peak-flux trigger, instead of a fluence trigger."
 Swift has the ability to operate with a [ence trigger. which potentially could lead to the detection of longer GRBs.," Swift has the ability to operate with a fluence trigger, which potentially could lead to the detection of longer GRBs."
 As an example of long diuration GRBs. we investigate a case whose duration in the source [rame is 7/(12-2)=1000 s. Other parameters are (he same as in the standard case.," As an example of long duration GRBs, we investigate a case whose duration in the source frame is $T/(1+z)=1000$ s. Other parameters are the same as in the standard case."
 Figure 7 shows the total fIuxes of the Forward and reverse shock emission at an observedfrequency vy=5 Gllz and at observed (times. /=1 hr. 1 day. 10 days and 100 days. as a [unetion of redshilt z. together with the 5o sensitivities of the VLA and SKA.," Figure \ref{fig:long:z} shows the total fluxes of the forward and reverse shock emission at an observedfrequency $\nu=5$ GHz and at observed times, $t=1$ hr, $1$ day, $10$ days and $100$ days, as a function of redshift $z$ , together with the $5 \sigma$ sensitivities of the VLA and SKA."
 Comparing Figures 7 and 1 we see that the detection of long bursts is easier (han lor the standarcl case ol duration Z/(12-2)=10 s. and even the VLA can easily detect such long burst afterglows bevond 2~30.," Comparing Figures \ref{fig:long:z} and \ref{fig:standard:z}
 we see that the detection of long bursts is easier than for the standard case of duration $T/(1+z)=10$ s, and even the VLA can easily detect such long burst afterglows beyond $z \sim 30$."
 This is because the reverse shock emission at early times /.<LO day is enhanced due (ο the long curation., This is because the reverse shock emission at early times $t \siml 10$ day is enhanced due to the long duration.
 Figure 8. shows the long duration GRB allerglow light curves αἱ z=6 and £p~200 AMIIz and at z=13 and v~100 MlIz., Figure \ref{fig:long} shows the long duration GRB afterglow light curves at $z=6$ and $\nu \sim 200$ MHz and at $z=13$ and $\nu \sim 100$ MHz.
 The5o sensitivities of the VLA. LOFAR and SIXA are also shown.," The$5 \sigma$ sensitivities of the VLA, LOFAR and SKA are also shown."
 Although the reverse shock emission is brighter than in the standard case in Figure 2.. it is still below the forward shock emission at low lrequencies ~100. MI.," Although the reverse shock emission is brighter than in the standard case in Figure \ref{fig:standard}, it is still below the forward shock emission at low frequencies $\sim 100$ MHz."
 Since the forward shock emission is similar (ο the standard case. the detectabilitv at (hese frequencies is similar to the standard case.," Since the forward shock emission is similar to the standard case, the detectability at these frequencies is similar to the standard case."
 LOFAR and SIXA should be able to detect the long duration GRB afterglows at low Irecquencies ~100 MlIIZ and hieh redshift 2~10. while it appears diffieult for the VLA to detect them.," LOFAR and SKA should be able to detect the long duration GRB afterglows at low frequencies $\sim 100$ MHz and high redshift $z \sim 10$, while it appears difficult for the VLA to detect them."
 As seen in Figure 8.. the peak (Iux is about e 1-10 pedy at the redshifted 21 em frequency. p=1420/(1+2) Mllz. for 2=6.," As seen in Figure \ref{fig:long}, the peak flux is about $\sim 1$ $10$ $\mu$ Jy at the redshifted 21 cm frequency, $\nu=1420/(1+z)$ MHz, for $z \simg 6$."
 Several observations suggest that the ejected shell may be strongly magnetized., Several observations suggest that the ejected shell may be strongly magnetized.
 A large linear polarization in the gamma-ray emission of GRB 021206 has been interpreted as implving a uniform ordered magnetic field over (he visible region (Coburn&Boges2003).. which could be a magnetic field advected [rom the central source (seehoweverItutledge&2004:Wiggeretal. 2004).," A large linear polarization in the gamma-ray emission of GRB 021206 has been interpreted as implying a uniform ordered magnetic field over the visible region \citep{coburn03}, which could be a magnetic field advected from the central source \citep[see however][]{rutledge04,wigger04}. ."
. The early afterglows of GRB 990123 and GRB 021211 also may imply that the reverse shock region has a stronger magnetic field than the forward shock region (Zhang.IXobavashi.&Mészáros2003:Fanetal.2002b).," The early afterglows of GRB 990123 and GRB 021211 also may imply that the reverse shock region has a stronger magnetic field than the forward shock region \citep{zhang03b,fan02b}."
. Although further studies are necessary to verily these suggestions (e.g..Zhang&Ixobavashi:2004:\latsumiva 2004).. it is useful to examine as a possibility the strongly maegnetized case.," Although further studies are necessary to verify these suggestions \citep[e.g.,][]{zhang04,matsumiya03,fan04}, , it is useful to examine as a possibility the strongly magnetized case."
" Here we adopt a ratio of reverse to forward magnetic field strengthsRy»,= 5. with the other parameters the same as in the standardcase."," Here we adopt a ratio of reverse to forward magnetic field strengths${\cal R}_{B}=5$ , with the other parameters the same as in the standardcase."
If interactions. spontaneous iustabilities. Or intermediate mechauisius a‘e the reasous for the origin aud the evoltion of these TBB galaxies hey may leave cliflerent traces which should be observect.,"If interactions, spontaneous instabilities, or intermediate mechanisms are the reasons for the origin and the evolution of these TBB galaxies they may leave different traces which should be observed."
 For tus durpose we have selected: a sample of 8 TBB galaxies. aud: we are investigaine the likely formation1 mechanisin of this class of oljects.," For this purpose we have selected a sample of 8 TBB galaxies, and we are investigating the likely formation mechanism of this class of objects."
 The galaxies were selecte from the Third Reference Catalogue of Briehte Calaxies (de Vaucoueurs et al., The galaxies were selected from the Third Reference Catalogue of Bright Galaxies (de Vaucouleurs et al.
 1991) on the basis of their orientation (nearly aud lelr diameters., 1991) on the basis of their orientation (nearly edge-on) and their diameters.
 The diameters «of tje galaxies are constraiued to je larger thar 2' at the Bos isophote [9] he Digital Sky $urvey (DSS)., The diameters of the galaxies are constrained to be larger than $'$ at the $_{25}$ isophote on the Digital Sky Survey (DSS).
 Base the (act that interaction events produce a highly asyiumetric distributioi and. complex sinenatics ‘the gaseous coupoleut. large deviations f‘OM syumetry in the iuorpholosy :uid kinematics will inclicate a galaxy which is strougly— interacting with nearby compauiols.," Based on the fact that interaction events produce a highly asymmetric distribution and complex kinematics of the gaseous component, large deviations from symmetry in the morphology and kinematics will indicate a galaxy which is strongly interacting with nearby companions."
 In orde‘to ciseern difTerent yal ormation scenarios (spolaneous iustabiitles or ba' triggeredMD by iuteractious) one of he cliaguostics is 11e frequency of peculiarities ο‘the TBB galaxies coup:wed to spheroical galaxies., In order to discern different bar formation scenarios (spontaneous instabilities or bar triggered by interactions) one of the diagnostics is the frequency of peculiarities of the TBB galaxies compared to spheroidal galaxies.
 We are stucdyine the statisties of war‘ps. teir shapes as well as lopsicleduess.," We are studying the statistics of warps, their shapes as well as lopsidedness."
 The atter is investigated yoth in the kinematics (compari& the approaching aud receiug side of the rotation curve) aud in the density distribution (compari180 he m:ws included iu the receding/approaching sice) using 21-cu line VLA and ATCA data., The latter is investigated both in the kinematics (comparing the approaching and receding side of the rotation curve) and in the density distribution (comparing the mass included in the receding/approaching side) using 21-cm line VLA and ATCA data.
 Since our investigation Las as input tje rotation curve FL‘conn Which we wi| derive the mass and the sinematical dillereuces between the twὉ sides in each gaaxy. we have to find the most reliable aud accurate metloc to obtain the rotation curve.," Since our investigation has as input the rotation curve from which we will derive the mass and the kinematical differences between the two sides in each galaxy, we have to find the most reliable and accurate method to obtain the rotation curve."
 Unfortuuatey. the procedure ος erive the rotation curve rom highly incliied ealanies is far [rou )elug sunple.," Unfortunately, the procedure to derive the rotation curve from highly inclined galaxies is far from being simple."
 It gives rise to severe ukerestimates of the velocities if couducted wi La Classical approach., It gives rise to severe underestimates of the velocities if conducted with a classical approach.
 This is principally due to the integratio1 aloug the line of sight ol a large porti Lol the disk., This is principally due to the integration along the line of sight of a large portion of the disk.
 Nevertheess. (lus study has o be performect 1 edge-on systems sitce the /p component In a vertical structure observable ouly in stch inclined galaxies.," Nevertheless, this study has to be performed in edge-on systems since the b/p component is a vertical structure observable only in such inclined galaxies."
 Usiug the tied-jug model (Begeman LOST) we have tle advantage to determine several kinematic:il j»aranmeters [rom iniial estimatecl values through an itera]ve fit to the velocity Held., Using the tilted-ring model (Begeman 1987) we have the advantage to determine several kinematical parameters from initial estimated values through an iterative fit to the velocity field.
 However. iu o objects the cominatiou of the edge-ou orientation -- )) aud the small angular size often. vie a lital )OOF salipliο in every ring of the tilted inodel (less tieu 15 points).," However, in our objects the combination of the edge-on orientation – ) and the small angular size often yield a final poor sampling in every ring of the tilted model (less then 15 points)."
 In this case. the Π Lai Or podices: DesIts or the rotation curve with poor coufideuce.," In this case, the fit fails or produces results for the rotation curve with poor confidence."
 Moreover. the velocity field derived as an intensitv-welelite€d mean velocity Cirst-moment analysi5) ὁ| by fitting a single-peaked. Crtaussian [9] the proiles do ol srovide a good estimate for the racia velelt. which was actually expected sinee velocity profiles lited by asynunetric distribution are not eliale.," Moreover, the velocity field derived as an intensity-weighted mean velocity (first-moment analysis) or by fitting a single-peaked Gaussian to the profiles do not provide a good estimate for the radial velocity, which was actually expected since velocity profiles fitted by a symmetric distribution are not reliable."
" Iu edge-on galaxies we are faced wih the inconvenienc etlat the beam intercepts a large portion of tje disk. the effect of the inclination. ai the peculiarities oftle galaxies (extra-plauar emission. ""beards”. in/outflow) which p'oduce a ail of t clist‘buion at lower velocities. towards the sysemic velocity."," In edge-on galaxies we are faced with the inconvenience that the beam intercepts a large portion of the disk, the effect of the inclination, and the peculiarities of the galaxies (extra-planar emission, “beards”, in/outflow) which produce a tail of the distribution at lower velocities, towards the systemic velocity."
 h ¢«ler to reduce this efect. the rotation curve coul be extracted as outlined in 5ancisi Allen (1979)," In order to reduce this effect, the rotation curve could be extracted as outlined in Sancisi Allen (1979)."
 The velocity is fitted bv μα ο Craussiau the extreme edge of the velocity proile at eac1 position along the major axis., The velocity is fitted by half a Gaussian to the extreme edge of the velocity profile at each position along the major axis.
 We «xrected the velocities for several effects. (raudom motlous. lusrurnent:il broacening. etc.," We corrected the velocities for several effects (random motions, instrumental broadening, etc.)"
 a explainec by Gentile et al. (, as explained by Gentile et al. (
2002J.,2002).
 Tje advantage of this nethod is evident., The advantage of this method is evident.
 We ¢ο LO expect to have a sinele-peakec Ciatussl Lin every velocity profile silice the profiles are uot symmetric. btt with this method we utilize t10 DOS seful halt (tlie external oue) of a Gaussian. avoiding the fit over the broadened half owing to tte lower velocities.," We do not expect to have a single-peaked Gaussian in every velocity profile since the profiles are not symmetric, but with this method we utilize the most useful half (the external one) of a Gaussian, avoiding the fit over the broadened half owing to the lower velocities."
 T1e disadvaitage stars When we have to investigae warped systems of all spiral οςilaxies) ancl the positiou-velocity diagrain (PVD) is along a fixed position angle. while in such systems bot1 tbe line «of uodes aud the kilelnalica axis are changing with radis.," The disadvantage starts when we have to investigate warped systems of all spiral galaxies) and the position-velocity diagram (PVD) is along a fixed position angle, while in such systems both the line of nodes and the kinematical axis are changing with radius."
 The effect of warps ou the procedure to extract rotation curves over the PVD in edge-on systems is etite severe., The effect of warps on the procedure to extract rotation curves over the PVD in edge-on systems is quite severe.
 Moreover. the phenomenon of warpine," Moreover, the phenomenon of warping"
(?)..,\citep{1992ApJS...83...29S}.
" This galaxy is detected across the bands at 0.2 Jy (25m), 2.4 Jy (60m) and 4.5 Jy (100m), implying warm dust."," This galaxy is detected across the bands at 0.2 Jy $25 \unit{\mu m}$ ), 2.4 Jy $60 \unit{\mu m}$ ) and 4.5 Jy $100 \unit{\mu m}$ ), implying warm dust."
" The implied radio luminosity, if the radio source is associated with the spiral galaxy, is Lp=5x10?ergs!Hz !."," The implied radio luminosity, if the radio source is associated with the spiral galaxy, is $L_{\nu} = 5 \times 10^{29} \unit{erg~s^{-1}~Hz^{-1}}$ ."
" As the MOST contours are centred on the optical source, AGN activity or ISS of an AGN is a possible explanation but AGNs in barred spiral galaxies are rare (?).."," As the MOST contours are centred on the optical source, AGN activity or ISS of an AGN is a possible explanation but AGNs in barred spiral galaxies are rare \citep{Wilson95}."
" The warm dust implies star formation, so a stellar event is conceivable."," The warm dust implies star formation, so a stellar event is conceivable."
" T'he 3 year time-scale argues strongly against a GRB afterglow interpretation, and the shape and time-scale are consistent with a Type II RSN."," The 3 year time-scale argues strongly against a GRB afterglow interpretation, and the shape and time-scale are consistent with a Type II RSN."
" The luminosity, once again, is higher than that of any known RSN."," The luminosity, once again, is higher than that of any known RSN."
 We conclude that SUMSS J200936—554236 is associated with an unusual stellar event or explosion in IC4957., We conclude that SUMSS $-$ 554236 is associated with an unusual stellar event or explosion in IC4957.
 The light curve for SUMSS J223225—615308 (Fig. D6]) , The light curve for SUMSS $-$ 615308 (Fig. \ref{fig:J223255-615313-lightcurve}) )
shows two pronounced dips in flux density over two years and it is the most dramatic of some five variable sources in this field., shows two pronounced dips in flux density over two years and it is the most dramatic of some five variable sources in this field.
" There are other sources at the same flux density level in this field that do not exhibit variability, ruling out a calibration effect."," There are other sources at the same flux density level in this field that do not exhibit variability, ruling out a calibration effect."
" An overlay of SUMSS J223225—615308 and the Parkes-MIT-NRAO (PMN) survey data (?) confirms an association with PMNJ2232—6153, whose reported flux density is 40+7mJy at 4.85 GHz."," An overlay of SUMSS $-$ 615308 and the Parkes-MIT-NRAO (PMN) survey data \citep{Wright94PMN} confirms an association with $-$ 6153, whose reported flux density is $40 \pm 7 \unit{mJy}$ at 4.85 GHz."
" This flux density together with the range of flux densities shown in the 843 MHz light curve, implies a spectral index between —0.8 and —1.0, although we note that the PMN and MOST observations are not contemporaneous."," This flux density together with the range of flux densities shown in the 843 MHz light curve, implies a spectral index between $-0.8$ and $-1.0$, although we note that the PMN and MOST observations are not contemporaneous."
" If the variation is due to scintillation, this implies a compact source or component, and together with the spectral index implies a classification as a compact steep spectrum source."," If the variation is due to scintillation, this implies a compact source or component, and together with the spectral index implies a classification as a compact steep spectrum source."
the efficiency of Comptonization is much higher than bremsstrahhime in ACNs. in contrast to the case of ταν radiation from solar flares.,"the efficiency of Comptonization is much higher than bremsstrahlung in AGNs, in contrast to the case of X-ray radiation from solar flares."
 It should be noted that the radiation cficiency of the thick-tarect Dremsstrabhme is generalle much lower than the unity because the electrous injected into dense material would lose their energv by ijouization or Coulomb losses rather than breimisstrallung., It should be noted that the radiation efficiency of the thick-target bremsstrahlung is generally much lower than the unity because the electrons injected into dense material would lose their energy by ionization or Coulomb losses rather than bremsstrahlung.
 Our results sugeestCoco that the majority. of AGN »pulatious that are responsible for the CXD should οπου] have a nonthermal component bevond the hermal exponential cutoff in their eamunarav spectra., Our results suggest that the majority of AGN populations that are responsible for the CXB should commonly have a nonthermal component beyond the thermal exponential cutoff in their gamma-ray spectra.
 Future sensitive AIeV observations iuav reveal the routhermal couponcuts frou nearby. ACN spectra., Future sensitive MeV observations may reveal the nonthermal components from nearby AGN spectra.
 For instance. the Advanced Compton Telescope (ACT. see (2006)). schectiled for launch around. 2015. will lave a continu sensitivity in the 0.210 MeV. baud with E24EF./dE.~1«10?CE./MeV)MeVeim7s|l. where dF./dE. is the differential photon flux.," For instance, the Advanced Compton Telescope (ACT, see (2006)), scheduled for launch around 2015, will have a continuum sensitivity in the 0.2–10 MeV band with $E_\gamma^2 dF_\gamma/dE_\gamma \sim 1 \times 10^{-5} (E_\gamma/{\rm
MeV}) \ \rm{MeV \ cm^{-2}s^{-1}}$, where $dF_\gamma/dE_\gamma$ is the differential photon flux."
 Using he hard N-rav fux of NGC 1151 2007). the brightest ρωσ ealaxyv. we estimate he expected nonthermal MeV flux απ ~δν10(E./MeV)95.MeVeim78 4 which can well be detected with the ACT.," Using the hard X-ray flux of NGC 4151 2007), the brightest Seyfert galaxy, we estimate the expected nonthermal MeV flux as $\sim 3 \times 10^{-5} (E_\gamma/{\rm
MeV})^{-0.8} \ \rm{MeV \ cm^{-2} s^{-1}}$ , which can well be detected with the ACT."
 The detection of suc[um components from nearby bright ACNs would eive a clear test for our model., The detection of such components from nearby bright AGNs would give a clear test for our model.
 Tn this paper. we have shown that MeV. eamunarav backeround can be explained by the same population of ACNs that inakes the CNB. by considering Comptonization by uouthermal electrons in AGN coronae that are theoretically expected to exist.," In this paper, we have shown that MeV gamma-ray background can be explained by the same population of AGNs that makes the CXB, by considering Comptonization by nonthermal electrons in AGN coronae that are theoretically expected to exist."
 The best ft to the MeV. eauuna-rav background is obtained when the noutheriial componeut has ~3.5% , The best fit to the MeV gamma-ray background is obtained when the nonthermal component has $\sim 3.5\%$ 
Apenk? 0946pom with an intrinsic dispersion 0—31 jum: 2) ==2642 hh with e-skk. The DOO sample consists of sources detected at Sa in at least one BLAST band.,$\left\langle \lambda_{\rm peak} \right\rangle$ $\pm$ $\mu$ m with an intrinsic dispersion $\sigma$ $\mu$ m; $\left\langle T \right\rangle$ $\pm$ K with $\sigma$ K. The D09 sample consists of sources detected at $\sigma$ in at least one BLAST band.
 Almost all are also detected at το ancl yam. although the MIPS. counterparts have fainter flux densities than the 809 sample.," Almost all are also detected at 70 and $\mu$ m, although the MIPS counterparts have fainter flux densities than the S09 sample."
 The average peak wavelength of the DOO sample is consistent with that of S09. although the characteristics of the BLAST ULIRCSs cannot be evaluated in an unbiased part of the Aposug-z space.," The average peak wavelength of the D09 sample is consistent with that of S09, although the characteristics of the BLAST ULIRGs cannot be evaluated in an unbiased part of the $\lambda_{\rm peak}$ -z space."
 For DOO we calculate. Άρωμα) ——89c4 with an intrinsic dispersion. a=15 pm: (2) ==290+1 WW with oe—5HFxlx. Note that the range in Ape is slightly different for the ALLS and BLAST samples. with the former extending to lower and higher Apa.," For D09 we calculate $\left\langle \lambda_{\rm peak} \right\rangle$ $\pm$ 4 with an intrinsic dispersion $\sigma$ $\mu$ m; $\left\langle T \right\rangle$ $\pm$ K with $\sigma$ K. Note that the range in $\lambda_{\rm peak}$ is slightly different for the MIPS and BLAST samples, with the former extending to lower and higher $\lambda_{\rm peak}$."
 Ln addition. their redshift) clistributions ave diferent. with most SOO ULIICs being below z=1 and most DOO ULIRGSs above z=1.," In addition, their redshift distributions are different, with most S09 ULIRGs being below z=1 and most D09 ULIRGs above z=1."
 The average peak wavelength of the COS SCUBA sample is also in agreement with DOO and 509., The average peak wavelength of the C08 SCUBA sample is also in agreement with D09 and S09.
 For COS we calculate. Ai) ασε Ξξθnn with an intrinsic dispersion e—11 jim and (7? ==204+1 with a=3hkh. however note that (i) there are large upper WWerrors on the temperature measurements. (ii) we are not. probing an unbiased part in the selection function and (iii) there are additional selection elfects due to the radio selection (see also Blain et al.2," For C08 we calculate $\left\langle \lambda_{\rm peak} \right\rangle$ $\pm$ $\mu$ m with an intrinsic dispersion $\sigma$ $\mu$ m and $\left\langle T \right\rangle$ $\pm$ K with $\sigma$ K, however note that (i) there are large upper errors on the temperature measurements, (ii) we are not probing an unbiased part in the selection function and (iii) there are additional selection effects due to the radio selection (see also Blain et al.;"
004b:: Coppin et al. 2009))., Coppin et al. ).
 We point out that the Ape distribution of these high redshift saniples extends to much longer peak wavelengths than what is seen for the local VLIRGs in Fig. 2..," We point out that the $\lambda_{\rm peak}$ distribution of these high redshift samples extends to much longer peak wavelengths than what is seen for the local ULIRGs in Fig. \ref{fig:fig2},"
 resulting in a higher average Apenk by at least 26 (hore o is the dispersion in the local sample. equal to ju)," resulting in a higher average $\lambda_{\rm peak}$ by at least $\sigma$ (here $\sigma$ is the dispersion in the local sample, equal to $\mu$ m)."
 In 809 we showed that a Iuminosity-tempoerature correlation is not apparent in the 70//m sample. although it is clearly seen in the BCS.," In S09 we showed that a luminosity-temperature correlation is not apparent in the $\mu$ m sample, although it is clearly seen in the BGS."
 Llowever. it has been proposed that he abundance of cold galaxies in the distant. Universe is a consequence of the local L-T relation evolving with redshift (c.g. Chapman et al.2," However, it has been proposed that the abundance of cold galaxies in the distant Universe is a consequence of the local L-T relation evolving with redshift (e.g. Chapman et al.;"
002: Lewis. Chapman and Helou2005: CLILAXO9) in the same wav that the knee of the infrared uminosity. [unction evolves by 2). where q~3 (e.g. Le Floeh et al.2," Lewis, Chapman and Helou; CHA09) in the same way that the knee of the infrared luminosity function evolves by $^q$, where $\sim$ 3 (e.g. Le Floc'h et al.,"
005.. Lluyvnh et al. 2007b))., Huynh et al. ).
 This suggests that although more luminous galaxies would still have higher empoeratures than their less luminous counterparts. they would be much colder than the objects we see locally. ie. he ULIRG temperature clistribution would. shift. towards onger Ajo (ower T) with increasing redshift.," This suggests that although more luminous galaxies would still have higher temperatures than their less luminous counterparts, they would be much colder than the objects we see locally, i.e. the ULIRG temperature distribution would shift towards longer $\lambda_{\rm peak}$ (lower T) with increasing redshift."
be equal to zero (by definition the solar metallicity). since we have neglected the influence of SN Ia events.,"be equal to zero (by definition the solar metallicity), since we have neglected the influence of SN Ia events."
" To quantify the enrichment of the ISM we introduce the concept of the polluted mass M, in a unit volume at time 7.", To quantify the enrichment of the ISM we introduce the concept of the polluted mass $M_{\mathrm{poll}}$ in a unit volume at time $\tau$.
 It is defined as the total mass which gets polluted by Vex SNe. where Nox is the number of SNe in the unit volume that occwred during the elapsed time 7.," It is defined as the total mass which gets polluted by $N_{\mathrm{SN}}$ SNe, where $N_{\mathrm{SN}}$ is the number of SNe in the unit volume that occurred during the elapsed time $\tau$ ."
 For a constant mixing-mass M. swept up by a SN event. Mi=Vax:le.," For a constant mixing-mass $M_{\mathrm{sw}}$ swept up by a SN event, $M_{{\rm poll}}=N_{\mathrm{SN}} \cdot M_{\mathrm{sw}}$."
 Since the polluted mass ts directly proportional to the number of SNe. it can become larger than the total ISM mass in the unit volume. τον.," Since the polluted mass is directly proportional to the number of SNe, it can become larger than the total ISM mass in the unit volume, $M_{\mathrm{tot}}$."
" Furthermore. the pollution factor f, is defined as the ratio M,/M,4 and only depends on Nyx. for fixed Af. and My."," Furthermore, the pollution factor $f_{{\rm poll}}$ is defined as the ratio $M_{\mathrm{poll}} /
M_{\mathrm{tot}}$ and only depends on $N_{\mathrm{SN}}$, for fixed $M_{\mathrm{sw}}$ and $M_{\mathrm{tot}}$."
 When fou=1. enough SNe have contributed to the chemical enrichment to theoretically pollute the entire ISM in the unit volume. even though there still may be patches of material which were not yet affected by any SN.," When $f_{\mathrm{poll}}=1$, enough SNe have contributed to the chemical enrichment to theoretically pollute the entire ISM in the unit volume, even though there still may be patches of material which were not yet affected by any SN."
 A higher pollution factor results in à better mixing of the halo ISM. decreasing the local abundance differences and the amount of material with primordial abundances.," A higher pollution factor results in a better mixing of the halo ISM, decreasing the local abundance differences and the amount of material with primordial abundances."
 Therefore. the ratio AMae/My determines the mixing efficiency in our model. 1.8. how many SNe in the unit volume are needed to reach a certain value of fii.," Therefore, the ratio $M_{\mathrm{sw}}/M_{\mathrm{tot}}$ determines the mixing efficiency in our model, i.e. how many SNe in the unit volume are needed to reach a certain value of $f_{\mathrm{poll}}$."
 Given fii. Ma and the mean. IMF integrated iron yield (Alp) of a typical SN IL. the mean metallicity of the ISM then is determined by where C is the solar iron abundance.," Given $f_{\mathrm{poll}}$, $M_{\mathrm{sw}}$ and the mean, IMF integrated iron yield $\left< M_{\mathrm{Fe}}
\right>$ of a typical SN II, the mean metallicity of the ISM then is determined by where $C$ is the solar iron abundance."
 The local inhomogeneities of the ISA begin to disappear when most of the gaseous SN remnants start to overlap., The local inhomogeneities of the ISM begin to disappear when most of the gaseous SN remnants start to overlap.
 This is the case when more or less every cloud in the halo was influenced at least once by a SN event. re. the pollution factor 1s about equal to one.," This is the case when more or less every cloud in the halo was influenced at least once by a SN event, i.e. the pollution factor is about equal to one."
 With the adopted mixing mass of Mow=5sWEA. this is the case at [Fe/H] ~—2.5.," With the adopted mixing mass of $M_{\mathrm{sw}} = 5 \times
10^4 \, \mathrm{M}_{\sun}$ this is the case at [Fe/H] $\approx -2.8$."
 This metallicity gives an upper limit for the end of the early phase and the beginning of the transition to the second. well-mixec enrichment phase.," This metallicity gives an upper limit for the end of the early phase and the beginning of the transition to the second, well-mixed enrichment phase."
 Table 2 shows the pollution factor needed to reach the mean metallicities shown in the panels of Fig. 1.., Table \ref{snnr} shows the pollution factor needed to reach the mean metallicities shown in the panels of Fig. \ref{density}.
 Also show! are the corresponding SN frequency Vex and elapsed time 7. which depend on our model parameters.," Also shown are the corresponding SN frequency $N_{\mathrm{SN}}$ and elapsed time $\tau$, which depend on our model parameters."
" Here. the S frequency is defined as the number of SNe per Κρο and depends on the total ISM mass in the unit volume. whereas the elapsed time scales with the average SER as where 1.06-10!M;vrtkpe"" is the mean SFR in the unit volume in our model."," Here, the SN frequency is defined as the number of SNe per $^3$ and depends on the total ISM mass in the unit volume, whereas the elapsed time scales with the average SFR as where $1.06 \cdot 10^{-4} \, \mathrm{M}_{\sun} \, \mathrm{yr}^{-1} \,
\mathrm{kpc}^{-3}$ is the mean SFR in the unit volume in our model."
 Note that the evolution of the abundance ratios as a function of |Fe/H] is independent of the star formation timescale and the SER specified in the model., Note that the evolution of the abundance ratios as a function of [Fe/H] is independent of the star formation timescale and the SFR specified in the model.
 The scatter in the [El/Fe]| ratios of the model stars as a function of [Fe/H] shows the same general trend for every element considered. independent of the individual stellar yields.," The scatter in the [El/Fe] ratios of the model stars as a function of [Fe/H] shows the same general trend for every element considered, independent of the individual stellar yields."
 The inhomogeneous mixing of the very metal-poor halo ISM at [Fe/H] <3.0 leads to a scatter in the [El/Fe] ratios of up to ] dex., The inhomogeneous mixing of the very metal-poor halo ISM at [Fe/H] $< -3.0$ leads to a scatter in the [El/Fe] ratios of up to 1 dex.
 This scatter continuously decreases for higher metallicities. reflecting the ongoing mixing of the ISM.," This scatter continuously decreases for higher metallicities, reflecting the ongoing mixing of the ISM."
 At [Fe/H] >2.0 the model stars show an IMF averaged abundance pattern with an intrinsic scatter of about 0.1 to 0.2 dex., At [Fe/H] $> -2.0$ the model stars show an IMF averaged abundance pattern with an intrinsic scatter of about 0.1 to 0.2 dex.
 This behaviour matches the general trend of the observations well. as can be seen in Fig. 2..," This behaviour matches the general trend of the observations well, as can be seen in Fig. \ref{scatter}."
 The observations also show a large scatter at low metallicities which again decreases for higher [Fe/H]. with some exceptions. however: the iron-group elements Cr and Mn show a strong decrease in the [Cr/Fe] and |Mn/Fe] ratio for lower metallicities.," The observations also show a large scatter at low metallicities which again decreases for higher [Fe/H], with some exceptions, however: the iron-group elements Cr and Mn show a strong decrease in the [Cr/Fe] and [Mn/Fe] ratio for lower metallicities."
 This behaviour can not be reproduced with our adopted metallicity-independent stellar yields and the. progenitor-independent mixing mass., This behaviour can not be reproduced with our adopted metallicity-independent stellar yields and the progenitor-independent mixing mass.
 Compared to the observations. the distribution of [Ni/Fe] ratios of the model stars in Fig.," Compared to the observations, the distribution of [Ni/Fe] ratios of the model stars in Fig."
 2. shows a scatter that is much toosmall., \ref{scatter} shows a scatter that is much toosmall.
 This is most likely due to the choice of mass cuts in the SNe II models. which have been set with the aim to reproduce the average solar [Ni/Fe] ratio.," This is most likely due to the choice of mass cuts in the SNe II models, which have been set with the aim to reproduce the average solar [Ni/Fe] ratio."
 Thielemann et al. (1996)), Thielemann et al. \cite{th96}) )
 discuss in detail that large variations can easily occur., discuss in detail that large variations can easily occur.
 See also the discussion in Sect. 3.., See also the discussion in Sect. \ref{nucleo}.
 We therefore now want to investigate whether the sequence of enrichment stages seen in our model is similar to the observed evolution. of abundance ratios even in cases when the employed yields may be incorrect., We therefore now want to investigate whether the sequence of enrichment stages seen in our model is similar to the observed evolution of abundance ratios even in cases when the employed yields may be incorrect.
 To this end we have normalized the scatter in [Ni/Fe] of the model-stars at low [Fe/H] to unity. and have similarly renormalized the range of values for the observed stellar |Ni/Fe| ratios to one.," To this end we have normalized the scatter in [Ni/Fe] of the model-stars at low [Fe/H] to unity, and have similarly renormalized the range of values for the observed stellar [Ni/Fe] ratios to one."
 The mean values of both distributions were left unchanged., The mean values of both distributions were left unchanged.
 The resulting renormalized distributions are shown in Fig. 3.., The resulting renormalized distributions are shown in Fig. \ref{ninormal}.
 The remarkably good agreement of both distributions after this procedure indicates that the enrichment history of the halo ISM implied by the model is consistent with the data. even though the employed Ni yields are not.," The remarkably good agreement of both distributions after this procedure indicates that the enrichment history of the halo ISM implied by the model is consistent with the data, even though the employed Ni yields are not."
 Based on similar comparisons. we conclude that the abundance ratio data of most elements except Mn and Cr are consistent with the predicted enrichment history. and the scatter plots in Fig.," Based on similar comparisons, we conclude that the abundance ratio data of most elements except Mn and Cr are consistent with the predicted enrichment history, and the scatter plots in Fig."
 2 can thus be used to compare the range of the theoretically predicted nucleosynthesis yields with observations., \ref{scatter} can thus be used to compare the range of the theoretically predicted nucleosynthesis yields with observations.
 To deseribe the transition from the metal-poor. unmixed to the enriched. well mixed ISM more quantitatively. the relativefrequency of stars at a given [E]/Fe] ratio has been analysed for the different enrichment phases.," To describe the transition from the metal-poor, unmixed to the enriched, well mixed ISM more quantitatively, the relativefrequency of stars at a given [El/Fe] ratio has been analysed for the different enrichment phases."
 In the case of silicon. this detailed enrichment history is shown in Fig. 4..," In the case of silicon, this detailed enrichment history is shown in Fig. \ref{sihist}. ."
 The different, The different
candidates.,candidates.
 The sensitivities of the data can be found in Table 2.., The sensitivities of the data can be found in Table \ref{spitzerdata}.
 We searched the public catalog (Sanders et al., We searched the public catalog (Sanders et al.
" 2007. v. ""GO2”. released May 2007) for sources associated with our candidates."," 2007, v. “GO2”, released May 2007) for sources associated with our candidates."
 In the IRAC bands. counterparts were searched for within a circle with 5 IRAC pixels C) radius around each candidate. and in the MIPS bands within a circle with 4 MIPS pixels (1.8) radius.," In the IRAC bands, counterparts were searched for within a circle with 5 IRAC pixels $3''$ ) radius around each candidate, and in the MIPS bands within a circle with 4 MIPS pixels $4.8''$ ) radius."
 In total [56. 41. 25. 15. 20] candidate counterparts were found in the [Chl. Ch2. Ch3. Ch4. MIPS- bands. see also Table 5 that includes all sub-sets of the candidates.," In total [56, 41, 25, 15, 20] candidate counterparts were found in the [Ch1, Ch2, Ch3, Ch4, MIPS-24] bands, see also Table \ref{spitzdet} that includes all sub-sets of the candidates."
 The random probability of finding an object within our search radit are 0.0096 in Chl. resulting in 1.6 random false detections in the whole sample.," The random probability of finding an object within our search radii are 0.0096 in Ch1, resulting in 1.6 random false detections in the whole sample."
 After visually inspecting the associations. two were excluded as random false detections and the list of Spitzer detected sources should. after removal of these two sources (detected in Chl and Ch2). be robust.," After visually inspecting the associations, two were excluded as random false detections and the list of Spitzer detected sources should, after removal of these two sources (detected in Ch1 and Ch2), be robust."
 The detection rate of our candidates is in Chl and in MIPS-24. which is à higher rate than found in. surveys for LAEs at redshifts three and beyond (Lai et al.," The detection rate of our candidates is in Ch1 and in MIPS-24, which is a higher rate than found in surveys for LAEs at redshifts three and beyond (Lai et al."
 2007. 2008) but in agreement with surveys at 2~2.3 (Colbert et al.," 2007, 2008) but in agreement with surveys at $z \sim 2.3$ (Colbert et al."
 2006)., 2006).
 The MIPS-24 detected candidates are by definition also ultra-luminous infrared galaxies (ULIRGs) due to their bright infrared fluxes., The MIPS-24 detected candidates are by definition also ultra-luminous infrared galaxies (ULIRGs) due to their bright infrared fluxes.
 For a further discussion on these LAE ULIRGs and their evolution with redshift. see Nilsson Moller (2009).," For a further discussion on these LAE ULIRGs and their evolution with redshift, see Nilsson ller (2009)."
 To test the public catalogues we performed aperture photometry on a number of objects in the catalogue., To test the public catalogues we performed aperture photometry on a number of objects in the catalogue.
 The catalogue fluxes were extracted in 1/44 radius apertures (to be compared to 1755 radius apertures for the optical broad-band images). and aperture corrected to give the total flux of the object according to the aperture corrections listed in the release notes of the catalogue.," The catalogue fluxes were extracted in 4 radius apertures (to be compared to 5 radius apertures for the optical broad-band images), and aperture corrected to give the total flux of the object according to the aperture corrections listed in the release notes of the catalogue."
 The fluxes measured in the image were in reasonable agreement with the catalogue values. however. the errors measured were in the cases of Chl - Ch3 roughly two times those quoted in the catalogue.," The fluxes measured in the image were in reasonable agreement with the catalogue values, however, the errors measured were in the cases of Ch1 - Ch3 roughly two times those quoted in the catalogue."
 For Ch4 and MIPS the errors were also 1n agreement., For Ch4 and MIPS the errors were also in agreement.
 Thus we multiply the published errors on our candidates in the Chl - Ch3 bands by two for the following analysis., Thus we multiply the published errors on our candidates in the Ch1 - Ch3 bands by two for the following analysis.
 There was a slight tendency of over-estimation of the fluxes in Chl. however. it was not significant enough to warrant a correction of the catalogue fluxes.," There was a slight tendency of over-estimation of the fluxes in Ch1, however, it was not significant enough to warrant a correction of the catalogue fluxes."
 It should be noted though. that the Ch! fluxes may be over-estimated by up to5%.," It should be noted though, that the Ch1 fluxes may be over-estimated by up to."
. In the subsequent SED fitting. an extra error of 10% of the flux of each object was included. in order to account for systematic errors in the data reduction (see also Muzzin et al.," In the subsequent SED fitting, an extra error of $10$ of the flux of each object was included, in order to account for systematic errors in the data reduction (see also Muzzin et al."
 2009)., 2009).
 The method used to fit the SEDs of the LAEs is an updated version of the code used in Nilsson et al. (, The method used to fit the SEDs of the LAEs is an updated version of the code used in Nilsson et al. (
2007). called NisseFit.,"2007), called NisseFit."
 It is based on the stellar populations catalogue GALAXEV (Bruzual Charlot 2003) and the fitting is done using a Monte-Carlo Markov-Chain (MCMC) algorithm., It is based on the stellar populations catalogue GALAXEV (Bruzual Charlot 2003) and the fitting is done using a Monte-Carlo Markov-Chain (MCMC) algorithm.
" The algorithm explores a multi-dimensional parameter space by stepping in a random fashion from one point P; in this space to another 7;,4.", The algorithm explores a multi-dimensional parameter space by stepping in a random fashion from one point $P_i$ in this space to another $P_{i+1}$ .
" The step is random in the sense that the projected distance from point 75; to P;4 along one of the parameter axes in the parameter space is a randomly chosen value ranging from O0 to the maximum step size. 77,,,,."," The step is random in the sense that the projected distance from point $P_i$ to $P_{i+1}$ along one of the parameter axes in the parameter space is a randomly chosen value ranging from 0 to the maximum step size, $\Delta P_{max}$."
 The direction of the step along an axis is also random. with a probability of that the direction is along the positive or negative direction respectively.," The direction of the step along an axis is also random, with a probability of that the direction is along the positive or negative direction respectively."
 We impose boundary conditions for all parameters and ensure that no step leads to a value outside these boundaries., We impose boundary conditions for all parameters and ensure that no step leads to a value outside these boundaries.
 The parameters and the boundary values we impose on them are listed in Table 4.., The parameters and the boundary values we impose on them are listed in Table \ref{tab:params}.
" Once a new point P,1 is determined. the current model is advanced to the new point with a probability p;.;;4 which is given by the ratio of the two model probabilities given the data D. where u, and 4$ are the reduced 4? values for the two points in the parameter space and T is a ""temperature"" parameter which can be used to adjust the convergence."," Once a new point $P_{i+1}$ is determined, the current model is advanced to the new point with a probability $p_{i\rightarrow i+1}$ which is given by the ratio of the two model probabilities given the data $D$, where $\chi^2_{i+1}$ and $\chi^2_{i}$ are the reduced $\chi^2$ values for the two points in the parameter space and $T$ is a “temperature” parameter which can be used to adjust the convergence."
 In our case 7—1., In our case $T=1$.
 If the model is not advanced to the new point. the parameters remain 75. so ει=P.," If the model is not advanced to the new point, the parameters remain $P_i$, so $P_{i+1}=P_i$."
" This algorithm has several advantages over more common maximization algorithms (such as steepest descend. amoeba, ete.)"," This algorithm has several advantages over more common maximization algorithms (such as steepest descend, amoeba, etc.)"
 in that it allows a full exploration of the parameter space., in that it allows a full exploration of the parameter space.
 The result of our algorithm after iterations is a list of points ο/—O.N that. if .V is sufficiently large. represents a good sampling of the underlying probability distribution function of the parameters.," The result of our algorithm after $N$ iterations is a list of points $P_i, i=0..N$ that, if $N$ is sufficiently large, represents a good sampling of the underlying probability distribution function of the parameters."
 Please note carefully that. even though we refer to the quantity V2 defined in Eq.," Please note carefully that, even though we refer to the quantity $\chi^2_r$ defined in Eq."
" ??. as the ""reduced chi-squared” here and throughout this paper. the underlying modelling errors are not known to sufficient accuracy. compared to the relatively high measurement accuracy of the data. to allow the usual interpretation of a reduced chi-square value."," \ref{eq:chi} as the “reduced chi-squared” here and throughout this paper, the underlying modelling errors are not known to sufficient accuracy, compared to the relatively high measurement accuracy of the data, to allow the usual interpretation of a reduced chi-square value."
 Given the large number of photometric bands and the small measurement errors in many of these. no stellar populationmodels are expected to give good fits to all the data in an absolute sense. and hence the 42 values are not actually expected to be close," Given the large number of photometric bands and the small measurement errors in many of these, no stellar populationmodels are expected to give good fits to all the data in an absolute sense, and hence the $\chi^2_r$ values are not actually expected to be close"
in the huninosity relations Chat use E.,in the luminosity relations that use $E_{peak}$.
 SUL. even the currently accepted laminosity relations have (heir drawbacks.," Still, even the currently accepted luminosity relations have their drawbacks."
 The best (ie. the Gehtest) of these relations. (he Ghirlanda relation. can only be applied if there is an observed jet break.," The best (i.e. the tightest) of these relations, the Ghirlanda relation, can only be applied if there is an observed jet break."
 Jet breaks are a well understood phenomena (Rhoads 1997: Sari el al., Jet breaks are a well understood phenomena (Rhoads 1997; Sari et al.
 1999)., 1999).
 Measuring a jet break is fairly clilficult for a variety of reasons. and has only been observed in a small percentage of bursts.," Measuring a jet break is fairly difficult for a variety of reasons, and has only been observed in a small percentage of bursts."
 Melandii οἱ al. (, Melandri et al. (
2008) and IxXocevski Butler (2008) have pointed out problems in identifving these jet breaks with the X-ray data.,2008) and Kocevski Butler (2008) have pointed out problems in identifying these jet breaks with the X-ray data.
 Alost notably. the Amati relation has been criticized [for several reasons.," Most notably, the Amati relation has been criticized for several reasons."
 Li (2006) originated a test (hat demonstrated an ambiguity when the measured. properties are used to determine the redshift., Li (2006) originated a test that demonstrated an ambiguity when the measured properties are used to determine the redshift.
 This result was confirmed by other eroups later (e.g. Schaefer Collazzi 2007)., This result was confirmed by other groups later (e.g. Schaefer Collazzi 2007).
 This ambiguity also exists for the Ghirlanda relation. but at a substantially higher redshift.," This ambiguity also exists for the Ghirlanda relation, but at a substantially higher redshift."
 This ambiguity does not exist [or any of the other confirmed: luminosity relations. and so (he ambieuily problem can go away if multiple relations are used {ο determine redshift.," This ambiguity does not exist for any of the other confirmed luminosity relations, and so the ambiguity problem can go away if multiple relations are used to determine redshift."
 This problem does affect current work on the GRB IIubble Diagram because those Iuminositv indicators were derived Irom a known reclshilt obtained spectroscopically., This problem does affect current work on the GRB Hubble Diagram because those luminosity indicators were derived from a known redshift obtained spectroscopically.
 Another major criticism towards the Amati relation came from Nakar and Piran (2005)., Another major criticism towards the Amati relation came from Nakar and Piran (2005).
 In this work. Nakar and Piran developed a test specifically for the Amati relation. the beauty ol the test being that a redshift was not needed.," In this work, Nakar and Piran developed a test specifically for the Amati relation, the beauty of the test being that a redshift was not needed."
 This test has since been generalized in several independent investigations (e.g. Dand Preece 2005: Schaefer Collazzi 2007: Goldstein et al., This test has since been generalized in several independent investigations (e.g. Band Preece 2005; Schaefer Collazzi 2007; Goldstein et al.
 2010)., 2010).
 Thev combined the Amati relation (equation 1)) with the inverse square law for [Inences (equation 2)) to eliminate £j; (equation 3)).," They combined the Amati relation (equation \ref{eq:AmatiRel}) ) with the inverse square law for fluences (equation \ref{eq:ISLF}) ) to eliminate $E_{\gamma,iso}$ (equation \ref{eq:NaP}) )."
" llere. E.;,, is the isotropic gama rav energy. d, is the luminosity clistance as derived with the concordance cosmology (O4=0.7. O,,=0.3. Il; = 14 km/s/Mpe). Shoe is the bolometric (hence (the fluence over the burst rest. frame 1-10.000. keV range). and is the redshift of the burst."," Here, $E_{\gamma,iso}$ is the isotropic gamma ray energy, $d_L$ is the luminosity distance as derived with the concordance cosmology $\Omega_\Lambda = 0.7$, $\Omega_m = 0.3$, $_0$ = 74 km/s/Mpc), $S_{bolo}$ is the bolometric fluence (the fluence over the burst rest frame 1-10,000 keV range), and is the redshift of the burst."
" The quantity ="" has been called the ‘energy ratio [or the Amati relation (e.g. Banc Preece 2005).", The quantity $\frac{E^{2.04}_{peak}}{S_{bolo}}$ has been called the `energy ratio' for the Amati relation (e.g. Band Preece 2005).
 The left side of equation 3 uses only directly observable quantities (albeit. thev are model dependent). while the right side is only a," The left side of equation 3 uses only directly observable quantities (albeit, they are model dependent), while the right side is only a"
where AZ» is the mass of the secondary star ancl C£ is the universal constant of gravitation.,where $M_2$ is the mass of the secondary star and $G$ is the universal constant of gravitation.
" If the secondary. star is near the giant branch. in the LR. diagram. we can estimate the mass of its core (and therefore a lower limit on the secondary star A2) using three basic relations obtained on the evolutionary mociels of ""stripped. giants”."," If the secondary star is near the giant branch in the HR diagram, we can estimate the mass of its core (and therefore a lower limit on the secondary star $M_2$ ) using three basic relations obtained on the evolutionary models of “stripped giants”."
 “Phe luminosity ancl radius of the core are strong functions of the core mass Aloe “PTaanm 1983: Webbink. Rappaport. Savonije 1983: also Phinney Kulkarni 1994): We also have from Roche geometry ancl Ixepler's Third Law a relationship between the mean density of the Roche lobe filling secondary star and the orbital period: where Q=ΑιΔΙ and Per(Q) is the sphere-equivalent radius of the Roche lobe for unit separation.," The luminosity and radius of the core are strong functions of the core mass $M_{\rm core}$ Taam 1983; Webbink, Rappaport, Savonije 1983; also Phinney Kulkarni 1994): We also have from Roche geometry and Kepler's Third Law a relationship between the mean density of the Roche lobe filling secondary star and the orbital period: where $Q=M_1/M_2$ and $R_{RL}(Q)$ is the sphere-equivalent radius of the Roche lobe for unit separation."
 For 2«Q<20. the quantity 5200)(11Q) 1;is approxiniatqv]els] constant (it varies between 9.7 and. 10.16).," For $2\le Q\le 20$, the quantity $R^{-3}_{RL}(Q)(1+Q)^{-1}$ is approximately constant (it varies between 9.7 and 10.16)."
 Thus. for our case here. the mean density of the secondary star is a function only of the orbital period to a good approximation.," Thus, for our case here, the mean density of the secondary star is a function only of the orbital period to a good approximation."
 Therefore the Roche radius is a function only of the mass of the secondary star., Therefore the Roche radius is a function only of the mass of the secondary star.
 The. procedure for finding. Ας is simple., The procedure for finding $M_{\rm core}$ is simple.
 For anassumed core mass Mo; we know its radius Roose and luminosity Lose refIcore..4)).," For an core mass $M_{\rm core}$ we know its radius $R_{\rm core}$ and luminosity $L_{\rm core}$ \\ref{lcore}, \ref{rcore}) )."
 For anassumed envelope mass Moe we know he total mass of the secondary. A and hence its racius Ro using ((5))., For an envelope mass $M_{\rm env}$ we know the total mass of the secondary $M_2$ and hence its radius $R_2$ using \ref{den}) ).
" The radius of the secondary. star aud he luminosity £o, can then be used to find the ellective emperature Zhi.", The radius of the secondary star and the luminosity $L_{\rm core}$ can then be used to find the effective temperature $T_{\rm eff}$ .
 relstripgplot shows a contour. plot of Zig in the Aus Al. plane for situations where Roo<2.," \\ref{stripgplot} shows a contour plot of $T_{\rm eff}$ in the $M_{\rm core}$ $M_{\rm env}$ plane for situations where $R_{\rm core}
< R_2$."
 Phe contour ines are nearly vertical. meaning the core mass Mo ds ightly constrained. whereas the envelope mass Mog is not.," The contour lines are nearly vertical, meaning the core mass $M_{\rm core}$ is tightly constrained whereas the envelope mass $M_{\rm env}$ is not."
 According to refstripgplot.. Z;4;=4300 corresponds to Mo;zc0.165M...," According to \\ref{stripgplot}, $T_{\rm eff}=4300$ corresponds to $M_{\rm core}\ge 0.165\,M_{\odot}$."
 llence the lower limit on the secondary star mass is Mo0.165AL. .," Hence the lower limit on the secondary star mass is $M_{2}\ge 0.165\,M_{\odot}$ ."
 We use a Monte Carlo procedure outlined in Orosz Wade (1999) to derive interesting binary parameters. and their uncertainties [rom the results of the light curve fitting., We use a Monte Carlo procedure outlined in Orosz Wade (1999) to derive interesting binary parameters and their uncertainties from the results of the light curve fitting.
 Since we have theracial velocity curve of the secondary star. each point in the mass ratio-inclination. plane corresponds," Since we have theradial velocity curve of the secondary star, each point in the mass ratio-inclination plane corresponds"
wines compared to the Sun are the consequence of the hieher effective teiiperature of ITD 166135.,wings compared to the Sun are the consequence of the higher effective temperature of HD 166435.
 No strong Lithium absorption liue is seen., No strong lithium absorption line is seen.
 The comparison with the Suus spectrum sugeests that. with our resolution. the sensitivity to the ‘Li doublet is limited to medium or strong features.," The comparison with the Sun's spectrum suggests that, with our resolution, the sensitivity to the $^7$ Li doublet is limited to medium or strong features."
 Moreover. m the case of 1166135. the Lithium doublet is blended with a nearby feature due to rotational broadening.," Moreover, in the case of 166435, the Lithium doublet is blended with a nearby feature due to rotational broadening."
" However. it appears that the ""Li feature in IID 166135 is no stronger than the one in the solar spectrum."," However, it appears that the $^7$ Li feature in HD 166435 is no stronger than the one in the solar spectrum."
 We cstimate an upper nuit of for the ‘Li doublet at., We estimate an upper limit of for the $^7$ Li doublet at.
 The curve of erowth frou Soderblometal.(1993a). them inuplies au upper luit for the πι abundance of N(Li)«1.7., The curve of growth from \cite{Sod93a} then implies an upper limit for the lithium abundance of $<1.7$.
 We computed the radial velocity of cach individua spectrin with the automatic reduction software. which uses a cross-correlation technique with binary mask templates.," We computed the radial velocity of each individual spectrum with the automatic reduction software, which uses a cross-correlation technique with binary mask templates."
 In addition to the stellar racia velocity. the cross-correlation function (CCF) provides additional information about features in the average spectral lines (see Quoeloz1991 for areview).," In addition to the stellar radial velocity, the cross-correlation function (CCF) provides additional information about features in the averaged spectral lines (see \cite{Queloz94} for a review)."
 The width of the CCF vields the of the stax. while the equivaleu width of the CCF can be used as a ietallicity estimate if the temperature of the star is known approximately (Mavor1980: Deuz&Mavor1981 :: Queloz1991)).," The width of the CCF yields the of the star, while the equivalent width of the CCF can be used as a metallicity estimate if the temperature of the star is known approximately \cite{Mayor80}; \cite{Benz81}; \cite{Queloz94}) )."
 The mean equivalent width of the CCF for the 70 individual spectra is simular το the value measured for the Pleiades stars of the same temperature Vy= 0.63)., The mean equivalent width of the CCF for the 70 individual spectra is similar to the value measured for the Pleiades stars of the same temperature $-$ $_0=0.63$ ).
 Therefore. a solar metallicity can be assmued for Πο 166135.," Therefore, a solar metallicity can be assumed for HD 166435."
 With the same technique and calibration described in. Quelozetal. 1998a.. we dervive a ican esin/=7.6£0.5," With the same technique and calibration described in \cite{Quelozetal98a}, , we dervive a mean $=7.6\pm0.5$."
 A simular value is measured by CORAVEL (esin/=7.740.7 1))., A similar value is measured by CORAVEL $=7.7\pm0.7$ ).
 Analysis of our eutire two-vear radial-velocity data set revealed a periodicity of 3.7987(+.000 1) davs., Analysis of our entire two-year radial-velocity data set revealed a periodicity of $\pm.0004$ ) days.
 The radial velocities are shown in 22-- where they are phase folded ou that period., The radial velocities are shown in 2 where they are phase folded on that period.
 We ft these data with a binary model and derived a slight orbital ecceutriev ο=0.2 and an auplitude A—δις corresponding to a lai nass for a planetary companion of MN;.," We fit these data with a binary model and derived a slight orbital eccentricy $e=0.2$ and an amplitude $K=83$, corresponding to a minimum mass for a planetary companion of $M_J$."
 The iis of the residuals to the fit is5., The rms of the residuals to the fit is.
.. A laree value compared to the tvpical precision ofο, A large value compared to the typical precision of.
"ν, If the binary inode is the correct interpretation ofthe observed radial-velocity variations. then additional radial-velocitv scatter intrinsic to the atiuosphiere of the star mist be Xxesent."," If the binary model is the correct interpretation of the observed radial-velocity variations, then additional radial-velocity scatter intrinsic to the atmosphere of the star must be present."
 Tn order to test the binary hwpothesis we first investigated the coherence time of he radial-welocitv variations.," In order to test the binary hypothesis, we first investigated the coherence time of the radial-velocity variations."
 Since a short-period planet iu a (presumed) circular orbit iuduces sinusoidal reflex motionin the star. we fit sine curves with a period of ddays to subsets," Since a short-period planet in a (presumed) circular orbit induces sinusoidal reflex motionin the star, we fit sine curves with a period of days to subsets"
We also define the one-sided emergent [ux which is the [lux that would be seen by an observer sitting at the disc photosphere ancl corotating with the disc (Page&Thorne1974)..,We also define the one-sided emergent flux which is the flux that would be seen by an observer sitting at the disc photosphere and corotating with the disc \citep{1974ApJ...191..499P}.
" We further neglect stresses in the tangential direction. Le. we set 5,—0."," We further neglect stresses in the tangential direction, i.e. we set $t_\phi{^\phi}=0$."
 Orthogonality with u then implies ἐν= 0., Orthogonality with ${\bmath u}$ then implies $t_\phi{^t}=0$ .
" We note that the requirement that 7,747=0. combined with the approximation that 2zv. gives us the integral As is the case with the time-steacdy thin accretion disk. it is convenient to use the conservation of barvonic rest mass. angular momentum. and energy to solve for the state of the system."," We note that the requirement that $t_\mu{^\nu}u^\mu=0$ , combined with the approximation that ${\bmath u}\approx{\bmath r}$, gives us the integral As is the case with the time-steady thin accretion disk, it is convenient to use the conservation of baryonic rest mass, angular momentum, and energy to solve for the state of the system."
 In our case. the equations will be time-dependent but their derivation is similar.," In our case, the equations will be time-dependent but their derivation is similar."
" For any current 1 satisfying where the source term E is the amount of charge added per unit. proper volume. we integrating this equation over z from ff to Lf. we get: This implies. for the rest-mass current. 7Hj which has no source. For: the angular momentum current ibi:77j""=s7"". there is à source. namely there is an angular momentum ddr added per unit radial coordinate per unit coordinate time."," For any current ${\bmath j}$ satisfying where the source term $\Gamma$ is the amount of charge added per unit proper 4-volume, we integrating this equation over $z$ from $-H$ to $H$, we get: This implies, for the rest-mass current $^{\rm(m)}j^\mu=\rho_0u^\mu$, which has no source, For the angular momentum current $^{\rm(L)}j^\mu = T_\phi{^\mu}$, there is a source, namely there is an angular momentum $\rmd T/\rmd r$ added per unit radial coordinate per unit coordinate time."
" ‘This is related to the source via ‘Thus For the energy current |j""=). the source dillers from the angular momentum source in that the energy added is equal to QO. times the angular momentum added."," This is related to the source via Thus For the energy current $^{\rm(E)}j^\mu = -T_t{^\mu}$, the source differs from the angular momentum source in that the energy added is equal to $\Omega_{\rm s}$ times the angular momentum added."
" This is a direct. consequence of the fact that the time dependence of the metric perturbation consists solely of a pattern speedος, ", This is a direct consequence of the fact that the time dependence of the metric perturbation consists solely of a pattern speed$\Omega_{\rm s}$.
"Phen 'P'p=0,7T. so Equations (182)) (184)). and (182)) provide 3 constraints for 4 unknowns (X. 9. £F. and Wi)."," Then $^{\rm(E)}\Gamma = \Omega_{\rm s}{^{\rm(L)}}\Gamma$, so Equations \ref{eq:cM}) ), \ref{eq:cL}) ), and \ref{eq:cM}) ) provide 3 constraints for 4 unknowns $\dot\Sigma$, $u^r$, $F$, and $W_\phi{^r}$ )."
 They can be solved if à. prescription is available for the shear stress Wo.. eg. an a-prescription o. (Shakura.&Sunvacy1973)..," They can be solved if a prescription is available for the shear stress $W_\phi{^r}$, e.g. an $\alpha$ -prescription \citep{1973A&A....24..337S}."
"=o) A special case of interest to us is the case where the viscosity of the disc is negligible (M,—0).", A special case of interest to us is the case where the viscosity of the disc is negligible $W_\phi{^r}=0$ ).
 This limit is appropriate in the final stages of a binary black hole inspiral where the viscous timescale becomes short compared to the merger timescale. as occurs in the Changctal.(2010) calculation.," This limit is appropriate in the final stages of a binary black hole inspiral where the viscous timescale becomes short compared to the merger timescale, as occurs in the \citet{2009arXiv0906.0825C} calculation."
 Then the disc evolution is dominated by angular momentum transport via the resonances and bv the inspiral of the secondary black bole (itself driven by radiation reaction)., Then the disc evolution is dominated by angular momentum transport via the resonances and by the inspiral of the secondary black hole (itself driven by radiation reaction).
 Writing Eq. (184)), Writing Eq. \ref{eq:cL}) )
" without the I, term. anc using Ίνα. (182))"," without the $W_\phi{^r}$ term, and using Eq. \ref{eq:cM}) )"
 to eliminate So we find using Eq. (185))," to eliminate $\dot\Sigma$, we find Similarly, using Eq. \ref{eq:cE}) )"
 gives rea gives us a linear svstem for’ and £F. with solution: ; 1dr ↾↓∖∪↓≻↓⋅⋯∙⋖⋅⋖⋅∠⇂⇂⋅⊔↓⋅⇂↓↥⋖⋅↓⋅⊳∖∖⋎⋖⋅⊔≱∖⋖⋅∟⊲⊏↥⋡≼≤⋗," gives This gives us a linear system for $u^r$ and $F$, with solution: and To proceed further, we use Eq. \ref{eq:dTdr}) )"
⇉⊐⊐↕↓↥↿↓↥⋖⋅↓↥⇂⇂⇀∖ equation., in the flux equation.
 We then reduce this using the relations and vielding finally Thus the emerging (ux is. as expected. proportional to the surface density of material at resonance and localizecl at the resonance.," We then reduce this using the relations and yielding finally Thus the emerging flux is, as expected, proportional to the surface density of material at resonance and localized at the resonance."
 In reality. the 8-function would be smeared out in a wav that depends on the dissipation mechanism.," In reality, the $\delta$ -function would be smeared out in a way that depends on the dissipation mechanism."
 We note further that ris not a proper racial coordinate: an observer sittingon the dise would. measure a proper radial distance element eclr instead. of dr.," We note further that $r$ is not a proper radial coordinate: an observer sittingon the disc would measure a proper radial distance element $\rme^\mmu\,\rmd r$ instead of $\rmd r$ ."
 That is. the emitted Dux per unit length (units: eres tem +) along the circumference as measured locally by an observer on the clise would be," That is, the emitted flux per unit length (units: $\,$ $^{-1}\,$ $^{-1}$ ) along the circumference as measured locally by an observer on the disc would be"
This research has mace use of data obtained. [rom the satellite. a collaborative mission between the space agencies of Japan (JANA) and the USA (NASA).,"This research has made use of data obtained from the satellite, a collaborative mission between the space agencies of Japan (JAXA) and the USA (NASA)."
 Data obtained withNALAI-Newtou has also been used. within this paper. an ESA science mission. with instruments and contributions cirectly funded by ESA Member States and NASA.," Data obtained with has also been used within this paper, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA."
with a mass greater than the mitinui inass of the solar nebula:: Weidenschilling LOTT. Hayashi 1951). and that the mecian disk mass isML.,"with a mass greater than the minimum mass of the solar nebula; Weidenschilling 1977, Hayashi 1981), and that the median disk mass is."
.. Further insights into disk evolution Ca1 be οMalned by using rich ¢usters as a tool to empirically measure he mass of disks as a fuiction « TSellar mass aud age |rinuch the same manner near-infrared sttdies have used clusters ic establish the frequency. of inier accretion disks (Haisch.Lada.&Laca2001b)., Further insights into disk evolution can be obtained by using rich clusters as a tool to empirically measure the mass of disks as a function of stellar mass and age in much the same manner near-infrared studies have used clusters to establish the frequency of inner accretion disks \citep{Haisch01b}.
. Continuum suΝους of clusters are also imporant since an appreciable fraction of stars in molecular clouds are found iu icl clusters (Ladaetal.1991:Carpenter2000).. aud the high ultraviolet raciatjon fields produced by O-stars in clusters 1jay iullueuce disk evolution (Jolinstone.Stórzer&Holeubach1999:ScallyClarke 2001).," Continuum surveys of clusters are also important since an appreciable fraction of stars in molecular clouds are found in rich clusters \citep{Lada91,Carp00}, and the high ultraviolet radiation fields produced by O-stars in clusters may influence disk evolution \citep{Johnstone98,Storzer99,Scally01}."
. The main observational chelenge to studying clusters in the 1ullimeter continuum is that high augular resollion is required to resolve the stars aud distiuglish disk eiission from the more extended. moleclar cloud., The main observational challenge to studying clusters in the millimeter continuum is that high angular resolution is required to resolve the stars and distinguish disk emission from the more extended molecular cloud.
" ΤΙe only rich cluster surveyed. to cl: "" interferometric techluieqes has been the Orion Nebula Custer (Muudsy.Loouey.&Lada1*2:Ballyetal.1993)."," The only rich cluster surveyed to date by interferometric techniques has been the Orion Nebula Cluster \citep{Mundy95,Bally98}."
. However. these observa10|Is weο 10-50 ines less sensitivel5 to dust mass th: je Observations of Taurus axd p Oph ix cdid 100 pace strigent limits οι the amount o[cire ellar 1nass arouucd individual stars.," However, these observations were 10-50 times less sensitive to dust mass than the observations of Taurus and $\rho$ Oph and did not place stringent limits on the amount of circumstellar mass around individual stars."
 Given t limitations iu inferdug cliss evolution froiu 1eal-]'ec excesses. it is important conduct milliijeter contluuuim obse'vallons o ‘additional star fort 'eelons inorder to uudersta the evolution of disk Lasses al voung stellar ages when plalets : in their formative stages.," Given the limitations in inferring disk evolution from near-infrared excesses, it is important to conduct millimeter continuum observations of additional star forming regions in order to understand the evolution of disk masses at young stellar ages when planets are in their formative stages."
 To fu‘ther measure the circiunstellar isk masses iu cliffert star for.ing environments. I obtained A3unu coutinuum observations of he vome clus DIC 9315 with tie OVRO πιοer wave interferometer.," To further measure the circumstellar disk masses in different star forming environments, I obtained $\lambda$ 3mm continuum observations of the young cluster IC 348 with the OVRO millimeter wave interferometer."
" Based ou st:πάσα. analysis cof near-l""arec star counts. the IC 318 cluser contains LOO stars distributed over a 20!x 'eglon (1.pex1.9 alt he assuimed dista of 320 pe: de Zeeuw 1999: Herbig 1998). wit about lia fthe stars located within the centr ToxT region (Lada&Lada1995:Carpenter2000."," Based on statistical analysis of near-infrared star counts, the IC 348 cluster contains 400 stars distributed over a $20'\times20'$ region $1.9~\rm{pc}\times1.9~\rm{pc}$ at the assumed distance of 320 pc; de Zeeuw 1999; Herbig 1998), with about half the stars located within the central $7'\times7'$ region \citep{Lada95,Carp00}."
. To date. 200 stars aud brown clwarls have been iudividually identilied as likely cluster membes based oi their spectroscopic aud photometr properties (Herbig1998:Lulunaielal.1905:Lulinan1999:Najita.Tiede.&Carr2000).. a 115-173 likely members have bee1 detected with x-rays (PreibiscL&Zinnecker2001).," To date, 200 stars and brown dwarfs have been individually identified as likely cluster members based on their spectroscopic and photometric properties \citep{Herbig98,Luhman98,Luhman99,Najita00}, and 115-173 likely members have been detected with x-rays \citep{PZ01}."
. A chster age of ~2 Myr (Lulunau 1999: see also Herbig 1995 has been infer‘eck by placing the low mass star ou the HR diagram auc using tleoretical pre-malsequence evolutionary tracks [roi1 (1997.98)., A cluster age of 2 Myr (Luhman 1999; see also Herbig 1998) has been inferred by placing the low mass stars on the HR diagram and using theoretical pre-main-sequence evolutionary tracks from \citet{DM98}.
. Near-infr:wed imagi18oO surveys of the cluser show that of the star contain a fy—L excess characterisic of au optically lick accretion disk (Lada&Lada1995:Lada 2001a).," Near-infrared imaging surveys of the cluster show that of the stars contain a $K-L$ excess characteristic of an optically thick accretion disk \citep{Lada95,Haisch01a}."
". By mosaicking the ceiral 5.2’x2.2"" region (0.18pex0.I8 pe) of the IC cluster in the millimeter continuuu. L investigae the circuiistellar clisk inasses in 95 known clt members."," By mosaicking the central $5.2'\times5.2'$ region $0.48~\rm{pc}\times0.48~\rm{pc}$ ) of the IC 348 cluster in the millimeter continuum, I investigate the circumstellar disk masses in 95 known cluster members."
 The OVRO observations of t1e IC 318 cltIser are described in Section 2.., The OVRO observations of the IC 348 cluster are described in Section \ref{obs}.
 The stellar prope‘ties of he cluster members within he OVRO mosaic botaries are reviewed in Section )..3.. aud constraints on the circumstellar ¢isk masses a'e derived it Section [.," The stellar properties of the cluster members within the OVRO mosaic boundaries are reviewed in Section \ref{cluster}, and constraints on the circumstellar disk masses are derived in Section \ref{constraints}."
 Section 5 colnpares these results with clisk masses in Tatrus aud the Orio1 Nebula Custer. and diseuses the implicatious lor plajet formation.," Section \ref{discussion} compares these results with disk masses in Taurus and the Orion Nebula Cluster, and discuses the implications for planet formation."
 The couclusious are sumanarized iu Section 6.., The conclusions are summarized in Section \ref{summary}. .
The Local Volume (LV). generally considered as the sphere of radius 10 Mpe centred on the Local Group. contains more than 500 galaxies.,"The Local Volume (LV), generally considered as the sphere of radius 10 Mpc centred on the Local Group, contains more than 500 galaxies."
 For the majority of these galaxies reliable distances are currently available (Ixarachentsev et al., For the majority of these galaxies reliable distances are currently available (Karachentsev et al.
 2004. 2008).," 2004, 2008)."
 Independent. distances. such as those obtained. from the luminosity of Cepheids. the tip of the red giant branch (PROB). and surface brightness [uctuations (SBE) are an essential ingredient. together with accurate velocities. and detailed multi-wavelength studies of each LV. galaxy. for the assembly of a dynamic 3D view of the Local Universe.," Independent distances, such as those obtained from the luminosity of Cepheids, the tip of the red giant branch (TRGB), and surface brightness fluctuations (SBF) are an essential ingredient, together with accurate velocities and detailed multi-wavelength studies of each LV galaxy, for the assembly of a dynamic 3D view of the Local Universe."
 This. in turn. leads to a better understanding of the local Dow Ποια. the local mass density anc the local star-formation density.," This, in turn, leads to a better understanding of the local flow field, the local mass density and the local star-formation density."
 Interferometric nineasurements. in particular. provide insight into the overall matter distribution (barvonic ancl non-barvonic) in the Local. Volume.," Interferometric measurements, in particular, provide insight into the overall matter distribution (baryonic and non-baryonic) in the Local Volume."
 The galaxy pai NGC 1512/1510. is located in the outskirts of the Local Volume and its study forms part of the ‘Local Volume, The galaxy pair NGC 1512/1510 is located in the outskirts of the Local Volume and its study forms part of the `Local Volume
"simulations, the calculated results show a decreasing values of the loss of the mass, momentum, and the energy from the cases A, B, and C to D, respectively.","simulations, the calculated results show a decreasing values of the loss of the mass, momentum, and the energy from the cases A, B, and C to D, respectively."
" Simultaneously, the inverse energy injected from downstream to precursor is also a decreasing values of (Ej;)4= 1.5861, 1.1742, (Ein)c=0.9707, and (Ein)p=0.8036 from the cases A, B, and C to D, respectively."," Simultaneously, the inverse energy injected from downstream to precursor is also a decreasing values of $(E_{in})_{A}=1.5861$ , $(E_{in})_{B}=1.1742$ , $(E_{in})_{C}=0.9707$, and $(E_{in})_{D}=0.8036$ from the cases A, B, and C to D, respectively."
" The accurate energy losses are the values of (Ejoss)A=0.7468, (Ej,,,)g=0.5861, (Ες=0.4397, and (Ejoss)p=0.3041 in each case."," The accurate energy losses are the values of $(E_{loss})_{A}=0.7468$, $(E_{loss})_{B}=0.5861$, $(E_{loss})_{C}=0.4397$, and $(E_{loss})_{D}=0.3041$ in each case."
 The inverse energy is the summation of the energy loss Ε]οςς and the net energy Fey in the precursor (i.e. Ein=Ejo;+E fen)., The inverse energy is the summation of the energy loss $E_{loss}$ and the net energy $E_{feb}$ in the precursor (i.e. $E_{in}=E_{loss}+E_{feb}$ ).
 So it is no wonder that the total shock ratios are all larger than four because of the existence of energy losses in all cases., So it is no wonder that the total shock ratios are all larger than four because of the existence of energy losses in all cases.
" Therefore, the difference of the energy losses and the inverse energycan directly affect all aspects of the simulationshocks."," Therefore, the difference of the energy losses and the inverse energycan directly affect all aspects of the simulationshocks."
Damped Lyman a (DLA) systems are clouds of ueutral atomic hydrogen with column densities A(ID1)=24.QUU 7 that are detected as absorbers against bright backeround quasars (QSOs) or guunma-ray bursts (GRBs) (Wolfeetal.2005:Prochaska2005.2007. 2008)..,"Damped Lyman $\alpha$ (DLA) systems are clouds of neutral atomic hydrogen with column densities $N(\hi) \geq 2 \times 10^{20}$ $^{-2}$ that are detected as absorbers against bright background quasars (QSOs) or gamma-ray bursts (GRBs) \citep{wolfe05a, prochaska05a, prochaska07a, prochaska08a}."
 These systems comprise the bulk of the neutral eas in the universe at redshifts up to at least 2~5., These systems comprise the bulk of the neutral gas in the universe at redshifts up to at least $z \sim 5$.
 Because of their ubiquity. the study of DLAs provides vital clues to the distribution of eas and metals. aud potentially also star formation. iu the uuiverse.," Because of their ubiquity, the study of DLAs provides vital clues to the distribution of gas and metals, and potentially also star formation, in the universe."
" Observations of DLAs show a clear zone of exclusion: none are observed with both hieh metallicity aud high οσοι density,", Observations of DLAs show a clear zone of exclusion: none are observed with both high metallicity and high column density.
 One possible explanation for this effect is that lines of sight with laree coluun densities aud metallicities produce huge dust extinctions that might lead to exclusion of the backeround QSO from selected samples (Boissectal.1998:Prautzos&Dolssier 2000).," One possible explanation for this effect is that lines of sight with large column densities and metallicities produce large dust extinctions that might lead to exclusion of the background QSO from optically-selected samples \citep{boisse98a, prantzos00a}."
". ILowewver. statistical analysis of the optically-selected QSO-DLA sample sugeests that few DLAs are nüssed due to extinction (Poutzen&Petting2009).. and radio-seclected QSO-DLA samples do not differ sienificautly frou, optically-sclected ones2006)."," However, statistical analysis of the optically-selected QSO-DLA sample suggests that few DLAs are missed due to extinction \citep{pontzen09a}, and radio-selected QSO-DLA samples do not differ significantly from optically-selected ones."
. An alternative hwvpothesis to explain the zoue of exclusion is that above some threshold total hwdroseu cohunn density. which cecreases with mereasiug uetallicitv. eas forms molecular lvdrogen that is nof detectable in Ly à absorption (Schave2001:ITirashita&Ferrara2005:Hirashitaetal. 2006)..," An alternative hypothesis to explain the zone of exclusion is that above some threshold total hydrogen column density, which decreases with increasing metallicity, gas forms molecular hydrogen that is not detectable in Ly $\alpha$ absorption \citep{schaye01a, hirashita05a, hirashita06a}."
 Large amounts of nolecular gas are not observed iu these DLAs because nolecular clouds have a very siuall covering fraction and are unlikely to be seen along random sightlines (Zwaan&Prochaska2006).. although iu some cases race amounts of molecular gas have been detected (e.g.Ledouxetal.2003:Noterdaecnme 2008)..," Large amounts of molecular gas are not observed in these DLAs because molecular clouds have a very small covering fraction and are unlikely to be seen along random sightlines \citep{zwaan06a}, although in some cases trace amounts of molecular gas have been detected \citep[e.g.][]{ledoux03a, noterdaeme08a}."
 In one GRBDB-DLÀ a substantial column of molecular hiydrogeu jas been detected. (Prochaskaetal.2009).. and. as we show below. this svstem is unique among DLAs in its Hel column density aud metallicity.," In one GRB-DLA a substantial column of molecular hydrogen has been detected \citep{prochaska09a}, and, as we show below, this system is unique among DLAs in its high column density and metallicity."
 While the molecule-formation hvpothesis avoids the woblems of the dust bias explanation. if also las significant weaknesses," While the molecule-formation hypothesis avoids the problems of the dust bias explanation, it also has significant weaknesses."
 In DLAs we can observe only colin density aud metallicity. so previous authors have con. forced to asstume values. which nav be incorrect. or other quautitics such as total eas volume density and radiation field that influence the molecule fraction.," In DLAs we can observe only column density and metallicity, so previous authors have been forced to assume values, which may be incorrect, for other quantities such as total gas volume density and radiation field that influence the molecule fraction."
 For example. Schave(2001). asses a Lymau-Werner (TW) radiation field within a factor of 3 of the," For example, \citet{schaye01a} assumes a Lyman-Werner (LW) radiation field within a factor of 3 of the"
The similarity of the Kinematics of the Ta absorption and hieh ionization cussion lines suggests that they arise roni the same region.,The similarity of the kinematics of the $\alpha$ absorption and high ionization emission lines suggests that they arise from the same region.
 To achieve this would require the asina to exist in both hot and cold phases simultancously., To achieve this would require the plasma to exist in both hot and cold phases simultaneously.
 Such a situation was chvisioued iu the overflowing stream uodel of Frank.Nine&Lasota(1987) with cold blobs clubedded im a hotter low density eas., Such a situation was envisioned in the overflowing stream model of \citet{frank87} with cold blobs embedded in a hotter low density gas.
 Towever. the cluperatures required in that mocel are much higher than hat which would produce the[um lines we observe.," However, the temperatures required in that model are much higher than that which would produce the lines we observe."
 It is Likely. herefore. that another mechanisin is at work.," It is likely, therefore, that another mechanism is at work."
 For example. he temperature separation may arise from differences in the effidenev of coolne between denser and rarer regions.," For example, the temperature separation may arise from differences in the efficiency of cooling between denser and rarer regions."
 The velocity amplitude of the ITJ/| absorption iu he trailed spectra clearly clhiauges between the VETI aud CTIO observations., The velocity amplitude of the $\beta$ absorption in the trailed spectra clearly changes between the VLT1 and CTIO observations.
 While the pliase rauge 0.5. 1.0 appears simular to the Πα absorption. the coustant velocity phases of the absorption requires a iore colplesx explanation.," While the phase range $0.5$ $1.0$ appears similar to the $\alpha$ absorption, the constant velocity phases of the absorption requires a more complex explanation."
 With a velocity ~650kuns|. this absorbing material has the correct velocity to be in EKepleriau rotation at the circularization radius.," With a velocity $\sim650~\mbox{km}~\mbox{s}^{-1}$, this absorbing material has the correct velocity to be in Keplerian rotation at the circularization radius."
 However. it is more problematic to explain why different sectious of any culauced ring of immaterial at this radius would be picked out with the observed phase dependence.," However, it is more problematic to explain why different sections of any enhanced ring of material at this radius would be picked out with the observed phase dependence."
 Why. for example. do we see an Savave absorption (from material in one region) at certain phases aud then coustaut velocity absorption Giuplving material that is at that imstaut on the receding edge of the ring) at other phases?," Why, for example, do we see an S-wave absorption (from material in one region) at certain phases and then constant velocity absorption (implying material that is at that instant on the receding edge of the ring) at other phases?"
 Qualitatively. we might uuderstand the behavior as arising from an extended reeion of absorbing material along an overflowing stream.," Qualitatively, we might understand the behavior as arising from an extended region of absorbing material along an overflowing stream."
 For carly phases. the absorption would preferentially pick out that part of the stream obscuring the hottest (and lus brightest) part of the iuner disk and consequently eive rise to an approximately coustaut velocity componcut.," For early phases, the absorption would preferentially pick out that part of the stream obscuring the hottest (and thus brightest) part of the inner disk and consequently give rise to an approximately constant velocity component."
 This coutinues uutil we have passed the phase at which he point where the overflowing stream mecerees with he disk inaterial no longer Les on a line between the observer and the neutron star., This continues until we have passed the phase at which the point where the overflowing stream merges with the disk material no longer lies on a line between the observer and the neutron star.
 For the remaining phases he absorption traces out the S-wawve appropriate to the nerecr poiut., For the remaining phases the absorption traces out the S-wave appropriate to the merger point.
 Confirmation of this would require some reasonably sophisticated radiative transter modelling., Confirmation of this would require some reasonably sophisticated radiative transfer modelling.
 The vchavior is also renauniscent of the simulated eniüssion ine kinematics produced by the method of Foulkesctal.(2001) in other as vet unpublished spectra., The behavior is also reminiscent of the simulated emission line kinematics produced by the method of \citet{foulkes04} in other as yet unpublished spectra.
 These uodels studied the eccentric. precessing accretion disks hat eive rise to ΜΠΡΟΣ in the SU UMa sub-eroup of DNe.," These models studied the eccentric, precessing accretion disks that give rise to superhumps in the SU UMa sub-group of DNe."
 Iuterestingly. the preferred mass ratio for this svsten (q—0.31. see section 3.L1. below) is right on the limut for which such ecceutricitv is possible.," Interestingly, the preferred mass ratio for this system $q=0.34$, see section \ref{sec:qconst} below) is right on the limit for which such eccentricity is possible."
 UU Aqr has the highest measured gq=0.30 for a superhumping system. whereas U Gem at 4=0.36 has only recently had a πηραη) period detected frou a single outburst in 1985 (Baptista.Waagen20014:Pattersonetal.," UU Aqr has the highest measured $q=0.30$ for a superhumping system, whereas U Gem at $q=0.36$ has only recently had a superhump period detected from a single outburst in 1985 \citep{baptista94,smak01,smak02,smak04,patterson05}."
 2005).. οοιπιαο. of such an explanation would require similar modelling to be undertaken with paramcters appropriate toGTO., Confirmation of such an explanation would require similar modelling to be undertaken with parameters appropriate to.
. Other svstems also show absorption in the lydrogen Bahuer Hines but noue with the same kinematics., Other systems also show absorption in the hydrogen Balmer lines but none with the same kinematics.
 The SW Sex systems are CVs which show the trausieut absorption durus the approximate phase range 0.1 0.6 (Szkodv&Piché1990:Thorestensenetal.1991:Warner 1995).," The SW Sex systems are CVs which show the transient absorption during the approximate phase range $0.4$ $0.6$ \citep{szkody90,thorestensen91,warner95}."
. Sinibudy. Ho iu the soft N-rayv transicut NTE J2123-058 shows transicut absorption from 0.35 0.55.," Similarly, $\alpha$ in the soft X-ray transient XTE J2123-058 shows transient absorption from $0.35$ $0.55$."
 In both cases the absorption is generally interpreted as arising frou stream immaterial overflowiug the disk (Warner1995:Πνιοςetal.2001).," In both cases the absorption is generally interpreted as arising from stream material overflowing the disk \citep{warner95,hynes01}."
. A contrasting LAINB system is 2A 1822-971 which shows broad absorption lues dominating and moving across the Balmer profiles in the approximate range ο=0.5 LO., A contrasting LMXB system is 2A 1822-371 which shows broad absorption lines dominating and moving across the Balmer profiles in the approximate range $\phi=0.5$ $1.0$.
 Again. this is interpreted as arising frou absorption bv material in a vertically extended: region resulting from a splash of material deflected around the hot spot (Casaresetal.P003).," Again, this is interpreted as arising from absorption by material in a vertically extended region resulting from a splash of material deflected around the hot spot \citep{casares03}."
. Tarlattis.Charles&Ποιο(1997) lüeasured a VOYV weak Fell aabsorption feature in 2A 1822-371 at orbital phase 0.75., \citet{harlaftis97} measured a very weak FeII absorption feature in 2A 1822-371 at orbital phase 0.75.
" ""They. ascribed this to the same “iron curtain” feature that was observed in OY Car by Horneetal.(1991).", They ascribed this to the same “iron curtain” feature that was observed in OY Car by \citet{horne94}.
.. These earlier observations were taken in the ultraviolet using aand showed a “forest of bleuded Fell features” that was interpreted as being due to material with supersonic. vot sub-Ikeplerian. velocity iu the outer disk.," These earlier observations were taken in the ultraviolet using and showed a “forest of blended FeII features” that was interpreted as being due to material with supersonic, yet sub-Keplerian, velocity in the outer disk."
 Close exanuination of our optical aud UV spectra show no convincing evidence for the presence of either feature iu this system., Close examination of our optical and UV spectra show no convincing evidence for the presence of either feature in this system.
 We have used the unsmoothed trailed spectra to eencrate Doppler tomograms using the maxinauu eutropy technique of Marsh&Ποιο (1988). , We have used the unsmoothed trailed spectra to generate Doppler tomograms using the maximum entropy technique of \citet{marsh88}. .
The tomograims formed from the optical observations are shown in Figure 8 and those from the IIST observatious in Figure 9.., The tomograms formed from the optical observations are shown in Figure \ref{fig:opttoms} and those from the HST observations in Figure \ref{fig:hsttoms}.
" Markings on the plots were generated using q=0.91. Af,=1.355, and i|=τοις"" (Model 3 of Paper D."," Markings on the plots were generated using $q=0.34$, $M_{1}=1.35M_{\odot}$ and $i=75.5^{\circ}$ (Model 3 of Paper I)."
 The velocities of the centers of mass of the system aud of the two stars are marked with crosses., The velocities of the centers of mass of the system and of the two stars are marked with crosses.
 The Roche lobe of the secoudary and the Iepleriau velocitics at the expected οσο of the disk and at the circularization radius are also plotted., The Roche lobe of the secondary and the Keplerian velocities at the expected edge of the disk and at the circularization radius are also plotted.
 Two trails are also indicated iu the figure., Two trails are also indicated in the figure.
 The solid line shows the expected ballistic trajectory of uaterial leaving the LI poiut., The solid line shows the expected ballistic trajectory of material leaving the L1 point.
 The cot-dashed me slows he Ieplerian velocity at cach point that the ballistic stream would pass through., The dot-dashed line shows the Keplerian velocity at each point that the ballistic stream would pass through.
 The Te aud ΤΠ) lines show consistent behavior between ith the CTIO and VET datasets with emission coufined o lower velocities than we would expect for αν disk uateridl., The $\alpha$ and $\beta$ lines show consistent behavior between both the CTIO and VLT datasets with emission confined to lower velocities than we would expect for any disk material.
 Both lines. however. suffer from the effects of he absorption feature that mean we iust treat the derived tomoerams with caution.," Both lines, however, suffer from the effects of the absorption feature that mean we must treat the derived tomograms with caution."
 Absorption violates an asstuuption in the recoustructive technique: that the observed fux is positive., Absorption violates an assumption in the reconstructive technique: that the observed flux is positive.
 The Hell is similay in both VLT aud CTIO datasets with cussion close to the ballistic stream. although the CTIO tomoecram has it in a position also cousistenut with the edge of the disk.," The HeII is similar in both VLT and CTIO datasets with emission close to the ballistic stream, although the CTIO tomogram has it in a position also consistent with the edge of the disk."
 The ΠΟΠ ttomoegranis are all rather noisy reflecting the weakness of the line and difficulty in effectiugan accurate continui subtraction., The HeII tomograms are all rather noisy reflecting the weakness of the line and difficulty in effectingan accurate continuum subtraction.
 Although they all show scattered knots of chussion about the disk. the lack of reproducibility," Although they all show scattered knots of emission about the disk, the lack of reproducibility"
For completeness. we beein by reaunniug the PCA on the actual Earth data obtained by the Deep Iupact spacecraft.,"For completeness, we begin by re-running the PCA on the actual Earth1 data obtained by the Deep Impact spacecraft."
 This cudeavor is not redundaut. since there are many differences between our current analysis and that of 19): 1) here we use a different solar spectrum in computing refiectauce (the change is most noticeade in the 950 win wavebaud): 2) we are now using rigoroush-defined apparent albedo: 3) we run the analysis individualvon the Earthl. raticr than on both equatorial observations simultaneously: and 1) we do not apply the cloud-variahbiitv uncertainties when running the PCA.," This endeavor is not redundant, since there are many differences between our current analysis and that of \cite{Cowan_2009}: 1) here we use a different solar spectrum in computing reflectance (the change is most noticeable in the 950 nm waveband); 2) we are now using rigorously-defined apparent albedo; 3) we run the analysis individually on the Earth1, rather than on both equatorial observations simultaneously; and 4) we do not apply the cloud-variability uncertainties when running the PCA."
 Iu Figure 16 we stummarize the results of the PCA performed on the 2008 EPOXI Equinox data., In Figure \ref{Earth1_all} we summarize the results of the PCA performed on the 2008 EPOXI Equinox data.
 These are the saue as he results presented in Cowanetal.(2009):: the dominant cigencolor is red (most non-zero at lo1ο wavelenueths). while the second eigeucolor is blue Guost non-zero at shor wavelengths).," These are the same as the results presented in \cite{Cowan_2009}: the dominant eigencolor is red (most non-zero at long wavelengths), while the second eigencolor is blue (most non-zero at short wavelengths)."
 Note that the sign of the eigeuspectra. aud hence its slope. is not important in describing its color.," Note that the sign of the eigenspectra, and hence its slope, is not important in describing its color."
 Altrough the two prinary cigencolors shown iu Figure 16 look simular at first glance. they are in fact orthogonal. by definition.," Although the two primary eigencolors shown in Figure \ref{Earth1_all} look similar at first glance, they are in fact orthogonal, by definition."
" We now ru1 five different versions of the VPL 3D Ert 11nodel: 1) Stauclare> this model is au excellent fit to the EPOXI Earthl observations: the remaining models are iceuical. but iu cach case a single model clement has been “turned off"": 2) Cloud Free: 3) No Rayleigh Scatteriie: L) Dack Oceans: 5) Black Laud."," We now run five different versions of the VPL 3D Earth model: 1) Standard: this model is an excellent fit to the EPOXI Earth1 observations; the remaining models are identical, but in each case a single model element has been “turned off”: 2) Cloud Free; 3) No Rayleigh Scattering; 4) Black Oceans; 5) Black Land."
 1) The Staidard model (Figure 17)) produces eigeucolcD indistiuguishiable youn those presented iu or the control case above: a donnant rec eleeicolor followed closely by a blue eigeucolor., 1) The Standard model (Figure \ref{standard_all}) ) produces eigencolors indistinguishable from those presented in \cite{Cowan_2009} or the control case above: a dominant red eigencolor followed closely by a blue eigencolor.
" The relative nuportance o| the cigencolors as a function of time. ""eleecnxojections. also match verv well"," The relative importance of the eigencolors as a function of time, “eigenprojections”, also match very well."
 This should not be surprising. eiven the excellent fit to the actual data (Robiwon et al.," This should not be surprising, given the excellent fit to the actual data (Robinson et al."
 2011)., 2011).
 2) The Clotd Free model (Figure 18)) has simular ine-averaged coOr to the Standard model. but is less reflective at all waveleneths (AA~-- 0.13.," 2) The Cloud Free model (Figure \ref{no_cloud_all}) ) has similar time-averaged colors to the Standard model, but is less reflective at all wavelengths $\Delta A^{*}\approx -0.1$ )."
 This is especially noticeable at lois waveleugths. where Ravleigh scattering docs rot operate.," This is especially noticeable at long wavelengths, where Rayleigh scattering does not operate."
 If the albedo were not on au absolute scale. as would be the case for a directlv-inaged plauct with no reliable radius estimate. it would be difficult to distiieuish this clou-free planct from its cloudy. counterpart.," If the albedo were not on an absolute scale, as would be the case for a directly-imaged planet with no reliable radius estimate, it would be difficult to distinguish this cloud-free planet from its cloudy counterpart."
 Unlike he Standard case. rowever. the Cloud Free model shows very little varjiabilitv at blue wavehauds.," Unlike the Standard case, however, the Cloud Free model shows very little variability at blue wavebands."
 As a result. the Cloud Free inodel srows the same doninaut red eigencolor as the Standard model. but the amplitude of excursious or the blue eigeucoor are much simaller than for the Standard model.," As a result, the Cloud Free model shows the same dominant red eigencolor as the Standard model, but the amplitude of excursions for the blue eigencolor are much smaller than for the Standard model."
 3) The No Ravleieh Scattering model (Figure 19)) has red time-averaged colors. with a sheht wpturn iu reflectance at he bluest scavebaucs due to oceans.," 3) The No Rayleigh Scattering model (Figure \ref{no_rayleigh_all}) ) has red time-averaged colors, with a slight upturn in reflectance at the bluest wavebands due to oceans."
 The cigencolors aud eigeuprojeclons are essentially the same as in the Standard uoclel., The eigencolors and eigenprojections are essentially the same as in the Standard model.
 8) The Black Oceans model (Figure 20)) has time-averaged colors. cigencolors aud cigcuprojectious indistinguisbhable roni those of the Sandard model.," 4) The Black Oceans model (Figure \ref{zero_albedo_ocean_all}) ) has time-averaged colors, eigencolors and eigenprojections indistinguishable from those of the Standard model."
 This indicates that at eibbous phases oceans on Earth cousist of a null surface ype. contributing neither to the time-averaged nor to the time-resolved disk-inteerated colors.," This indicates that at gibbous phases oceans on Earth consist of a null surface type, contributing neither to the time-averaged nor to the time-resolved disk-integrated colors."
 This does not preclude. rowever. the iniportauce of specular reflection at crescent phases.," This does not preclude, however, the importance of specular reflection at crescent phases."
 5) The Black Laud model (Figure 21)) has similar time-averaged colors to the Standard model. but without the upturn at near-IR wavelengths.," 5) The Black Land model (Figure \ref{zero_albedo_land_all}) ) has similar time-averaged colors to the Standard model, but without the upturn at near-IR wavelengths."
 There is a single dominant. eray. cigeucolor.," There is a single dominant, gray eigencolor."
Galaxies of different morphological types show different clustering properties.,Galaxies of different morphological types show different clustering properties.
 It is well khown. for example. that elliptical galaxies are preferentially found in high density environments. such as the centres of rich galaxy clusters (?).. while the dominant populatio| of the field are mainly spiral galaxies 990(??)..," It is well known, for example, that elliptical galaxies are preferentially found in high density environments, such as the centres of rich galaxy clusters \citep{dressler1980}, while the dominant population of the field are mainly spiral galaxies \citep{davis1976,dressler1980}."
 Second order characteristics as the two point correlation function have been used to quantify the clustering of galaxies with differert morphologies. different spectral characteristics. different colours or belonging to different luminosity ranges »(222222)...," Second order characteristics as the two point correlation function have been used to quantify the clustering of galaxies with different morphologies, different spectral characteristics, different colours or belonging to different luminosity ranges \citep{phillipps1987,hamilton1988,davis1988,loveday1995,hermit1996, guzzo1997}."
 Bright galaxies show stronger spatial correlatiot than faint ones., Bright galaxies show stronger spatial correlation than faint ones.
 Other clustering measures have been also used to quantify the luminosity or morphological segregation: multifractals (22).. void probability functions (??).. distributions of the distances to the nearest neighbours (?).. ete.," Other clustering measures have been also used to quantify the luminosity or morphological segregation: multifractals \citep{dominguez1989, dominguez1994}, , void probability functions \citep{vogeley1991, croton2004}, distributions of the distances to the nearest neighbours \citep{salzer1990}, , etc."
 The two-point correlation function &(7) measures the excess probability of finding à ieighbour at a distance 7 from a given galaxy when compared with that probability for a homogeneous Poisson process., The two-point correlation function $\xi(r)$ measures the excess probability of finding a neighbour at a distance $r$ from a given galaxy when compared with that probability for a homogeneous Poisson process.
 Morphological segregation is encapsulated by the behaviour of &*(r) when it is calculated separately for different populations of galaxies., Morphological segregation is encapsulated by the behaviour of $\xi(r)$ when it is calculated separately for different populations of galaxies.
 Elliptical galaxies show at small scales a correlation function with steeper slopes and larger amplitudes than spirals (?).., Elliptical galaxies show at small scales a correlation function with steeper slopes and larger amplitudes than spirals \citep{loveday1995}.
 A recent analysis of the Two Degree Field Galaxy Redshift Survey (2dFGRS) has shown the same trend when comparing populations for different spectral types. being the two-point correlation function steeper for passive galaxies than for active galaxies (?)..," A recent analysis of the Two Degree Field Galaxy Redshift Survey (2dFGRS) has shown the same trend when comparing populations for different spectral types, being the two-point correlation function steeper for passive galaxies than for active galaxies \citep{mad03a}."
" Also. ? have analysed the distribution of red and blue galaxies in the Sloan Digital Sky Survey (SDSS) by means of the projected correlation funeion wj(G,) showing that red galaxies display a more prominent and steeper real-space correlation function than blue galaxies do."," Also, \citet{zehavi2002} have analysed the distribution of red and blue galaxies in the Sloan Digital Sky Survey (SDSS) by means of the projected correlation funcion $w_p(r_p)$ showing that red galaxies display a more prominent and steeper real-space correlation function than blue galaxies do."
 The galaxy distribution can be considered a realisation of a point process., The galaxy distribution can be considered a realisation of a point process.
 However. in many situations. each galaxy (point in the process) carries additional information regarding a given characteristic (e.g. morphological type) or a given numerical value that measures a given galaxy property: luminosity. colour. spectral type.," However, in many situations, each galaxy (point in the process) carries additional information regarding a given characteristic (e.g. morphological type) or a given numerical value that measures a given galaxy property: luminosity, colour, spectral type."
 If we attach this characteristic (mark) to the point in the process. we end up at a marked point process. as itis called in mainstream spatial statistics (222)..," If we attach this characteristic (mark) to the point in the process, we end up at a marked point process, as it is called in mainstream spatial statistics \citep{sto94a, martsaar02,ili08a}."
 In this work. we compare different statistical methods for the study of the marked galaxy distribution.," In this work, we compare different statistical methods for the study of the marked galaxy distribution."
 We also introduce — for the first time in this context — the mark connection function., We also introduce – for the first time in this context – the mark connection function.
 We illustrate the usefulness of these methods by applying them to a volume-limited sample drawn from the 2dFGRS with marks given by the galaxy spectral type., We illustrate the usefulness of these methods by applying them to a volume-limited sample drawn from the 2dFGRS with marks given by the galaxy spectral type.
 In Sectioi 2. we describe the sample and the marks assigned to the galaxies.," In Section 2, we describe the sample and the marks assigned to the galaxies."
 In Section 3 we describe the different statistical methods considered. and in Section 4+ we show the results of applying them to our galaxy sample.," In Section 3 we describe the different statistical methods considered, and in Section 4 we show the results of applying them to our galaxy sample."
 In the conclusions. we stress the capabilities of the mark connection function to characterise the spatial correlation between the marks.," In the conclusions, we stress the capabilities of the mark connection function to characterise the spatial correlation between the marks."
 To illustrate the different mark clustering measures. we used a nearly volume-limited sample drawn from the 2dFGRS and prepared by the 2dF team (?)..," To illustrate the different mark clustering measures, we used a nearly volume-limited sample drawn from the 2dFGRS and prepared by the 2dF team \citep{croton2004}."
 It contains galaxies with absolute magnitudes in the range -20<Με«-19 at redshifts ς<0.13., It contains galaxies with absolute magnitudes in the range $-20 < M_{b_J} < -19$ at redshifts $z<0.13$.
 In order to avoid the effects of complicated boundaries while using a simple estimator. we selected galaxies inside a rectangular parallelepiped inscribed in the North slice of 2dFGRS.," In order to avoid the effects of complicated boundaries while using a simple estimator, we selected galaxies inside a rectangular parallelepiped inscribed in the North slice of 2dFGRS."
 The final sample used contains N=7741] galaxies ane covers a volume of V~10° Mpe)? where 7i is the Hubble constant in units of 100 km s! Mpe!., The final sample used contains $N=7741$ galaxies and covers a volume of $V \sim 10^6$ $^3$ where $h$ is the Hubble constant in units of 100 km $^{-1}$ $^{-1}$.
 We characterized the galaxies in the sample using the spectral classification parameter 7 (?).., We characterized the galaxies in the sample using the spectral classification parameter $\eta$ \citep{mad02a}.
" Lower values of 7 correspond to more passive or ‘early-type’ galaxies. while larger values correspond to active or ""late-type' ones."," Lower values of $\eta$ correspond to more passive or `early-type' galaxies, while larger values correspond to active or `late-type' ones."
 In order to avoid negative values of the marks. we defined the mark used as ntΞ77+10.," In order to avoid negative values of the marks, we defined the mark used as $m = \eta + 10$."
 This shift does not affect our conclusions., This shift does not affect our conclusions.
 Based on this 77 parameter. we divided our sample in two populations. following ?:: population l (passive galaxies) with 7<—1.4. and population 27 (active galaxies) with η>—1.4.," Based on this $\eta$ parameter, we divided our sample in two populations, following \citet{mad03a}: population `1' (passive galaxies) with $\eta \leq -1.4$, and population `2' (active galaxies) with $\eta > -1.4$."
" These subsamples contain N,=3828 and No=3913 galaxies. respectively."," These subsamples contain $N_1 = 3828$ and $N_2 = 3913$ galaxies, respectively."
 We show the sample used in Fig. Τ.., We show the sample used in Fig. \ref{fig:slice}.
 In order totest the existence of mark segregation. we compared the results obtained for the different statistics with random relabelling simulations.," In order totest the existence of mark segregation, we compared the results obtained for the different statistics with random relabelling simulations."
 In these. we keep the originalpositions of galaxies. but redistribute the marks randomly," In these, we keep the originalpositions of galaxies, but redistribute the marks randomly"
 Lo E Dy L D)+FuaL d The total acdvective energve. [lux out of the laver can be estimated asΈμνὸ (pur/2 dT 5nkgT)9. where the first term is the {his of kinetic energv and the second is the fIux of thermal enthalpy of a two-species gas.," L E B_0 L + L. The total advective energy flux out of the layer can be estimated as u^2/2 + 5, where the first term is the flux of kinetic energy and the second is the flux of thermal enthalpy of a two-species gas."
 As we showed above. the condition of pressure balance across the laver dictates that 2n/pT. be equal. or at least. comparable. to Da/8z.," As we showed above, the condition of pressure balance across the layer dictates that $2nk_BT$ be equal, or at least comparable, to $B_0^2/8\pi$."
 At the same lime. (he equation of motion along the laver dictates that the plasma kinetic energy is pur[2cABZ," At the same time, the equation of motion along the layer dictates that the plasma kinetic energy is $\rho u^2/2 \sim
A B_0^2/8\pi$."
 ΗΕ although the two energy f[hixes ave comparable in the incompressible SweelParker case. in the strong-compression ;1X1 case. (he kinetic energy. flix always dominates over (thermal enthalpy Πας.," Thus, although the two energy fluxes are comparable in the incompressible Sweet–Parker case, in the strong-compression $A\gg 1$ case, the kinetic energy flux always dominates over thermal enthalpy flux."
 It is then easy to see that in this case (lie ratio of the total advective energy flix out of the laver to the total Povnting flux into the laver can be estimated as BUsing the continuity. equation (2.2)). we (hus immediately see (hat u O(1)," It is then easy to see that in this case the ratio of the total advective energy flux out of the layer to the total Poynting flux into the layer can be estimated as ).Using the continuity equation \ref{eq-mass-conserv}) ), we thus immediately see that = O(1)"
 It is then easy to see that in this case (lie ratio of the total advective energy flix out of the laver to the total Povnting flux into the laver can be estimated as BUsing the continuity. equation (2.2)). we (hus immediately see (hat u O(1) ," It is then easy to see that in this case the ratio of the total advective energy flux out of the layer to the total Poynting flux into the layer can be estimated as ).Using the continuity equation \ref{eq-mass-conserv}) ), we thus immediately see that = O(1)"
 It is then easy to see that in this case (lie ratio of the total advective energy flix out of the laver to the total Povnting flux into the laver can be estimated as BUsing the continuity. equation (2.2)). we (hus immediately see (hat u O(1) o," It is then easy to see that in this case the ratio of the total advective energy flux out of the layer to the total Poynting flux into the layer can be estimated as ).Using the continuity equation \ref{eq-mass-conserv}) ), we thus immediately see that = O(1)"
 It is then easy to see that in this case (lie ratio of the total advective energy flix out of the laver to the total Povnting flux into the laver can be estimated as BUsing the continuity. equation (2.2)). we (hus immediately see (hat u O(1) oe," It is then easy to see that in this case the ratio of the total advective energy flux out of the layer to the total Poynting flux into the layer can be estimated as ).Using the continuity equation \ref{eq-mass-conserv}) ), we thus immediately see that = O(1)"
"estimated to be (4.4+0.3)x10714 erg cm? s7! and (3.5E0.3)x10714 erg cm? s~!, corresponding to and of the total flux from the unresolved nucleus corrected for absorption, respectively.","estimated to be $(4.4\pm0.3)\times10^{-14}$ erg $^{-2}$ $^{-1}$ and $(3.5\pm0.3)\times10^{-14}$ erg $^{-2}$ $^{-1}$, corresponding to and of the total flux from the unresolved nucleus corrected for absorption, respectively."
" Model A consists of a direct component from the nucleus (a cutoff power law absorbed by cold matter), a scattered component (a cutoff power law without absorption), and an iron-K emission line (a Gaussian)."," Model A consists of a direct component from the nucleus (a cutoff power law absorbed by cold matter), a scattered component (a cutoff power law without absorption), and an iron-K emission line (a Gaussian)."
 'The high energy cutoff is fixed at 200 keV based on the BAT only results (see above)., The high energy cutoff is fixed at 200 keV based on the BAT only results (see above).
 The scattered component is assumed to have the same slope as the direct one with a fraction of fic., The scattered component is assumed to have the same slope as the direct one with a fraction of $f_{\rm scat}$.
" In Model B, a Compton reflection component of the direct continuum from optically thick matter model), absorbed with a column density of is further added to Model A. This emission is expectedNye, from the inner wall of the torus and/or the accretion disk irradiated by the central source."," In Model B, a Compton reflection component of the direct continuum from optically thick matter model), absorbed with a column density of $N_{\rm H}^{\rm refl}$, is further added to Model A. This emission is expected from the inner wall of the torus and/or the accretion disk irradiated by the central source."
" The absorption for the reflection component is set to be independent of that of the transmitted one, because the emission region is different and the line-of-sight column density may not always be the same, depending on the viewing geometry."," The absorption for the reflection component is set to be independent of that of the transmitted one, because the emission region is different and the line-of-sight column density may not always be the same, depending on the viewing geometry."
" Model C has the same emission components as Model B including an absorbed reflection component, but we consider two layers of absorber with different hydrogen column densities for the transmitted component, corresponding to the “partial covering” case where the absorbers in the line of sight consist of gas blobs smaller than the size of the X-ray emitting region (e.g.,Elitzur&Shlosman"," Model C has the same emission components as Model B including an absorbed reflection component, but we consider two layers of absorber with different hydrogen column densities for the transmitted component, corresponding to the “partial covering” case where the absorbers in the line of sight consist of gas blobs smaller than the size of the X-ray emitting region \citep[e.g.,][]{Eli06}."
 We first perform simultaneous2006).. fit only to theSuzaku XIS and HXD/PIN spectra to select the most appropriate model for each object among the three., We first perform simultaneous fit only to the XIS and HXD/PIN spectra to select the most appropriate model for each object among the three.
" To avoid complex effects of time variability, the BAT spectra averaged for 58 months are not utilized in this stage."," To avoid complex effects of time variability, the BAT spectra averaged for 58 months are not utilized in this stage."
" We start from the simplest model (Model A), and adopt a more complex model (Models B or C) only if we find statistically significant improvement of the fit or à physicallya more reasonable solution."," We start from the simplest model (Model A), and adopt a more complex model (Models B or C) only if we find a statistically significant improvement of the fit or a physically more reasonable solution."
" After selecting the best model describing the data in this way, we finally include the BAT spectra in the joint fit to better constrain the continuum up to 200 keV. We allow only the normalization of the direct component to vary while keeping the continuum shape (i.e., spectral slope and cutoff energy) the same between theSuzaku and epoch."," After selecting the best model describing the data in this way, we finally include the BAT spectra in the joint fit to better constrain the continuum up to 200 keV. We allow only the normalization of the direct component to vary while keeping the continuum shape (i.e., spectral slope and cutoff energy) the same between the and /BAT epoch."
" The normalizations of the reflection and Swift/BATscattered component are also linked betweenSuzaku and Swift/BAT, considering that the time scale of their variability should be larger than years if the emission region size is typical (71 pc) of the scale size of tori."," The normalizations of the reflection and scattered component are also linked between and /BAT, considering that the time scale of their variability should be larger than $>$ years if the emission region size is typical $>$ 1 pc) of the scale size of tori."
" Unlike our previous papers (Uedaetal.2007;Eguchial.2009, 2011), we define the reflection strength and scattered fraction relative to the BAT flux, not to theSuzaku flux, since the BAT spectra integrated over 58 months should be a good indicator of the averaged flux level responsible for these reprocessed emission."," Unlike our previous papers \citep{Ued07,Egu09,Egu11}, we define the reflection strength and scattered fraction relative to the BAT flux, not to the flux, since the BAT spectra integrated over 58 months should be a good indicator of the averaged flux level responsible for these reprocessed emission."
" From the results by Kraftetal.(2005) obtained withChandra, we are able to estimate the X-ray fluxes from the radio and compact features in the jets (knots and hot lobes/wingsspots) that should contribute to theSuzaku spectra, where these jet-related structures and the nucleus are not spatially resolved."," From the results by \citet{Kra05} obtained with, we are able to estimate the X-ray fluxes from the radio lobes/wings and compact features in the jets (knots and hot spots) that should contribute to the spectra, where these jet-related structures and the nucleus are not spatially resolved."
" Since neither of these components are expected to be variable on time scale of years, we fix their fluxes at the best-fitChandra values; we confirm that the uncertainties do not affect our results as their contributions in the total flux are minor."," Since neither of these components are expected to be variable on time scale of years, we fix their fluxes at the best-fit values; we confirm that the uncertainties do not affect our results as their contributions in the total flux are minor."
" The component from the radio lobes/wings and jets are represented as a power law with a photon index of 1.8 and 2.0 with a normalization at 1 keV of 9.8x10- and 9.6x107?ergcm-?s-!keV- respectively, both are always added to the above 1,three models representing the nucleus emission."," The component from the radio lobes/wings and jets are represented as a power law with a photon index of 1.8 and 2.0 with a normalization at 1 keV of $9.8 \times 10^{-15}$ and $9.6 \times 10^{-15} {\rm erg \
cm^{-2} s^{-1} keV^{-1}}$, respectively, both are always added to the above three models representing the nucleus emission."
" Since photon index of the power law in the lobes/wings componentis poorly constrained from theChandra data, we fix its slope to that of the radio emission Dennett-Thorpeetal.(2002),, assuming that the radio and X-ray emission correspond to the synchrotron and inverse Comptonization from the same electrons, respectively."," Since photon index of the power law in the lobes/wings componentis poorly constrained from the data, we fix its slope to that of the radio emission \citet{Den02}, assuming that the radio and X-ray emission correspond to the synchrotron and inverse Comptonization from the same electrons, respectively."
" To model optically thin thermal emission from the hot interstellar medium (ISM) detected by Kraftetal. (2005),, we also add an"," To model optically thin thermal emission from the hot interstellar medium (ISM) detected by \citet{Kra05}, , we also add an"
of the wwing. by overlaving various forbidden lines on to the line.,"of the wing, by overlaying various forbidden lines on to the line."
 From this. we obtained a rather couscrvative upper luit onthe fraction ofthe scattered light to be (this corresponds to the intrinsic 2 of the scattered light to be zLO%.. since the observed P for the σοιπα is about 14).," From this, we obtained a rather conservative upper limit on the fraction of the scattered light to be (this corresponds to the intrinsic $P$ of the scattered light to be $\gtrsim 10$, since the observed $P$ for the continuum is about )."
 For the iregion. essentiallv the same limit was obtained from the red side of the |[NTI lines (though in the blue side there seem to be some more residuals}.," For the region, essentially the same limit was obtained from the red side of the +[NII] lines (though in the blue side there seem to be some more residuals)."
 This upper Ματ is calculated. to be 10Mere1. by adopting the total flux of ~τν1016 aat Ι500Α (Cexcluding an old stellar population: Tran 1995. Heckmanet al.," This upper limit is calculated to be $\sim 7 \times 10^{-17}$, by adopting the total flux of $\sim 7 \times 10^{-16}$ at $4800$ (excluding an old stellar population; Tran 1995, Heckman et al."
 1997)., 1997).
 Now. this upper Init should be compared with the optical dux of the hotspot. but unfortunately there is not an adequate OST optical continuum image: the existing archival F606W nuages taken by WEPC2 (ou PC chip: A~ 600043 are saturated at the hotspot. aud also lave a significant enüssiou-line contribution of ~ (estimated using the spectrumof Tran 1995).," Now, this upper limit should be compared with the optical flux of the hotspot, but unfortunately there is not an adequate HST optical continuum image: the existing archival F606W images taken by WFPC2 (on PC chip; $\lambda \sim$ ) are saturated at the hotspot, and also have a significant emission-line contribution of $\sim$ (estimated using the spectrum of Tran 1995)."
 We obtain a conservative lower limit of the optical iotspot coutimmun to be ~3«10.1s by implementius a formal svuthetic photometry with a 0.8 pixel radius aperture on he hotspot. correspouding to the 2.5 pixel radius aperture used below for the POC images. and assuning a enission line contribution.," We obtain a conservative lower limit of the optical hotspot continuum to be $\sim
3 \times 10^{-17}$, by implementing a formal synthetic photometry with a 0.8 pixel radius aperture on the hotspot, corresponding to the 2.5 pixel radius aperture used below for the FOC images, and assuming a emission line contribution."
 This would not be too constraining., This would not be too constraining.
 However. we cau conipare the above upper Iit on the total optical scattered light with the hotspot fluxes at other wavelengths.," However, we can compare the above upper limit on the total optical scattered light with the hotspot fluxes at other wavelengths."
 Using our two broad-band images aud the FOC/F210M. image (A~2180À: see previous section: Heckmauet al.," Using our two broad-band images and the FOC/F210M image $\lambda \sim
2180$; see previous section; Heckman et al."
 1997). we have constructed the UV/optical spectra of the hotspot aud surrounding reeions. by implementing svuthetic aperture photometry witli several aperture sizes.," 1997), we have constructed the UV/optical spectra of the hotspot and surrounding regions, by implementing synthetic aperture photometry with several aperture sizes."
 This is shown in Figure 11ι, This is shown in Figure \ref{fig_sed}.
 The dusxes have been corrected for Calactic reddening (see refsec-intro))., The fluxes have been corrected for Galactic reddening (see \\ref{sec-intro}) ).
 The smallest aperture (2.5 pixel radius) is essentially for the hotspot., The smallest aperture (2.5 pixel radius) is essentially for the hotspot.
 Ifthe hotspot is dominated by scattered light. the above upper lut ou the total scattered liebt. indicated with across. gives a rather blue color for the hotspot between aad[NOOA.. 3<2.0 where FyxA) for a>O where FQXvw).," If the hotspot is dominated by scattered light, the above upper limit on the total scattered light, indicated with a cross, gives a rather blue color for the hotspot between and, $\beta <
-2.0$ where $F_{\lambda} \propto \lambda^{\beta}$ (or $\alpha > 0$ where $F_{\nu} \propto \nu^{\alpha}$ )."
 The scattered helt from the hotspot would be uch less than this upper liuüt. sjuce this is the upper hit for the sui of the scattered light.," The scattered light from the hotspot would be much less than this upper limit, since this is the upper limit for the sum of the scattered light."
" In our polarization unage with the F312W alter. the polarized fux from the ceutral Q.""11SOWLL bin is roughly comparable to that detected in the NE iuiror."," In our polarization image with the F342W filter, the polarized flux from the central $0.''14 \times 0.''14$ bin is roughly comparable to that detected in the NE mirror."
 Based ou this. if we assune that half of the total scattered light at iis frou the hotspot. the luit of the color becoiies joLO fa|2.0).," Based on this, if we assume that half of the total scattered light at is from the hotspot, the limit of the color becomes $\beta < - 4.0$ $\alpha > +2.0$ )."
 Therefore. although we cannot exclude the possibility that the hotspot is dominated by scattered light. these colors secu to sugeest the existence of another siguificaut conrponeut in addition to the scattered lielt.," Therefore, although we cannot exclude the possibility that the hotspot is dominated by scattered light, these colors seem to suggest the existence of another significant component in addition to the scattered light."
 Note that the observed optical polarized flux is uot too blue. 9=1.6 (or a=OL Tran 1995).," Note that the observed optical polarized flux is not too blue, $\beta = -1.6$ (or $\alpha = -0.4$; Tran 1995)."
 The ratio of the polarized flux iu the 0.1L dianeter aperture in our two images formally eives >=O06 (4=LL). though this is subject to several uucertaiuties as discussed iu rofsec-res..," The ratio of the polarized flux in the $0.''14$ diameter aperture in our two images formally gives $\beta
= -0.6$ $\alpha = -1.4$ ), though this is subject to several uncertainties as discussed in \\ref{sec-res}."
 We do not expect that the hotspot is a heavily absorbed Seyfert 1 nucleus. if the size of the melous ix mnaller than the broad-line region as usually thought.," We do not expect that the hotspot is a heavily absorbed Seyfert 1 nucleus, if the size of the nucleus is smaller than the broad-line region as usually thought."
 We clearly do not see any strong direct broad lines in the total flux. so the direct xoad lines. if there are any. ust be heavily absorbed. (," We clearly do not see any strong direct broad lines in the total flux, so the direct broad lines, if there are any, must be heavily absorbed. ("
For iustance. conservatively. even if the unabsorbed direct broad componcuts have peal Hux ouly comparable to the narrow components. it would have to be suppressed at least by a factor of ~50. based on the above upper limit on the broad ine componcnt: this absorption corresponds to roughly o 1.),"For instance, conservatively, even if the unabsorbed direct broad components have peak flux only comparable to the narrow components, it would have to be suppressed at least by a factor of $\sim 50$, based on the above upper limit on the broad line component; this absorption corresponds to roughly $A_V \sim 4$ .)"
 The direct Sevfert 1 coutinmin would be absorbed even more., The direct Seyfert 1 continuum would be absorbed even more.
 This would be inconsistent with the UV spectra of the hotspot shown in Figure ll. which is not too red. uuless Ay(E(BV) is extremely high (note that the intrinsic color of direct continuum should be no er than quasars. be. àS oor 32 eg. Neugebauer et al.," This would be inconsistent with the UV spectrum of the hotspot shown in Figure \ref{fig_sed} which is not too red, unless $A_V/E(B-V)$ is extremely high (note that the intrinsic color of direct continuum should be no bluer than quasars, i.e. $\alpha \lesssim 0$ or $\beta \gtrsim -2$ [e.g. Neugebauer et al."
 1987]. aud possibly redder than," 1987], and possibly redder than"
Figure (12)).,Figure \ref{tophat}) ).
 There is a shallow rise to a maximum between 24.0 and 24.5. a drop therealter. then a rise again to the limit of the follow-up observations.," There is a shallow rise to a maximum between 24.0 and 24.5, a drop thereafter, then a rise again to the limit of the follow-up observations."
 The reconstruction of the faint. end. as shown bv (he (wo methods involved. is uncertzn.," The reconstruction of the faint end, as shown by the two methods involved, is uncertain."
 But it is clear Chat. since the 2.1m showed anv objects at all. there must be several detected by (he eve-and-plate method.," But it is clear that, since the 2.1m showed any objects at all, there must be several detected by the eye-and-plate method."
 It is in this tail. we suggest. that (he objects not detected by follow-up imaging lie.," It is in this tail, we suggest, that the objects not detected by follow-up imaging lie."
 To work out specifically the selection function of the eve-plate combination. even as [ar as the limitations of follow-up observations allow. requires a knowledge of the actual (surface brightness) Iuminosity felon.," To work out specifically the selection function of the eye-plate combination, even as far as the limitations of follow-up observations allow, requires a knowledge of the actual (surface brightness) luminosity function."
 Unfortunately. it is simply not known for galaxies this faint.," Unfortunately, it is simply not known for galaxies this faint."
 If there is a sudden great increase in the number of objects fainter than 24.5 or 25 magnitudes per square arc second in f our sensitivity Chere could be low indeed., If there is a sudden great increase in the number of objects fainter than 24.5 or 25 magnitudes per square arc second in $R$ our sensitivity there could be low indeed.
 But we note that both Blantonetal...(2005) and Driverοἱal.(2005) have the surface brightness Iuninosity function actually Falling at their faint limits., But we note that both \citet{BL05} and \citet{DL05} have the surface brightness luminosity function actually falling at their faint limits.
 Since we go deeper (than either study it is certainly not impossible for there to be such a faint upturn. but it would require some line-tuning to have it eut in at just the least convenient point.," Since we go deeper than either study it is certainly not impossible for there to be such a faint upturn, but it would require some fine-tuning to have it cut in at just the least convenient point."
 The quantitative{ shape| of Figureeure (123) should not be taken too seriously., The quantitative shape of Figure \ref{tophat}) ) should not be taken too seriously.
 As we have noted. our data are relatively inaccurate and sparse. especially at the fant end.," As we have noted, our data are relatively inaccurate and sparse, especially at the faint end."
 However. we believe our overall result is robust: if the actual surface brightness5 distribution of 5galaxies is not rising rapidly faintward of 25. and extrapolation of current information has it indeed [alling. then the combination of photographic survey plates ancl visual examination retains most of its sensitivity out to 25.5 magnitudes per square are second in 2.," However, we believe our overall result is robust: if the actual surface brightness distribution of galaxies is not rising rapidly faintward of 25, and extrapolation of current information has it indeed falling, then the combination of photographic survey plates and visual examination retains most of its sensitivity out to 25.5 magnitudes per square arc second in $R$."
 From our survev we conclude that the current. list of Local Group dwarf galaxies is essentially complete for objects brighter (han some limit between 25 and 26 magnitudes per square arc second in Rand larger than about a minute of are over of the sky. (, From our survey we conclude that the current list of Local Group dwarf galaxies is essentially complete for objects brighter than some limit between 25 and 26 magnitudes per square arc second in $R$ and larger than about a minute of arc over of the sky. (
In total Iuminositv. 26 mag ? over a one-minute diameter translates to M=—7.6 at a distance ol 1 Alpe.,"In total luminosity, 26 mag $^{-2}$ over a one-minute diameter translates to $M = -7.6$ at a distance of 1 Mpc."
 We donof claim an absolute magnitude limit on our survev. however.)," We do claim an absolute magnitude limit on our survey, however.)"
 There av remain one more (probably two) to be found., There may remain one more (improbably two) to be found.
 Concealed behind the Milky Way we estimate another dozen: due to the uncertainty about the luminosity function and spatial distribution of concealed galaxies this number is uncertain. but unlikely to be as high as (wenly.," Concealed behind the Milky Way we estimate another dozen; due to the uncertainty about the luminosity function and spatial distribution of concealed galaxies this number is uncertain, but unlikely to be as high as twenty."
 Our survey was nol capable of detecting all known Local Group galaxies., Our survey was not capable of detecting all known Local Group galaxies.
 Those whose stars must be picked out from the field individually. such as Sextus. Sagittarius ancl Andromeda," Those whose stars must be picked out from the field individually, such as Sextans, Sagittarius and Andromeda"
The total flux of the free-free radio continuum emission can be used as an observable reflecting the total Lyman continuum luminosity of à region.,The total flux of the free-free radio continuum emission can be used as an observable reflecting the total Lyman continuum luminosity of a region.
 As Orton covers a very large area of the sky (~600 Deg) only a part of it has been measured by radio telescopes., As Orion covers a very large area of the sky $\sim600$ $^2$ ) only a part of it has been measured by radio telescopes.
 Observations of the Greater Orion Nebula (M42) covering the most luminous parts of Orion OBId. report radio luminosities in the 1-25 GHz band of 300-500 Jy (Fellietal.1993;vanderWerf&Goss 1989).," Observations of the Greater Orion Nebula (M42) covering the most luminous parts of Orion OB1d, report radio luminosities in the 1-25 GHz band of 300-500 Jy \citep{Felli1993,vanderWerf1989}."
. This translates to a emission of hydrogen ionizing photons of 5—8x10? ph s! (Condon1992)., This translates to a emission of hydrogen ionizing photons of $5-8\times10^{48}$ ph $^{-1}$ \citep{Condon1992}.
. This is significantly smaller than our estimate of ~3xI0? ph s! on average., This is significantly smaller than our estimate of $\sim3\times10^{49}$ ph $^{-1}$ on average.
 However. the UV output is strongly dependent on the most massive star in a cluster. making it highly sensitive to small-number statistics.," However, the UV output is strongly dependent on the most massive star in a cluster, making it highly sensitive to small-number statistics."
 Indeed the number of observed massive stars in OBId is significantly smaller than that from a population synthesis view. and thus the UV radiation is statistically very uncertain and almost unconstrained. with a l-sigma confidence interval of 3x101’- 3x107? ph s'.," Indeed the number of observed massive stars in OB1d is significantly smaller than that from a population synthesis view, and thus the UV radiation is statistically very uncertain and almost unconstrained, with a 1-sigma confidence interval of $\times10^{47}$ $\times10^{49}$ ph $^{-1}$."
 The absence of stars more massive than 45 M. in OBId indicates that the UV radiation should be well below the population-synthesis predicted. average found by integrating over the entire mass function., The absence of stars more massive than 45 $M_{\odot}$ in OB1d indicates that the UV radiation should be well below the population-synthesis predicted average found by integrating over the entire mass function.
 Indeed an integration over the expected output from the observed stars yield an ionizing UV output of 107? ph s7!., Indeed an integration over the expected output from the observed stars yield an ionizing UV output of $10^{49}$ ph $^{-1}$.
 With a leakage of of the ionizing photons. similar to what has been inferred in the Carina region (Smith&Brooks2007) this number would agree well with the radio continuum observations.," With a leakage of of the ionizing photons, similar to what has been inferred in the Carina region \citep{Smith2007} this number would agree well with the radio continuum observations."
 Therefore. we do not consider this a significant discrepancy between predicted and observrd ionizing energy.," Therefore, we do not consider this a significant discrepancy between predicted and observrd ionizing energy."
 The COMPTEL y-ray telescope has mapped the all sky distribution of the -°Al decay line at 1.809 MeV emission over 9 years of observations., The COMPTEL $\gamma$ -ray telescope has mapped the all sky distribution of the $^{26}$ Al decay line at 1.809 MeV emission over 9 years of observations.
 The results for the Orion region are presented in Diehl (2002).., The results for the Orion region are presented in \citet{Diehl2002}. .
 Depending on the spatial model. the emission from the Orion region is found at à confidence level of 7—9i. and a total flux of 2.8)—3.7x107 ph em s! is found.," Depending on the spatial model, the emission from the Orion region is found at a confidence level of $7-9\sigma$, and a total flux of $2.8-3.7\times 10^{-5}$ ph $^{-2}$ $^{-1}$ is found."
 This corresponds to a mass of ~4—5x107 M. of 76 A] at a distance of 400 pc. in good agreement with the results shown in figure 3..," This corresponds to a mass of $\sim4-5\times10^{-4}$ $M_{\odot}$ of $^{26}$ Al at a distance of 400 pc, in good agreement with the results shown in figure \ref{fig:onecluster}."
 Calculating the emission separately for the 5 groups and taking into account their individual distances. we get an expected flux of 4.575)x107? ph s! from the OBI association. in good agreement with the observations.," Calculating the emission separately for the 5 groups and taking into account their individual distances, we get an expected flux of $4.5^{+2.1}_{-2.0}\times10^{-5}$ ph $^{-1}$ from the OB1 association, in good agreement with the observations."
 A map of the observed signal. although limited by the total signal weakness. shows ΑΙ emission in the Orion region. with a mam peak consistent with the position of Orion OBI. and extended emission towards lower latitudes. suggestively aligned with the direction of the Orion-Eridanus bubble.," A map of the observed signal, although limited by the total signal weakness, shows $^{26}$ Al emission in the Orion region, with a main peak consistent with the position of Orion OB1, and extended emission towards lower latitudes, suggestively aligned with the direction of the Orion-Eridanus bubble."
 Nearly all the flux is coming from the OBIb.c groups which are producing equally strong signals.," Nearly all the flux is coming from the OB1b,c groups which are producing equally strong signals."
 A modest addition of 1079 ph s! is expected to come from vt Ori. which was not included in the observational analysis.," A modest addition of $\sim3\times10^{-6}$ ph $^{-1}$ is expected to come from $\lambda$ Ori, which was not included in the observational analysis."
 We analyzed the population of massive stars m the nearby star-forming Orion region. including the four OBI subgroups (a-d) and the 4| Ort group.," We analyzed the population of massive stars in the nearby star-forming Orion region, including the four OB1 subgroups (a-d) and the $\lambda$ Ori group."
 We analyzed the stellar contents of the individual groups. providing updated lists of the stars more massive than 8 Ms.," We analyzed the stellar contents of the individual groups, providing updated lists of the stars more massive than 8 $M_{\odot}$."
 Ages of the individual groups were constramed based on comparison between the updated properties of the most massive stars and stellar isochrones., Ages of the individual groups were constrained based on comparison between the updated properties of the most massive stars and stellar isochrones.
 Based on these results. we performed a study of the ejection of kinetic energy and radioactive elements from the young massive stars in Orion.," Based on these results, we performed a study of the ejection of kinetic energy and radioactive elements from the young massive stars in Orion."
 We showed that the current state of the region only depends modestly on the properties of the model. such às the star formation history and the stellar evolutioαυ] models.," We showed that the current state of the region only depends modestly on the properties of the model, such as the star formation history and the stellar evolution models."
 Main uncertainties are due to the unknown populatioαυ] of very massive stars that exploded over the past 10 Myr., Main uncertainties are due to the unknown population of very massive stars that exploded over the past 10 Myr.
 The population synthesis results were compared to the energy needed to form the Eridanus superbubble. the emission of hydrogen tonizing photons. and the intensity of the 1.809 MeV line from the decay of ΑΙ. showing good agreement between our model estimates and the observations.," The population synthesis results were compared to the energy needed to form the Eridanus superbubble, the emission of hydrogen ionizing photons, and the intensity of the 1.809 MeV line from the decay of $^{26}$ Al, showing good agreement between our model estimates and the observations."
 The ΑΙ observations provide a valuable tracer of the population of (now not any more observable) stars and thus of the cumulative action of massive star groups. and of the kinematics of the outflows from the massive stars.," The $^{26}$ Al observations provide a valuable tracer of the population of (now not any more observable) stars and thus of the cumulative action of massive star groups, and of the kinematics of the outflows from the massive stars."
 Our current understanding of stellar. evolution and supernova models is far from complete., Our current understanding of stellar evolution and supernova models is far from complete.
 Different models ofter rely on similar assumptions., Different models often rely on similar assumptions.
 Showing consistency betweer models and observations is important. as it supports confidence that the most important effects are accounted for in models.," Showing consistency between models and observations is important, as it supports confidence that the most important effects are accounted for in models."
 We have employed different models for characterizing the Ortor region's stellar population. and for the stellar-evolution inputs to population synthesis.," We have employed different models for characterizing the Orion region's stellar population, and for the stellar-evolution inputs to population synthesis."
 The results show that the observed properties of the Orion region are consistent with these models., The results show that the observed properties of the Orion region are consistent with these models.
 Differences among models are smaller than the statistical effects caused by the relatively small number of massive stars., Differences among models are smaller than the statistical effects caused by the relatively small number of massive stars.
 Some recent UV studies (Bouretetal.2003:Fullertonal.2006) have called for a more fundamental mass-loss rate reduction. invoking clumping factors up to ~ 100. much higher than the currently favoured values of ~5. and mass-loss rate reductions of order 10.," Some recent UV studies \citep{Bouret2003,Fullerton2006} have called for a more fundamental mass-loss rate reduction, invoking clumping factors up to $\sim$ 100, much higher than the currently favoured values of $\sim 5$, and mass-loss rate reductions of order 10."
 However. other studies cast doubt on these conclusions based on theoretical studies of “macro-clumping” (Oskinovaetal.2007:Sundqvist2010) and emission in the extreme UV band (Waldron&Cassinelli 2010).," However, other studies cast doubt on these conclusions based on theoretical studies of ""macro-clumping"" \citep{Oskinova2007,Sundqvist2010} and emission in the extreme UV band \citep{Waldron2010}."
. As we find good agreement between our population synthesis and the observations of Orion. this could either suggest that our mass-loss rates are realistic (and the very large clumping factors exaggerated). or alternatively that some unknown process is also missing in the stellar models.," As we find good agreement between our population synthesis and the observations of Orion, this could either suggest that our mass-loss rates are realistic (and the very large clumping factors exaggerated), or alternatively that some unknown process is also missing in the stellar models."
" However. we note that the wind and supernova contributions to the interstellar ""AI have not been disentangled observationally. and models with weak winds to some degree compensate for the low 7° Al wind yields by having larger core masses and therefore producing higher supernova yields (seediscussioninLimongi&Chieti 2006).. and the production of ""AI in high-clumping models have not yet been explored."," However, we note that the wind and supernova contributions to the interstellar $^{26}$ Al have not been disentangled observationally, and models with weak winds to some degree compensate for the low $^{26}$ Al wind yields by having larger core masses and therefore producing higher supernova yields \citep[see discussion in][]{Limongi2006}, and the production of $^{26}$ Al in high-clumping models have not yet been explored."
 On the other had. we emphasize that our models are in agreementwith both the kinematic and the radioactive tracers. which would be hard to achieve with models involving very large clumping factors.," On the other hand, we emphasize that our models are in agreementwith both the kinematic and the radioactive tracers, which would be hard to achieve with models involving very large clumping factors."
 The Galaxy contains hundreds of regions of massive star-, The Galaxy contains hundreds of regions of massive star-formation.
 It is important to extend our approach to other, It is important to extend our approach to other
modified by absorption associated with a high compactness region (in agreement with our analytical estimate).,modified by absorption associated with a high compactness region (in agreement with our analytical estimate).
 During interval a. the source is likely to be optically thick. whereas during interval c. photons with energies of a few GeVs were observed by the Fermi/LAT thus requiring the source to be optically thin in the GeV range.," During interval a, the source is likely to be optically thick, whereas during interval c, photons with energies of a few GeVs were observed by the Fermi/LAT thus requiring the source to be optically thin in the GeV range."
 As discussed in the previous section for interval a. and because the fundamental parameter determining the source compactness is the Lorentz factor of the relativistic shell where the observed radiation 15 produced. a scenario explaining the observations could be the following.," As discussed in the previous section for interval a, and because the fundamental parameter determining the source compactness is the Lorentz factor of the relativistic shell where the observed radiation is produced, a scenario explaining the observations could be the following."
" The central engine emits a first shell with Lorentz factor L;,. responsible for the emission observed during interval à. with DL, such that the source is optically thick above MeV because of the small radius at which the first IS takes place (see previous section)."," The central engine emits a first shell with Lorentz factor $\Gamma_{a}$, responsible for the emission observed during interval a, with $\Gamma_{a}$ such that the source is optically thick above $\sim 30$ MeV because of the small radius at which the first IS takes place (see previous section)."
" Later on. the central engine emits a series of shells responsible for the other multiple peaks observed during intervals b and c. These shells are characterized by a Lorentz factorin-between I, and [.. where D.>Τι ts such that the source ts thin to GeV photons (as discussed in the next section)."," Later on, the central engine emits a series of shells responsible for the other multiple peaks observed during intervals b and c. These shells are characterized by a Lorentz factorin-between $\Gamma_{a}$ and $\Gamma_{c}$, where $\Gamma_{c}>\Gamma_{a}$ is such that the source is thin to GeV photons (as discussed in the next section)."
 In the above scenario. spectra observed during interval b and e should follow a progressive transition from an optically thick to an optically thin spectrum in the GeV range.," In the above scenario, spectra observed during interval b and c should follow a progressive transition from an optically thick to an optically thin spectrum in the GeV range."
 Since both of these intervals contain multiple peaks of the corresponding light curve. we expect that. especially during the transition phase b. the integrated spectrum Is a superimposition of spectra emitted by shells with increasing Γ factors. progressively more transparent to GeV photons.," Since both of these intervals contain multiple peaks of the corresponding light curve, we expect that, especially during the transition phase b, the integrated spectrum is a superimposition of spectra emitted by shells with increasing $\Gamma$ factors, progressively more transparent to GeV photons."
 The best-fit spectrum obtained by Fermi during interval b. does indeed show the contribution from a component peaking around a few MeV (a Band or exponential cutoff component). plus a second component with substantial emission in the GeV range (power-law component).," The best-fit spectrum obtained by Fermi during interval b, does indeed show the contribution from a component peaking around a few MeV (a Band or exponential cutoff component), plus a second component with substantial emission in the GeV range (power-law component)."
 Thus. on general lines. the observed spectral evolution is consistent with our hypothesis.," Thus, on general lines, the observed spectral evolution is consistent with our hypothesis."
 This picture also naturally explains the delayed onset of the GeV tail observed by the LAT., This picture also naturally explains the delayed onset of the GeV tail observed by the LAT.
 As emphasized before. the observation of GeV photons during interval e requires the Lorentz factor of the late shell generating such emission being sufficiently. high for the source to be optically thin at that energies.," As emphasized before, the observation of GeV photons during interval c requires the Lorentz factor of the late shell generating such emission being sufficiently high for the source to be optically thin at that energies."
 We thus again use Eq. (5), We thus again use Eq. \ref{gammap}) )
" assuming that C=Cy.107. where the vF,. flux at ~2 GeV is about 107 erg/em-/s1).. and using a photon index of p=-1.6 (as the observed one). 1.8. We also assume that E,,,,z|GeV. and thus so that Ε>T,."," assuming that $C=C_{pow}\sim 10^{-4}$, where the $\nu F_{\nu}$ flux at $\sim 2$ GeV is about $10^{-7}$ $^{2}$ /s, and using a photon index of $\beta=-1.6$ (as the observed one), i.e. We also assume that $E_{max}\gtrsim 1{\rm ~GeV}$, and thus so that $\Gamma_c \gtrsim \Gamma_a$."
" We note that Ε,. is not much higher than Γ, because. as can be see from Eq. (5))."," We note that $\Gamma_c$ is not much higher than $\Gamma_a$ because, as can be see from Eq. \ref{gammap}) ),"
 in interval e photons of much higher energy are observed (i.e. 2 GeV >>30 MeV). although from interval a to ¢ the emitted flux becomes much lower (Chav<<Cp.," in interval c photons of much higher energy are observed (i.e. $2~$ GeV $>> 30$ MeV), although from interval a to c the emitted flux becomes much lower $C_{pow}<<C_{Band}$ )."
 In the (optically thin) IS model. the synchrotron peak energy is given by where La» is the source luminosity in units of 107 erg(2).," In the (optically thin) IS model, the synchrotron peak energy is given by where $L_{52}$ is the source luminosity in units of $10^{52}$ erg."
. We estimate this last parameter by considering the 100 MeV - 10 GeV fluence measured during interval e (and its scatter caused by the measured errors. see Sect. 2)).," We estimate this last parameter by considering the 100 MeV - 10 GeV fluence measured during interval c (and its scatter caused by the measured errors, see Sect. \ref{osservazioni}) ),"
 and taking into accountthe observed duration of this interval Using Eq. (15)), and taking into accountthe observed duration of this interval Using Eq. \ref{reqgamma2}) )
" into (16)). and setting Ls.~107. we derive It is evident that even after setting e;~eg0.5. p~5. and Of,s,~| ms. the requirement on the Lorentz factor in Eq. (15))"," into \ref{piccosincr}) ), and setting $L_{52}\sim10^{-3}$, we derive It is evident that even after setting $\epsilon_e\sim\epsilon_B\sim0.5$, $p\sim5$, and $\delta t_{obs}\sim 1$ ms, the requirement on the Lorentz factor in Eq. \ref{reqgamma2}) )"
" for the source to be optically thin implies that the peak of the synchrotron emission by IS is at energies below ~500 keV <<2 GeV. We thus conclude that synchrotron emission from late IS cannot explain the high energy tail observed during interval ο, since the transparency condition in the GeV range implies values of the synchrotror peak energy much lower than ~| GeV. in conflict with the observations."," for the source to be optically thin implies that the peak of the synchrotron emission by IS is at energies below $\sim 500$ keV $<< 2$ GeV. We thus conclude that synchrotron emission from late IS cannot explain the high energy tail observed during interval c, since the transparency condition in the GeV range implies values of the synchrotron peak energy much lower than $\sim 1$ GeV, in conflict with the observations."
 Another mechanism that may be responsible for the ~ GeV emission is SSC?)., Another mechanism that may be responsible for the $\sim$ GeV emission is SSC.
". The peak frequency of the SSC component is given by Setting Lis= 107.054,=| ms. &=0.5. eg=—0.01. 29. z=0.1. into Eq. (19))."," The peak frequency of the SSC component is given by Setting $L_{52}=10^{-3}$, $\delta t_{obs} =1$ ms, $\epsilon_e=0.5$, $\epsilon_B = 0.01$, $p = 2.9$ , $z=0.1$, into Eq. \ref{piccoSSC}) ),"
 we obtain EX~1 GeV. for (see Fig. 2)).," we obtain $E_p^{SC}\sim 1$ GeV, for $\Gamma=300$ (see Fig. \ref{Fig2}) )."
 For this solution. we note that a variability timescale as short as 1 ms can indeed be present (?).. and was found in at least one short GRB. in which a very bright <1 ms pulse was observed (?).," For this solution, we note that a variability timescale as short as $1$ ms can indeed be present , and was found in at least one short GRB, in which a very bright $< 1$ ms pulse was observed ."
. Moreover. we emphasize that these values of the physical parameters are of course not necessarily unique.," Moreover, we emphasize that these values of the physical parameters are of course not necessarily unique."
 However. our aim is to show that a possible solution," However, our aim is to show that a possible solution"
Tn this work we couceutrate on GRD 050121. whic[um has the best data.,"In this work we concentrate on GRB 050421, which has the best data."
 Our aim is to perform afterelov calculations to obtain for different scenarios the limits ou the external density that are compatible with the absence of an afterglow., Our aim is to perform afterglow calculations to obtain for different scenarios the limits on the external density that are compatible with the absence of an afterglow.
 For a given density we also coustrain the mucroplivsics parameters e. aud ep aud the distributio1 of the Loreutz factor in the ejecta., For a given density we also constrain the microphysics parameters $\epsilon_e$ and $\epsilon_B$ and the distribution of the Lorentz factor in the ejecta.
 The paper is organized as follows: we briefly sununarize the observational data on GRB 050121 iu Sect., The paper is organized as follows: we briefly summarize the observational data on GRB 050421 in Sect.
 2 and estimate the isotropic A.inetic cnerey released by this burst., 2 and estimate the isotropic kinetic energy released by this burst.
 We cousider in Sect., We consider in Sect.
 3 several possible origins for the afterglow., 3 several possible origins for the afterglow.
" Fist. the standard case. where it is made by the forward shock oxopaesatimg in the external mecdimm. then the alternative nodel where it comes from the reverse shock that sweeps yack iuto the ejecta. and finally ai few more exotic yossibilities,"," First, the standard case, where it is made by the forward shock propagating in the external medium, then the alternative model where it comes from the reverse shock that sweeps back into the ejecta, and finally a few more exotic possibilities."
 Our results are discussed ii Sect., Our results are discussed in Sect.
 l. which is also the conclusion.," 4, which is also the conclusion."
 GRB 050121 belongs to the faintest bursts of the siauple., GRB 050421 belongs to the faintest bursts of the sample.
 Its flueuce in the 15 150 keV energy rauge integrated over του=LO s was 545150=l.l40.7«10[ erg P 7.," Its fluence in the 15 – 150 keV energy range integrated over $t_{90}=10$ s was $S_{15\,-\,150}= 1.1\pm 0.7 \times 10^{-7}$ erg $^{-2}$ ."
 The light curve duriug του approximately had a FRED shape., The light curve during $t_{90}$ approximately had a FRED shape.
" It was followed by a weak tail and at least two flares at 110 and 1515s. Between 15 aud 150 keV the prompt spectrum can be fitted by a mele power-law Fy,1xv 7, sich suggestsoo hat the peak cucrey Γρ was hieher than 150 keV. (Code et al."," It was followed by a weak tail and at least two flares at 110 and 154 s. Between 15 and 150 keV the prompt spectrum can be fitted by a single power-law $F_{\nu}\propto \nu^{-0.7}$ , which suggests that the peak energy $E_{\rm p}$ was higher than 150 keV (Godet et al."
 2006)., 2006).
 The NRT was able to follow the Invst frou1 about 100 s to 1000 after trigeer., The XRT was able to follow the burst from about 100 s to 1000 s after trigger.
 Later. iu an interva running frou 5000 to 5107 s. the source was no detectd. leading te yan upper luit Posaon<δ101 cre lo7 Ss1," Later, in an interval running from 5000 to $5\,10^5$ s, the source was not detected, leading to an upper limit $F_{0.3\,-\,10\,{\rm keV}}< 8\,10^{-14}$ erg $^{-2}$ $^{-1}$."
 Auv long-lasting afterglow component. if present. should trerefore be very dim. ling after a few hours a0ut five ordrs of magnitude below the flux recorded at 100 s. Between LOO aud 1000 s the flux exhibited a power law clecline of iudex 3.1+1 together with a lard-to-soft evolution. indicating tiat the peak energy ¢ft the spectruni was probably crossiιο the ART band «urne the observations.," Any long-lasting afterglow component, if present, should therefore be very dim, lying after a few hours about five orders of magnitude below the flux recorded at 100 s. Between 100 and 1000 s the flux exhibited a power law decline of index $3.1\pm 0.1$ together with a hard-to-soft evolution, indicating that the peak energy of the spectrum was probably crossing the XRT band during the observations."
 This stroely sueeests that what was observed was the hieh-latitice enission of the last shocked shells in the ejecta of CRB 350121 (Codet et al., This strongly suggests that what was observed was the high-latitude emission of the last shocked shells in the ejecta of GRB 050421 (Godet et al.
 2006)., 2006).
 The isotropic kinetic energy of the burst ejecta at the eud of the prompt phase (after a fraction f. of the initial amount has been converted to e@auuna-ravs) is a key ingredient for anv afterelow calculation., The isotropic kinetic energy of the burst ejecta at the end of the prompt phase (after a fraction $f_{\gamma}$ of the initial amount has been converted to gamma-rays) is a key ingredient for any afterglow calculation.
 Unfortunately. he redshift of CRB 050121 is not known auc. iu a first step. we just estimate the total gamunatrav fluence 5. roni the flucnce in the 1 150 keV band.," Unfortunately, the redshift of GRB 050421 is not known and, in a first step, we just estimate the total gamma-ray fluence $S_{\gamma}$ from the fluence in the 15 – 150 keV band."
 We obtain S.=L510*η ere 7 assuming that t1ο spectrum is a Baud function (Baud et al.," We obtain $S_{\gamma}=4.5\,10^{-7}$ erg $^{-2}$ assuming that the spectrum is a Band function (Band et al."
" 1993) with a=1.7. )j2,5 aud £j,=350 keV. Frou the ueuce we then obtain the otal energy release iu Galina rayvs as a fuaction of redshift where D,6:)L is the luminosity distance."," 1993) with $\alpha=-1.7$, $\beta=-2.5$ and $E_{\rm p}=350$ keV. From the fluence we then obtain the total energy release in gamma rays as a function of redshift where $D_{\rm L}(z)$ is the luminosity distance."
" The kinetic ↸∖∐↸∖↥⋅∶↴∙⊾⋅↖⇁≿↕↕↕∖⋚⊔↸⊳⋜⋯∐∪↖↖↽↴⋈∖↸∖↴∖↴↑↕⋯⋜↧↑↸∖≼⊔≯↥⋅∪⋯↑∐∖↸∖↕−⊔↸⊳↕↸∖∐↸⊳⋅↖↽⋅↗⊔↜ Iu the case of imuterual shocks we have f.2e;« Pains: where fan. is the fraction of the kinetic energv cissipate by the shocks aud e, the fraction trausterred to electrons aud eventually radiated (assuming fast cooling electrons)."," The kinetic energy ${\cal E}_{\rm K}^{\rm iso}$ can now be estimated from the efficiency $f_{\gamma}$ In the case of internal shocks we have $f_{\gamma}\simeq \epsilon_e\times f_{\rm diss}$ , where $f_{\rm diss}$ is the fraction of the kinetic energy dissipated by the shocks and $\epsilon_e$ the fraction transferred to electrons and eventually radiated (assuming fast cooling electrons)."
 We take fai. 0.1. which is typical for internal srocks (Daigue AMochkovitch. 1998).," We take $f_{\rm diss}\sim 0.1$ , which is typical for internal shocks (Daigne Mochkovitch, 1998)."
 To cusure a sufficietit elobal efficiency. it is then necessary to have - ]l. ," To ensure a sufficient global efficiency, it is then necessary to have $\epsilon_e\sim 0.1$ - 1."
"We adopt e,1/3. which leads to F "," We adopt $\epsilon_e= 1/3$, which leads to $f_{\gamma}\sim 3\%$."
We also cousider he possibility. that he promptenission nav result frou a more efficient proc such as Conmptouization at the photosphere (Rees A\ésszarros. 2005: Lazzati. orsonv Degehuan. 20 Deloborodov. 2010) Or maejietie reconnection (Spiut. Daigue Dreukhan. 2001: Dreukhan Spruit. 202: Cüanuos Spruit. 2006: \IcTsinnev Uxeusky. 2011). for which we adopt a radiative efficiency of30%.," We also consider the possibility that the prompt emission may result from a more efficient process such as Comptonization at the photosphere (Rees Mésszárros, 2005; Lazzati, Morsony Begelman, 2009; Beloborodov, 2010) or magnetic reconnection (Spruit, Daigne Drenkhan, 2001; Drenkhan Spruit, 2002; Giannos Spruit, 2006; McKinney Uzdensky, 2011), for which we adopt a radiative efficiency of."
. Our results for ep aud σιcise are sununuarized in Table 1 for different redshifts., Our results for ${\cal E}_{\gamma}^{\rm iso}$ and ${\cal E}_{\rm K}^{\rm iso}$ are summarized in Table 1 for different redshifts.
" They can vary bw 1:p to oe the parameters of the Baud fuuctiou. (especially £,) are changed.", They can vary by up to if the parameters of the Band function (especially $E_{\rm p}$ ) are changed.
 This nucertainty remains mnuch smaller than the one resulting from the unknown distance aud radiative efficienev of the burst., This uncertainty remains much smaller than the one resulting from the unknown distance and radiative efficiency of the burst.
 Tu the standard model. where the afterglow is mace by the forward shock. the predicted X-ray fiux is Ίο above the observationallimit aslong as the burst paraimcters keep “usual” values.," In the standard model, where the afterglow is made by the forward shock, the predicted X-ray flux is much above the observationallimit aslong as the burst parameters keep “usual” values."
" This can be checked using the analytical formmlac provided by Panaiteseu I&wunar (2000).The relevant radiative regime corresponds to jx>ÓQ4, (vosp.", This can be checked using the analytical formulae provided by Panaitescu Kumar (2000).The relevant radiative regime corresponds to $\nu_{\rm X} > \nu_{m}$ (resp.
the propagation of the linear as well as nonlinear EAWSs has received a ereat deal of renewed interest not only because the two electrou temperature plana Is very common in laboratory experiments (Derftler aud Sinonenu. 1969: Παν and Treguier. 1972) aud in space (Dubouloz et al.,"the propagation of the linear as well as nonlinear EAWs has received a great deal of renewed interest not only because the two electron temperature plasma is very common in laboratory experiments (Derfler and Simonen, 1969; Henry and Treguier, 1972) and in space (Dubouloz et al.,"
 1991. 1993: Pottelette et al.," 1991, 1993; Pottelette et al.,"
 1999: Berthomicr et al..," 1999; Berthomier et al.,"
 2000: Singh aud. Lakhbina. 2001). but so because of the potential importance in interpreting ectrostatic coniponeut of the broadband electrostatic noise (BEN) as being solitary EA structures observed in the cusp of the terrestrial maguetosphere (Tolar iid Cary. 19st: Sineh aud Lakhina. 2001). in the ecolmagnetic tail (Schriver aud Ashom-Abdalla. 1989). in auroral region (Dubouloz et al..," 2000; Singh and Lakhina, 2001), but also because of the potential importance in interpreting electrostatic component of the broadband electrostatic noise (BEN) as being solitary EA structures observed in the cusp of the terrestrial magnetosphere (Tokar and Gary, 1984; Singh and Lakhina, 2001), in the geomagnetic tail (Schriver and Ashour-Abdalla, 1989), in auroral region (Dubouloz et al.,"
 1991. 1993: Potteletteli al.," 1991, 1993; Pottelette et al.,"
 1999). iu the uunercal simulation (Lu. Wang xb Dou. 2005: Lu. Wang and Wang. 2005). aud iu laboratory experiment (Lefebvre. et al.," 1999), in the numerical simulation (Lu, Wang and Dou, 2005; Lu, Wang and Wang, 2005), and in laboratory experiment (Lefebvre, et al.,"
 2011). etc.," 2011), etc."
 Ou the other side. since Alfvéun aud Carlqvist (1967) had sugeested the current disruption theory for solar flare. the subject of DL (sometimes also called. shock or kinks) has attracted ereat attention (Li. 198E: Liu. 2010: reference therein).," On the other side, since Alfvénn and Carlqvist (1967) had suggested the current disruption theory for solar flare, the subject of DL (sometimes also called shock or kinks) has attracted great attention (Li, 1984; Liu, 2010; reference therein)."
 DLs Occur raturally in a variety of space plasiia cuvirouments., DLs occur naturally in a variety of space plasma environments.
 It turus ou that DLs have the electrostatic potential auc other relevaut paranieters ionotouicallv changing from oue value at one extreme to another at the other cud. lence “kinks”.," It turns out that DLs have the electrostatic potential and other relevant parameters monotonically changing from one value at one extreme to another at the other end, hence “kinks”."
" This is associated with adjacent positive and negative charge regions. which eive rise to the name ""double avers."," This is associated with adjacent positive and negative charge regions, which give rise to the name “double layers""."
 Such DLs are more difficult to ecuerate and require a fine tuniug of the plasma parameters. hence a more complicated plasma compositions with enough eocwav to obey the necessary constraints (Verhecst. 2006: ITellbere. 1992: Moslem. 2007).," Such DLs are more difficult to generate and require a fine tuning of the plasma parameters, hence a more complicated plasma compositions with enough leeway to obey the necessary constraints (Verheest, 2006; Hellberg, 1992; Moslem, 2007)."
 The study of nonlinear EAWSs has been focused woinany authors with different particle distribution. Le. Cairns distribution (Pakzad aud Tribeche. 2010). Vortes-like distribution (Moiuun and Shukla. 2002). q-honextensive distribution (CGougam aud Tribeche. 2011). quantum plasimas (Masood anc Mushtaq. 2008). et al.," The study of nonlinear EAWs has been focused by many authors with different particle distribution, i.e., Cairns distribution (Pakzad and Tribeche, 2010), Vortex-like distribution (Mamun and Shukla, 2002), q-nonextensive distribution (Gougam and Tribeche, 2011), quantum plasmas (Masood and Mushtaq, 2008), et al."
 Aud it had beeu found that the particles distributions plav a crucial role in characterizing the plivsics of nonlinear waves., And it had been found that the particles distributions play a crucial role in characterizing the physics of nonlinear waves.
 Receutly. the plasma with superthermal particles has gained much attention.," Recently, the plasma with superthermal particles has gained much attention."
 Superthermal clectrous are often observed in laboratory. space. aud astrophysical plasina cuviromments. viz..," Superthermal electrons are often observed in laboratory, space, and astrophysical plasma environments, viz.,"
 the ionosphere. auroral zones. nesosplicre. lower thermosplere. ete (Picrrard. 2010. and reference fherein).," the ionosphere, auroral zones, mesosphere, lower thermosphere, etc (Pierrard, 2010, and reference therein)."
 The EKappa functions (Vasvliunas. 1968) characterized by the spectral iudex Ho are found to represent more suitably the particles velocity distributions observed in umber of space and astrophysical cuviromment.," The Kappa functions (Vasyliunas, 1968) characterized by the spectral index $\kappa $ are found to represent more suitably the particle's velocity distributions observed in number of space and astrophysical environment."
 The Kappa function may recover the Maxwellian distribution in the lauit of #»ox and its mathematical characteristics aud physical origin have receutlv been addressed bv Tau and Fu (2007. the references within).," The Kappa function may recover the Maxwellian distribution in the limit of $\kappa \to
\infty $ and its mathematical characteristics and physical origin have recently been addressed by Hau and Fu (2007, the references within)."
 It is worth noting hat some theoretical work focused on the effects of superthermal particles on different types of lincar aud ronlinear collective processes in plasmas., It is worth noting that some theoretical work focused on the effects of superthermal particles on different types of linear and nonlinear collective processes in plasmas.
 For instance. he linear properties of plasmas in the presence of a Kappa distribution with excess superthermal particles wave been investigated) rather extensively (Sunuuers alc Thorne. 1991: Mace and Iellberg. 1995).," For instance, the linear properties of plasmas in the presence of a Kappa distribution with excess superthermal particles have been investigated rather extensively (Summers and Thorne, 1991; Mace and Hellberg, 1995)."
 More recently. eniployiug a Sagdeev pseudopoteutia nethod. the nonlinear arbitrary amplitude EAWs were studied. the weak stationary solitons aud DLs were also given by expanding the Sagdeev poteutial in smal züuplitude luit (Sahnu. 2010: Youusi and Tribeche. 2010).," More recently, employing a Sagdeev pseudopotential method, the nonlinear arbitrary amplitude EAWs were studied, the weak stationary solitons and DLs were also given by expanding the Sagdeev potential in small amplitude limit (Sahu, 2010; Younsi and Tribeche, 2010)."
 Iu their model. the plasina systenis Were assuniec consisting of cold fluid clectrous. supertlermal hot electrons and stationary donus.," In their model, the plasma systems were assumed consisting of cold fluid electrons, superthermal hot electrons and stationary ions."
 The same procedure also was founded for the q-uonexteusive distribute hot electrons plasina systema (Cougam and Tribeche. 2011).," The same procedure also was founded for the q-nonextensive distributed hot electrons plasma system (Gougam and Tribeche, 2011)."
 Baboolal et al. (, Baboolal et al. (
1991) have showed that. when ion-acoustic DLs in a plasma with negative ions are isidered. one uust be especially careful to ensure that one’s solutions iicet the criteria for convergence of the original expansions.,"1991) have showed that, when ion-acoustic DLs in a plasma with negative ions are considered, one must be especially careful to ensure that one's solutions meet the criteria for convergence of the original expansions."
 Verheest (1993) has arrived at a similar conclusion cousideriug DLs iu dusty plasimas., Verheest (1993) has arrived at a similar conclusion considering DLs in dusty plasmas.
 Mace and Ποσο (1993) showed that EA DLs can not be supported in an infinite. homogeneous. unmnaenetized aud collisionless plasma svstem cousistincl6 of cool fluid ions. cold fluid electrous aud hot Boltzmann distributed electrons based ou the midV model.," Mace and Hellberg (1993) showed that EA DLs can not be supported in an infinite, homogeneous, unmagnetized and collisionless plasma system consisting of cool fluid ions, cold fluid electrons and hot Boltzmann distributed electrons based on the mKdV model."
 Some sale conclusions were also cau be found (IHellberg. et al.," Some same conclusions were also can be found (Hellberg, et al.,"
 1992)., 1992).
 Thus. with these ideas iu wind. we rce-investisate here the s2all but finite amplitude solitary structures iu such two-clectron-temperatiure asma with superthenuall electron. based on the iisdV moctel.," Thus, with these ideas in mind, we re-investigate here the small but finite amplitude solitary structures in such two-electron-temperature plasma with superthermal electron based on the mKdV model."
 Ounce of our objective here is to study the noulinear effects of super-thermal distribution of hot electrous on the nature of the sinall amplitude solitary waves., One of our objective here is to study the nonlinear effects of super-thermal distribution of hot electrons on the nature of the small amplitude solitary waves.
 Another one is to show whether the DL solution exist or not., Another one is to show whether the DL solution exist or not.
 This paper is organized as follows: iu Section 2. the basic set of equations is introduced.," This paper is organized as follows: in Section 2, the basic set of equations is introduced."
 Iu Section 3. we derive the iulXdV equation. aud the solutious of both solitons aud. DLs are given.," In Section 3, we derive the mKdV equation, and the solutions of both solitons and DLs are given."
 Finally. some conclusions and discussions are eiven iu Section L.," Finally, some conclusions and discussions are given in Section 4."
 We consider a homogeneous system of au uunaenetized collisionless plasima cousisting of a cold electron. fluid. and superthermal hot olectrous obeving a Ikappa," We consider a homogeneous system of an unmagnetized collisionless plasma consisting of a cold electron fluid, and superthermal hot electrons obeying a Kappa"
(uncalibrated) light curve for eclipse 1 is shown. for the whole array and for the two corner pixels.,"(uncalibrated) light curve for eclipse 1 is shown, for the whole array and for the two corner pixels."
 Aso described. under step. (d). if. theenergydependent pixel-to-pixel response variations are large (and uncorrected). atmospheric-induced. image motion would. alfect the Light curves through the interdependence of image position and array sensitivity.," As described under step (d), if theenergy-dependent pixel-to-pixel response variations are large (and uncorrected), atmospheric-induced image motion would affect the light curves through the interdependence of image position and array sensitivity."
 We have performed experiments in which the data are binnecl into. e.g. los time bins. and the image centroid positions in we and y are compared with the corresponding intensity variations (ligure 3)).," We have performed experiments in which the data are binned into, e.g., 1 s time bins, and the image centroid positions in $x$ and $y$ are compared with the corresponding intensity variations (Figure \ref{fig:motion}) )."
 In practice. the image centroid moves by. at most —O0.1 pixels. and even for our cata before energy calibration there is no evident correlation between image motion and intensity [ickering.," In practice, the image centroid moves by at most $\pm0.1$ pixels, and even for our data before energy calibration there is no evident correlation between image motion and intensity flickering."
" AX small part of the high-frequency structure of the light curves can formally be. attributed to the time-dependent loss of flux into the small inter-pixel gaps (dead: zones) between the array elements. as the atmospheric phase Iluetuations move the ""seeing profile’ around the array."," A small part of the high-frequency structure of the light curves can formally be attributed to the time-dependent loss of flux into the small inter-pixel gaps (dead zones) between the array elements, as the atmospheric phase fluctuations move the `seeing profile' around the array."
 Some improvement in this instrumental contribution to the light curve flickering could be made by taking into account the varying contribution to the dead zones as a function of image location., Some improvement in this instrumental contribution to the light curve flickering could be made by taking into account the varying contribution to the dead zones as a function of image location.
 This could be done by determining a Gaussian profile fit to the data binned over. sav. 1s. taking account of the dead: zones in the fitting process. then normalising the measured [ux to the total area covered by the image during that interval.," This could be done by determining a Gaussian profile fit to the data binned over, say, 1 s, taking account of the dead zones in the fitting process, then normalising the measured flux to the total area covered by the image during that interval."
 The effect is expected to be rather small. and a detailed study. is deferred to a future paper.," The effect is expected to be rather small, and a detailed study is deferred to a future paper."
 The pixel-to-pixel light curves Figure 1)) show structure inconsistent with Poisson noise. and only roughly. correlated between neighbouring pixels.," The pixel-to-pixel light curves Figure \ref{fig:pixels}) ) show structure inconsistent with Poisson noise, and only roughly correlated between neighbouring pixels."
 From the clean behaviour of the total light curve. we infer that this structure is consistent with atmospheric phase Iuctuations. and again return to this issue in a future study.," From the clean behaviour of the total light curve, we infer that this structure is consistent with atmospheric phase fluctuations, and again return to this issue in a future study."
 lo assess the fidelity of our data further. we have investigated: some specific features. of the light curves. in detail.," To assess the fidelity of our data further, we have investigated some specific features of the light curves in detail."
" For example. one low data point appears as a single outlier in all three energy. bins at about phase 0.938 in the 2 s binned data of Figure ο,"," For example, one low data point appears as a single outlier in all three energy bins at about phase 0.938 in the 2 s binned data of Figure \ref{fig:colour1}."
 At a time binning of 0.02 s. this feature is seen to arise from a rapid but not instantaneous drop to zero source counts. which persists for almost. 1 s. and which can be attributed to a known but. infrequent telescope pointing glitch in azimuth. with an amplitude of several aresec (CLR. Benn. private communication).," At a time binning of 0.02 s, this feature is seen to arise from a rapid but not instantaneous drop to zero source counts, which persists for almost 1 s, and which can be attributed to a known but infrequent telescope pointing glitch in azimuth, with an amplitude of several arcsec (C.R. Benn, private communication)."
 Figure 2. displays a number of prominent features observed previously in UZ For through the optical citealtabs| 89: Bailey&Cropper 19011: Imamura&Steiman-Camoeron 1998)) to ultraviolet (Warrenetal. 1995:: Stockman&Schmidt 1996)). ancl related to the variable viewing geometry with orbital phase Figure S ofFerrarioetal. 1989: Figure 4 of Bailey&Cropper 19011," Figure \ref{fig:lightcurve} displays a number of prominent features observed previously in UZ For through the optical \\citealt{abs+89}; \citealt{bc91}; \citealt{is-c98}) ) to ultraviolet \citealt{wsv95}; ; \citealt{ss96}) ), and related to the variable viewing geometry with orbital phase Figure 8 of\citealt{fwb+89}; ; Figure 4 of \citealt{bc91}; ;"
 Figure 2. displays a number of prominent features observed previously in UZ For through the optical citealtabs| 89: Bailey&Cropper 19011: Imamura&Steiman-Camoeron 1998)) to ultraviolet (Warrenetal. 1995:: Stockman&Schmidt 1996)). ancl related to the variable viewing geometry with orbital phase Figure S ofFerrarioetal. 1989: Figure 4 of Bailey&Cropper 19011:," Figure \ref{fig:lightcurve} displays a number of prominent features observed previously in UZ For through the optical \\citealt{abs+89}; \citealt{bc91}; \citealt{is-c98}) ) to ultraviolet \citealt{wsv95}; ; \citealt{ss96}) ), and related to the variable viewing geometry with orbital phase Figure 8 of\citealt{fwb+89}; ; Figure 4 of \citealt{bc91}; ;"
 substituting equations (13)) and (14)) in equation (12)). we obtain where the F parameter is defined in equation (10)).,"2 Substituting equations \ref{eeta}) ) and \ref{mu}) )in equation \ref{Lsimu}) ), we obtain )^2 where the $F$ parameter is defined in equation \ref{nu}) )."
" As outlined in PaperL. heating rates are given by Il,= where //4, is the heatingrale associated wilh a generic camping mechanism. is the wave flux and LyBl is the damping5 length."," As outlined in \citeauthor{vasc..00}, heating rates are given by H_A = where $H_A$ is the heatingrate associated with a generic damping mechanism, $\Phi_w = \rho\langle \delta v^{2}\rangle v_{A}$ is the wave flux and $L_A$ is the damping length."
5 We derived the heating5 rates [or both the nonlinear and turbulent damping mechanisms in Paper I. , We derived the heating rates for both the nonlinear and turbulent damping mechanisms in \citeauthor{vasc..00}. .
They are. respectively:," They are, respectively: , and"
Polarization is a powerful tool in understanding diverse astrophysical phenomena.,Polarization is a powerful tool in understanding diverse astrophysical phenomena.
 Net polarization in the continuum and spectral lines can measure spatial. kinematic and compositional structure that could not otherwise be detected in unresolved sources.," Net polarization in the continuum and spectral lines can measure spatial, kinematic and compositional structure that could not otherwise be detected in unresolved sources."
 It can also be used as a diagnostic of magnetic fields in both resolved and unresolved sources., It can also be used as a diagnostic of magnetic fields in both resolved and unresolved sources.
 Continuum polarization can be produced by Thomson scattering: in lines it can be created via the Hanle and tranverse- and Jongitudinal-Zeeman effects., Continuum polarization can be produced by Thomson scattering; in lines it can be created via the Hanle and tranverse- and longitudinal-Zeeman effects.
 In this paper we focus on the Hanle effect. but our results can also apply to other magnetically-induced linear polarization mechanisms.," In this paper we focus on the Hanle effect, but our results can also apply to other magnetically-induced linear polarization mechanisms."
 The Hanle effect is a weak field case of the Zeeman effect with consequence for resonance line scattering polarization in the presence of a magnetic field (e.g.. Moruzzi Strumia 1991; Stenflo 1994: Landi Deel’ Innocenti Landolfi 2004).," The Hanle effect is a weak field case of the Zeeman effect with consequence for resonance line scattering polarization in the presence of a magnetic field (e.g., Moruzzi Strumia 1991; Stenflo 1994; Landi Degl' Innocenti Landolfi 2004)."
 The Hanle effect describes the influence of the field for the polarization of line scattering: unlike the Zeeman effect. the Hanle effect does not generate circularly polarized emissions.," The Hanle effect describes the influence of the field for the polarization of line scattering; unlike the Zeeman effect, the Hanle effect does not generate circularly polarized emissions."
 The Hanle effect has proven to have diagnostic value in a number of applications to solar physics., The Hanle effect has proven to have diagnostic value in a number of applications to solar physics.
 Examples from the recent literature include coronal magnetic field (e.g.. Derouich 22010). turbulent magnetic fields (e.g.. Frisch 22009; Rachkovskii 2009; Kleint 22010). chromospheric magnetic fields (e.g.. Faurobert 22009). and prominences (e.g.. Merenda 22006). to name only a few.," Examples from the recent literature include coronal magnetic field (e.g., Derouich 2010), turbulent magnetic fields (e.g., Frisch 2009; Rachkovskii 2009; Kleint 2010), chromospheric magnetic fields (e.g., Faurobert 2009), and prominences (e.g., Merenda 2006), to name only a few."
 There have also been efforts to develop diagnostics based on the Hanle effect for molecular lines (e.g.. Berdyugina Fluri 2004; Shapiro 22007).," There have also been efforts to develop diagnostics based on the Hanle effect for molecular lines (e.g., Berdyugina Fluri 2004; Shapiro 2007)."
" Many of these diagnostics have been developed to interpret the so-called ""Second Solar Spectrum"" (Stenflo Keller 1997).", Many of these diagnostics have been developed to interpret the so-called “Second Solar Spectrum” (Stenflo Keller 1997).
 There has even been a consideration of the Hanle effect for the magnetic field of Jupiter (Ben-Jaftel 22005)., There has even been a consideration of the Hanle effect for the magnetic field of Jupiter (Ben-Jaffel 2005).
 For stars other than the Sun. considerations of the Hanle effect have so far been restricted to theoretical calculations. such as simplified considerations in stellar wind lines (e.g.. Ignace. Nordsieck. Cassinelli 2004). circumstellar disks (Yan Lazarian 2008: Ignace 2010). and maser sources (Asenio Ramos. Landi DeglInnocenti. Trujillo Bueno 2005).," For stars other than the Sun, considerations of the Hanle effect have so far been restricted to theoretical calculations, such as simplified considerations in stellar wind lines (e.g., Ignace, Nordsieck, Cassinelli 2004), circumstellar disks (Yan Lazarian 2008; Ignace 2010), and maser sources (Asenio Ramos, Landi Degl'Innocenti, Trujilo Bueno 2005)."
 So far. no definitive detections of the Hanle effect in the stellar context have been reported.," So far, no definitive detections of the Hanle effect in the stellar context have been reported."
 A new consideration of the Hanle effect in photospheric lines of unresolved stars has been proposed by Lopez Ariste. Asensio Ramos. Gonzalez Fernandez (2011).," A new consideration of the Hanle effect in photospheric lines of unresolved stars has been proposed by Lopez Ariste, Asensio Ramos, Gonzalez Fernandez (2011)."
 Our paper makes a contribution to these new and interesting results by extending them to a more general case through a consideration of perspective effects for oblique magnetic rotators., Our paper makes a contribution to these new and interesting results by extending them to a more general case through a consideration of perspective effects for oblique magnetic rotators.
 We demonstrate that for a given field topology and field strength. aspects of the variable polarization due to geometry can be disentangled from the mechanism of the Hanle effect and generalized to apply to any net polarization due to a bipolar magnetic field.," We demonstrate that for a given field topology and field strength, aspects of the variable polarization due to geometry can be disentangled from the mechanism of the Hanle effect and generalized to apply to any net polarization due to a bipolar magnetic field."
 Section 2 presents the background for our models: section 2.1 describes polarization conventions and gives an overview of the nature of the Hanle effect.," Section \ref{sec:hanle}
 presents the background for our models: section \ref{sub:pol} describes polarization conventions and gives an overview of the nature of the Hanle effect."
 Adopted geometry and assumptions are defined in section. 2.2.. and solutions for perspective effects for polarimetric lighteurves are given in section 2.3..," Adopted geometry and assumptions are defined in section \ref{sub:conventions}, and solutions for perspective effects for polarimetric lightcurves are given in section \ref{sub:solns}."
 There are three parts to the discussion: (a) a consideration of an edge-on (or equator-on) rotating star as discussed by Lopez Ariste (2011): (b) a generalization to arbitrary viewing inclination of the stellar rotation axis; and (c) a review of a special case in which the dependence of amplitude on the Hanle effect is a known function of the inclination between the field and observer axes., There are three parts to the discussion: (a) a consideration of an edge-on (or equator-on) rotating star as discussed by Lopez Ariste (2011); (b) a generalization to arbitrary viewing inclination of the stellar rotation axis; and (c) a review of a special case in which the dependence of amplitude on the Hanle effect is a known function of the inclination between the field and observer axes.
 Concluding remarks are given in section 3.., Concluding remarks are given in section \ref{sec:concs}.
 An extra figure. exclusive to the version of this paper. is included in the Appendix.," An extra figure, exclusive to the version of this paper, is included in the Appendix."
 Polarization is measured 1n. terms of the four Stokes vector components. 7. Q. U and V.," Polarization is measured in terms of the four Stokes vector components, $I$ , $Q$, $U$ and $V$."
 Here { ts total intensity: Q and U measure the intensity of linearly polarized light relative to two axes offset by a rotation of 43i and V is a measure of the circularly polarized light — 1n our case zero., Here $I$ is total intensity; $Q$ and $U$ measure the intensity of linearly polarized light relative to two axes offset by a rotation of $45^\circ$; and $V$ is a measure of the circularly polarized light – in our case zero.
 For convenience we introduce normalized parameters g=Q/I and u=U/T., For convenience we introduce normalized parameters $q=Q/I$ and $u=U/I$.
 Measured Stokes parameters are defined with respectto one orientation in the sky — by convention. g is measured along," Measured Stokes parameters are defined with respectto one orientation in the sky – by convention, $q$ is measured along"
study. primarily devoted to the effective temperature scale of E. € «uid [dx stars.,"study primarily devoted to the effective temperature scale of F, G and K stars."
 We believe we have iniproved. on their resuts by (1) severely restricting the stellar. sample to the hiehest quality metallicities: (2) providing error estiniates on the quoted. colours and (3) we concentrate on Sunlike stars in the (Liye. esl) region closest. to the Sun. rather than interpolating the solar colours from fitting relations valid for a much wider range in temperatures and metalicities.," We believe we have improved on their results by (1) severely restricting the stellar sample to the highest quality metallicities; (2) providing error estimates on the quoted colours and (3) we concentrate on Sun–like stars in the $\Teff$, [Fe/H]) region closest to the Sun, rather than interpolating the solar colours from fitting relations valid for a much wider range in temperatures and metallicities."
 Combined with the requirement of highest quality nxtallicity data. this restricts our sample to a rather small number of stars (especially in CDVI). which we plan to extend in the near future.," Combined with the requirement of highest quality metallicity data, this restricts our sample to a rather small number of stars (especially in $UBVRI$ ), which we plan to extend in the near future."
 However we remark that our sample is not significantly smaller than that of rez Moelénndez.applied.," However we remark that our sample is not significantly smaller than that of rez Melénndez,."
 As mentioned in Section 2. the requirement of good metallicitv cata reduces their sample by (from 115 to G7 stars). anc their subsamples with available DBVIU photometry would. count. LL37 stars cour 912 stars in Table 1..," As mentioned in Section 2, the requirement of good metallicity data reduces their sample by (from 115 to 67 stars), and their subsamples with available BVRI photometry would count 11–37 stars our 9–12 stars in Table \ref{fits}."
 The lower number of stars in our sample is compensated for by the increased accuracy and homogeneity in the metallicities. the smaller number of. parameters and the decreased. dispersion in the fits for this restricted temperature range (see below).," The lower number of stars in our sample is compensated for by the increased accuracy and homogeneity in the metallicities, the smaller number of parameters and the decreased dispersion in the fits for this restricted temperature range (see below)."
 Notice also that. for D.V. our direct determination based. on just 9 objects is in excellent. agreement with the indirect. determination. from Jvcho BpVp colours. which is based on 51 objects.," Notice also that, for $B-V$, our direct determination based on just 9 objects is in excellent agreement with the indirect determination from Tycho $B_{\rm T}-V_{\rm T}$ colours, which is based on 51 objects."
 Actually. all our colours were found to be. within our error estimates. in excellent agreement with irez Melénndez. with the possible exception of οV.," Actually, all our colours were found to be, within our error estimates, in excellent agreement with rez Melénndez, with the possible exception of $B-V$ ."
 For this colour. we find (D.V).=0.642£0.016. while rez Melénndez find (5.V).=0.619 (no error given)," For this colour, we find $(B-V)_\odot = 0.642 \pm 0.016$, while rez Melénndez find $(B-V)_\odot = 0.619$ (no error given)."
 We have attempted to reconstruct the size of their error. ancl believe it to be about twice our own error. or about 0.03 mag.," We have attempted to reconstruct the size of their error, and believe it to be about twice our own error, or about 0.03 mag."
 This is based on their estimate of a scatter in the (10 parameter) fit of elfective temperature to colour and metallicity of SS Ix [or main sequence stars (their table 2). whereas our own (3 parameter) fit. produces a scatter of 43 Ix. Our reconstruction of the size of their error appears o be correct rez 2005. ccomnm.).," This is based on their estimate of a scatter in the (10 parameter) fit of effective temperature to colour and metallicity of 88 K for main sequence stars (their table 2), whereas our own (3 parameter) fit produces a scatter of 43 K. Our reconstruction of the size of their error appears to be correct rez 2005, comm.),"
 hence the two estimates of (£213. agree within the errors., hence the two estimates of $(B-V)_\odot$ agree within the errors.
 Sekiguchi Fukugita (2000) jwe also studied the BoV colourtemperature relation. using a very similar method. and deriving (13το.=1.626£ 0.018.," Sekiguchi Fukugita (2000) have also studied the $B-V$ colour–temperature relation, using a very similar method, and deriving $(B-V)_\odot = 0.626 \pm 0.018$ ."
 Our solar colours are also in &ood agreement with Cavrel de Strobel (1996): (D.V).=0.642+0.004. (bJj).=O404+0.005: Cirav (1995): (D1)-648+ 0.006. CR1).=(0.338+0.002: Tavlor (1998): (Ro1).—0.3535x0.002.," Our solar colours are also in good agreement with Cayrel de Strobel (1996): $(B-V)_\odot = 0.642 \pm 0.004$, $(b-y)_\odot =
0.404 \pm 0.005$; Gray (1995): $(B-V)_\odot = 0.648 \pm 0.006$ , $(R-I)_\odot =
0.338 \pm 0.002$; Taylor (1998): $(R-I)_\odot = 0.335 \pm 0.002$."
 Another method to determine the colours of the Sun is by applving svnthetic photometry to he observed. absolute flux calibrated solar spectrum: this results in (0.D).—0.13.Olt and (D.V).=0.631.65 (Colina. Bohlin Castelli 1996: Bessel et 11998). again in good agreement with our determinations.," Another method to determine the colours of the Sun is by applying synthetic photometry to the observed, absolute flux calibrated solar spectrum; this results in $(U-B)_\odot = 0.13-0.14$ and $(B-V)_\odot = 0.63-0.65$ (Colina, Bohlin Castelli 1996; Bessel et 1998), again in good agreement with our determinations."
 Finally. also the predictions of the most updated theoretical stellar atmosphere models: (0.V).~0.640.65. (Casagrande et 22005. in prep.)," Finally, also the predictions of the most updated theoretical stellar atmosphere models: $(B-V)_{\odot} \sim 0.64-0.65$ (Casagrande et 2005, in prep.)"
 are well compatible with our results., are well compatible with our results.
 In summary. we have provided an estimate of the colours of the Sun in a large variety of photometric svstenis. bv comparison to Sunlike stars in the same temperature and metallicity range as the Sun.," In summary, we have provided an estimate of the colours of the Sun in a large variety of photometric systems, by comparison to Sun–like stars in the same temperature and metallicity range as the Sun."
 We made use of the most accurate and internally homogeneous data available for colours and metallicitv. anc took advantage of the recently firmily-cstablishecl direct. ancl LREAL temperature scale.," We made use of the most accurate and internally homogeneous data available for colours and metallicity, and took advantage of the recently firmly-established direct and IRFM temperature scale."
 We also give a careful estimate of the presentuncertainties., We also give a careful estimate of the presentuncertainties.
 Within the errors. our solar colours are in excellent. agreement with the analogous recent work by," Within the errors, our solar colours are in excellent agreement with the analogous recent work by"
Dunn due to the use of the 907 sit isa secondary effect. while the responsivity iu both NIS ciumnels has been steadily dropping.,"burn-in due to the use of the $^{''}$ slit is a secondary effect, while the responsivity in both NIS channels has been steadily dropping."
 DelZamnact:id.(2010) provided a waveleugth-«depeudeut long-term c'orrectiou for this drop over the period 1996-2010., \citet{del10} provided a wavelength-dependent long-term correction for this drop over the period 1996-2010.
 The DelZamnaetal.(2010) lone-teri corrections. combined witi the. DelZanuaetal.(2001) responsivitics provide eood agreement between he mradiauces of most CDS lines with those meastred with the prototvpe of the Solar Dynamics Observatxv (SDO) EVE 1ustrumocnut. flown on a rocket on April |1. 2008.," The \citet{del10} long-term corrections, combined with the \citet{del01} responsivities provided good agreement between the irradiances of most CDS lines with those measured with the prototype of the Solar Dynamics Observatory (SDO) EVE instrument, flown on a rocket on April 14, 2008."
 The EUNIS LW channel has a wavelength rauge overlappiis with that of CDS/NIS 1 80 cal provide a direct calibration. update for it.," The EUNIS LW channel has a wavelength range overlapping with that of CDS/NIS 1, so can provide a direct calibration update for it."
 The lab-calibrated SERTS-97 was successfully used to improve the response curve for the CDS NIS. 1 wavebaud based on their coordinated. cospatial spectra (Thomas2002).," The lab-calibrated SERTS-97 was successfully used to improve the response curve for the CDS NIS 1 waveband based on their coordinated, cospatial spectra \citep{tho02}."
". Based ou observations of active region spectra. EUNIS-06 provided a new calibration update for CDS NIS (Wanectal. 2010).. which showed au overall decrease in NIS 1 responsivity bv a factor about 1.7 compared to that of the previously implemented calibration (version. 1. 2002) with the NIS ""standard loug-teru corrections. while the responsivitv in NIS 2 second order at 301 wwith the NIS. standard long-eterur corrections remained nearly conustaut (Fig. a(("," Based on observations of active region spectra, EUNIS-06 provided a new calibration update for CDS NIS \citep{wan10}, which showed an overall decrease in NIS 1 responsivity by a factor about 1.7 compared to that of the previously implemented calibration (version 4, 2002) with the NIS “standard"" long-term corrections, while the responsivity in NIS 2 second order at $-$ 304 with the NIS “standard"" long-term corrections remained nearly constant (Fig. \ref{fgcdscal}( ("
aj).,a)).
 It —uecds to be, It needs to be
Rees Gunn (1974) prosposed a theoretical description of interaction between pulsar and its nebula.,Rees Gunn (1974) prosposed a theoretical description of interaction between pulsar and its nebula.
 They suggested that the central pulsar can generate a highly relativistic parücle dominated wind that passes through the medium in the supernova remuant. forming a shock front.," They suggested that the central pulsar can generate a highly relativistic particle dominated wind that passes through the medium in the supernova remnant, forming a shock front."
 The electrons and positrons in (ie shock are envisioned to be accelerated to a power-law energy distribution and (to radiation svuchrotvon radiation in the downstream region., The electrons and positrons in the shock are envisioned to be accelerated to a power-law energy distribution and to radiation synchrotron radiation in the downstream region.
 Llowever. it is unlikely Chat electrons/poistrons can carry away all the spin-down power of pulsars near (he light evlinder.," However, it is unlikely that electrons/poistrons can carry away all the spin-down power of pulsars near the light cylinder."
 Kennel Coroniti (1984) have introduced a magnetization parameter. σ={πμD. where B is the magnetic field. n is the particle number density. ος is the Lorentz [actor of relativistic particles in (he wind and n ds the particle mass.," Kennel Coroniti (1984) have introduced a magnetization parameter, $\sigma = \frac{B^2}{4\pi n\gamma_w mc^2}$, where $B$ is the magnetic field, $n$ is the particle number density, $\gamma_w$ is the Lorentz factor of relativistic particles in the wind and $m$ is the particle mass."
 In order (o explain the observed radiation properties in the Crab nebula. 6~0.003.," In order to explain the observed radiation properties in the Crab nebula, $\sigma \sim 0.003$."
 επ pairs are produced inside the light evlinder in the polar gap (e.g. Ruderman Sutherland 1975: Fawley. Arons Scharlemann 1977) and/or outergap (e.g. Cheng. Ilo Ruderman 1956).," $e^{\pm}$ pairs are produced inside the light cylinder in the polar gap (e.g. Ruderman Sutherland 1975; Fawley, Arons Scharlemann 1977) and/or outergap (e.g. Cheng, Ho Ruderman 1986)."
 When electvons/positrons leave the light cvlinder. they can onlv carry a very small fraction of spin-down power. which implies &>>1.," When electrons/positrons leave the light cylinder, they can only carry a very small fraction of spin-down power, which implies $\sigma>>1$."
 Therefore the magnetization parameter of pulsar wind must evolve from high-o to low-7 in the down-stream., Therefore the magnetization parameter of pulsar wind must evolve from $\sigma$ to $\sigma$ in the down-stream.
 Coroniti (1990) has shown that the pulsar spin-down power initially carried awav by low lrequency electromagnetic waves can be converted into particle kinetic energy via magnetic reconnection process before reaching the shock radius., Coroniti (1990) has shown that the pulsar spin-down power initially carried away by low frequency electromagnetic waves can be converted into particle kinetic energy via magnetic reconnection process before reaching the shock radius.
" Cheng. Taam Wang (2004. 2006) studied the noupulsed X-ray. enission of pulsars. they found that the nonpulsed. X-ray. luminosity (L7?) is proportional to the pulsar spin-down power (Lay) as Lue""xLi "," Cheng, Taam Wang (2004, 2006) studied the nonpulsed X-ray emission of rotation-powered pulsars, they found that the nonpulsed X-ray luminosity $L_x^{npul}$ ) is proportional to the pulsar spin-down power $L_{sd}$ ) as $L_x^{npul} \propto L_{sd}^{1.4\pm 0.1}$."
Thev argued that the nonpulsed X-rays should be emitted by the pulsar wind in the shock radius via svnclirotron radiation., They argued that the nonpulsed X-rays should be emitted by the pulsar wind in the shock radius via synchrotron radiation.
 Thev used (he simple one-zone model developed by Chevalier (2000) to estimate the relation between (he spin-down power ancl nonpulsed X-ray. Iuminosity., They used the simple one-zone model developed by Chevalier (2000) to estimate the relation between the spin-down power and nonpulsed X-ray luminosity.
 They. assumed that, They assumed that
 define the equilibrium p'essure. deusity aid entropy scale heights.," + define the equilibrium pressure, density and entropy scale heights."
 We have included the vertical component of the velocity in orde‘to make contac with au axisviunmetric convective instability that is present in two cdimensious. alter which we wi[set A. to zero.," We have included the vertical component of the velocity in order to make contact with an axisymmetric convective instability that is present in two dimensions, after which we will set $k_z$ to zero."
 We will be mainly interestec in the incompressive shiwaves because the short-waveleieth upressive shwaves are uichaneed at leadiug order by st'alification., We will be mainly interested in the incompressive shwaves because the short-wavelength compressive shwaves are unchanged at leading order by stratification.
 We will therefore wcork ely in the Boussiuesq In addition to the asstunption of incompressibiity. is approximationcousideiders ὁ2 o be negligible in the ent‘opy eclatlou: pressure changes are ermined by whatever is requirec to maintaln uearly iucomp'essible flow.," We will therefore work solely in the Boussinesq In addition to the assumption of incompressibility, this approximationconsiders $\delta P$ to be negligible in the entropy equation; pressure changes are determined by whatever is required to maintain nearly incompressible flow."
 Tie original Boussitοσα ooxinatiou applies onM7 to incoupressible fluids., The original Boussinesq approximation applies only to incompressible fluids.
 Π was extened to Compressible [Iuids by Je[revs(1930) aud Spiegel&\'eronis(1960)., It was extended to compressible fluids by \cite{jeff30} and \cite{sv60}.
. We show i1 the Appenclix that it is formally eauivalent to taking the slolt-waveeneth. low-frequency limiit of tle full set of linear equatious.," We show in the Appendix that it is formally equivalent to taking the short-wavelength, low-frequency limit of the full set of linear equations."
" Fromthis viewpoint. asstmune tha HEPD, is of the sane order as the other terms in the dynamical equations implies that àPÍDyo(Hu).IXNX. tls justiving its neglect iu the eutrορν equation."," Fromthis viewpoint, assuming that $H k_y \delta P/P_0$ is of the same order as the other terms in the dynamical equations implies that $\delta P/P_0 \sim (H k_y)^{-1} \delta
\Sigma/\Sigma_0$, thus justifying its neglect in the entropy equation."
" We therefore replace equaious ??7)) and (??)) witl ""de, hydty kde. =0(51) and 26£=0.", We therefore replace equations \ref{LIN1a}) ) and \ref{LIN5a}) ) with _x v_x + k_y v_y + k_z v_z = 0 and - = 0.
"(52) Using equatious (?2)) aud (2? ?)) and the time derivative of equation (??)). one can express ov, and 07? in terius of ov, aud δὲ: Eliminating 62 in equation (??))via equation (??)) gives"," Using equations \ref{LIN3}) ) and \ref{LIN5}) ) and the time derivative of equation \ref{LIN1}) ), one can express $\dot{\delta v}_y$ and $\delta P$ in terms of $\delta v_x$ and $\dot{\delta v}_x$ : = -i _y = Eliminating $\delta P$ in equation \ref{LIN2}) )via equation \ref{DH}) ) gives"
The 4? contours are shown in Ligure 1. while the renorndised data and best-fit SED are plotted in Figure 2.,"The $\chi^2$ contours are shown in Figure 1, while the renormalised data and best-fit SED are plotted in Figure 2."
 The best self-consistent fit corresponds to 3=1.95d0.3. T—41£5 (lo errors).," The best self-consistent fit corresponds to $\beta=1.95\pm0.3$, $T=41\pm5\K$ $\sigma$ errors)."
 A similar procedure applied to the low-recdshift. less-Iumimous samples of LIRGs (Lisenfeld. Isaak Llills. 190)) and local galaxies (Dunneal... 2000) gives results inconsistent at the >20 level (Figure 1).," A similar procedure applied to the low-redshift, less-lumimous samples of LIRGs (Lisenfeld, Isaak Hills, 1999) and local galaxies (Dunne, 2000) gives results inconsistent at the $>2\sigma$ level (Figure 1)."
 We can use the \2 contours to predict the outcome of curve-Litting in which 3 is held fixed. while the temperature is varied.," We can use the $\chi^2$ contours to predict the outcome of curve-fitting in which $\beta$ is held fixed, while the temperature is varied."
 For other studies of high-redshift’ quasar SEDs. he 3=L5 adopted by Benforc (1999) ancl Buller (in prep.)," For other studies of high-redshift quasar SEDs, the $\beta=1.5$ adopted by Benford (1999) and Buffey (in prep.)"
 would give 7=50 aas mean best-fit. which is indeed. close to that found. by hose authors. ancl consistent with the 7=50 aassumecd by MeMahon al.(1999).," would give $T$ as mean best-fit, which is indeed close to that found by those authors, and consistent with the $T$ assumed by McMahon (1999)."
 Variation in οσον (hence. eventually. star-formation rates) estimated. from such best-fits cdo not vary substantially. cause Leyx(3|ονd. whilst the best-fit Z. is monotonically decreasing with 3: the clotdashed line in Figure 1. a locus of constant luminosity. illustrates. this.," Variation in luminosities (hence, eventually, star-formation rates) estimated from such best-fits do not vary substantially, because $L_{\rm FIR} \propto (3+\beta)!\times T^{4+\beta}$, whilst the best-fit $T$ is monotonically decreasing with $\beta$: the dot–dashed line in Figure 1, a locus of constant luminosity, illustrates this."
 This is to be expected. since Luminosity is an integral under the curve defined by the cata points.," This is to be expected, since luminosity is an integral under the curve defined by the data points."
 On the other hand. using best fits to the datasets consisting of other objects (listed in Table 1). would give a discrepaney in luminosity oL up to a factor three at the redshifts of our quasars.," On the other hand, using best fits to the datasets consisting of other objects (listed in Table 1), would give a discrepancy in luminosity of up to a factor three at the redshifts of our quasars."
Pileup is not significant.,Pileup is not significant.
 The X-ray core position (J2000.0) is measured to be O4 37 04.30 429 40 11.2., The X-ray core position (J2000.0) is measured to be 04 37 04.30 +29 40 11.2.
 The core position measured from the VLA radio map of H97 is 04 37 04.375 429 40 13.86. and this is expected to be accurate to within about 0.05 aresec.," The core position measured from the VLA radio map of H97 is 04 37 04.375 +29 40 13.86, and this is expected to be accurate to within about 0.05 arcsec."
 The X-ray core position is therefore offset from the (true) radio position by about 3 aresec., The X-ray core position is therefore offset from the (true) radio position by about 3 arcsec.
 We attribute this to uncertainties in aspect determination in the early version ofthe pipeline software (R4CUAUPD7.4) used to process the data (see URL: « http://asc.harvard.edu/mti/ASPECT/-)., We attribute this to uncertainties in aspect determination in the early version of the pipeline software (R4CU4UPD7.4) used to process the data (see URL: $<$ $>$ ).
 In refimage we have aligned the radio data with the X-ray core., In \\ref{image} we have aligned the radio data with the X-ray core.
 The spectrum of the nucleus is well fitted with an absorbed. flat-spectrum power law model.," The spectrum of the nucleus is well fitted with an absorbed, flat-spectrum power law model."
 Fitting with free galactic absorption. the best-fit values of photon index bL and NH are 1.16+0.14 and 1.45n1077 -. respectively.," Fitting with free galactic absorption, the best-fit values of photon index $\Gamma$ and $N_{\rm H}$ are $1.16
\pm 0.14$ and $1.48_{-0.24}^{+0.32} \times 10^{22}$ $^{-2}$, respectively."
 If we fix galactic absorption at the value derived from the cluster fits and requireour the absorber to be at the redshift of the galaxy. the best- Ny forg the reintrinsic absorber is epo1.60.Ont1755107722 7. 2044with the photon index unchanged.," If we fix galactic absorption at the value derived from the cluster fits and require the absorber to be at the redshift of the galaxy, the best-fit $N_{\rm H}$ for the intrinsic absorber is $1.69_{-0.41}^{+0.51} \times 10^{22}$ $^{-2}$, with the photon index unchanged."
 This implies a rest-frame 2-10 keV luminosity (assumed isotropic) of L0! ergs s+. comparable to the luminosity of the nuclear component in 2295 (Harris 22000).," This implies a rest-frame 2–10 keV luminosity (assumed isotropic) of $10^{44}$ ergs $^{-1}$, comparable to the luminosity of the nuclear component in 295 (Harris 2000)."
 Fits in which the absorbing column is constrained to the galactic value are much poorer and require an inverted nuclear spectrum., Fits in which the absorbing column is constrained to the galactic value are much poorer and require an inverted nuclear spectrum.
" The column density required for the intrinsic absorber is considerably lower than the 4.107* > a,inferred for Cygnus A by Ueno (19943. and more comparable to that inferred for the much lower luminosity nucleus of Hydra A by Sambruna (2000)."," The column density required for the intrinsic absorber is considerably lower than the $4 \times
10^{23}$ $^{-2}$ inferred for Cygnus A by Ueno (1994), and more comparable to that inferred for the much lower luminosity nucleus of Hydra A by Sambruna (2000)."
 The best-fit photon index is flatter than might be expected from. for example. the photon indices of radio-loud quasars LLawsonTurner 1997) or other radio galaxies (Sambruna. Eracleous Mushotzky 1999) although the errors are large: as shown in refspeccont... more reasonable values of DL are allowed in conjunction with somewhat higher intrinsic absorbing columns.," The best-fit photon index is flatter than might be expected from, for example, the photon indices of radio-loud quasars LawsonTurner 1997) or other radio galaxies (Sambruna, Eracleous Mushotzky 1999) although the errors are large; as shown in \\ref{speccont}, more reasonable values of $\Gamma$ are allowed in conjunction with somewhat higher intrinsic absorbing columns."
 The inferred absorbing column in front of the nucleus explainsthe non-detection of this core component in theROSAT HRI image (tHardeastle Worrall 1999)., The inferred absorbing column in front of the nucleus explainsthe non-detection of this core component in the HRI image (Hardcastle Worrall 1999).
 The E hotspot complex is detected with 145+32 0.5-7.0 keV counts. using a 2.5-aresee source circle and concentric 3—5 aresec background annulus.," The E hotspot complex is detected with $145 \pm 32$ 0.5–7.0 keV counts, using a 2.5-arcsec source circle and concentric 3–5 arcsec background annulus."
 The X-ray hotspot is positionally coincident with the larger. “secondary” hotspot of the eastern hotspot pair in the radi» (after the X-ray and radio cores have been aligned).," The X-ray hotspot is positionally coincident with the larger, `secondary' hotspot of the eastern hotspot pair in the radio (after the X-ray and radio cores have been aligned)."
 The X-ray emission appears to be slightly elongated in an east-west direction. matching the radio. (," The X-ray emission appears to be slightly elongated in an east-west direction, matching the radio. ("
The X-ray structure will be discussed in more detail in a subsequent paper which will include results of further radio observations now in progress.),The X-ray structure will be discussed in more detail in a subsequent paper which will include results of further radio observations now in progress.)
 The X-ray spectrum of the hotspot is well fitted with a power law with FL=1.6+0.3. with the absorbing column fixed at the galactic value.," The X-ray spectrum of the hotspot is well fitted with a power law with $\Gamma = 1.6 \pm 0.3$, with the absorbing column fixed at the galactic value."
 The corresponding unabsorbed |-keV flux density is 4.6+0.9 nJy., The corresponding unabsorbed 1-keV flux density is $4.6 \pm 0.9$ nJy.
 We used the synchrotron-self-Compton code described by Hardcastle ((1998) to predict the SSC flux density expected at this frequency from the hotspots., We used the synchrotron-self-Compton code described by Hardcastle (1998) to predict the SSC flux density expected at this frequency from the hotspots.
 The basic model for the hotspots is described by Looney Hardcastle (2000)., The basic model for the hotspots is described by Looney Hardcastle (2000).
" The larger hotspot is treated as a cylinder of 1.140.54 aresec (length times radius): the fainter ""primary (nore compact) hotspot is a cylinder of 0.74.«0.14 aresec. based on the MERLIN maps of H97."," The larger hotspot is treated as a cylinder of $1.14 \times 0.54$ arcsec (length times radius); the fainter `primary' (more compact) hotspot is a cylinder of $0.74 \times 0.14$ arcsec, based on the MERLIN maps of H97."
 Radio flux densities of the two components are taken from Looney Hardeastle., Radio flux densities of the two components are taken from Looney Hardcastle.
 In addition to these. we have used infra-red and optical upper limits and a 231-GHz data point from Meisenheimer (1950. 1997) and archival HST observations. and low-frequency radio data from Readhead Hewish (1974) and Stephens (1987).," In addition to these, we have used infra-red and optical upper limits and a 231-GHz data point from Meisenheimer (1989, 1997) and archival HST observations, and low-frequency radio data from Readhead Hewish (1974) and Stephens (1987)."
 As these data do not resolve the two hotspot components. we have corrected them by scaling by the appropriate factors measured from the 5-GHz data.," As these data do not resolve the two hotspot components, we have corrected them by scaling by the appropriate factors measured from the 5-GHz data."
 Looney Hardcastle showed that the radio-to-mm spectra of the two hotspots are well modelled as broken power laws. and we adopt the break energies they found.," Looney Hardcastle showed that the radio-to-mm spectra of the two hotspots are well modelled as broken power laws, and we adopt the break energies they found."
 The apparent low-frequency turnover in the spectrum observed by Stephens (1987) requires a low-energy cutoff in the electron energy spectrum corresponding at equipartition to a minimum Lorentz factor sin71000. and we adopt this value. although Stephens’ flux densities are inconsistent with a larger flux at a lower frequency derived from the scintillation measurements of Readhead Hewish.," The apparent low-frequency turnover in the spectrum observed by Stephens (1987) requires a low-energy cutoff in the electron energy spectrum corresponding at equipartition to a minimum Lorentz factor $\gamma_{\rm min} \approx
1000$, and we adopt this value, although Stephens' flux densities are inconsistent with a larger flux at a lower frequency derived from the scintillation measurements of Readhead Hewish."
 If we were to adopt the scintillation measurements as our low-frequency constraint. we would obtain sin7400. which is more consistent with the value inferred for the hotspots of Cygnus A by Carilli (1991): but this would not significantly affect our conclusions. (," If we were to adopt the scintillation measurements as our low-frequency constraint, we would obtain $\gamma_{\rm min} \approx 400$, which is more consistent with the value inferred for the hotspots of Cygnus A by Carilli (1991); but this would not significantly affect our conclusions. ("
Scheduled. low-frequency VLBA observations should give a definitive answer.),Scheduled low-frequency VLBA observations should give a definitive answer.)
" An upper limit on the maximum Lorentz factor is given by the non-detection in the IR. 5,44<3.6« 107: alower limit is given by the detection at 231 GHz. is78 107."," An upper limit on the maximum Lorentz factor is given by the non-detection in the IR, $\gamma_{\rm max} < 3.6 \times
10^5$ ; a lower limit is given by the detection at 231 GHz, $\gamma_{\rm max} > 8 \times 10^4$ ."
 The, The
For nuu vears the fact that pq falls short of Ho.Toonre Was believed to rule out the formation of planctesimals by collective effects. sclf-gravitational or otherwise (e.g.Weideuschilling&Cuzzi1993).,"For many years the fact that $\mu_{\rm 0,Ri}$ falls short of $\mu_{\rm
 0,Toomre}$ was believed to rule out the formation of planetesimals by collective effects, self-gravitational or otherwise \citep[e.g.,][]{weidenschillingcuzzi93}."
.. But there are more wavs to achieve the Toomre density than vertical settling., But there are more ways to achieve the Toomre density than vertical settling.
 A dissipative form of gravitational instability cau. iu principle. collect particles racially iuto overdense rings even when sclferavity is weaker than stellar tidal forces (Ward1976: Ward2000: Coraclinietal. 1981: Youdiu 2005: for a simple explanation of je instability. see the introduction of Goodman&Pin-dor 2000)).," A dissipative form of gravitational instability can, in principle, collect particles radially into overdense rings even when self-gravity is weaker than stellar tidal forces \citealt{ward76}; \citealt{ward00}; \citealt{coradinietal81}; \citealt{youdin05a}; for a simple explanation of the instability, see the introduction of \citealt{goodmanpindor00}) )."
 It is not clear whether this iustabilitv. which operates over lengthscales aud timescales longer than rose characterizing the Toonmre instability by at least a actor of (toTous/P0). ca compete with other effects iat seek to rearrange dust and eas (6.9...Youdin2005)..," It is not clear whether this instability, which operates over lengthscales and timescales longer than those characterizing the Toomre instability by at least a factor of $(\mu_{\rm 0,Toomre}/\mu_0)^2$, can compete with other effects that seek to rearrange dust and gas \citep[e.g.,][]{youdin05a}."
 Another alternative is to invoke larger dust particles iat are only iuueinally coupled to eas: these cau clump w the acrodvnamic streunius instability (SE: 2005: Johansenetal. 2009: Dai&Stone 20102: Dai&Stone 2010€6))., Another alternative is to invoke larger dust particles that are only marginally coupled to gas; these can clump by the aerodynamic streaming instability (SI; \citealt{youdingoodman05}; \citealt{johansenetal09}; \citealt{baistone10}; \citealt{baistone10b}) ).
" In. their 3D nuicrical shuulationus. Johansenctal.(2009) reported that particles having z,—0.1 0.Lcorresponding to sizes of a few centimeters at kr—5 AU if F=1. aud lavecr sizes if F1 couceutrated so strougly by acrodvuauuc effects that planetesimals effectivele hundreds of kilometers across coalesced within just a few orbits."," In their 3D numerical simulations, \citet{johansenetal09} reported that particles having $\taus = 0.1$ –0.4—corresponding to sizes of a few centimeters at $r= 5$ AU if $F=1$, and larger sizes if $F>1$ —concentrated so strongly by aerodynamic effects that planetesimals effectively hundreds of kilometers across coalesced within just a few orbits."
 To obtain this result. Johausenetal.(2009) initialized their simulations by placing the bulk of the disks solid mass iuto particles approaching decimeters in size.," To obtain this result, \citet{johansenetal09} initialized their simulations by placing the bulk of the disk's solid mass into particles approaching decimeters in size."
 Dai&Stone(20104) ercatly expanded the range of 7 modeled aud fouud simular results for thei 3D simulations: iu the highly urbuleut states driven by the SI. iustautaueous clensitics exceeded the Roche when the disks solids were all composed of particles having 7=0.1 1 aud the bulk wight-inteerated mctallicity was about twice solar: see mu R10Z23-3D in their Figure 5.," \citet{baistone10} greatly expanded the range of $\taus$ modeled and found similar results for their 3D simulations: in the highly turbulent states driven by the SI, instantaneous densities exceeded the Roche when the disk's solids were all composed of particles having $\taus = 0.1$ –1 and the bulk height-integrated metallicity was about twice solar; see run R10Z3-3D in their Figure 5."
 For this same run. the Inc-averaged dust-to-gas ratio at the iidplanue was 12. a factor of a few less than the Toonmre threshold: see heir Figure. E aud compare with our equation (10)).," For this same run, the time-averaged dust-to-gas ratio at the midplane was $\sim$ 12, a factor of a few less than the Toomre threshold; see their Figure 4 and compare with our equation \ref{eqn:muToomre}) )."
 By contrast. when half or more of the disks solid mass had mr<OL. or when disks had smaller metallicities. their simulated censities fell short of the Roche aud. Tooine densities by more than an order of magnitude.," By contrast, when half or more of the disk's solid mass had $\taus < 0.1$, or when disks had smaller metallicities, their simulated densities fell short of the Roche and Toomre densities by more than an order of magnitude."
 Note tha we are quoting from the 3D simulatious of Bai&Stone (2010a)., Note that we are quoting from the 3D simulations of \citet{baistone10}.
". Given how sensitive the SI is to the existence of uarginallv coupled particles (ceutimeter to meter size Or 7,(0.1 ler~ 130 AU. and order uuitv £F). whether enough such particles actually exist iu protoplauctary disks for the SI to play a dominant role im planetesinia ormnation remains an open and delicate issue."," Given how sensitive the SI is to the existence of marginally coupled particles (centimeter to meter sized for $\taus \sim 0.1$ –1, $r \sim
1$ –30 AU, and order unity $F$ ), whether enough such particles actually exist in protoplanetary disks for the SI to play a dominant role in planetesimal formation remains an open and delicate issue."
 Appea is often made to observed spectral energy. distributions and images of T Taun disks at centimeter waveleusthlis: hese suggest that much of the solid mass is in 1illinieter ο centimeter sized particles (e.g...D'Alessioetal.2001:Wilneretal. 2005).," Appeal is often made to observed spectral energy distributions and images of T Tauri disks at centimeter wavelengths; these suggest that much of the solid mass is in millimeter to centimeter sized particles \citep[e.g.,][]{dalessioetal01,wilneretal05}."
. Larger sized particles are plausibly also preseut but are not interred for want of data probing he disk at longer wavelengths., Larger sized particles are plausibly also present but are not inferred for want of data probing the disk at longer wavelengths.
 Oue problem concerus how quickly z0.1 particles can be grown. aud how they can survive orbital decay by eas drag.," One problem concerns how quickly $\taus \gtrsim 0.1$ particles can be grown, and how they can survive orbital decay by gas drag."
 In the 3D simulations of Dai&Stone(2010a).. the SI clumped particles strouely enough for sclberavity to be significant when nom. particles comprised more than half of the disks solid mass.," In the 3D simulations of \citet{baistone10}, the SI clumped particles strongly enough for self-gravity to be significant when $\taus \gtrsim 0.1$ particles comprised more than half of the disk's solid mass."
 It is unclear whether particle-particle sticking cau build up such a population before it is lost to the star bv eas drag., It is unclear whether particle-particle sticking can build up such a population before it is lost to the star by gas drag.
 This concern is ameliorated by chhancements in particle density (pileups) that may occur as particles diift racially award (Youdin&Shu2002:Youdin&Chiang2001)... aud by the reduction of drift speeds brought about by multiple particle sizes &Stone2010a:: see their Figure 8).," This concern is ameliorated by enhancements in particle density (pileups) that may occur as particles drift radially inward \citep{youdinshu02,youdinchiang04}, and by the reduction of drift speeds brought about by multiple particle sizes \citealt{baistone10}; see their Figure 8)."
 Reeardless of which scenario nature prefers—particle concentration by the streamine instability: dissipative eravitation into riues: or dynamical collapse of a vertically settled sublaver. which is the subject of this paperall the proposed wavs of formine planctesimals depend on knowing how far down dust settles aud what maximum dust-to-gas ratios fy cau be attained at the midplane.," Regardless of which scenario nature prefers—particle concentration by the streaming instability; dissipative gravitation into rings; or dynamical collapse of a vertically settled sublayer, which is the subject of this paper—all the proposed ways of forming planetesimals depend on knowing how far down dust settles and what maximum dust-to-gas ratios $\mu_0$ can be attained at the midplane."
 Our order-ofmaguitude estimate in equation (11)) requires testing., Our order-of-magnitude estimate in equation \ref{eqn:muRi}) ) requires testing.
 Amoue the most realistic siuulations of particle settling are those by Jolauseuetal.(2000) and Bai&Stone(2010a).. both of which conccutrated on the οἱ.," Among the most realistic simulations of particle settling are those by \citet{johansenetal09} and \citet{baistone10}, both of which concentrated on the SI."
 Johansenetal.(2009) reported that super-ceutineter sized particles settled nnο sublavers in which the widplanc-averaged pj ranged from 0.6 to 9.0 as the bulk metallicity ranged from 1 to 3 solar., \citet{johansenetal09} reported that super-centimeter sized particles settled into sublayers in which the midplane-averaged $\mu_0$ ranged from 0.6 to 9.0 as the bulk metallicity ranged from 1 to $3$$\times$ solar.
 Dai&Stone(20108). found that the highest 7 particles settled the most. driving turbulence that lofted sanaller 7 particles to ereater heights.," \citet{baistone10}
 found that the highest $\taus$ particles settled the most, driving turbulence that lofted smaller $\taus$ particles to greater heights."
" They argued that in their simulations. all of which were characterized bv axnr,c0.1. particles were so strougly stirred by the SI that the IXIII never mauifested."," They argued that in their simulations, all of which were characterized by $\max \taus \geq 0.1$, particles were so strongly stirred by the SI that the KHI never manifested."
 To complement these studies. we would like to nuderstand the settled equilibrium states of disks composed cutirely of small particles. well but not vertectly coupled to gas (0<maxz- 1). isolated roni the complicating effects of the streaming instability mut not other instabilities like the INT.," To complement these studies, we would like to understand the settled equilibrium states of disks composed entirely of small particles, well but not perfectly coupled to gas $0< \max \taus \ll 1$ ), isolated from the complicating effects of the streaming instability but not other instabilities like the KHI."
 Some previous attempts in this regard relied on asstimed forms for the density profile of settled dust., Some previous attempts in this regard relied on assumed forms for the density profile of settled dust.
 Barranco(2009) presuned he dust density profile was Cuussiau in shape. aud did rot seek to determine the παΠΠ value of fry ," \citet{barranco09} presumed the dust density profile was Gaussian in shape, and did not seek to determine the maximum value of $\mu_0$ ."
se. Chiang(2008) aud Paper L following Sekiva(1998) aud Youdin&Shu(2002).. assumed the dust density xofile had a spatially coustaut Richardson nmuuber.," \citet{chiang08}
 and Paper I, following \citet{sekiya98} and \citet{youdinshu02}, assumed the dust density profile had a spatially constant Richardson number."
 We ound in Paper I that under this assuniption. iu a disk of bulk solar iictallicitv (X= 0.015). the sublaver could remain WO stable for jy as high as ὃa value hat is nearly an order of mmaenitude higher than our crude estimate in CELT)). aud as such lowers the ladle to ornmiue planctesimals by eravitational instability.," We found in Paper I that under this assumption, in a disk of bulk solar metallicity $\Sigmad/\Sigmag = 0.015$ ), the sublayer could remain KH stable for $\mu_0$ as high as 8—a value that is nearly an order of magnitude higher than our crude estimate in \ref{eqn:muRi}) ), and as such lowers the hurdle to forming planetesimals by gravitational instability."
 Weidensclilling(2006) and Weidenschilline(2010) did uot asstune a shape for the mareially stable density profile to which dust relaxes., \citet{weiden06} and \citet{weiden10} did not assume a shape for the marginally stable density profile to which dust relaxes.
 Instead the profile was calculated from a one-dimensional model that balanced the dowmward fux of particlesby eravity Gucluding vertical sclteravity) with the upward fiux due to turbulent diffusion., Instead the profile was calculated from a one-dimensional model that balanced the downward flux of particlesby gravity (including vertical self-gravity) with the upward flux due to turbulent diffusion.
 The model used prescriptions for ID turbulence. with a number of parameters chosen to match the 3D calculatious of Cuzzietal. which also relied on a prescribed form of," The model used prescriptions for KH turbulence, with a number of parameters chosen to match the 3D calculations of \citet{cuzzietal93}- —which also relied on a prescribed form of"
enussjon. and thus the detection of such e1uission may in turn provide us a valuable chance to test those IR backeround absorption models.,"emission, and thus the detection of such emission may in turn provide us a valuable chance to test those IR background absorption models."
 Tn our calculations. as anu illustration. we take Έρως=102(004ΤΟΝ (Above which there is LO observation available). which is conservative.," In our calculations, as an illustration, we take $E'_{\rm
up,cut}=10.2~(1+z){\rm TeV}$ (Above which there is no observation available), which is conservative."
 Even sO. with the three correction models takeu 11i Aharoniaιο al. {," Even so, with the three correction models taken in Aharonian et al. ("
2003a). the predicted time-averaged scattered photon enerev flux are far above (case b. c). or at least comparable with (case a) that of the well studied Blazay MkEn50! (see Dai ct al.,"2003a), the predicted time-averaged scattered photon energy flux are far above (case b, c), or at least comparable with (case a) that of the well studied Blazar Mkn501 (see Dai et al."
 2002 for detail)., 2002 for detail).
 Oue problem arises. jus as shown in figure l1 c. the predicted now hard 5rax enission at the energy ~0.21TeV is about ten times tha observed.," One problem arises, just as shown in figure 1 c, the predicted new hard $\gamma-$ ray emission at the energy $\sim0.24~{\rm TeV}$ is about ten times that observed."
 Iu principle. such emission may be absorbed bx the backeround IR/UV photons again. but the resulting flux is still high. above the observed (for E.~0.21/TeV. TU~ 1].," In principle, such emission may be absorbed by the background IR/UV photons again, but the resulting flux is still high above the observed (for $E_{\rm \gamma}\sim
0.24{\rm TeV}$, $\tau_{\gamma\gamma}^{\rm ex}\sim 1$ )."
 Two possibilities exist: oue is that the derived lutrinsic spectrum based ou the correctio 1inodel xoposed bv Malkeu Stecker (2001) is much harder than what it really is., Two possibilities exist: one is that the derived intrinsic spectrum based on the correction model proposed by Malken Stecker (2001) is much harder than what it really is.
" Another is that the IGME imieht 1)o0 strong οπως], ιο observable CeV-TeV. emission flux. was heen suppressed significantly."," Another is that the IGMF might be strong enough, the observable GeV-TeV emission flux has been suppressed significantly."
 For Dlazar T1126|128. due to the poorv kuowu X-ray baud spectrum. we cannot provide a definite SSC spectrmm as Dai ct al. (," For Blazar H1426+428, due to the poorly known X-ray band spectrum, we cannot provide a definite SSC spectrum as Dai et al. ("
2002) lave done for Mknu5ül.,2002) have done for Mkn501.
" Even so. as shown in Figure 1. at a first elaice, the SSC colmponcut is likely far below than the externally scattered photon flux."," Even so, as shown in Figure 1, at a first glance, the SSC component is likely far below than the externally scattered photon flux."
 The UBLs T1126)128 is distinguished 1 odis relatively hieh redshift as well as its strong TeV energev enisson., The HBLs H1426+428 is distinguished by its relatively high redshift as well as its strong TeV energy emission.
 —ji this Letter. with the recently observed data as well as the derived. iutriusic spectrin. we have studied the possible accompauviug Ce enission. which is due to the IC scattering of CAIBPs|w the eT4 pairs produced i interactions of high energy plotous with the cosmic meeeinfrared-UoooV. backerouud photons.," In this Letter, with the recently observed data as well as the derived intrinsic spectrum, we have studied the possible accompanying GeV emission, which is due to the IC scattering of CMBPs by the $e^\pm$ pairs produced in interactions of high energy photons with the cosmic infrared-UV background photons."
 If the IGAIF is weak rough. there is very strong hitherto uudiscovered GeV-TeV cunission. whose flux is far above or at least comparable with that of the well-studied WBLs MXxn501 (Dai et al.," If the IGMF is weak enough, there is very strong hitherto undiscovered GeV-TeV emission, whose flux is far above or at least comparable with that of the well-studied HBLs Mkn501 (Dai et al."
 2002)., 2002).
 With the upcoming satellite GLAST. planned for launch iu 2005. if is casy for us to detect such enussion directly.," With the upcoming satellite GLAST, planned for launch in 2005, it is easy for us to detect such emission directly."
 We also noted that he shape of the interred source spectra is uost sensitive to the characteristics of the extragalacticbackground light., We also noted that the shape of the inferred source spectra is most sensitive to the characteristics of the extragalactic background light.
 A different correctioi model leads to a differen intriusc spectruni. so does the accompanyie GeV enission (see figure l for detail).," A different correction model leads to a different intrinsic spectrum, so does the accompanying GeV emission (see figure 1 for detail)."
 Thus the detection of such cussion lay in turn provide us a valuable chance to test those IR backeround absorption models., Thus the detection of such emission may in turn provide us a valuable chance to test those IR background absorption models.
 Tn Aharonian et al. (, In Aharonian et al. (
"200210), the detection of Τον ~ ravs from the BL Lac 1ES1959|650 has been reported.","2003b), the detection of TeV $\gamma-$ rays from the BL Lac 1ES1959+650 has been reported."
 LES1959|650 is located at a redshift of 2=0.017. providing an intermeciate distance between the nearby azars Miki121 and Πιο. and the much iore cüstaut ject ITE126|128.," 1ES1959+650 is located at a redshift of $z=0.047$, providing an intermediate distance between the nearby blazars Mkn421 and Mkn501, and the much more distant object H1426+428."
" Without douM. for such a source. the observed TeV emission lias been absorbed sieuificautlv bx the iufrared-UV 1vackeround photons. aud thus a strong GeV cussion is expected. as long as the IGME is weak οποιο],"," Without doubt, for such a source, the observed TeV emission has been absorbed significantly by the infrared-UV background photons, and thus a strong GeV emission is expected, as long as the IGMF is weak enough."
 We would like to thank Drs Y. E. Huang. N. Y. Wang X. EF. Wu or valuable comments.," We would like to thank Drs Y. F. Huang, X. Y. Wang X. F. Wu for valuable comments."
 We also jiink the anonymous referee [or jer/his useful suggestions jw enable us to improve the paper significantly., We also thank the anonymous referee for her/his useful suggestions that enable us to improve the paper significantly.
 This work was supported in the National Natural Science-- of China (grantsINKGLSE 10073022.10225314 and 10233010).ο. the National 3 Project 619990754) and the for the Author of National Excellent. Doctoral Dissertation of D. 1t. China. (," This work was supported by the National Natural Science Foundation of China (grants 10073022,10225314 and 10233010), the National 973 Project (NKBRSF G19990754) and the Foundation for the Author of National Excellent Doctoral Dissertation of P. R. China. ("
Project No:200125).,Project No:200125).
Eq.7)),Eq.\ref{Fourier2}) )
 simply means that under lensing. the Fourier transformation of the galaxy image is changed from. fs(&) to [dettΑΙ.(AA).," simply means that under lensing, the Fourier transformation of the galaxy image is changed from $\widetilde{f_S}(\vec{k})$ to $\vert \mathrm{det} (\mathbf{A})\vert\widetilde{f_S}(\mathbf{A}\vec{k})$."
 Due to the presence of the PSE. the Fourier transformation of the observed image fo is related to that of the lensecl image mn via: where WA) is the Fourier transformation of the PSE.," Due to the presence of the PSF, the Fourier transformation of the observed image $\widetilde{f_O}$ is related to that of the lensed image $\widetilde{f_L}$ via: where $\widetilde{W}(\vec{k})$ is the Fourier transformation of the PSF."
 Without loss of generalitv. in the rest of our cliscussion. weuse the isotropic Caussian PSE.ie... Wik)=Walk)expAyo 2).," Without loss of generality, in the rest of our discussion, weuse the isotropic Gaussian PSF, $\widetilde{W}(\vec{k})=\widetilde{W}_{\beta}(\vec{k})=\exp(-\beta^2\left\vert\vec{k}\right\vert^2/2)$ ."
 The advantage of working in Fourier space is that the PSE is included as a multiplicative factor. rather than a convolution as in real space.," The advantage of working in Fourier space is that the PSF is included as a multiplicative factor, rather than a convolution as in real space."
 Combining eq.(67)) and eq.(68)). we get: Since the PSE profile in Fourier space typically falls olf quickly when the wave number exceeds the inverse of the size of the PSE. it strongly suppresses the power of the observed images on small scales.," Combining \ref{Fourier2}) ) and \ref{f_O}) ), we get: Since the PSF profile in Fourier space typically falls off quickly when the wave number exceeds the inverse of the size of the PSF, it strongly suppresses the power of the observed images on small scales."
 Therefore. only a finite number of Fourier modes are available for providing shape information.," Therefore, only a finite number of Fourier modes are available for providing shape information."
 Recovering information on arbitrarily small scales is never feasible in practice due to noise and numerical problems., Recovering information on arbitrarily small scales is never feasible in practice due to noise and numerical problems.
 Yo form CSEs. let us use the multipole moments of galaxy images to represent the shape information. which are defined as: where { and. j are non-negative integers.," To form CSEs, let us use the multipole moments of galaxy images to represent the shape information, which are defined as: where $i$ and $j$ are non-negative integers."
 Note that due to the finite degrees of freedom. of the shape information. one can cquivalenthy choose other basis(e.g... shapelets) to study the same issue without allecting the conclusion.," Note that due to the finite degrees of freedom of the shape information, one can equivalently choose other basis, shapelets) to study the same issue without affecting the conclusion."
 For simplicity but without loss of generality.let us only consider galaxies that are invariant under the parity transformation Fosd.," For simplicity but without loss of generality,let us only consider galaxies that are invariant under the parity transformation $\vec{x}\to -\vec{x}$."
 Note that weal lensing does not change this property., Note that weak lensing does not change this property.
 For this twpe of galaxies. the imaginary part of folk) is always zero. ancl AM;j' are real.," For this type of galaxies, the imaginary part of $\widetilde{f_O}(\vec{k})$ is always zero, and $M_{ij}$ 's are real."
 Furthermore. Adj; is zero when #|j is an odd number.," Furthermore, $M_{ij}$ is zero when $i+j$ is an odd number."
"s In this case. the shear estimators DL, and Vs can be written as functions of the Al, with i| being even numbers only."," In this case, the shear estimators $\Gamma_1$ and $\Gamma_2$ can be written as functions of the $M_{ij}$ with $i+j$ being even numbers only."
 For some of the lowest order Adjjs. we can find out how they transform under lensing using eq.(69)): The last step in the above equation is achieved. by redelining AF as k.," For some of the lowest order $M_{ij}$ 's, we can find out how they transform under lensing using \ref{f_O2}) ): The last step in the above equation is achieved by redefining $\mathbf{A}\vec{k}$ as $\vec{k}$."
 By keeping the terms in matrix A up to the first order in shear. one can straightlorwardly show the Following: where The conventional cosmic shear estimators (Ly.bs) are functions of A;;.," By keeping the terms in matrix $\mathbf{A}$ up to the first order in shear, one can straightforwardly show the following: where The conventional cosmic shear estimators $\Gamma_1, \Gamma_2$ ) are functions of $M_{ij}$."
" According to our discussion in relsping,sli. fhelwofunclionshavetosalis fylhe followingretation In Lthe presenceΌσο of PSE. we are unable to find out whether one can find CSEs that satisfy the most general requirement eiven in eq.(5.3))."," According to our discussion in \\ref{spin_2_esti}, the two functions have to satisfy the following relation: In the presence of PSF, we are unable to find out whether one can find CSEs that satisfy the most general requirement given in \ref{requirement_again}) )."
 However. we can show that there do not exist. CSEs satisfving a slightlv stronger condition: In aclelition to eq. (5.3)). eq.(75))," However, we can show that there do not exist CSEs satisfying a slightly stronger condition: In addition to eq. \ref{requirement_again}) ), \ref{requirement_stronger}) )"
 simply. imposes. another requirement that the spin-+ parts of the derivatives of the shear estimators with respect to the shears are zero., simply imposes another requirement that the spin-4 parts of the derivatives of the shear estimators with respect to the shears are zero.
" We can rewrite eq.(75)) for.eg... Py. using the chain rule as: Since there are only a finite number. of. multipole moments available for constructing the shear estimators. we assume the maximum value of 7|j is N (N is an even integer).Le. we have: Because the right side of cq.77)) is evaluated at 5,=---- 0. both OL)/0M;; and OAL;ὅτι are functions of only Ad?s.c... the multipole moments in the absence of lensing."," We can rewrite \ref{requirement_stronger}) ) for, $\Gamma_1$ , using the chain rule as: Since there are only a finite number of multipole moments available for constructing the shear estimators, we assume the maximum value of $i+j$ is $N$ (N is an even integer), we have: Because the right side of \ref{Gamma_1_chain_rule2}) ) is evaluated at $\gamma_1=\gamma_2=\kappa=0$ , both $\partial\Gamma_1/\partial M_{ij}$ and $\partial M_{ij}/\partial \gamma_1$ are functions of only $M_{ij}^S$ 's, the multipole moments in the absence of lensing."
 As in eq.(72)). one can show in general that OAL)Ότι involves higher order multipole moments.ie... with FILIj.," As in \ref{Mij_trans}) ), one can show in general that $\partial M_{ij}/\partial \gamma_1$ involves higher order multipole moments, $M_{i'j'}^S$ 's with $i'+j'>i+j$."
" dn particular. when i|j=N. Alpi.OAL;sf depends linearly on M7, rs with Zo| "," In particular, when $i+j=N$, $\partial M_{ij}/\partial \gamma_1$ depends linearly on $M_{i'j'}^S$ 's with $i'+j'>N$ ."
"‘To satisfy the constraint in. eq.607)). the coelficients in front. of the terms. proportional to Mz os G|jz UN) must. vanish because they are independentof the multipole moments with PE EUN. As a result. we find that OU,/0ÀM;; has to vanish when?|j= AN."," To satisfy the constraint in \ref{Gamma_1_chain_rule2}) ), the coefficients in front of the terms proportional to $M_{i'j'}^S$ 's $i'+j'>N$ ) must vanish because they are independentof the multipole moments with $i+j\le N$ As a result, we find that $\partial\Gamma_1/\partial M_{ij}$ has to vanish when $i+j=N$ ."
 ln other words. we have:," In other words, we have:"
2009).,.
. Fieure 2. displays the 3D structure of magnetic field lines (red curves). temperature variations. ancl the velocity field (arrows).," Figure \ref{3D} displays the 3D structure of magnetic field lines (red curves), temperature variations, and the velocity field (arrows)."
 The top horizontal slice corresponds to the solar surface., The top horizontal slice corresponds to the solar surface.
 The results demonstrate a strong coupling between the fluid flow and magnetic field., The results demonstrate a strong coupling between the fluid flow and magnetic field.
 In particular. the upflows correspond to magnetic field lines rising above (he surface (positive polarity) while the downward flows correlate with the negative polarity.," In particular, the upflows correspond to magnetic field lines rising above the surface (positive polarity) while the downward flows correlate with the negative polarity."
 This corresponds verv well to the observed properties of the penumbra and (he sea-serpent model., This corresponds very well to the observed properties of the penumbra and the sea-serpent model.
 In this Letter. we have used the results of numerical simulations of magnetoconvection in strong inclined magnetic field to interpret polarimetric observations of a sunspot penunbra.," In this Letter, we have used the results of numerical simulations of magnetoconvection in strong inclined magnetic field to interpret polarimetric observations of a sunspot penumbra."
 The results reproduce the moving bipolar magnetic elements observed in high-resolution SOIIO/MDI and IHinode/SOT data and also (heir properties. supporting (he sea-serpent model proposed by SainzDalda&BellotRubio(2003).," The results reproduce the moving bipolar magnetic elements observed in high-resolution SOHO/MDI and Hinode/SOT data and also their properties, supporting the sea-serpent model proposed by \cite{dalda08}."
. The simulations explain the serpent structure and dynamics of the pemmubral field as a consequence of solar magnetoconvection in a highly inclined. strong magnetic field. which forms filamentary structures ancl has properties of traveling convective wave.," The simulations explain the sea-serpent structure and dynamics of the penumbral field as a consequence of solar magnetoconvection in a highly inclined, strong magnetic field, which forms filamentary structures and has properties of traveling convective wave."
 The physical picture schematically illustrated in Figure 3. is the following.," The physical picture schematically illustrated in Figure \ref{scheme}
 is the following."
 Convective cells in sunspot penunbrae are delormed under (he action of the inclined magnetic field. forming filamentary structures and producing high-speed IEvershed flows 2009a).," Convective cells in sunspot penumbrae are deformed under the action of the inclined magnetic field, forming filamentary structures and producing high-speed Evershed flows \citep{kiti09a}."
. The magnetic field lines are stretched by the downward flows and dragged under the surface., The magnetic field lines are stretched by the downward flows and dragged under the surface.
 The points where the magnetic field lines cross the solar surface are observed as magnetic patches of positive and negative polarities., The points where the magnetic field lines cross the solar surface are observed as magnetic patches of positive and negative polarities.
 Note that the negative patch is closer {ο the mubra. in agreement with the observations.," Note that the negative patch is closer to the umbra, in agreement with the observations."
 The convective cells move in the direction of ihe magnetic field inclination because of the traveling convective wave behavior., The convective cells move in the direction of the magnetic field inclination because of the traveling convective wave behavior.
 Therefore. the bipolar magnetic patches also move in the same direction.," Therefore, the bipolar magnetic patches also move in the same direction."
 Thus. (he numerical simulations connect the sea-serpent structure of the moving bipolar magnetic pathes observed in (he penumbra with Che process of overturning maenetoconvection. traveling convective waves. and the Evershed flow.," Thus, the numerical simulations connect the sea-serpent structure of the moving bipolar magnetic pathes observed in the penumbra with the process of overturning magnetoconvection, traveling convective waves, and the Evershed flow."
 This work was partly supported by NASA. the Center for Turbulence Research (Stanford University). NORDITA. AlbaNova Univ.," This work was partly supported by NASA, the Center for Turbulence Research (Stanford University), NORDITA, AlbaNova Univ."
 Center (Stockholm). and the Spanish Ministerio de Ciencia e Innovaciónn through project. AYA2009-14105-C06-06 and by Junta de Andaluctaa through project POT-TEP-2687.," Center (Stockholm), and the Spanish Ministerio de Ciencia e Innovaciónn through project AYA2009-14105-C06-06 and by Junta de a through project P07-TEP-2687."
during the Blazhko evele. like it was proposed by Prestonetal.(1965) . would. also olfer an explanation for the changing bump The dramatic change not only in the strength but also in the appearance of the Blazhko clleet certainly provides strong constraints for the models. as an explanation for the Blazhko elfect would need. to be able to account for strong changes of the phasing of the two types of moctulations (amplitude as well as phase modulation) which can be present in a Blazhko star.,"during the Blazhko cycle, like it was proposed by \citet{preston}, would also offer an explanation for the changing bump The dramatic change not only in the strength but also in the appearance of the Blazhko effect certainly provides strong constraints for the models, as an explanation for the Blazhko effect would need to be able to account for strong changes of the phasing of the two types of modulations (amplitude as well as phase modulation) which can be present in a Blazhko star."
 As we have shown in section 4.2.. the phase variation is getting stronger in CoRoT 105288363. while at the same time the amplitude modulation is getting weaker.," As we have shown in section \ref{OC}, the phase variation is getting stronger in CoRoT 105288363, while at the same time the amplitude modulation is getting weaker."
 Also. we have seen in section 4.3. that. suddenly a phase shift between the two types of modulation appears. and ceases again.," Also, we have seen in section \ref{loopsect} that suddenly a phase shift between the two types of modulation appears and ceases again."
 Never before have such drastic: changes in the Blazhko behaviour of an RR Lyrae star been documented., Never before have such drastic changes in the Blazhko behaviour of an RR Lyrae star been documented.
 I is certainly a big challenge for the models to reproduce these The excitation of additional modes is an open issue in he modeling of the pulsation of RR Lyr stars., It is certainly a big challenge for the models to reproduce these The excitation of additional modes is an open issue in the modeling of the pulsation of RR Lyr stars.
 Two requencics not related with the Blazhko modulation were convineinely found in the case of ColtoT. 101128793 (Porettietal.2010)., Two frequencies not related with the Blazhko modulation were convincingly found in the case of CoRoT 101128793 \citep{por}.
 One of them is perhaps related with the period doubling bifurcation. the other supplies he ratio (0.582 with the main pulsation [requency (i.c... 2.119/3.630—0.582).," One of them is perhaps related with the period doubling bifurcation, the other supplies the ratio 0.582 with the main pulsation frequency (i.e., 2.119/3.630=0.582)."
 Moreover. the same authors ound similar ratio values when rediscussing the cases of V1I27. Aql (Chadidetal2010) and. AIW Lye (Juresik et al.," Moreover, the same authors found similar ratio values when rediscussing the cases of V1127 Aql \citep{cha} and MW Lyr (Jurcsik et al."
 2008). Le. 2.8090/4.8254—0.582 and 2.5146/4.2738—0.588. In the case of ColtoT 105288363. we found a possible additional mode only. ie. 2.984 .," 2008), i.e., 2.8090/4.8254=0.582 and 2.5146/4.2738=0.588, In the case of CoRoT 105288363 we found a possible additional mode only, i.e., 2.984 $^{-1}$."
 The ratio 1.762/2.984=0.591 is very similar to those reported above and this strengthens our confidence on the reliability. of the detection of such small amplitude fi term., The ratio 1.762/2.984=0.591 is very similar to those reported above and this strengthens our confidence on the reliability of the detection of such small amplitude $f_1$ term.
 The identification of the additional mode as the second: radial overtone. as in the case of Coltot 101128793. is still the most plausible A few similar stars in which frequencies close to the expected value of the overtones appear. were also found in the sample of RR. Lyrae stars observed by the satellite(Denkóοἱal.2010).," The identification of the additional mode as the second radial overtone, as in the case of CoRoT 101128793, is still the most plausible A few similar stars in which frequencies close to the expected value of the overtones appear, were also found in the sample of RR Lyrae stars observed by the satellite \citep{ben10}."
. This research has made use of the Exo-Dat database. operated. at LAM-OAALP. Marseille: France. on behalf of the CoRoT/Exoplanct program.," This research has made use of the Exo-Dat database, operated at LAM-OAMP, Marseille, France, on behalf of the CoRoT/Exoplanet program."
 Ixlx. and EX: acknowledge support) from the Austrian Fonds. zur Forrderung cer wissenschaftlichen Forschung. (ENTE). project number D359-NI6 and. P19962-N16.," KK and EG acknowledge support from the Austrian Fonds zur Förrderung der wissenschaftlichen Forschung (FWF), project number T359-N16 and P19962-N16."
 EP acknowledges support. from the PRIN-INAI 2010stars., EP acknowledges support from the PRIN-INAF 2010.
 MP. JMD. and ltSz acknowledge the support of the ESA PECS projects No.," MP, JMB, and RSz acknowledge the support of the ESA PECS projects No."
 98022 98114., 98022 98114.
 ItSz and JMD are supported by the llungarian OTI grant. τος., RSz and JMB are supported by the Hungarian OTKA grant K83790.
"Au expression for the loop imaxinuun temperature To=Toyayf(108 I) can be derived from fitting livdrostatic model loops with isothermal models: We obtain log(7,44)77.6.",An expression for the loop maximum temperature $T_7=T_{max}/(10^7$ K) can be derived from fitting hydrostatic model loops with isothermal models: We obtain $\log (T_{max}) \approx 7.6$.
 From Fig. 2..," From Fig. \ref{fig:datnt},"
 it cau be noted that the iuitial decay D1 is very short aud ouly two points are defined iu the u-T diagram. too few to obtain a well-defined decay. trend.," it can be noted that the initial decay D1 is very short and only two points are defined in the n-T diagram, too few to obtain a well-defined decay trend."
 Tf one assumes the initial decay DI is eutirelyv due to plasina cooling. with negligible heating. the οληΊσα expression of loop leugth (Eqs. (2)). (3))," If one assumes the initial decay D1 is entirely due to plasma cooling, with negligible heating, the empirical expression of loop length (Eqs. \ref{eq:lreale}) ), \ref{eq:fzeta}) )"
" aud €1))) vields an upper nuit to the loop ilf length L,,,=1.6&1ye) on, ", and \ref{eq:t7}) )) yields an upper limit to the loop half length $L_{up} \approx 1.6 \times 10^{10}$ cm.
The cussion nieasure shows a second peak during hase R2. as the light curve does. while the temperature is practically flat.," The emission measure shows a second peak during phase R2, as the light curve does, while the temperature is practically flat."
 Phase D3 includes just two points with large error bars., Phase D3 includes just two points with large error bars.
" Phase DI is better defined: the eniperature and EM of the lot component both decay uonotonicallv. the temperature more slowly,"," Phase D4 is better defined: the temperature and EM of the hot component both decay monotonically, the temperature more slowly."
 The general approach to model this flare is an evolved version of the inodeliug of another flare observed on Proxima Contaur in 1980 with the Tagine Proportional Counter (Reale et al., The general approach to model this flare is an evolved version of the modeling of another flare observed on Proxima Centauri in 1980 with the Imaging Proportional Counter (Reale et al.
 1988)., 1988).
 At variance with the previous modeling effort. here the modeling will iuclude later phases of the fare aud more than oue loop component. allowing us to diagnose contributions of flaring structures other than the main loop and the heating fiction at late times.," At variance with the previous modeling effort, here the modeling will include later phases of the flare and more than one loop component, allowing us to diagnose contributions of flaring structures other than the main loop and the heating function at late times."
 The nodel asstuuptions are those typical of a solar coronal flare loop modeling (e.g. Reale 2002): the flare in each loop is triggered by a stroug heat pulse: the oop is initially at equilibrium (Serio e al., The model assumptions are those typical of a solar coronal flare loop modeling (e.g. Reale 2002): the flare in each loop is triggered by a strong heat pulse; the loop is initially at equilibrium (Serio et al.
 1981) at the enrperature {ον ADI) of an active region loop. nof ar from the peak of the EM distribution in quiesceut conditious (23 MIN iu Paper ID.," 1981) at the temperature $\sim~4$ MK) of an active region loop, not far from the peak of the EM distribution in quiescent conditions $\approx~3$ MK in Paper II)."
 The faring plasuia is described as a fluid confined iu a closed semücireular oop with fixed ogeometry and constaut CYOss-section. oxrpendieular to the stellar surface and unchausged πιο he flare.," The flaring plasma is described as a fluid confined in a closed semicircular loop with fixed geometry and constant cross-section, perpendicular to the stellar surface and unchanged during the flare."
 The plasma moves aud trausports enerev ouly along the magnetic field lines runing parallel to the loop. and cau therefore be described with a sinele curvilinear coordinate.," The plasma moves and transports energy only along the magnetic field lines running parallel to the loop, and can therefore be described with a single curvilinear coordinate."
 The plasina evolution is them described by the time-dependent hvdrodynuanüc equations of mass. moment aud energy conservation as done in many previous works (see references in Section 1)). iuncludiug. as sieuificaut physical effects. the eravity. the compressional viscosity. the radiative losses frou optically thin plasma. aud the thermal conduction.," The plasma evolution is then described by the time-dependent hydrodynamic equations of mass, momentum and energy conservation as done in many previous works (see references in Section \ref{sec:intro}) ), including, as significant physical effects, the gravity, the compressional viscosity, the radiative losses from optically thin plasma, and the thermal conduction."
 The stellar gravity aud radius have been assumed gs=l0g: aud R.=0158... respectively (Pettersen 1980. Séeercusan et al.," The stellar gravity and radius have been assumed $g_* = 10 g_{\sun}$ and $R_*
= 0.15 R_{\sun}$, respectively (Pettersen 1980, Séggrensan et al."
 2003)., 2003).
 There are two external energy inputs: a low. coustaut and nuiform one. which keeps the loop initially at equilibrimui: a hieh and highly transient one. Qs.£). which triggers the flare. and is asstued to be a separable function of space gs) and time f(t) (e.g. Peres et al.," There are two external energy inputs: a low, constant and uniform one, which keeps the loop initially at equilibrium; a high and highly transient one, $Q(s,t)$, which triggers the flare, and is assumed to be a separable function of space $g(s)$ and time $f(t)$ (e.g. Peres et al."
 1987): wheref) fy is the peak value of the heating rate. s ds the coordinate along the loop. f is the time.," 1987): where $H_0$ is the peak value of the heating rate, $s$ is the coordinate along the loop, $t$ is the time."
 We consider Gaussian spatial distributions. centered on sy and with width o: There is no reliable way to determine a prion the intensity. the spatial distribution. the duration aud the time dependence of the heating function.," We consider Gaussian spatial distributions, centered on $s_0$ and with width $\sigma$: There is no reliable way to determine a priori the intensity, the spatial distribution, the duration and the time dependence of the heating function."
 We therefore proceed. by educated. guesses aud refine the choices with the feedback coming from the comparison of the data to the mocel results., We therefore proceed by educated guesses and refine the choices with the feedback coming from the comparison of the data to the model results.
 We will consider. in particular. lee alternative distributions g(s): two thin Caussiaus centered at the footpoiuts. a single wide (απορία centered at the apex. and a uniform heating (6<>£).," We will consider, in particular, three alternative distributions $g(s)$: two thin Gaussians centered at the footpoints, a single wide Gaussian centered at the apex, and a uniform heating $\sigma \gg L$ )."
 As for the time dependence. we will cousider a heat pulse. described as ft)=1 tor Ofο aud f(t)=0 at any other due.," As for the time dependence, we will consider a heat pulse, described as $f(t) = 1$ for $0 < t \leq \delta t_H$, and $f(t) =
0$ at any other time."
 The heating decay is assumed exponential: The tine-depeudent lvdrodvuamic equations have oen solved using the revised version of the Palerino-Tarvard umuerical code with adaptive reeridding (Betta ot al., The heating decay is assumed exponential: The time-dependent hydrodynamic equations have been solved using the revised version of the Palermo-Harvard numerical code with adaptive regridding (Betta et al.
 1997. Betta et al.," 1997, Betta et al."
 2001)., 2001).
 Svnunetry with respect to he apex las been assunned. aud a half-Ioop modelled.," Symmetry with respect to the apex has been assumed, and a half-loop modelled."
 A flaring loop iunodel is set up bw selectiug the oop length aud the heating function., A flaring loop model is set up by selecting the loop length and the heating function.
 The details and conditious of the loop vefore heat ignition are not critical or the simulation results. provided that the pressure is Heh enough to have a significant amount of mass in the chromosphere for evaporation (see Sect. 1)).," The details and conditions of the loop before heat ignition are not critical for the simulation results, provided that the pressure is high enough to have a significant amount of mass in the chromosphere for evaporation (see Sect. \ref{sec:res}) )."
 The uuuerical solutious of the 1-D hivdrodyvuauic plaua equations are in the form of plasma deusitv. teniperature and velocity distributions along the loop at progressing times.," The numerical solutions of the 1-D hydrodynamic plasma equations are in the form of plasma density, temperature and velocity distributions along the loop at progressing times."
 For comparison with observational data. from cach density aud temperature distribution. the plasma N-rav spectitun at the focal plaue of the EPIC-PN detector is svuthesized as done in several previous works (c.g. Reale ot al.," For comparison with observational data, from each density and temperature distribution, the plasma X-ray spectrum at the focal plane of the EPIC-PN detector is synthesized as done in several previous works (e.g. Reale et al."
 1988. Reale et al.," 1988, Reale et al."
 1997. Reale ποσα 1998).," 1997, Reale Micela 1998)."
 We ider the MEKAL spectral code (Alewe et al., We consider the MEKAL spectral code (Mewe et al.
 1995) with a metallicity Z=0.5. as on average found iu the spectral fits (Paper ID.," 1995) with a metallicity Z=0.5, as on average found in the spectral fits (Paper II)."
 The MEINAL spectra are folded with the EPIC-PN response function used in Caideel et al. (, The MEKAL spectra are folded with the EPIC-PN response function used in Güddel et al. (
2001).,2001).
 The final results are weakly dependent ou the details (or nüuor changes) of the response function. suce they are mainly based on the analvsis of elobal observables. such as the Πο curve in a broad spectral baud (0.15 - 10 keV.," The final results are weakly dependent on the details (or minor changes) of the response function, since they are mainly based on the analysis of global observables, such as the light curve in a broad spectral band (0.15 - 10 keV)."
 The normalization of the light curve obtained from the loop model to the observed one provides, The normalization of the light curve obtained from the loop model to the observed one provides
Mass uncertainties are also indicated for all white dwarls in the OIIDIIS sample with neasured parallaxes (LIIS. 147. LIIS 542. and LIIS 4033) and for the white dwarls in the DLR sample with e>200 (LIIS 56. LIIS 147. and LIIS 542: the last two objects are in common with the OIIDIIS sample and they have identical error bars).,"Mass uncertainties are also indicated for all white dwarfs in the OHDHS sample with measured parallaxes (LHS 147, LHS 542, and LHS 4033) and for the white dwarfs in the BLR sample with $\vtan>200$ (LHS 56, LHS 147, and LHS 542; the last two objects are in common with the OHDHS sample and they have identical error bars)."
 Unlortunatelv. these mass uncertainties are ailv large. with the exception of LIIS 4033 at M.~1.3M... which corresponds to a nodern parallax measurement (Dahnetal.2004).," Unfortunately, these mass uncertainties are fairly large, with the exception of LHS 4033 at $M\sim 1.3$, which corresponds to a modern parallax measurement \citep{dahn04}."
. As discussed in 4.2. however. both LIIS 147 and LIIS 542 have been measured with comparable accuracy. ancl (he parallax values have not changed significantly [rom those used in Figure 9. (II. C. Harris. 2004. private communication).," As discussed in 4.2, however, both LHS 147 and LHS 542 have been measured with comparable accuracy, and the parallax values have not changed significantly from those used in Figure \ref{fg:f9}
 (H. C. Harris, 2004, private communication)."
 Also superposed on this plot are the theoretical isochrones from the white dwarf cooling sequences discussed above with C/O-cores. q(He)=Ady./AL10?. and ΟΠ)=10.+.," Also superposed on this plot are the theoretical isochrones from the white dwarf cooling sequences discussed above with C/O-cores, $q({\rm
He})\equiv M_{\rm He}/M_{\star}=10^{-2}$, and $q({\rm H})=10^{-4}$."
 The solid lines represent (he white dwarf cooling ages only., The solid lines represent the white dwarf cooling ages only.
 These parabola-shaped isochrones are the result of the onset of ervstallization oceuring first in the higher mass models. reducing the cooling timescales considerably.," These parabola-shaped isochrones are the result of the onset of crystallization occuring first in the higher mass models, reducing the cooling timescales considerably."
 With decreasing effective temperature. crvstallization eracduallv occurs in lower mass models. and the turning point of these parabola moves slowly towards lower masses.," With decreasing effective temperature, crystallization gradually occurs in lower mass models, and the turning point of these parabola moves slowly towards lower masses."
 Sinceages and not white dwarl cooling ages are the crucial aspect we want (o investigate here. we must take into account the lime spent on the main sequence.," Since and not white dwarf cooling ages are the crucial aspect we want to investigate here, we must take into account the time spent on the main sequence."
 To do so. we follow the procedure outlined in Wood(1992) and we add to the white dwarl cooling age (he main sequence lifetime /j calculated as Gyr where Mais is the mass on the main sequence of the white dwarl progenitor.," To do so, we follow the procedure outlined in \citet{wood92} and we add to the white dwarf cooling age the main sequence lifetime $t_{\rm MS}$ calculated as $t_{\rm MS}=10(M_{\rm MS}/M_\odot)^{-2.5}$ Gyr where $M_{\rm MS}$ is the mass on the main sequence of the white dwarf progenitor."
 The latter is obtained from the mitial-final mass relation for white dwarls. a relation that is not particularly well determined. especiallyatlow mass (seefora review)..," The latter is obtained from the initial-final mass relation for white dwarfs, a relation that is not particularly well determined, especiallyatlow mass \citep[see][for a review]{weidemann00}."
 Llere we use (he parameterization used by Wood(1992) where Vp is the mass of the white cdwarL. and je and By represent constants that need to be determined empirically.," Here we use the parameterization used by \citet{wood92}
 where $M_{\rm WD}$ is the mass of the white dwarf, and $A_{\rm IF}$ and $B_{\rm IF}$ represent constants that need to be determined empirically."
 Wood(1992) used the spectroscopic mass distribution of DA white chwarls obtained by Bergeronοἱal.(1992) and derived jj=0.4 and 0.125., \citet{wood92} used the spectroscopic mass distribution of DA white dwarfs obtained by \citet{bsl} and derived $A_{\rm IF}=0.4$ and $B_{\rm IF}=0.125$ .
 The mass distribution of Bergeron et al., The mass distribution of Bergeron et al.
 relied on (hin hydrogen laver models. while thick hvdrogen models vield larger masses (Bragaglia.Renzini.&Bergeron1995).," relied on thin hydrogen layer models, while thick hydrogen models yield larger masses \citep{brb95}."
. Since the weight of evidence now is that most DÀ white chwarls have thick outer hvdrogen lavers. we redetermined the constants in equation (4) by using the mass distribution obtained Lor ihe 348 DA stars from the Palomar-Green survey sample (Liebertetal.2005).. which is based on the thick hydrogen evolutionary models of Wood (1995)..," Since the weight of evidence now is that most DA white dwarfs have thick outer hydrogen layers, we redetermined the constants in equation (4) by using the mass distribution obtained for the 348 DA stars from the Palomar-Green survey sample \citep{lbh05}, which is based on the thick hydrogen evolutionary models of \cite{wood95}. ."
 We obtain the following constants. Aye=0.45 and Dj= 0.144.," We obtain the following constants, $A_{\rm IF}=0.45$ and $B_{\rm IF}=0.144$ ."
 Thus a main sequence star with a 12 Gvr lifetime, Thus a main sequence star with a 12 Gyr lifetime –
no difference.,no difference.
" However, if the MID stem from gradual mass loss from individual clusters, any features in V/; (such as the cut-off mass for the Schechter function) will be shifted downwards with time, whereas only the normalization of V; will change with time for constant number loss."," However, if the MID stem from gradual mass loss from individual clusters, any features in $\Psi_i$ (such as the cut-off mass for the Schechter function) will be shifted downwards with time, whereas only the normalization of $\Psi_i$ will change with time for constant number loss."
" In order to apply Eq. (1)),"," In order to apply Eq. \ref{eq:dndl}) ),"
 some constraints on cluster disruption are necessary., some constraints on cluster disruption are necessary.
" Models and empirical constraints on cluster disruption have been discussed in recent years by different authors (e.g.????7?,amongothers),, and ? for different types of galaxies such as the LMC, SMC, Milky Way, M83, or Antennae."," Models and empirical constraints on cluster disruption have been discussed in recent years by different authors \citep[e.g.][ among others]{BL03,lamers05,whitmorechandarfall07,larsen09,zhang99,fall04}, and \citet{fall09}
 for different types of galaxies such as the LMC, SMC, Milky Way, M83, or Antennae."
" Given that it is currently uncertain to what extent MID or MDD dominates the cluster disruption, we carried out our analysis for both scenarios."," Given that it is currently uncertain to what extent MID or MDD dominates the cluster disruption, we carried out our analysis for both scenarios."
" Figure 12 shows the age distributions (ADs) for clusters with masses between 10 and 10? Mo for the galaxies NGC 1313, NGC 5236, and NGC 7793."," Figure \ref{fig:agedist} shows the age distributions (ADs) for clusters with masses between $10^4$ and $10^5$ $_\odot$ for the galaxies NGC 1313, NGC 5236, and NGC 7793."
 NGC 45 has too few clusters to derive meaningful ADs., NGC 45 has too few clusters to derive meaningful ADs.
 We show fits for both the Accepted and Accepted+Suspected samples., We show fits for both the Accepted and $+$ Suspected samples.
" The slopes of the age distributions, obtained by carrying out fits of the form log(dN/dt)=axlog(r)+6 to the data in Fig. 12,,"," The slopes of the age distributions, obtained by carrying out fits of the form $\log(dN/dt)=a\times \log(\tau)+b$ to the data in Fig. \ref{fig:agedist},"
 are given in Table 6.., are given in Table \ref{tab:agedist}.
 There are no large differences between the slopes derived for the Accepted and Accepted+Suspected sample., There are no large differences between the slopes derived for the Accepted and $+$ Suspected sample.
" Figure 11 shows that most of the clusters in the suspected sample have masses below our limit of log(M) [Mo]=4.0, explaining the similarity of the age distributions above this limit."," Figure \ref{fig:agemass} shows that most of the clusters in the suspected sample have masses below our limit of $\log(M)$ $_{\odot}]=4.0$, explaining the similarity of the age distributions above this limit."
" As a consistency check for the slope of the age distributions, we performed a maximum likelihood fit to the data, assuming a power-law relation and using the power-law index as a free parameter."," As a consistency check for the slope of the age distributions, we performed a maximum likelihood fit to the data, assuming a power-law relation and using the power-law index as a free parameter."
" Using the accepted and accepted plus suspected sample of clusters, we estimated the slope of the age distributions using the same age and mass ranges as shown in Fig."," Using the accepted and accepted plus suspected sample of clusters, we estimated the slope of the age distributions using the same age and mass ranges as shown in Fig."
 12 (i.e. ages between 4 Myrs up to 1 Gyr and masses between 10* and 10° Mo)., \ref{fig:agedist} (i.e. ages between 4 Myrs up to 1 Gyr and masses between $10^4$ and $10^5$ $_{\odot}$ ).
 The results obtained are presented in Table 7.., The results obtained are presented in Table \ref{tab:mls}.
" 'The derived slopes agree very well with those in table 6,, within the errors."," The derived slopes agree very well with those in table \ref{tab:agedist}, within the errors."
 Using clusters with ages between 1099<7«108 yr and a mass 104<M10° Mo we checked for (possible) variations over the slope of the age distributions., Using clusters with ages between $10^{6.6}\le \tau \le10^8$ yr and a mass $10^4\le M \le10^5$ $_{\odot}$ we checked for (possible) variations over the slope of the age distributions.
" The best fit for these slopes in the new age interval are —0.17+ 0.39, —0.38+2.34, and 0.78+0.43 using the accepted sample, and —0.39+0.31, 0.05+0.91, and 0.59+0.91 using the accepted plus suspected sample, for the galaxies NGC 5236, NGC 7793, and NGC 1313 respectively."," The best fit for these slopes in the new age interval are $-0.17\pm0.39$ , $-0.38\pm2.34$, and $0.78\pm0.43$ using the accepted sample, and $-0.39\pm0.31$, $0.05\pm0.91$, and $0.59\pm0.91$ using the accepted plus suspected sample, for the galaxies NGC 5236, NGC 7793, and NGC 1313 respectively."
" The new slopes are to be flatter than the values for the whole age range, showing even positive values; however, in most of the cases, the error is larger than the estimation itself."," The new slopes are to be flatter than the values for the whole age range, showing even positive values; however, in most of the cases, the error is larger than the estimation itself."
" The possibility of having shallower slopes indicate that there is a possible curvature of the age distribution of star cluster systems, which is not consistent with a (simple) power law."," The possibility of having shallower slopes indicate that there is a possible curvature of the age distribution of star cluster systems, which is not consistent with a (simple) power law."
" The slopes found here are, however, somewhat shallower than the value of a=—0.9+0.2 found for NGC 5236 by ?.."," The slopes found here are, however, somewhat shallower than the value of $a=-0.9\pm0.2$ found for NGC 5236 by \citet{chandarwhitmore10}."
" If interpreted within the MID scenario, the slopes derived here correspond to MID disruption rates of41%,,81%,, and per decade in age if we use the accepted sample, and45%,,62%,, and if we use the sample of accepted plus suspected objects, for the galaxies NGC 5236, NGC 7793, and NGC 1313, respectively."," If interpreted within the MID scenario, the slopes derived here correspond to MID disruption rates of, and per decade in age if we use the accepted sample, and, and if we use the sample of accepted plus suspected objects, for the galaxies NGC 5236, NGC 7793, and NGC 1313, respectively."
 A weighted average of the slopes for the Accepted samples leads to a mean slope of (a)=—0.42+0.07 and an MID disruption rate of (62+6)% per decade in age., A weighted average of the slopes for the Accepted samples leads to a mean slope of $\langle a \rangle = -0.42\pm0.07$ and an MID disruption rate of $(62\pm6)$ per decade in age.
" We use this mean weighted value for all the galaxies in our sample, including NGC 45 and NGC 4395 where the numbers of detected clusters are too low to allow us to estimate the slopes of the age distributions independently."," We use this mean weighted value for all the galaxies in our sample, including NGC 45 and NGC 4395 where the numbers of detected clusters are too low to allow us to estimate the slopes of the age distributions independently."
where we have used the substitution vw=ero. and Tone ds the envelope temperature.,"where we have used the substitution $\omega=R/r_{crit}$, and $\rm T_{env}$ is the envelope temperature."
 Ehe. first. term of this equation is the contribution to the signal [rom the envelope. while the second term is the contribution from the core.," The first term of this equation is the contribution to the signal from the envelope, while the second term is the contribution from the core."
" This equation can be solved numerically for anv value of à, or er. to predict the brightness profile LOR)."," This equation can be solved numerically for any value of $\alpha_{\rho}$ or $\alpha_{T}$, to predict the brightness profile I(R)."
 Numerical solution of equation 7 in the isothermal case allows us to compare the continuum racial flux. density variation observed in Paper LH. with that predicted. by the parameterised. model we have presented here;," Numerical solution of equation 7 in the isothermal case allows us to compare the continuum radial flux density variation observed in Paper II, with that predicted by the parameterised model we have presented here."
" We find that models with. pxrcUSCTdU.1 (he.. a,=05+ 0.1) best match the data presented in Paper LL.", We find that models with $\rho\propto r^{-0.5\pm0.1}$ (i.e. $\alpha_{\rho}=0.5\pm0.1$ ) best match the data presented in Paper II.
" A more general. non-isothermal. solution to the continuum appearance of L168913 can be expressed approximately as: This solution was found by numerically solving equation 7 for all values of a, between 0 and 2. and ay between 0 and 2. and then finding which range of values give solutions best matching the data in Paper LL."," A more general, non-isothermal, solution to the continuum appearance of L1689B can be expressed approximately as: This solution was found by numerically solving equation 7 for all values of $\alpha_{\rho}$ between 0 and 2, and $\alpha_{T}$ between 0 and 2, and then finding which range of values give solutions best matching the data in Paper II."
 This is à new and clillerent constraint to that discovered in the above modelling of the C270 data., This is a new and different constraint to that discovered in the above modelling of the $^{18}$ O data.
" Figure 9 illustrates this additional constraint introduced by the continuum cata by. reproducing the contours [rom Figure 9(b) the values of the ratio of Ta at a radius of 32 arcsec [from the centre. to Tus at core centre for the οσο s1) transition as a function of varving o, and ar."," Figure 9 illustrates this additional constraint introduced by the continuum data by reproducing the contours from Figure 9(b) – the values of the ratio of $\rm T_{mb}$ at a radius of 32 arcsec from the centre, to $\rm T_{mb}$ at core centre for the $^{18}$ O $\rightarrow$ 1) transition – as a function of varying $\alpha_{\rho}$ and $\alpha_{T}$."
 Once again the part of this plot that is consistent with the CO data from Figures 1 2 is shown as a shaded area on Figure 7T(b)., Once again the part of this plot that is consistent with the CO data from Figures 1 2 is shown as a shaded area on Figure 7(b).
 However. now we have added an additional shaded: strip at the upper left of the plot illustrating the constraint placed. by the continuum data. as cleseribecl by equation S.," However, now we have added an additional shaded strip at the upper left of the plot illustrating the constraint placed by the continuum data, as described by equation 8."
 We see that the two shaded areas do not overlap. indicating that there is no simultaneous fit to the CO data and the continuum cata.," We see that the two shaded areas do not overlap, indicating that there is no simultaneous fit to the CO data and the continuum data."
 Hence. à more complex model is required to siniultaneously fit all of the data.," Hence, a more complex model is required to simultaneously fit all of the data."
 The simplest way to try to reconcile the CO cata to the continuum data is to vary the abundance of gas-phase CO relative to Hl»., The simplest way to try to reconcile the CO data to the continuum data is to vary the abundance of gas-phase CO relative to $_2$.
 This is predicted. to occur in regions of high density. as the CO freezes out onto the dust. grains. and it has been observed. qualitatively in many regions on many occasions (e.g. Mezger ct al.," This is predicted to occur in regions of high density, as the CO freezes out onto the dust grains, and it has been observed qualitatively in many regions on many occasions (e.g. Mezger et al."
 1990: Gibb Little 1998: Ward-Phomipson et al., 1990; Gibb Little 1998; Ward-Thompson et al.
 2000)., 2000).
 It is thought to occur at temperatures less than ΙΤ (Nakagawa 1980. Dergin Langer 1997).," It is thought to occur at temperatures less than 17K (Nakagawa 1980, Bergin Langer 1997)."
 So we ran a set of models to investigate the οσοι of decreasing the CO abundance towards the centre of the core., So we ran a set of models to investigate the effect of decreasing the CO abundance towards the centre of the core.
" These models had a single temperature of 20Ix. an inner density gradient as before. of pxr"". and à CO abundance fraction xxr’."," These models had a single temperature of 20K, an inner density gradient as before, of $\rho \propto r^{-\alpha_{\rho}}$, and a CO abundance fraction $\chi \propto r^{\alpha_{\chi}}$ ."
" We then investigated the regime O<a,«2and 0«a,2.", We then investigated the regime $0<\alpha_{\rho}<2$ and $0<\alpha_{\chi}<2$.
" Figure 10 shows two contour plots that illustrate the cllects of varving a, and ay simultaneously.", Figure 10 shows two contour plots that illustrate the effects of varying $\alpha_\rho$ and $\alpha_\chi$ simultaneously.
 Figure 10(a) shows contours of the values of the ratio of Ἑμισο +2) to Vu 1)., Figure 10(a) shows contours of the values of the ratio of $\rm T_{mb}$ $ \rm \rightarrow$ 2) to $\rm T_{mb}$ $ \rm \rightarrow$ 1).
 The area of this plot that is consistent with the CO cata is shaded., The area of this plot that is consistent with the CO data is shaded.
" Figure LO(b) shows contours of the values of the ratio of Tin, at a radius of 32 arcsee from the centre to μι, at core centre for the C4°O <1) transition.", Figure 10(b) shows contours of the values of the ratio of $\rm T_{mb}$ at a radius of 32 arcsec from the centre to $\rm T_{mb}$ at core centre for the $^{18}$ O $\rightarrow$ 1) transition.
 As noted in section 2 above. the value observed in the data of LI680D for this ratio was 1.02:0.1.," As noted in section 2 above, the value observed in the data of L1689B for this ratio was $\pm$ 0.1."
 Once again the part of this plot that is consistent with the data from Figures 1 2 is shown as à shaded: area in the lower right hand corner of Figure 10b)., Once again the part of this plot that is consistent with the data from Figures 1 2 is shown as a shaded area in the lower right hand corner of Figure 10(b).
" Including the continuum data in this case. with ay—0. equation 10 simplifies to à,=0.5+0.1."," Including the continuum data in this case, with $\alpha_T=0$, equation 10 simplifies to $\alpha_{\rho} = 0.5 \pm 0.1$."
 Figure. 10(b) illustrates this additional constraint as an horizontal shaded strip in the lower half of the plot., Figure 10(b) illustrates this additional constraint as an horizontal shaded strip in the lower half of the plot.
 Again we see that the wo shacled areas do not overlap. indicating that there is no simultaneous formal fit to the CO data and the continuum data.," Again we see that the two shaded areas do not overlap, indicating that there is no simultaneous formal fit to the CO data and the continuum data."
" Llowever. this is only at the lo level. and we find that he shaded: regions would overlap at the 2o level for the values ay~LO2 and à,~0.4."," However, this is only at the $\sigma$ level, and we find that the shaded regions would overlap at the $\sigma$ level for the values $\alpha_\chi \sim 1.9-2$ and $\alpha_\rho \sim 0.4$."
 This abundance ellect is quite extreme — it implies a drop in CO abundance rom edge to centre although not unprecedented., This abundance effect is quite extreme – it implies a drop in $^{18}$ O abundance from edge to centre – although not unprecedented.
 Cibb and Little (1998) found a similar reduction in the €4°O abundance in H1I23.26., Gibb and Little (1998) found a similar reduction in the $^{18}$ O abundance in HH23–26.
 Furthermore. if there is such à large amount of freeze- taking place. this will increase the average grain size towards the core centre ancl consequently. the dust. grain miss Opacity.," Furthermore, if there is such a large amount of freeze-out taking place, this will increase the average grain size towards the core centre and consequently the dust grain mass opacity."
" In this case we would over-estimate the central density profile ""*ponent. a, derived from the continu data."," In this case we would over-estimate the central density profile exponent, $\alpha_\rho$ derived from the continuum data."
 Vhis would then act to shift the horizontal shaded region in Figure I0(b) downwards. causing a genuine overlap region at the Ί-σ level.," This would then act to shift the horizontal shaded region in Figure 10(b) downwards, causing a genuine overlap region at the $\sigma$ level."
" Thus we have a Π to the data wilh ay~2 and à,0.4.", Thus we have a fit to the data with $\alpha_\chi\sim 2$ and $\alpha_\rho\leq 0.4$.
 The spectra produced. by the model were compared with those observed ancl there was eood agreement within the errors., The spectra produced by the model were compared with those observed and there was good agreement within the errors.
 This is an isothermal fit., This is an isothermal fit.
 Llowever we cannot rule out a slight temperature eracient. depending upon how much the dust opacity parameters that are not well constrained can vary.," However we cannot rule out a slight temperature gradient, depending upon how much the dust opacity parameters that are not well constrained can vary."
 We ran this set of simulations for several teniperatures from 10 to 25k. We found that. the. predicted: surface brightness did not vary significantly. with T. even at. very low temperatures.," We ran this set of simulations for several temperatures from 10 to 25K. We found that the predicted surface brightness did not vary significantly with T, even at very low temperatures."
 However. the predicted. ratio of C70 22) 10 C70 1) di fall with T. and for mocels with P< lth the predicted values were too low to match our observations.," However, the predicted ratio of $^{18}$ O $\rightarrow$ 2) to $^{18}$ O $\rightarrow$ 1) did fall with T, and for models with $<$ 14K the predicted values were too low to match our observations."
 There ave other factors than those discussed above that may allect the conclusions of the modelling., There are other factors than those discussed above that may affect the conclusions of the modelling.
 One suchfactor is that the ortho- to para-Il» ratio in these cores is not well defined., One suchfactor is that the ortho- to $_2$ ratio in these cores is not well defined.
" Since ortho-HI» has a higher cross section for collisions with CO. the ratio of ortho- to para-Ll, may alfect"," Since $_2$ has a higher cross section for collisions with CO, the ratio of ortho- to $_2$ may affect"
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particularly good (Table 1).,particularly good (Table 1).
 We accepted a lower completeness level at the flux limit for GOODS-North (=50%)) in order to get the maximum range of luminosity at each redshift., We accepted a lower completeness level at the flux limit for GOODS-North $\simeq$ ) in order to get the maximum range of luminosity at each redshift.
" When calculating the luminosity function ($3), we used the curves in Fig."," When calculating the luminosity function 3), we used the curves in Fig."
 1 to correct for incompleteness., 1 to correct for incompleteness.
 All the sources above these flux limits are detected at >5c., All the sources above these flux limits are detected at $\bf \ge 5 \sigma$.
 Fig., Fig.
 1 does not account for any objects that are missing because their 24-um flux density falls below the limit of the catalogue used in the cross-ID method., 1 does not account for any objects that are missing because their $\mu$ m flux density falls below the limit of the catalogue used in the cross-ID method.
 There are two arguments that suggest this is not a serious problem., There are two arguments that suggest this is not a serious problem.
" First, Roseboom et show that the number-density of 250-um sources in the cross-ID catalogues agree well with the source counts determined by Oliver et ((2010) down to 225 mJy in and 240 mJy in LH."," First, Roseboom et show that the number-density of $\mu$ m sources in the cross-ID catalogues agree well with the source counts determined by Oliver et (2010) down to $\simeq$ 25 mJy in LH-North and $\simeq$ 40 mJy in LH."
" Second, they compare the results of using a shallow and a deepSpitzer catalogue in several fields and conclude that using the deeper catalogue does not produce a large increase in the number of 250-um sources found by the cross-ID method."," Second, they compare the results of using a shallow and a deep catalogue in several fields and conclude that using the deeper catalogue does not produce a large increase in the number of $\mu$ m sources found by the cross-ID method."
 Fig., Fig.
 2 illustrates this clearly for the North field., 2 illustrates this clearly for the LH-North field.
" The figure shows a histogram of the 24-um flux densities of the sources in the inputSpitzer catalogue, whereas the red line shows the 24-um flux densities of the objects found by the cross-ID method."," The figure shows a histogram of the $\mu$ m flux densities of the sources in the input catalogue, whereas the red line shows the $\mu$ m flux densities of the objects found by the cross-ID method."
" It is important to note that the pum flux densities of the sources in the input catalogue are not used as information in the cross-ID method, so the very different distributions for the input catalogue and for the objects found by the cross-ID method is evidence that the method is working well."," It is important to note that the $\mu$ m flux densities of the sources in the input catalogue are not used as information in the cross-ID method, so the very different distributions for the input catalogue and for the objects found by the cross-ID method is evidence that the method is working well."
" The small number of objects with faint 24-~m flux densities found by the cross-ID method, despite the very large number of faint 24-μπι sources in the input catalogue, strongly suggests that we are not missing objects that have too low 24-um flux densities to be included in the catalogues."," The small number of objects with faint $\mu$ m flux densities found by the cross-ID method, despite the very large number of faint $\mu$ m sources in the input catalogue, strongly suggests that we are not missing objects that have too low $\mu$ m flux densities to be included in the catalogues."
 We have used the optical and near-infrared images for these fields to find the counterparts to the 24-um sources., We have used the optical and near-infrared images for these fields to find the counterparts to the $\mu$ m sources.
" Table 1 shows we have redshifts for all of the GOODS-North sources, either a spectroscopic redshift from the catalogue of Barger et ((2008) or, for of the sources, a photometric redshift, which we have estimated from the available multi-wavelength images (in typically nine optical and near-infrared bands Raymond et al.,"," Table 1 shows we have redshifts for all of the GOODS-North sources, either a spectroscopic redshift from the catalogue of Barger et (2008) or, for of the sources, a photometric redshift, which we have estimated from the available multi-wavelength images (in typically nine optical and near-infrared bands -- Raymond et al.,"
 in prep)., in prep).
" The situation for our other deep field is a little less satisfactory, although we still have redshifts for of the sources, a mixture of spectroscopic redshifts and photometric redshifts, mostly taken from an unpublished catalogue of Owen and collaborators, which was produced from images in eight optical and near-infrared bands."," The situation for our other deep field is a little less satisfactory, although we still have redshifts for of the sources, a mixture of spectroscopic redshifts and photometric redshifts, mostly taken from an unpublished catalogue of Owen and collaborators, which was produced from images in eight optical and near-infrared bands."
 The data for LH is described in Rowan-Robinson et ((2008) and Vaccari et ((in prep)., The data for LH is described in Rowan-Robinson et (2008) and Vaccari et (in prep).
 Fig., Fig.
 3 shows the redshift distributions for our two deep samples., 3 shows the redshift distributions for our two deep samples.
 The differences between the two can probably be explained by cosmic variance as the result of the small area of the GOODS-North sample., The differences between the two can probably be explained by cosmic variance as the result of the small area of the GOODS-North sample.
 The similarity of the distributions at high redshift suggests that the sources without redshifts in LH-North are not preferentially at high redshift., The similarity of the distributions at high redshift suggests that the sources without redshifts in LH-North are not preferentially at high redshift.
" We have estimated the rest-frame 250-um luminosity function in six redshift intervals: 0.0<z 0.2,0.2<z<04,04 < z<0.8,0.8<z< 1.2,1.2<z<1.6, 1.6<zx2.0."," We have estimated the rest-frame $\mu$ m luminosity function in six redshift intervals: $\rm 0.0 < z \le 0.2$, $\rm 0.2 < z \le 0.4$, $\rm 0.4 < z \le 0.8$ , $\rm 0.8 < z \le 1.2$, $\rm 1.2 < z \le 1.6$, $\rm 1.6 < z \le 2.0$."
" Because the optical/IR data is less sensitive for this field than the other two, we have only used the LH sample for the two low-redshift intervals."," Because the optical/IR data is less sensitive for this field than the other two, we have only used the LH sample for the two low-redshift intervals."
 We have not estimated the luminosity function at z2 because of the low number of sources above this redshift., We have not estimated the luminosity function at $\rm z > 2$ because of the low number of sources above this redshift.
" At this early stage of the HerMES project, we do not have large numbers of measurements of the spectral energy distributions (SED) of individual galaxies."," At this early stage of the HerMES project, we do not have large numbers of measurements of the spectral energy distributions (SED) of individual galaxies."
" We have therefore made the assumption that all galaxies have the same SED, which we have taken to be a grey body with a dust-emissivity index of 1.5 and a temperature of 26 K, the average of the SEDs found for the galaxies detected at the same wavelength by the Balloon-borne Large-Aperture Sub-millimeter Telescope (BLAST; Dye et 22009)."," We have therefore made the assumption that all galaxies have the same SED, which we have taken to be a grey body with a dust-emissivity index of 1.5 and a temperature of 26 K, the average of the SEDs found for the galaxies detected at the same wavelength by the Balloon-borne Large-Aperture Sub-millimeter Telescope (BLAST; Dye et 2009)."
" If the typical temperature of the dust in a SPIRE galaxy does change systematically with redshift, this will have little effect on the shape of a galaxy SED at A>100um and thus on the luminosity functions at z«1 but"," If the typical temperature of the dust in a SPIRE galaxy does change systematically with redshift, this will have little effect on the shape of a galaxy SED at $\rm \lambda > 100\ \mu m$ and thus on the luminosity functions at $\rm z < 1$ but"
 , 
The present cosmological paradigm of structure formation relies on indirect evidence that a dark matter component dominates the dynamics of large structures (e.g.?.andreferences therein)..,The present cosmological paradigm of structure formation relies on indirect evidence that a dark matter component dominates the dynamics of large structures \citep[e.g.][and references therein]{Pad06}.
 Gravitational instabilities increase the initially small amplitude fluctuations in the primordial universe. resulting in the evolution towards virialized systems like galaxies and clusters of galaxies (222)..," Gravitational instabilities increase the initially small amplitude fluctuations in the primordial universe, resulting in the evolution towards virialized systems like galaxies and clusters of galaxies \citep{Pee80,Col95,Dod03}."
 However. this rather simple mechanism is in reality exceedingly more complicated. mainly because of non-linear effects. such as the role of dissipation of the baryonic component inside dark matter halos (?) and the nature of dark matter itself (e.g.2)..," However, this rather simple mechanism is in reality exceedingly more complicated, mainly because of non-linear effects, such as the role of dissipation of the baryonic component inside dark matter halos \citep{Sil81} and the nature of dark matter itself \citep[e.g.][]{Gao07}."
 In addition. in the hierarchical scenario of structure formation. low-mass objects are formed first. and then larger systems are formed by subsequent merging of smaller subunits. resulting to a greater or lesser degree in a dynamically complicated history of fusions for probably any given selferavitating object seen today (e.g.. 22)).," In addition, in the hierarchical scenario of structure formation, low-mass objects are formed first, and then larger systems are formed by subsequent merging of smaller subunits, resulting to a greater or lesser degree in a dynamically complicated history of fusions for probably any given selfgravitating object seen today (e.g., \citealt{DeL07,McI08}) )."
 Despite the evident difficulties reaching complete understanding of these mechanisms. it is remarkable that virialized systems do present some kind of global regularity in. their scaling relations.," Despite the evident difficulties reaching complete understanding of these mechanisms, it is remarkable that virialized systems do present some kind of global regularity in their scaling relations."
 For instance. it 15 found that all virtalized stellar systems are reasonably confined to à two-dimensional sheet in their parameter space defined by three independent variables. derivable from quantities such as luminosity. radius. and projected velocity dispersion (e.g.??)..," For instance, it is found that all virialized stellar systems are reasonably confined to a two-dimensional sheet in their parameter space defined by three independent variables, derivable from quantities such as luminosity, radius, and projected velocity dispersion \citep[e.g.][]{Sch93,Bur97}."
" The study of elliptical galaxies. for instance. is of paramount importance in this respect. given that their 2-D manifold of physical observables are a very well-defined plane (the so-called ""fundamental"," The study of elliptical galaxies, for instance, is of paramount importance in this respect, given that their 2-D manifold of physical observables are a very well-defined plane (the so-called `fundamental"
Star formation and stellar feedback are followed by a recipe similar to tlie one presented bv Cen Ostriker (1993). which has been implemented and (tested in detail by O'Shea et al. (,"Star formation and stellar feedback are followed by a recipe similar to the one presented by Cen Ostriker (1993), which has been implemented and tested in detail by O'Shea et al. ("
2002. in preparation).,"2002, in preparation)."
 Some of the relevant details of this algorithm are summarized below., Some of the relevant details of this algorithm are summarized below.
" When a contracting region (hat shows rapid cooling (its cooling timescale /4,4 becomes shorter than the dynamical timescale faq.) and is Jeans unstable is identified it is converted into a collisionless stellar particle with a mininmm mass of 105M...", When a contracting region that shows rapid cooling (its cooling timescale $\tcool$ becomes shorter than the dynamical timescale $\tdyn$ ) and is Jeans unstable is identified it is converted into a collisionless stellar particle with a minimum mass of $10^6\msun$ .
" The mass m. of a stellar particle is recorded at the tme of its creation /5,44. and also we store /44 derived from the average density of the region at that moment."," The mass $m_*$ of a stellar particle is recorded at the time of its creation $t_{\rm form}$ , and also we store $\tdyn$ derived from the average density of the region at that moment."
 The star formation rate (Fig. 1)), The star formation rate (Fig. \ref{fig:all1}) )
 accounted for bv this particle is spread over several {ανν according to with a corresponding UV luminosity of simply where we have assumed a range 5xLO°—ei<4107.," accounted for by this particle is spread over several $\tdyn$ according to with a corresponding UV luminosity of simply where we have assumed a range $5\times 10^{-6}\le\euv\le 4\times
10^{-5}$."
 The justification for eq. (2- 3)), The justification for eq. \ref{eq:sfrate}- \ref{eq:lumin}) )
 have been discussed in Cen Ostriker (1993)., have been discussed in Cen Ostriker (1993).
 This range gives reionization before z6 and vields moderate values of the UV background after complete overlap. for the run with quenchecl star lormation due to strong stellar feedback.," This range gives reionization before $z\sim 6$ and yields moderate values of the UV background after complete overlap, for the run with quenched star formation due to strong stellar feedback."
 Note that this range is slightly higher (han the interval adopted by Guedin (2000)., Note that this range is slightly higher than the interval adopted by Gnedin (2000).
 Clearly. εν depends on a number of hidden parameters. such as the initial mass function (AIF). the stellar spectral energy distribution (SED) and the escape fraction [ο of ionizing radiation from host halos.," Clearly, $\euv$ depends on a number of hidden parameters, such as the initial mass function (IMF), the stellar spectral energy distribution (SED) and the escape fraction $\fesc$ of ionizing radiation from host halos."
 At a grid resolution ol TOkpe comoving. we are unable (ο accurately compute the internal absorption of UV radiation inside galaxies.," At a grid resolution of $70\kpc$ comoving, we are unable to accurately compute the internal absorption of UV radiation inside galaxies."
 As such. our UV emission parameter εν must be viewed as the amount of ionizing radiation escaping the galaxy.," As such, our UV emission parameter $\euv$ must be viewed as the amount of ionizing radiation escaping the galaxy."
" For comparison. our range ofchosen values of eiy mapsinto arange of escape fractions Q.07<fi,0.55 if we adopt the model of Ciardiοἱal. (2000).."," For comparison, our range ofchosen values of $\euv$ mapsinto arange of escape fractions $0.07\le\fesc\le 0.55$ if we adopt the model of \citet{ciardi00}. ."
more sigmificant contributions from galaxies with a hiecor inclination.,more significant contributions from galaxies with a high inclination.
 These models also converge to a ΟὉΟ value if only ealasxies with low inclination are cousidered., These models also converge to a common value if only galaxies with low inclination are considered.
 The distribution of Wy of au observed sample of spiral ealaxies would be a superposition of a continuous set of model distributions similar to tle nine curves iu Figure 5.., The distribution of $\Pi_0$ of an observed sample of spiral galaxies would be a superposition of a continuous set of model distributions similar to the nine curves in Figure \ref{Pi_PDF-fig}.
 A simulated PDF for 20.000. &alaxies wit1 model parameters varied over the ranges given in Table is shown in Fieure 6..," A simulated PDF for 20,000 galaxies with model parameters varied over the ranges given in Table \ref{model_var-tab} is shown in Figure \ref{Pi_PDF-sim-fig}. ."
 At Ls GIIz (Figure 62a). the distribution of Wy is quite broad. with a peak between l4 and 2% polarization.," At 4.8 GHz (Figure \ref{Pi_PDF-sim-fig}a a), the distribution of $\Pi_0$ is quite broad, with a peak between $1\%$ and $2\%$ polarization."
 The location of the peak and he depth of the minimum near Ty=0% depends on the nuuber of galaxies with strong Faraday depolarization., The location of the peak and the depth of the minimum near $\Pi_0 = 0\%$ depends on the number of galaxies with strong Faraday depolarization.
" At 1.1 GIIz (Figure 6010), Faraday depolarization is mach «ποσο aud the distribution is sharply peaked towards II, 4."," At 1.4 GHz (Figure \ref{Pi_PDF-sim-fig}b b), Faraday depolarization is much stronger and the distribution is sharply peaked towards $\Pi_0 =
0\%$ ."
 For the distributions in Figure 6 we find ha of galaxies has Uy>1% at L8 GIIz. while at Lt αν has Wy] ," For the distributions in Figure \ref{Pi_PDF-sim-fig} we find that of galaxies has $\Pi_0 > 1\%$ at 4.8 GHz, while at 1.4 GHz has $\Pi_0 > 1\%$."
The broad tail of the distribution iu Figure lbh contains galaxies with low to uoderate inclination., The broad tail of the distribution in Figure \ref{model_var-tab}b b contains galaxies with low to moderate inclination.
 The mecian inclination for galaxics with Ty25% at 1.1 GIIz is 11, The median inclination for galaxies with $\Pi_0 > 5\%$ at 1.4 GHz is $41\degr$.
 Iuteerated polarimetry of an uubiased sample of a few iucdred spiral galaxies would allow a statistical analysis or the Wy distributions of spiral galaxies. including subsets by inchuation. morphological type and star oration rate.," Integrated polarimetry of an unbiased sample of a few hundred spiral galaxies would allow a statistical analysis for the $\Pi_0$ distributions of spiral galaxies, including subsets by inclination, morphological type and star formation rate."
 The Uy distribution can be retrieved yon the data in the presence of noise through maxim ikchhood fits presented by Tavloretal.(2007)., The $\Pi_0$ distribution can be retrieved from the data in the presence of noise through maximum likelihood fits presented by \citet{taylor2007}.
.. The skewed shape on the PDF in Figure Gaa. sugeests that he best theoretical functiou to represent the PDF of spiral galaxies would be the lowest order entisynuuetric deviation from a Camssian that shifts the peak of the distribution to a finite value of Wy.," The skewed shape on the PDF in Figure \ref{Pi_PDF-sim-fig}a a, suggests that the best theoretical function to represent the PDF of spiral galaxies would be the lowest order -symmetric deviation from a Gaussian that shifts the peak of the distribution to a finite value of $\Pi_0$."
 Iu terms of the Cass- series used in Tavloretal.(2007).. the lowest order term would include coeffcieut fs (Vauder\larel&Frans 1995).," In terms of the Gauss-Hermite series used in \citet{taylor2007}, the lowest order term would include coefficient $h_3$ \citep{vdmarel1993}."
. We preseuted.— observatious of the integrate polarization of nearbv spiral galaxies to/— studv the polarization properties of spiral galaxies as unuresolve radio sources., We presented observations of the integrated polarization of nearby spiral galaxies to study the polarization properties of spiral galaxies as unresolved radio sources.
 It ais shown that unresolved spira ealaxics are polarized radio sources with fractiona polarization up to ~20% at Ls ον., It is shown that unresolved spiral galaxies are polarized radio sources with fractional polarization up to $\sim 20\%$ at 4.8 GHz.
 This lich degree of fractional polarization arises from the regular azimuthal componcut of the magnetic field in the spira ealaxies observed. that is projected iuto a conponent in the plane of the sky that is predominantly oreuted aloug the apparent major axis of the disk seeu at inclination 7.," This high degree of fractional polarization arises from the regular azimuthal component of the magnetic field in the spiral galaxies observed, that is projected into a component in the plane of the sky that is predominantly oriented along the apparent major axis of the disk seen at inclination $i$."
 The projected maguetic field direction as iuplied by the plane of polarization. rotated by 907. is well correlate with the position angele of the major axis for galaxies observed at ligher inclination.," The projected magnetic field direction as implied by the plane of polarization, rotated by $90\degr$, is well correlated with the position angle of the major axis for galaxies observed at higher inclination."
 The highest integrates polarization is expected for galaxies at intermediate inclination., The highest integrated polarization is expected for galaxies at intermediate inclination.
 For a sample of randomly oriented spira ealaxies. has an melinatioun between 50° and 80°.," For a sample of randomly oriented spiral galaxies, has an inclination between $50\degr$ and $80\degr$."
 Calaxies in this inclination range are mucer-represcutcc iu the present sample because the data used in this paper were obtained for polarization studies that prefere low-iuclinatioun or high-inclination galaxies., Galaxies in this inclination range are under-represented in the present sample because the data used in this paper were obtained for polarization studies that preferred low-inclination or high-inclination galaxies.
 The ΙΟ of galaxies with a high fractional polarization in Figure 1 iav therefore be muder represented compared with an unbiased sample.," The number of galaxies with a high fractional polarization in Figure \ref{diskpol_model-fig}
 may therefore be under represented compared with an unbiased sample."
 Three of the eight. Virgo spirals in our data set have inteerated fractional polarization Wy2WA., Three of the eight Virgo spirals in our data set have integrated fractional polarization $\Pi_0 \geqq 8\%$.
 The rauge of Ty of the Vireo spirals is similar to that of the nearby “field” spirals., The range of $\Pi_0$ of the Virgo spirals is similar to that of the nearby “field” spirals.
 We do not fud evidence im the present data that the inteerated polarization of spiral ealaxies in a cluster enviroment would be different frou field galaxies., We do not find evidence in the present data that the integrated polarization of spiral galaxies in a cluster environment would be different from field galaxies.
 Although cluster galaxies are distorted by interactions with other galaxies aud the iutracluster medi (Wezegowiecetal.2007:ClyzvctVollmeretal.2007).. the Vireo galaxies m our sample cannot be distinguished from field galaxies in their integrated polarization.," Although cluster galaxies are distorted by interactions with other galaxies and the intracluster medium \citep{wezgowiec2007,chyzy2007,vollmer2007}, the Virgo galaxies in our sample cannot be distinguished from field galaxies in their integrated polarization."
 This result should be verified. with a larger. complete sample of cluster ealaxies.," This result should be verified with a larger, complete sample of cluster galaxies."
 The barred galaxies in Table ὁ show that a high inteerated polarization also occurs for barred galaxies., The barred galaxies in Table \ref{barred-tab} show that a high integrated polarization also occurs for barred galaxies.
 Iu some of these barred galaxics. polarized emission froni the bar is negligible compared to polarized omission from the disk.," In some of these barred galaxies, polarized emission from the bar is negligible compared to polarized emission from the disk."
 In other barred spirals. polarized eiission from the bar region dominates. aud the integrated polarization depends on the orieutatiou of the bar. as well as the inclination of the ealaxy.," In other barred spirals, polarized emission from the bar region dominates, and the integrated polarization depends on the orientation of the bar, as well as the inclination of the galaxy."
 The effect of à bar is not included in the present models. so the existence of significant departures from the models is uot unexpected.," The effect of a bar is not included in the present models, so the existence of significant departures from the models is not unexpected."
 Nou-axially svuuuetric models of the inteerated polarization of spiral galaxies are deferred to a later paper., Non-axially symmetric models of the integrated polarization of spiral galaxies are deferred to a later paper.
 Figure 23 suggests a difference between Lbhuuimnous and less huninous spiral galaxies., Figure \ref{PI_L-fig} suggests a difference between luminous and less luminous spiral galaxies.
 The three sub saluples separately also show a smaller integrated fractional polarization for luminous spiral galaxies., The three sub samples separately also show a smaller integrated fractional polarization for luminous spiral galaxies.
 Face-on galaxies aud depolarized edgc-ou galaxies should exist at every Iuninositv. although they fori a minority m a SC of randomly orieuted spiral galaxies.," Face-on galaxies and depolarized edge-on galaxies should exist at every luminosity, although they form a minority in a set of randomly oriented spiral galaxies."
 The presence of sole galaxies with low II at every huuinosity iu Figure 3 is therefore not surprising., The presence of some galaxies with low $\Pi_0$ at every luminosity in Figure \ref{PI_L-fig} is therefore not surprising.
 The luminous galaxies in the BHuple cover the same rauge in inclination as the galaxies with lower hDnuuinositv., The luminous galaxies in the sample cover the same range in inclination as the galaxies with lower luminosity.
 This excludes selection effects iu inclination as a possible origin of the correlation., This excludes selection effects in inclination as a possible origin of the correlation.
 No SCection effect could be ideuti&ed that would exclude luminous galaxies with a high Wy from the sample., No selection effect could be identified that would exclude luminous galaxies with a high $\Pi_0$ from the sample.
 The lack of luminous galaxies with a hieh I gains sienificauce im view of the results from Section 3.3.., The lack of luminous galaxies with a high $\Pi_0$ gains significance in view of the results from Section \ref{Pi_PDF-sec}.
 Cüven certain physical conditions. the inclination dependence of Ty favors high values of Hy.," Given certain physical conditions, the inclination dependence of $\Pi_0$ favors high values of $\Pi_0$."
 The lower polarization of luminous spiral galaxies therefore indicates different conditions in these ealaxies., The lower polarization of luminous spiral galaxies therefore indicates different conditions in these galaxies.
 A higher rate of star formation increases the random component of the magnetic field through the effect of superuova explosions and stellar winds., A higher rate of star formation increases the random component of the magnetic field through the effect of supernova explosions and stellar winds.
 A stronger total magnetic field anc lower polarization are found locally in regious of galaxies where the star formation rate is high (Beck2005:Chyzy 2008).," A stronger total magnetic field and lower polarization are found locally in regions of galaxies where the star formation rate is high \citep{beck2005,chyzy2008}."
. The correlation iu Figure 3bb may be explaince sinularly in terms of a generally higher star formation rate., The correlation in Figure \ref{PI_L-fig}b b may be explained similarly in terms of a generally higher star formation rate.
 The correlation of polarization with hunüinositv is an important factor for predictions of the number of spiral galaxies that will be detected in deep polarization survevs., The correlation of polarization with luminosity is an important factor for predictions of the number of spiral galaxies that will be detected in deep polarization surveys.
 Larger samples of spiral galaxies are required to confirm this result. aud to allowmore detailed modeling.," Larger samples of spiral galaxies are required to confirm this result, and to allowmore detailed modeling."
 Suuple axially svunuuetric modelsfor the iuteeratec polarization of spiral galaxies successfully describe. the distribution of observed galaxies iu the Hy - /diagram (Figure laa)., Simple axially symmetric modelsfor the integrated polarization of spiral galaxies successfully describe the distribution of observed galaxies in the $\Pi_0$ - $i$diagram (Figure \ref{diskpol_model-fig}a a).
 The results in Table 1 show that for iS50° the model is iost scusitive to the paralcter fp., The results in Table \ref{model_var-tab} show that for $i \lesssim 50\degr$ the model is most sensitive to the parameter $f_{\rm B}$ .
 This is so because waveleueth-depenudoeut, This is so because wavelength-dependent
clusters with Z = 0.02. the location of the sharp peak moves from about 2860 to around 1920 for and shifts from about 130 to around 95 forAv.,"clusters with Z = 0.02, the location of the sharp peak moves from about 2860 to around 1920 for and shifts from about 130 to around 95 for."
. These peaks also exist in the distributions of and of the cluster with Z = 0.008 and age = 7.0 Gyr., These peaks also exist in the distributions of and of the cluster with Z = 0.008 and age = 7.0 Gyr.
 are from the models with mass between |.02 and 1.04 for all clusters., are from the models with mass between 1.02 and 1.04 for all clusters.
 The mean density of the models decreases with age., The mean density of the models decreases with age.
 Thus. the locations of the sharp peaks move from a high frequency to a lower one.," Thus, the locations of the sharp peaks move from a high frequency to a lower one."
 Using Eggleton's stellar evolution code. detailed model calculations.," Using Eggleton's stellar evolution code, detailed model calculations."
 find any particularity in the evolutions of the models., find any particularity in the evolutions of the models.
. Comparing evolutionary tracks computed using Eggleton’s codecode. we tind that the Hurley code cannot reproduce exactly the evolutionary tracks of late phases of MS of the models with mass between 1.02 and 1.04.," Comparing evolutionary tracks computed using Eggleton's code, we find that the Hurley code cannot reproduce exactly the evolutionary tracks of late phases of MS of the models with mass between 1.02 and 1.04."
.. mean densities of the models., mean densities of the models.
 are almost equal. which leads to the appearance of the sharp peaks.," are almost equal, which leads to the appearance of the sharp peaks."
 In fact. the mean densities of the models given by Eggleton's code are not equal.c," In fact, the mean densities of the models given by Eggleton's code are not equal.,"
ase.. the sharp peaks are artefacts., the sharp peaks are artefacts.
 the Hurley code in effect models on top of another in the and plots., the Hurley code in effect models on top of another in the and plots.
 mean density as well as the evolutionary tracks of early phases of MS of the models with mass between about 1.02 and 1.04M., mean density as well as the evolutionary tracks of early phases of MS of the models with mass between about 1.02 and 1.04.
.. Thus the sharp peaks do not appear in the distributions of and of clusters with age < 3.0 Gyr., Thus the sharp peaks do not appear in the distributions of and of clusters with age $\leq$ 3.0 Gyr.
 The distributions of and of clusters with Z = 0.03 and 0.008 are shown in Figs., The distributions of and of clusters with Z = 0.03 and 0.008 are shown in Figs.
 6 and 7.. respectively.," \ref{pz3} and \ref{pz08}, respectively."
 For young clusters. have similar characteristics: a gap and three peaks.," For young clusters, have similar characteristics: a gap and three peaks."
 Figs. 1.6," Figs. \ref{fig1},"
 and 7 show that the distributions of and are by metallicity.," \ref{pz3}
 and \ref{pz08} show that the distributions of and are by metallicity."
 In spite of the fact that there are many stars hotter than the red edge of the instability strip. Fig.," In spite of the fact that there are many stars hotter than the red edge of the instability strip, Fig."
 8 shows that the location of dominant MS peak is to age. but also to metallicity.," \ref{fmsp} shows that the location of dominant MS peak is to age, but also to metallicity."
 When age increases from 0.5 Gyr to 1.0 Gyr. the frequency of the peak location decreases rom 83 ΓΗΣ to 79 Hz for clusters with Z= 0.02. but decreases rom 98 ΓΗΣ to 88 ΤΗΣ for clusters with Z = 0.008.," When age increases from 0.5 Gyr to 1.0 Gyr, the frequency of the peak location decreases from 83 $\mu$ Hz to 79 $\mu$ Hz for clusters with Z= 0.02, but decreases from 98 $\mu$ Hz to 88 $\mu$ Hz for clusters with Z = 0.008."
 However. the ocation of dominant RC peak is not sensitive to metallicity.," However, the location of dominant RC peak is not sensitive to metallicity."
 For example. for clusters with age = 1.0 Gyr. the peak location shifts only ~ | when the metallicity decreases from 0.03 to 0.008.," For example, for clusters with age = 1.0 Gyr, the peak location shifts only $\sim$ 1 when the metallicity decreases from 0.03 to 0.008."
 In young clusters with age 2.0 Gyr. there are many stars hotter han the red edge of the instability strip.," In young clusters with age $\lesssim$ 2.0 Gyr, there are many stars hotter than the red edge of the instability strip."
 survey solar-like oscillations. may be discarded.," survey solar-like oscillations, may be discarded."
 MS yeak be affected., MS peak be affected.
 For the cluster with Z = 0.008 and age = 0.5 Gyr. the MS peak is mainly composed of stars: MS peak in the distribution of solar-like oscillation frequencies.," For the cluster with Z = 0.008 and age = 0.5 Gyr, the MS peak is mainly composed of stars; MS peak in the distribution of solar-like oscillation frequencies."
 For clusters with Z 0.02. the stars hotter than the red edge of the instability strip are on the left of the dominant MS peaks of andAv.," For clusters with Z $\gtrsim$ 0.02, the stars hotter than the red edge of the instability strip are on the left of the dominant MS peaks of and."
. Hence MS peak may exist in these clusters., Hence MS peak may exist in these clusters.
 The asteroseismical observation of young clusters with a high metallicity. especially for MS stars. may aid in determining the age and metallicity of clusters.," The asteroseismical observation of young clusters with a high metallicity, especially for MS stars, may aid in determining the age and metallicity of clusters."
 In our simulations. we calculated the evolutions of 5» 107 binaries for a cluster.," In our simulations, we calculated the evolutions of 5 $\times
10^{4}$ binaries for a cluster."
 However. even the number of initial models decreases to 2000 binaries. our results affected.," However, even the number of initial models decreases to 2000 binaries, our results affected."
 hotter than the red edge of the instability strip are not discarded in our they have been shown in black., hotter than the red edge of the instability strip are not discarded in our they have been shown in black.
 For clusters with age 2.0 Gyr except the one with Z = 0.008. the distributions of and are not affected by these stars.," For clusters with age $\gtrsim$ 2.0 Gyr except the one with Z = 0.008, the distributions of and are not affected by these stars."
 Although these stars are not expected to exhibit solar-like oscillations. they may exhibit other oscillation..," Although these stars are not expected to exhibit solar-like oscillations, they may exhibit other ."
 The evolutions of wide binary stars are similar to those of, The evolutions of wide binary stars are similar to those of
"particle is equal to the number of supernovae that would occur in a simple stellar population of the same mass and metallicity multiplied bv a constant value. ον=4x10°"" eres per supernova (S06).","particle is equal to the number of supernovae that would occur in a simple stellar population of the same mass and metallicity multiplied by a constant value, $E_{SN} = 4\times 10^{50}$ ergs per supernova (S06)."
 The enerev is then distributed through (he surrounding gas particles ancl the cooling is disabled for a length of time and distance determined by the blastwave model., The energy is then distributed through the surrounding gas particles and the cooling is disabled for a length of time and distance determined by the blastwave model.
 Feedback from stellar particles also returns mass and metals to the ISM., Feedback from stellar particles also returns mass and metals to the ISM.
 The 5elobal SFR of a 5galaxv (the mass of stellar particles formed in one vear in the entire ealaxyv) is important (o establish in part because it can be ascertained even in relatively low- observational survevs of galaxies (??)— and [rom observations of high-redshift ealaxies (??77)..," The global SFR of a galaxy (the mass of stellar particles formed in one year in the entire galaxy) is important to establish in part because it can be ascertained even in relatively low-resolution observational surveys of galaxies \citep{Bell03, Brinchmann04} and from observations of high-redshift galaxies \citep{Madau98, Papovich01, Shapley01, Stanway03}."
 Furthermore. the global SFR is kev to the integrity of the simulation because of the significant5 impact of stellar feedback on the structure of the 5galaxy.," Furthermore, the global SFR is key to the integrity of the simulation because of the significant impact of stellar feedback on the structure of the galaxy."
 Through5 ihe injection of metals ancl energy by. stellar feedback. gas content. chemical evolution. morphology. aud future SFR of the galaxy. are all dependent on the global SFR.," Through the injection of metals and energy by stellar feedback, gas content, chemical evolution, morphology, and future SFR of the galaxy are all dependent on the global SFR."
 Trencls in the global SFR as a function of mass and force resolution can set lower limits on (he appropriate resolution for simulations ol different mass galaxies., Trends in the global SFR as a function of mass and force resolution can set lower limits on the appropriate resolution for simulations of different mass galaxies.
 The top panel of Figure shows the average SFR over 3 Gvr for different. masses of galaxies over our range of mass resolution., The top panel of Figure \ref{fig:sf} shows the average SFR over 3 Gyr for different masses of galaxies over our range of mass resolution.
 For galaxies with masses of 1072M. or more. SFRs in simulations do not converge until 101 DM particles are used: galaxies with these masses and LO? DM particles or fewer do not form stars at all.," For galaxies with masses of $10^{12} M_{\odot}$ or more, SFRs in simulations do not converge until $10^4$ DM particles are used; galaxies with these masses and $10^2$ DM particles or fewer do not form stars at all."
" For 101, galaxies and smaller. low mass resolution simulations are still able to form stars but the SFRs differ greatly [rom those of simulations with high mass resolution."," For $10^{11} M_{\odot}$ galaxies and smaller, low mass resolution simulations are still able to form stars but the SFRs differ greatly from those of simulations with high mass resolution."
 These low mass. low resolution galaxies form stars in our simulations because the absolute mass resolution is still relatively high. allowing the gas to more easily reach sufficient density for our SF criteria.," These low mass, low resolution galaxies form stars in our simulations because the absolute mass resolution is still relatively high, allowing the gas to more easily reach sufficient density for our SF criteria."
 For example. chiving the initial collapse about of the gas particles in the LOMAL.. 100 DAL particle simulation are sullicientlv dense to form stars.," For example, during the initial collapse about of the gas particles in the $10^{10} M_{\odot}$, 100 DM particle simulation are sufficiently dense to form stars."
 In comparison. none of the gas in the 102M... 100 DM particle simulation is capable of SE.," In comparison, none of the gas in the $10^{12} M_{\odot}$, 100 DM particle simulation is capable of SF."
 In all cases. the SFR increases dramatically once 1000 DM particles are used as more of the gas particles in all the simulations are able to reach the density threshold.," In all cases, the SFR increases dramatically once 1000 DM particles are used as more of the gas particles in all the simulations are able to reach the density threshold."
 The LOMM. ealaxy is unique in showing a comparatively huge increase in the SFR from 1000 to 10 DAL particles., The $10^{10} M_{\odot}$ galaxy is unique in showing a comparatively large increase in the SFR from $1000$ to $10^4$ DM particles.
 This increase in SFR corresponds to an increase in disk strength and will be discussed in more detail in 83.3., This increase in SFR corresponds to an increase in disk strength and will be discussed in more detail in 3.3.
" As the number of initial gas particles is further increased to LO"". the SER in this galaxy again declines."," As the number of initial gas particles is further increased to $10^6$, the SFR in this galaxy again declines."
 We will show that this can be linked to an increase in the effectiveness of stellar [eedback (83.2)., We will show that this can be linked to an increase in the effectiveness of stellar feedback 3.2).
 $-dependence (see Section 3.4)).,$\phi$ -dependence (see Section \ref{sct:circimage}) ).
" While the Scwharzschild lens model produces two images for each source position, we only consider the more highly magnified image outside of the Einstein radius."," While the Scwharzschild lens model produces two images for each source position, we only consider the more highly magnified image outside of the Einstein radius."
" Significant variation between the source shapes, À and C, is an indication that we are in a regime where the second order Taylor series expression for flexion is not valid for extended sources - this is the true strong lensing regime where images are arcs rather than arclets."," Significant variation between the source shapes, A and C, is an indication that we are in a regime where the second order Taylor series expression for flexion is not valid for extended sources - this is the true strong lensing regime where images are arcs rather than arclets."
" We examine the level of agreement between the Taylor expansion, equation (6)), and the forwards RBM solution by comparing the relative locations of each image or source ray in the bundle."," We examine the level of agreement between the Taylor expansion, equation \ref{eqn:Dijk}) ), and the forwards RBM solution by comparing the relative locations of each image or source ray in the bundle."
" We introduce two quantities: where the two-dimensional vectors, Ip,;, and Ip,,, are the Nray light rays in the actual (B) and elliptical (D) images, and similarly where the two-dimensional vectors, S4,, and are the light rays in the initial (A) and recovered (C) Όσο,source bundles."," We introduce two quantities: where the two-dimensional vectors, $\mathbf{I}_{B,n}$ and $\mathbf{I}_{D,n}'$, are the $N_{\rm ray}$ light rays in the actual (B) and elliptical (D) images, and similarly where the two-dimensional vectors, $\mathbf{S}_{A,n}$ and $\mathbf{S}_{C,n}'$, are the light rays in the initial (A) and recovered (C) source bundles."
cosinological paraiucters fixed at (O1.Opp.ty.wy)(3.07.0.5. 1.0).,"cosmological parameters fixed at $(\Om,\Ode,w_0,w_a) = (0.3,0.7,-0.5,-1.0)$ ."
 The niue data sets are distinguished according to the number of SNe iu the sample. aud the source of redshift inforiiation for cach object.," The nine data sets are distinguished according to the number of SNe in the sample, and the source of redshift information for each object."
 The A. D and C data sets have 500 SNe: D. E. aud F have 2000: while C. IT. aud I have 10000 objects.," The A, B and C data sets have 500 SNe; D, E, and F have 2000; while G, H, and I have 10000 objects."
 The first cobluun (CÀA.D.G) assunnes an uiunfonuative zZ prior for the redshitt.," The first column (A,D,G) assumes an uninformative $z^2$ prior for the redshift."
 The second columu (B.E.II) uses (simulated) host-ealaxy photometric redshifts.," The second column (B,E,H) uses (simulated) host-galaxy photometric redshifts."
 The final column (C.E.I) uses spectroscopic redshift priors.," The final column (C,F,I) uses spectroscopic redshift priors."
" The process of “bootstrapping” a cloned observation out of the seed data is as follows: At the eund of this process we lave a new cloned data point. which has been ""observed"" at a )osition 45fobs."," The process of “bootstrapping” a cloned observation out of the seed data is as follows: At the end of this process we have a new cloned data point, which has been “observed” at a position $z_{\rm obs},\mu_{\rm obs}$."
 Chis redshift aud distauce pair (along with associated uncertainties} incorporates he desired. variable DE τος]. and also reflects he real errors and observational uncertainties of the original seed object.," This redshift and distance pair (along with associated uncertainties) incorporates the desired variable DE model, and also reflects the real errors and observational uncertainties of the original seed object."
 The sequence ds repeated N times (where N=S500. 2000. or 10000) o generate a complete Monte Carlo sample.," The sequence is repeated N times (where N=500, 2000, or 10000) to generate a complete Monte Carlo sample."
 With cach bootstrap Moute Carlo data sot we then fit for cosmological paraiaeters using he variable DE nodel., With each bootstrap Monte Carlo data set we then fit for cosmological parameters using the variable DE model.
 Tn addition to the simmlated SN data. these cosmological fits are constrained by observations of Barvon Acoustic Oscillations (BAO) aud the Cosmic Microwave Dackeround. (CMDB).," In addition to the simulated SN data, these cosmological fits are constrained by observations of Baryon Acoustic Oscillations (BAO) and the Cosmic Microwave Background (CMB)."
". We use the BAO coustraimt on the souud barrier rr./Dy- frou, SDSS DR7 (7?) aud the CAIB constraint on the ""hift parauecter” RA frou the 7-vear WALAP results (2).", We use the BAO constraint on the sound barrier $r_s/D_V$ from SDSS DR7 \citep{Percival:2010} and the CMB constraint on the “shift parameter” $R$ from the 7-year WMAP results \citep{Komatsu:2010}.
 The likehhood contours from all ume Moute Carlo sinulatious are shown in Figure 6 ane the παν likelihood. values are sununuurized in Table 3.., The likelihood contours from all nine Monte Carlo simulations are shown in Figure \ref{fig:darkmcContours} and the maximum likelihood values are summarized in Table \ref{tab:darkmcResults}.
 The error contours aud quoted uncertainties reflect statistical errors only., The error contours and quoted uncertainties reflect statistical errors only.
 As is to ο expected. the precision of the DE coustraiuts iuproves as the sample size is increased. and as +he redshift prior is strengthened.," As is to be expected, the precision of the DE constraints improves as the sample size is increased, and as the redshift prior is strengthened."
 A couvenieut quantity for comparing the DE conustraiuts from ifferent experiments or simmlatious is the Figure of Merit (FoM) proposed by the Dark Encrev Task Force (DETF)., A convenient quantity for comparing the DE constraints from different experiments or simulations is the Figure of Merit (FoM) proposed by the Dark Energy Task Force (DETF).
" The DETF FoM is defined as the reciprocal of the area in the wyuy, plane that eucloses the confidence limit region (?)..", The DETF FoM is defined as the reciprocal of the area in the $w_0-w_a$ plane that encloses the confidence limit region \citep{Albrecht:2006}.
 In Table 3. we report the FoAl values achieved with from the SN data alone. as well as the FoM. from combined SN|CAMBBAO coustrauts.," In Table \ref{tab:darkmcResults} we report the FoM values achieved with from the SN data alone, as well as the FoM from combined SN+CMB+BAO constraints."
 Both values are normalized to the corresponding FoM from simulation C. This simulation. with spectroscopic constraints from 500 SNe. roughly correspouds to the current state of the art (cfο η.," Both values are normalized to the corresponding FoM from simulation C. This simulation, with spectroscopic constraints from 500 SNe, roughly corresponds to the current state of the art \citep[cf][]{Davis:2007,Sollerman:2009,Komatsu:2009,Komatsu:2010}. ."
The demonstration by SNela that the Universe is undergoing an accelerated expansion has stimulated a vigorous search of models to explain this unexpected fact.,The demonstration by SNeIa that the Universe is undergoing an accelerated expansion has stimulated a vigorous search of models to explain this unexpected fact.
 Since the dynamics of the Universe is conventionally described by the Friedmann equations which follow from the Einstein equation in four dimensions. all modifications ultimately affect the Einstein equation.," Since the dynamics of the Universe is conventionally described by the Friedmann equations which follow from the Einstein equation in four dimensions, all modifications ultimately affect the Einstein equation."
 The left-hand-side of the Einstein equation encodes the geommetry of the Universe in the Einstein tensor Gy. the right-hand-side encodes the energy content in the stress-energy tensor Των.," The left-hand-side of the Einstein equation encodes the metry of the Universe in the Einstein tensor $G_{\mu\nu}$, the right-hand-side encodes the energy content in the stress-energy tensor $T_{\mu\nu}$."
" Thus modifications to G,,, imply some alternative geommetry. modifications in Των involve new forms of energy densities that have not been observed. and which therefore are called dark energy."," Thus modifications to $G_{\mu\nu}$ imply some alternative metry, modifications in $T_{\mu\nu}$ involve new forms of energy densities that have not been observed, and which therefore are called dark energy."
 A well-studied model of modified gravity is the Dvali-Gabadadze-Porrati (DGP) braneworld model (Dvali 2000.. Deffayet 2001)) in which our four-dimensional world is a FRW brane embedded in a five-dimensional Minkowski bulk.," A well-studied model of modified gravity is the Dvali-Gabadadze-Porrati (DGP) braneworld model (Dvali \cite{Dvali}, Deffayet \cite{Deffayet}) ) in which our four-dimensional world is a FRW brane embedded in a five-dimensional Minkowski bulk."
" The model ts characterized by a cross-over length scale 7. such that gravity Is a four-dimensional theory at scales ¢@«7, where matter behaves as pressureless dust.", The model is characterized by a cross-over length scale $r_c$ such that gravity is a four-dimensional theory at scales $a\ll r_c$ where matter behaves as pressureless dust.
" In the self-accelerating DGP branch gravity ""leaks out into the bulk at scales eδα, and the cosmology approaches the behavior of à cosmologicalconstant."," In the self-accelerating DGP branch gravity ""leaks out"" into the bulk at scales $a \gg r_c$ and the cosmology approaches the behavior of a cosmologicalconstant."
 To explain the accelerated expansion which is of recent date (z=0.5 orax 2/3). r. must be of the order of 1.," To explain the accelerated expansion which is of recent date $z\approx 0.5$ or $a\approx 2/3$ ), $r_c$ must be of the order of 1."
" In the self-decelerating DGP branch gravity “leaks in” from the bulk at scales α>>r,. counteracting the observed dark energy acceleration."," In the self-decelerating DGP branch gravity ""leaks in"" from the bulk at scales $a\gg r_c$, counteracting the observed dark energy acceleration."
" Another well-studied model introduces into 7,, the density p, and pressure p, of a fluid called Chaplygin gas (Kamenshchik 2001.. Bilic 2002)) following historical work in aerodynamies (Chaplygin 1904))."," Another well-studied model introduces into $T_{\mu\nu}$ the density $\rho_{\varphi}$ and pressure $p_{\varphi}$ of a fluid called Chaplygin gas (Kamenshchik \cite{Kamenshchik}, Bilic \cite{Bilic}) ) following historical work in aerodynamics (Chaplygin \cite{Chaplygin}) )."
 This model is similar to the DGP model in the sense that it is also characterized by a cross-over length scale below which the gas behaves as pressureless dust. and above which it approaches the behavior of a cosmological constant.," This model is similar to the DGP model in the sense that it is also characterized by a cross-over length scale below which the gas behaves as pressureless dust, and above which it approaches the behavior of a cosmological constant."
 This length scale is expected to be of the same order of magnitude as the ας. scale in the DGP model., This length scale is expected to be of the same order of magnitude as the $r_c$ scale in the DGP model.
 Both the self-accelerating DGP model in flat space and the standard Chaplygin gas model have problems fitting present supernova data. as demonstrated by Davis (2007)).," Both the self-accelerating DGP model in flat space and the standard Chaplygin gas model have problems fitting present supernova data, as demonstrated by Davis \cite{Davis}) )."
" In the standard Chaplygin gas model the Jeans instability of perturbations behaves like CDM fluctuations in the dust-dominated stage (¢<r,). but disappears in the acceleration stage (¢>>5)."," In the standard Chaplygin gas model the Jeans instability of perturbations behaves like CDM fluctuations in the dust-dominated stage $a\ll r_c$ ), but disappears in the acceleration stage $a\gg r_c$ )."
 The combinedeffect of suppression of perturbations and non-zero Jeans length leads to à strong ISW effect and thus of loss of power in CMB anisotropies (Amendola 2003.. Bento 2003)).," The combinedeffect of suppression of perturbations and non-zero Jeans length leads to a strong ISW effect and thus of loss of power in CMB anisotropies (Amendola \cite{Amendola}, Bento \cite{Bento}) )."
 This has led to generalizations to higher-dimensional braneworld models which appear less motivated. and which require more parameters.," This has led to generalizations to higher-dimensional braneworld models which appear less motivated, and which require more parameters."
 We. instead. combine the standard DGP model with the standard Chaplygin gas model.," We, instead, combine the standard DGP model with the standard Chaplygin gas model."
 This paper is organized as follows., This paper is organized as follows.
 | Section 2 we discuss how to identify the cross-over scales in the DGP and Chaplygi gas models., In Section 2 we discuss how to identify the cross-over scales in the DGP and Chaplygin gas models.
 This idea is motivated by the similarities in the asymptotic properties of the models. and was first presented in (Roos 2007)).," This idea is motivated by the similarities in the asymptotic properties of the models, and was first presented in (Roos \cite{Roos}) )."
 In Section 3 we discuss the flat-space self-accelerating basic DGP model with and without standarc Chaplygin gas dark energy. and in Section 4+ we turn to the self- DGP model combined with standard Chaplygn gas.," In Section 3 we discuss the flat-space self-accelerating basic DGP model with and without standard Chaplygin gas dark energy, and in Section 4 we turn to the self-decelerating DGP model combined with standard Chaplygin gas."
 In Section 5 we summarize our results. and in Section 6we discuss them and conclude.," In Section 5 we summarize our results, and in Section 6we discuss them and conclude."
" On the four-dimensional brane in the DGP model. the action of gravity is proportional to M7,Μπ whereas in the bulk it is proportional to the corresponding quantity in 5 dimensions. Mz."," On the four-dimensional brane in the DGP model, the action of gravity is proportional to $M^2_{Pl}$ whereas in the bulk it is proportional to the corresponding quantity in 5 dimensions, $M^3_5$."
" The cross-over length scale is defined as It is customary to associate a density parameter with this. The Friedmann equation in the DGP model may be written (Deffayet 20010) where ¢2(1z)!.&= 81G/3. and p is the total cosmic fluid energy density p=pm+ p,."," The cross-over length scale is defined as It is customary to associate a density parameter with this, The Friedmann equation in the DGP model may be written (Deffayet \cite{Deffayet}) ) where $a=(1+z)^{-1},\ \kappa=8\pi G/3$ , and $\rho$ is the total cosmic fluid energy density $\rho=\rho_m+\rho_{\varphi}$ ."
" Clearly the standard FRW cosmology is recovered in the limit 7;>ο and p,- 0.", Clearly the standard FRW cosmology is recovered in the limit $r_c\rightarrow\infty$ and $\rho_{\varphi}\rightarrow 0$ .
 In the following we shall only consider k=0 flat geometry., In the following we shall only consider $k=0$ flat geometry.
 (PerhuutterRiessetal1998) p|3p<0. (Salud&Starobiusky (Copelandetal2006).. (Peeb," \citep{perl,ries} $\rho+3p<0$ \citep{sahni,paddy}. \citep{cope},"
les&Ratra2006) potential term which dominates over the kinetic term thus generating chough pressure to drive acceleration.," \citep{pee}
 potential term which dominates over the kinetic term thus generating enough pressure to drive acceleration."
 Presently we live in ai epoch where the densities of the dark energy aud the dark matter are comparable., Presently we live in an epoch where the densities of the dark energy and the dark matter are comparable.
 It becomes difficult to solve this coincidence problem without a suitable interaction., It becomes difficult to solve this coincidence problem without a suitable interaction.
 Generally interacting dark euergv models are studied to explain the cosmic coincidence problem (Jamiletal2010:Jamil&Sari-Juil&Rahman 2009).," Generally interacting dark energy models are studied to explain the cosmic coincidence problem \citep{jamil1,jamil2,jamil3,jamil4,jamil5}."
. Also the transition from matter domination to dark cucrey domination can be explained through an appropriate energy exchange ra5, Also the transition from matter domination to dark energy domination can be explained through an appropriate energy exchange rate.
 Therefore. to obtain a suitable evolution of the Universe al interaction is assunied aud the decay rate should be proportional to the preseut value of the IIubble paramcter for good f o the expansion history of the Universe as determined by the Superuovae aud CMD data (Jamiletal2010:Jamil&Saridakis2010).," Therefore, to obtain a suitable evolution of the Universe an interaction is assumed and the decay rate should be proportional to the present value of the Hubble parameter for good fit to the expansion history of the Universe as determined by the Supernovae and CMB data \citep{jamil1,jamil2}."
. A varicty of interacting dark energv nodels have becu proposed and studied for this purpose (Setare2007.Setare 2006)..," A variety of interacting dark energy models have been proposed and studied for this purpose \citep{setare1,setare2,hu,wu,jamil6,setare67}."
 Iu recent vears. the model of interacting dark οπου has been explored in the framework of loop quanti cosinoloey (LQC) as well: It is shown in (Wu&Yu2008) that for the quintessence model. the cosmological evolution in LQC is the same as that in classical Einstein cosmology. whereas for the phantom dark energv the loop quantum effec sjeuificautlv reduce the xuwanmeter spacetime required by stabilitv.," In recent years, the model of interacting dark energy has been explored in the framework of loop quantum cosmology (LQC) as well: It is shown in \citep{wu1} that for the quintessence model, the cosmological evolution in LQC is the same as that in classical Einstein cosmology, whereas for the phantom dark energy the loop quantum effect significantly reduce the parameter spacetime required by stability."
 In (Chemetal 2008).. the authors used a uore eeneral mteraction ena to study the interacting dark energy.," In \citep{chen}, the authors used a more general interaction term to study the interacting dark energy."
 They showed hat in LOC. the parameter space for the existeuce of he accelerated scaling attractor is found to be sinaller hen that in Etustein cosmology.," They showed that in LQC, the parameter space for the existence of the accelerated scaling attractor is found to be smaller then that in Einstein cosmology."
 Ii another study (Fuetal 2008).. the authors studied themodel with an interacting phantom scalar field with :ui exponential »otential aud deduced. that. the futire sineularity," In another study \citep{fu}, the authors studied themodel with an interacting phantom scalar field with an exponential potential and deduced that the future singularity"
In figure 11 we consider the variation of magnetic-field magnitude within the interior of two different NS models.,In figure \ref{Btor_magnitude} we consider the variation of magnetic-field magnitude within the interior of two different NS models.
 The left-hand plot shows a star with normal protons and hence subject to the usual Lorentz force of MHD., The left-hand plot shows a star with normal protons and hence subject to the usual Lorentz force of MHD.
 It is also unstratified., It is also unstratified.
 The field strength is seen to drop off fairly slowly before vanishing at the stellar surface., The field strength is seen to drop off fairly slowly before vanishing at the stellar surface.
" In the right-hand plot we show a toroidal magnetic field in a superconducting star, with a particular choice of toroidal-field function which we refer to as 'C?-superconductivity! — see section 3.2."," In the right-hand plot we show a toroidal magnetic field in a superconducting star, with a particular choice of toroidal-field function which we refer to as $\zeta^3$ -superconductivity' — see section $3.2$."
" This star is also stratified, and both this and the choice of toroidal-field function act to ‘bury’ the field deeper into the star."," This star is also stratified, and both this and the choice of toroidal-field function act to `bury' the field deeper into the star."
" Our other choice for the toroidal-field function, ‘¢?-superconductivity’, produces configurations which are (in the unstratified case) indistinguishable from the left-hand plot."," Our other choice for the toroidal-field function, $\zeta^2$ -superconductivity', produces configurations which are (in the unstratified case) indistinguishable from the left-hand plot."
" This is not surprising, since the expression for the toroidal field in this case is of the same form as for normal MHD (again, see section 3.2)."," This is not surprising, since the expression for the toroidal field in this case is of the same form as for normal MHD (again, see section $3.2$ )."
 In figure 12 we show density distributions for three NS models with toroidal magnetic fields., In figure \ref{norm_vs_sc_dens} we show density distributions for three NS models with toroidal magnetic fields.
" We consider very highly magnetised stars, which serve to emphasise the magnetic distortions."," We consider very highly magnetised stars, which serve to emphasise the magnetic distortions."
" All three models are broadly similar: each has a spherical neutron-fluid distribution, coincident neutron and proton-fluid surfaces, and prolate distortions of the proton fluid."," All three models are broadly similar: each has a spherical neutron-fluid distribution, coincident neutron and proton-fluid surfaces, and prolate distortions of the proton fluid."
" Comparing the density contours for each model, we see that the superconducting models have less distortion to the proton fluid in the outer region, and more in the centre."," Comparing the density contours for each model, we see that the superconducting models have less distortion to the proton fluid in the outer region, and more in the centre."
 The central panel (¢?-superconductivity) has the unusual feature of cusps in its distribution around the pole., The central panel $\zeta^2$ -superconductivity) has the unusual feature of cusps in its proton-fluid distribution around the pole.
" We show unstratified models, but the only obvious effect of stratification is that the spacing of the proton-fluid density contours is altered, as seen earlier in figure 7.."," We show unstratified models, but the only obvious effect of stratification is that the spacing of the proton-fluid density contours is altered, as seen earlier in figure \ref{pol_densconts}."
" We mentioned that figure 12 shows models with extremely strong magnetic fields, and we will show models with similar field strengths in the next figure too."," We mentioned that figure \ref{norm_vs_sc_dens} shows models with extremely strong magnetic fields, and we will show models with similar field strengths in the next figure too."
" Whilst these high fields are useful for emphasising certain features, the main reason for"," Whilst these high fields are useful for emphasising certain features, the main reason for"
MS stars in these clusters will reveal (he same twpes of bandstreneth variations as reported in previous studies.,MS stars in these clusters will reveal the same types of bandstrength variations as reported in previous studies.
 The possibility that CN enrichment is linked in some way with various physical parameters of (he parent cluster has been examined extensively in previous studies., The possibility that CN enrichment is linked in some way with various physical parameters of the parent cluster has been examined extensively in previous studies.
 For example. identilied a possible correlation between CN bandstrenetl and the apparent ellipticitv of the cluster using data from 12 Galactic GCs.," For example, identified a possible correlation between CN bandstrength and the apparent ellipticity of the cluster using data from 12 Galactic GCs."
 This suggested correlation was confirmed by (1990).. who combined (heir observations ol M2 with the set [rom (1937).. but was not seen by using data from eight elusters (of which three were in common between the (wo studies).," This suggested correlation was confirmed by , who combined their observations of M2 with the set from , but was not seen by using data from eight clusters (of which three were in common between the two studies)."
 They concluded Chat the correlation with ellipticitv is not as significant as initially believed., They concluded that the correlation with ellipticity is not as significant as initially believed.
 also reported a correlation between CN enrichment ancl cluster central velocity dispersion. which was again disputed by (2008).," also reported a correlation between CN enrichment and cluster central velocity dispersion, which was again disputed by ."
. The claim of a CN enrichment correlation with integrated cluster luminosity received moderate support from the observations of , The claim of a CN enrichment correlation with integrated cluster luminosity received moderate support from the observations of .
(2008)... Figure 6 shows the number ratio of CN-strong to CN-weak RGB stars for the clusters in our sample. denoted by r. plotted against various cluster parameters drawn [rom the These values are tabulated in Table 4..," Figure \ref{figcnratioparams} shows the number ratio of CN-strong to CN-weak RGB stars for the clusters in our sample, denoted by $r$, plotted against various cluster parameters drawn from the These values are tabulated in Table \ref{tabcnrationums}."
 The number ratio is useful because it reveals the relative population sizes of the individual CN groups. and provides a constraint on the ehemical evolution of the cluster.," The number ratio is useful because it reveals the relative population sizes of the individual CN groups, and provides a constraint on the chemical evolution of the cluster."
Alternativelv.. epochs where f is found to be only a small fraction of the elobal star formation density. psp; must be dominated bv relatively dilluse star formation.,", epochs where $f$ is found to be only a small fraction of the global star formation density, $\rho_{SFR}$ must be dominated by relatively diffuse star formation."
 Finally. if it were to be found that fzLat any epoch. it would suggest a significant contribution from faint chwarl galaxies which are being unaccounted for in the current or UV surveys vet have high enough SER. surface densities to drive winds.," Finally, if it were to be found that $f > 1$ at any epoch, it would suggest a significant contribution from faint dwarf galaxies which are being unaccounted for in the current or UV surveys yet have high enough SFR surface densities to drive winds."
 We have presented a deep imaging and spectroscopic study of the fields of two svstemis. from the NTTI sample of ssvstems., We have presented a deep imaging and spectroscopic study of the fields of two systems from the NTRQ sample of systems.
 In cach field we find that there are two galaxies at the absorption redshift. having strong emission lines ofOn].Oj. and 1L2.," In each field we find that there are two galaxies at the absorption redshift having strong emission lines of, and ."
. The emission line lluxes indicate the galaxies are metal rich anc have significant ongoing star formation., The emission line fluxes indicate the galaxies are metal rich and have significant ongoing star formation.
 We emplovecl SED template fitting to estimate stellar masses. which indicates relatively hiehssbkits.," We employed SED template fitting to estimate stellar masses, which indicates relatively high."
. Analysis of the bbreak and Balmer absorption strengths indicate the zστtubs galaxies toward QOTLT1035 underwent a starburst  1 Gyr in the past. while those towards OQ1417|001 are currently in a starburst phase.," Analysis of the break and Balmer absorption strengths indicate the $z\simeq z_{abs}$ galaxies toward Q0747+035 underwent a starburst $\sim$ 1 Gyr in the past, while those towards Q1417+001 are currently in a starburst phase."
 It is extremely. unlikely. to find galaxies with such properties at ie same location as the aabsorption unless they are related in some way to the ion velocity spreads that define ssvstenmis., It is extremely unlikely to find galaxies with such properties at the same location as the absorption unless they are related in some way to the low-ion velocity spreads that define systems.
 We consider various popular models for the nature of aabsorption svstems., We consider various popular models for the nature of absorption systems.
 Given the (post-)starburst natures of the galaxies. their velocities relative to the observed absorption kinematics. the burst ages. together with the impact parameters of the sightlines to the galaxies. we conclude that starburst-driven galactic winds are the most ikely causes of the aabsorption.," Given the (post-)starburst natures of the galaxies, their velocities relative to the observed absorption kinematics, the burst ages, together with the impact parameters of the sightlines to the galaxies, we conclude that starburst-driven galactic winds are the most likely causes of the absorption."
 Llowever. a scenario in which gas is tically stripped by galaxy-galaxy interactions which simultaneously rigger starbursts is also consistent with the data.," However, a scenario in which gas is tidally stripped by galaxy-galaxy interactions which simultaneously trigger starbursts is also consistent with the data."
 While past studies have found bbueshifted absorption in the spectra of ealaxies at cosmological distances. identifving outllows in his manner unambiguously demonstrates that the material reaches the Finally. we estimate that the star ormation density traced by. aabsorbers is. roughly. within at least an order of magnitude of the total &lobal density. indicating that. though rare. aabsorbers are a powerful tracer of star formation in the Universe.," While past studies have found blueshifted absorption in the spectra of galaxies at cosmological distances, identifying outflows in this manner unambiguously demonstrates that the material reaches the Finally, we estimate that the star formation density traced by absorbers is, roughly, within at least an order of magnitude of the total global density, indicating that, though rare, absorbers are a powerful tracer of star formation in the Universe."
 DBN and BDJ acknowledge support from the STEC-funded Galaxy Formation and Evolution programme at the Institute of Astronomy., DBN and BDJ acknowledge support from the STFC-funded Galaxy Formation and Evolution programme at the Institute of Astronomy.
 VW acknowledges European Union support from a Marie Curie. Intra-IE2uropean: fellowship., VW acknowledges European Union support from a Marie Curie Intra-European fellowship.
 Dased on observations obtained at the Gemini Observatory. which is operated. by the Association of Universities Lor Research in Astronomy. Inc.. under à cooperative agreement," Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement"
lis form involves (he dust particle densitv 24. the particle radius a; (assuming that the dust particles ave spherical). the velocity difference between dust and gas Av=v—vy and the thermal speed of the gas ο=S/3p/p (wok1975).,"Its form involves the dust particle density $\nd$, the particle radius $a_d$ (assuming that the dust particles are spherical), the velocity difference between dust and gas $\Delta\,\vecv=\vecv-\vd$ and the thermal speed of the gas $v_{\rm t}=\tiny{\frac{3}{4}}\sqrt{3p/\rho}$ \citep{k75}."
 It also includes the sticking coefficient a. which is a measure of the percentage of atoms that stick to the dust grain after collision.," It also includes the sticking coefficient $\alpha$, which is a measure of the percentage of atoms that stick to the dust grain after collision."
 This treatment neelects interactions between the different dust species., This treatment neglects interactions between the different dust species.
 However. because of the low particle densities (<1cecm ) and the small collision cross-section Lyon?) of the individual grains. the gas-dust interaction will dominate over the interaction between dust particles.," However, because of the low particle densities $\ll\,1$ $^{-3}$ ) and the small collision cross-section $<\,1\,\mu$ $^2$ ) of the individual grains, the gas-dust interaction will dominate over the interaction between dust particles."
 As in INwok(1975) we assume that a=0.25. so of the collisions are supposed to be elastic.," As in \citet{k75} we assume that $\alpha\,=\,0.25$, so of the collisions are supposed to be elastic."
 For our simulation we use a 2D cvlindrical grid with r=0 (o 2 pe and 2=—2 (o 2pc., For our simulation we use a 2D cylindrical grid with $r=0$ to 2 pc and $z=-2$ to $2$ pc.
 The base grid has a resolution of 80x160 eridpoints. and we allow grid adaptivitv up lo à maximum of six additional refinement levels. which translates in an effective resolution of 51120x102240 exidpoints.," The base grid has a resolution of $\times$ 160 gridpoints, and we allow grid adaptivity up to a maximum of six additional refinement levels, which translates in an effective resolution of $\times$ 240 gridpoints."
 The adaptive mesh is handled dvnamically and (races the presence of dust. ensuring that the front of each expanding dust (vpe is abwavs fully resolved.," The adaptive mesh is handled dynamically and traces the presence of dust, ensuring that the front of each expanding dust type is always fully resolved."
 We initialize the stellar wind bx filling a spherical area of radius ppc around the origin with wind material., We initialize the stellar wind by filling a spherical area of radius pc around the origin with wind material.
 Since the star is moving through the ISM. we let the ISM flow past the star al a constant. velocity.," Since the star is moving through the ISM, we let the ISM flow past the star at a constant velocity."
 As input parameters lor our simulations we use the observations ofa-Orionis.. a typical example of a fast moving evolved star. as obtained by Uetaοἱal.(2008).," As input parameters for our simulations we use the observations of, a typical example of a fast moving evolved star, as obtained by \citet{uetal08}."
". This gives us a gas mass-loss rate of Ma—3x10""ML,/vi. injected at wind velocity (ing=15 km/s. We estimate the dust mass-loss rate to be 2.5x10?Ma (Verhoelstetal.2006)."," This gives us a gas mass-loss rate of $\dot{M}_{\rm gas}=3\times10^{-6}\Msoy$, injected at wind velocity $v_{\rm wind}=15$ km/s. We estimate the dust mass-loss rate to be $2.5\times10^{-3}\dot{M}_{\rm gas}$ \citep{vetal06}."
. Since the winds of evolved LIMS are believed to be clust-driven (νοκ1975).. whieh means that the eas is dragged along with the grains. we assume that the dust and gas in tlie free-streaming wind are closely. coupled. so Chat the velocity difference vanishes.," Since the winds of evolved LIMS are believed to be dust-driven \citep{k75}, which means that the gas is dragged along with the grains, we assume that the dust and gas in the free-streaming wind are closely coupled, so that the velocity difference vanishes."
 Therefore. we initialize the dust grains with the same terminal velocity as the gas.," Therefore, we initialize the dust grains with the same terminal velocity as the gas."
" This wind collicles with an assumed homogeneous ISAL which has a particle density of nga;= 2eemoE and. in the lrame of relerence of the star. flows past the star wilh ej=28.3 kkm/s. For the dust particles we assume a minimum racius of e,=0.005 ja and a maximum of diya,=0.25 jan 2006).. with particle density distributed over the grainsizes as n(a)ea77."," This wind collides with an assumed homogeneous ISM, which has a particle density of $n_{\rm ISM}=2$ $^{-3}$ and, in the frame of reference of the star, flows past the star with $v_{\rm ISM}=28.3$ km/s. For the dust particles we assume a minimum radius of $a_{\rm min}=0.005\,\mu$ m and a maximum of $a_{\rm max}=0.25\,\mu$ m \citep{detal06}, with particle density distributed over the grainsizes as $n(a)\sim\,a^{-3.5}$."
 We represent(his distribution with particles of ten different sizes. taking »=10 im Eq.," We representthis distribution with particles of ten different sizes, taking $n=10$ in Eq."
 1-2. logarithmically distributed over (he total erainsize interval.," 1-2, logarithmically distributed over the total grainsize interval."
 Each dust species effectively represents all dust erains within part of an interval Aa.," Each dust species effectively represents all dust grains within part of an interval $\Delta\,a_{\rm d}$ ."
 The size of each grain type is given bv, The size of each grain type is given by
phenomena while preserviip causality in regions where spatial varlatlols occur over distances sinaller than a mean [ree path.,phenomena while preserving causality in regions where spatial variations occur over distances smaller than a mean free path.
 Pomrauiug (1983) included relativistic teri15 of order u/c iba moving fluid., Pomraning (1983) included relativistic terms of order $v/c$ in a moving fluid.
 FLD iuethods have since been used in pure scattering inedla (Melia Zylst‘a 1991). and for fully general-relativistie calculations (Anie Romano 1992).," FLD methods have since been used in pure scattering media (Melia Zylstra 1991), and for fully general-relativistic calculations (Anile Romano 1992)."
 TIe key inerectieut in all cases is the asstuuption that the specific intensity is a slowly-varyiug fuuctiou of space aud tiue., The key ingredient in all cases is the assumption that the specific intensity is a slowly-varying function of space and time.
 In one space cdimeusion. this assumption is valid in botithe optically-thick clifusion limit aud the optically-tlin [ree-streanuiug limit.," In one space dimension, this assumption is valid in both the optically-thick diffusion limit and the optically-thin free-streaming limit."
 One hopes it. holds approximately iu the 1utermediate regiire and in and this may be tested by coriparison witli results o- Full-transport caculatious.," One hopes it holds approximately in the intermediate regime and in multi-dimensions, and this may be tested by comparison with results of full-transport calculations."
 Cüven slow spatial aud time variation. analytic 'elations may be obtained between the angular momeuts ol the radiation fied.," Given slow spatial and time variation, analytic relations may be obtained between the angular moments of the radiation field."
 LP showed that the radiatiou flux may be written in the form of Fick's law oL ciffusion. as with a ciffusiou coeflicient D given by The dimeusiouless funetion A=ACE) is called the flux limiter.," LP showed that the radiation flux may be written in the form of Fick's law of diffusion, as with a diffusion coefficient $D$ given by The dimensionless function $\lambda=\lambda(E)$ is called the flux limiter."
 In this framework. the racdiatiO1 pressure teusor inay be expressed in terms of the radiation energy deusity via where the components of the Exldington tensor f are given by n=VE/VE| is the unit vector in the direcion of the radiation energy deusity gradient. aud the climensionless scalar function f=(CE) is σαled the Ecclingtou factor.," In this framework, the radiation pressure tensor may be expressed in terms of the radiation energy density via where the components of the Eddington tensor $\mathsf f$ are given by ${\bf n}=\nabla E/|\nabla E|$ is the unit vector in the direction of the radiation energy density gradient, and the dimensionless scalar function $f=f(E)$ is called the Eddington factor."
 The flux limiter A and Eddington factor f are related through iuplicit coustraints between the moments F aud P. so tliat where £? is the dimensionless quantity /2=[VE/(\E).," The flux limiter $\lambda$ and Eddington factor $f$ are related through implicit constraints between the moments ${\bf F}$ and ${\mathsf P}$ , so that where $R$ is the dimensionless quantity $R=|\nabla E|/(\chi E)$."
 Equatious (10)) through (11 ) close the equations of RHD. eliminating the need to solve he radiation momentum equation (5)). and greatly sinmplifviug the computation.," Equations \ref{eqn:fick}) ) through \ref{eqn:flambda}) ) close the equations of RHD, eliminating the need to solve the radiation momentum equation \ref{eqn:radmomentum}) ), and greatly simplifying the computation."
 Since the augilar distribution of the radiation fiek is not explicitly computed. no formal solution of the trausfer equation is needed.," Since the angular distribution of the radiation field is not explicitly computed, no formal solution of the transfer equation is needed."
 At important choice which must be iade to achieve this simplification is expression to be used for the flux uniter A., An important choice which must be made to achieve this simplification is the expression to be used for the flux limiter $\lambda$.
 Mauy expressions are possible which preserve causality. aud are consistent with the assum»tion of smoothness in the radiation field.," Many expressions are possible which preserve causality, and are consistent with the assumption of smoothness in the radiation field."
These are distiuguisl,These are distinguished
Observations of the CO J=5-1 lite (redshifted frequency 576.2679220/(14+5.73)=85.627 GHz) were conducted on two days in October 2001.,Observations of the CO J=5–4 line (redshifted frequency $576.2679220/(1+5.73) = 85.627$ GHz) were conducted on two days in October 2001.
" These observations used 10 autenuas iu D couliguration. eiving ~20"" resolution."," These observations used 10 antennas in D configuration, giving $\sim20''$ resolution."
 As for the Setember 2001 observations with the 1 cui receiver system. the correlator was configured to spau ue:uly 800 MHz centered near the revised redshitt of z—5E)).," As for the September 2001 observations with the 1 cm receiver system, the correlator was configured to span nearly 800 MHz centered near the revised redshift of $z=5.73$."
 The system temperatures raiced [rou 150 to 600 Ix (SSB)., The system temperatures ranged from 150 to 600 K (SSB).
 Frequent observatious of the nearby calibrator JLOS8+015 were 1sed to track amplitude and plase. and: baucdpass calibration was checked. with short observaticns of tie strong source 3C273.," Frequent observations of the nearby calibrator J1058+015 were used to track amplitude and phase, and bandpass calibration was checked with short observations of the strong source 3C273."
 The flux density scale was derived from observations of Mars auc should be accurate to20%., The flux density scale was derived from observations of Mars and should be accurate to.
". The frequency coverage and parameters of the resulting images are: 85.22 t0 85.92 GHz. beam 26""x20"" p.a. 20°."," The frequency coverage and parameters of the resulting images are: 85.22 to 85.92 GHz, beam $26''\times20''$ p.a. $^{\circ}$,"
 rs 3)0 iJv. for 200 kin 1 resolution.," rms 3.0 mJy, for 200 km $^{-1}$ resolution."
 Figure L shows the CO J=2-1 aud CO J-25-1 spectra obtaliecl at quasar position., Figure \ref{fig:spectrum} shows the CO J=2–1 and CO J=5–4 spectra obtained at quasar position.
 The velocity biuniugs for the two lines are 2(X) and 162 km . respectively.," The velocity binnings for the two lines are 200 and 162 km $^{-1}$, respectively."
 The noise in the CO J=2-1 spectrum is uot uniform. aud empirical lo error bars derived from the rus 1oise measured (rom the innages ‘e shown for each velocity binu.," The noise in the CO J=2–1 spectrum is not uniform, and empirical $\pm1\sigma$ error bars derived from the rms noise measured from the images are shown for each velocity bin."
 There are soije tantalizing liinis of signal in adjacent channels close to the expeced velocities. but features with similar (low Sg€»ülicance are present elsewhere in the data. and we do not coiskler any of these feattres to be rellable liue detections.," There are some tantalizing hints of signal in adjacent channels close to the expected velocities, but features with similar (low) significance are present elsewhere in the data, and we do not consider any of these features to be reliable line detections."
 Figure 2 lows a series of naps witli 2(ο kins 1 width hat span the fill half power field of view (6/6) for the J=2-1 line., Figure \ref{fig:channels} shows a series of maps with 200 km $^{-1}$ width that span the full half power field of view $6\farcm6$ ) for the J=2–1 line.
 V:wious attempts at smoothing in bot1 space and requency did not uncover aly iguificant CO enssion in either of the observed transitious., Various attempts at smoothing in both space and frequency did not uncover any significant CO emission in either of the observed transitions.
 Two mechailsius have been suggestedMOD or heating arge masses of dust aud gas it hieh τος» quasar systems: {1) high energy. photous euitted [ro1 gases accreted oWo a massive black hole aud (2) bursts of star formiatioun., Two mechanisms have been suggested for heating large masses of dust and gas in high redshift quasar systems: (1) high energy photons emitted from gases accreted onto a massive black hole and (2) bursts of star formation.
 If the cus is heated yw tlie activity of a inassive black hole. then bright emission uay be expected from hig excltatio CO lines iu a cotipact region close to the exciting source. from large amounts of war1. clense gas involved in fuelinD>oO aud accretion.," If the dust is heated by the activity of a massive black hole, then bright emission may be expected from high excitation CO lines in a compact region close to the exciting source, from large amounts of warm, dense gas involved in fueling and accretion."
 The CO J=5-1| line. whose upper enerey level lies 58 Ix above te ground state. rectives warn gas (>30 A) at hieh densities (>10* 7) to be populated siguificantly by Πο collisious.," The CO J=5–4 line, whose upper energy level lies 88 K above the ground state, requires warm gas $>30~K$ ) at high densities $>10^3$ $^{-3}$ ) to be populated significantly by $_2$ collisions."
 Consequently. the upper limits on CO emission from the J—25-1 line σοιintvaius primarily je amount of molecular eas with these coucitious close to the massive black hoe or other powerfu| heating sources.," Consequently, the upper limits on CO emission from the J=5–4 line constrains primarily the amount of molecular gas with these conditions close to the massive black hole or other powerful heating sources."
 Ou the other laud. such extreme physical couditious are not 1ecessarily appro»riate for starbursts. which are likely to be distributed over larger spatlal scales aud involve cooler. nore diffuse molecular gas.," On the other hand, such extreme physical conditions are not necessarily appropriate for starbursts, which are likely to be distributed over larger spatial scales and involve cooler, more diffuse molecular gas."
 If the dust is heated by primarily by star formation. then emission it CO J=2-] line may be a more appropriate tracer of molecular gas content. eiven that the upper everey level lies just 16 Ix above ground aud the excitation requirements are significantly less striIgel.," If the dust is heated by primarily by star formation, then emission in CO J=2–1 line may be a more appropriate tracer of molecular gas content, given that the upper energy level lies just 16 K above ground and the excitation requirements are significantly less stringent."
 Following Solomon. Downes Radford (1992). we calculate upper linits to CO line luininosities," Following Solomon, Downes Radford (1992), we calculate upper limits to CO line luminosities"
 (A7065A. ABSTGA. AJ4471.X) 7 w=90° Let us elaborate on the fourth. argument., $\lambda7065\rm{\AA}$ $\lambda5876\rm{\AA}$ $\lambda4471\rm{\AA}$ $\eta$ $\omega=90^\circ$ Let us elaborate on the fourth argument.
 Let us consider an alternative model where the Le I lines origin is the acceleration zone of the primary wind. and the change in the Doppler shift of the absorbed. part is attributed to a change in the distance from the star where the lines are formed.," Let us consider an alternative model where the He I lines origin is the acceleration zone of the primary wind, and the change in the Doppler shift of the absorbed part is attributed to a change in the distance from the star where the lines are formed."
 The Doppler shift changes as the wine velocity inside the acceleration zone is ügher at [arger distances from the star., The Doppler shift changes as the wind velocity inside the acceleration zone is higher at larger distances from the star.
 In. such a model we would expect the width of the emission part of the line to change. but its center to μίαν at about he primary stellar velocity.," In such a model we would expect the width of the emission part of the line to change, but its center to stay at about the primary stellar velocity."
 Phese two properties are opposite to observations., These two properties are opposite to observations.
 Observations show that the Doppler shift of the emission part. e.g.. of He L ATO67. ollows that of the absorption. and its width: does not change much (Nielsen et al.," Observations show that the Doppler shift of the emission part, e.g., of He I $\lambda7067$, follows that of the absorption, and its width does not change much (Nielsen et al."
 2007)., 2007).
 This observed »havior is expected in a model where the entire source of the line changes its velocity. as in a model where he line is formed in the secondary stellar wind.," This observed behavior is expected in a model where the entire source of the line changes its velocity, as in a model where the line is formed in the secondary stellar wind."
 The variation in the Doppler shift is attributed. to the orbital motion of the secondary star., The variation in the Doppler shift is attributed to the orbital motion of the secondary star.
 In a recent paper. Alehner et al. (," In a recent paper, Mehner et al. ("
2011) present he AA5668 5712 lines in y Car. observed: across he spectroscopic event of 2009.,"2011) present the $\lambda\lambda5668$ $5712\rm{\AA}$ lines in $\eta$ Car, observed across the spectroscopic event of 2009."
 Alehner et al. (, Mehner et al. (
2011) associate the lines with N LL. as previously. classified » {μου οἱ al. (,"2011) associate the lines with N II, as previously classified by Hillier et al. ("
2001).,2001).
 Phe Doppler shift. variation with orbital phase ofthe N LE lines closely follows the yvchavior of the Lle E lines (Alehner et al., The Doppler shift variation with orbital phase of the N II lines closely follows the behavior of the He I lines (Mehner et al.
 2011)., 2011).
 Since : HL lines come from lower ionization regions. Mehner 6 al. (," Since N II lines come from lower ionization regions, Mehner et al. ("
2011) conclude that neither the He E nor the N LL ines can originate in the secondary. wind.,2011) conclude that neither the He I nor the N II lines can originate in the secondary wind.
 Alehner ct al. (, Mehner et al. (
2011) do not provide a consistent explanation to 1e similar behavior of the N HH and Le LE lines. and to 16 Doppler variation with orbital phase.,"2011) do not provide a consistent explanation to the similar behavior of the N II and He I lines, and to the Doppler variation with orbital phase."
 Γον only comment that the observations of the N LL probably excludes some proposed. models. such as those where Le E lines originate in the secondary stellar wind or in an accretion disk.," They only comment that the observations of the N II probably excludes some proposed models, such as those where He I lines originate in the secondary stellar wind or in an accretion disk."
 We disagree with this conclusion of Alehner et al. (, We disagree with this conclusion of Mehner et al. (
2011).,2011).
 Below we argue that the behavior of the N LL lines might be accounted for in a model where the N LL lines originate in the acceleration zone of he secondary wind., Below we argue that the behavior of the N II lines might be accounted for in a model where the N II lines originate in the acceleration zone of he secondary wind.
 Although even this model is not perfect. it is the only model that quantitatively accounts for thevariation of the Doppler shift.," Although even this model is not perfect, it is the only model that quantitatively accounts for thevariation of the Doppler shift."
"We have performed many tests of the ORION2 MHD module, including the well-known standard tests, such as the EM wave families (e.g.Crockettetal.2005),, the Ryu&Jones shock-tube tests, the Brio&Wu shock-tube (1995)test, the field-loop advection test, and the (1988)MHD blast-wave test as in Gardiner&Stone(2005).","We have performed many tests of the ORION2 MHD module, including the well-known standard tests, such as the EM wave families \citep[e.g.][]{cro05}, the \citet{ryu95} shock-tube tests, the \citet{bri88} shock-tube test, the field-loop advection test, and the MHD blast-wave test as in \citet{gar05}."
. We present the results of only two of the shock-tube tests and the field-loop advection test here to demonstrate the second-order accuracy of the MHD module., We present the results of only two of the shock-tube tests and the field-loop advection test here to demonstrate the second-order accuracy of the MHD module.
 Ryu&Jones(1995) developed a suite of shock-tube tests that are commonly used for testing MHD algorithms., \citet{ryu95} developed a suite of shock-tube tests that are commonly used for testing MHD algorithms.
" In Figure 1, we present the results of just one of the tests with the setting of initial conditions (,vz,vy,vz,Bz,By,B:,P)=(1,10,0,0,5/(4)!/2,5/(4x)V/?, 0,20) on the left and (1,—10,0,0,5/(41)1/2,5/(41)/?,0,1) on the right of the contact discontinuity; here p is the density, v the velocity and P the gas pressure."," In Figure \ref{rjf}, we present the results of just one of the tests with the setting of initial conditions $(\rho,v_x,v_y,v_z,B_x,B_y,B_z,P) = (1,10,0,0,5/(4\pi)^{1/2},5/(4\pi)^{1/2},$ $0,20)$ on the left and $(1,-10,0,0,5/(4\pi)^{1/2},5/(4\pi)^{1/2},0,1)$ on the right of the contact discontinuity; here $\rho$ is the density, $v$ the velocity and $P$ the gas pressure."
" The contact discontinuity is located at the middle of the shock tube, and we set the adiabatic index of the gas to be y— 5/3."," The contact discontinuity is located at the middle of the shock tube, and we set the adiabatic index of the gas to be $\gamma = 5/3$ ."
 The length of the shock tube is 1 and is resolved by 512 cells along the x-direction., The length of the shock tube is 1 and is resolved by 512 cells along the $x$ -direction.
 The initial condition on the velocity is a colliding flow with a magnetic field at an angle of 45? in the x—y plane., The initial condition on the velocity is a colliding flow with a magnetic field at an angle of $45^\circ$ in the $x-y$ plane.
" The results at a time 0.08 in code units (corresponding to 0.46 sound crossing times at the left side of the shock tube initially) are shown in Figure 1,, and they agree with the magnitudes and locations of the shocks found by Ryu&Jones(1995) to almost within the thickness of the lines."," The results at a time 0.08 in code units (corresponding to 0.46 sound crossing times at the left side of the shock tube initially) are shown in Figure \ref{rjf}, and they agree with the magnitudes and locations of the shocks found by \citet{ryu95} to almost within the thickness of the lines."
" In Figure 2, we show the results of another commonly used shock-tube problem, that of Brio&Wu(1988) ."," In Figure \ref{briowu}, we show the results of another commonly used shock-tube problem, that of \citet{bri88} ."
" The initial conditions of this test are (p,Uz,Br,By,Bz,P)=(1,0,0,0,0.75, 1,0,1) on the leftVy, and (0.125,0,0,0,0.75,—1,0,0.1) on the right; here P is the gas pressure."," The initial conditions of this test are $(\rho,v_x,v_y,v_z,B_x,B_y,B_z,P) = (1,0,0,0,0.75,$ $1,0,1)$ on the left and $(0.125,0,0,0,0.75,-1,0,0.1)$ on the right; here $P$ is the gas pressure."
 The contact discontinuity is located at the middle of the shock tube and y=2., The contact discontinuity is located at the middle of the shock tube and $\gamma = 2$.
 The length of the shock tube is 1 and is resolved by 800 cells along the «x-direction., The length of the shock tube is 1 and is resolved by 800 cells along the $x$ -direction.
 The gas has no movement initially., The gas has no movement initially.
 'The y-component of the magnetic field changes sign at the contact discontinuity and has a pressure jump of 10., The $y$ -component of the magnetic field changes sign at the contact discontinuity and has a pressure jump of 10.
 Figure 2 shows the results at a time of 0.1 (corresponding to 0.14 sound crossing times at the left side of the shock tube initially)., Figure \ref{briowu} shows the results at a time of 0.1 (corresponding to 0.14 sound crossing times at the left side of the shock tube initially).
" We can see the compound wave, which is composed of an wave and a slow wave, in the figure."," We can see the compound wave, which is composed of an wave and a slow wave, in the figure."
" Since Gardiner&Stone(2005) first suggested using the advection of a magnetic field loop to show the difference between operator split and unsplit schemes, field-loop advection has become a standard test for MHD algorithms."," Since \citet{gar05} first suggested using the advection of a magnetic field loop to show the difference between operator split and unsplit schemes, field-loop advection has become a standard test for MHD algorithms."
" Our setup of the 3D test is exactly the same as in Gardiner&Stone(2008):: the magnetic field loop is created inside a rectangular box of size (2,1,1) resolved ona2NxNx grid with periodic boundaries."," Our setup of the 3D test is exactly the same as in \citet{gar08}: the magnetic field loop is created inside a rectangular box of size (2,1,1) resolved on a $2N \times N \times N$ grid with periodic boundaries."
" The loop of magnetic fieldN is generated from a vector potential on a coordinate system (z1,22,23), with Ay=A»0 and where Bo=1073, r=\/z?+z2, and the size of the loop is R=0.3."," The loop of magnetic field is generated from a vector potential on a coordinate system $x_1,x_2,x_3$ ), with $A_1 = A_2 = 0$ and where $B_0 = 10^{-3}$, $r = \sqrt{x_1^2+x_2^2}$, and the size of the loop is $R = 0.3$."
" The computational coordinate system (x,y, 2) is transformed to (x1,x2, x3) by corresponding to a rotation about the y-axis."," The computational coordinate system $x,y,z$ ) is transformed to $x_1,x_2,x_3$ ) by corresponding to a rotation about the $y$ -axis."
" The density (p= and pressure (P= are uniform and the whole region1) is advected with a velocity1) (2,1,1)."," The density $\rho = 1$ ) and pressure $P = 1$ ) are uniform and the whole region is advected with a velocity (2,1,1)."
" Therefore, after one unit of time, a loop starting in the middle of the rectangular region will travel across the 3D diagonal of the box and return back to the initial position."," Therefore, after one unit of time, a loop starting in the middle of the rectangular region will travel across the 3D diagonal of the box and return back to the initial position."
 The advection continues for 2 cycles and the images of the magnetic field loop at the beginning and the end of this test are shown in Figure 3.., The advection continues for 2 cycles and the images of the magnetic field loop at the beginning and the end of this test are shown in Figure \ref{loop1}.
" The top part of the figure shows the simpler case in which the field loop is aligned with the z-axis, which is similar to a 2D advection test."," The top part of the figure shows the simpler case in which the field loop is aligned with the $z$ -axis, which is similar to a 2D advection test."
 The loops diffuse slightly but maintain their shapes nicely after 2 cycles of advection., The loops diffuse slightly but maintain their shapes nicely after 2 cycles of advection.
" The time evolution of the volume mean óB?/ is similar to that of the 3D inclined field-loop test, and B, remains zeroto the machine accuracy."," The time evolution of the volume mean $\delta B^2 / B^2$ is similar to that of the 3D inclined field-loop test, and $B_z$ remains zeroto the machine accuracy."
" In the rest of this section, we focus on the 3D inclined field-loop test results."," In the rest of this section, we focus on the 3D inclined field-loop test results."
" We have performed the inclined field-loop test 3 times on a single level grid (unigrid) with 3 different resolutions: N=32,64 and 128, as in Gardiner&Stone (2008).."," We have performed the inclined field-loop test 3 times on a single level grid (unigrid) with 3 different resolutions: $N = 32,\,64$ and 128, as in \citet{gar08}. ."
dispersed the original D.T. wishes to thank David Nesvorny for the. fruitful discussions and the help in studying the collisional evolution of the irregular satellites in Saturn svstem.,dispersed the original D.T. wishes to thank David Nesvorny for the fruitful discussions and the help in studying the collisional evolution of the irregular satellites in Saturn system.
 All the authors wish to thank the anonymous referee for the help and the suggestions to improve this paper., All the authors wish to thank the anonymous referee for the help and the suggestions to improve this paper.
The study of the ICM properties has been tackled so far through X-ray observations.,The study of the ICM properties has been tackled so far through X–ray observations.
 Data from the Chandra and XMM-Newton satellites are providing precise measures of the temperature and surface brightness profiles for a fairly large number of nearby 2 0.3) clusters. reaching >—0.5 for the brightest objects (e.g.2]," Data from the Chandra and XMM--Newton satellites are providing precise measures of the temperature and surface brightness profiles for a fairly large number of nearby $z\mincir 0.3$ ) clusters, reaching $z\simeq 0.5$ for the brightest objects \citep[e.g.,
][]{2005A&A...433..101P,2005A&A...429..791P,2005ApJ...628..655V,2006ApJ...641..752K}."
 These observations have indeed allowed to trace in detail the mass distribution in galaxy clusters for the first time., These observations have indeed allowed to trace in detail the mass distribution in galaxy clusters for the first time.
 However in the X-rays the accessible dynamic range is limited by the ος dependence of the emissivity which causes measurements of the temperature profiles to be generally limited to 2-3 core radii. extending out to rzoo only in the most favorable cases.," However in the X-rays the accessible dynamic range is limited by the $\rho_{gas}^2$ dependence of the emissivity which causes measurements of the temperature profiles to be generally limited to 2–3 core radii, extending out to $r_{500}$ only in the most favorable cases."
 This is not the case for clusters’ studies performed with the Sunyaev—Zeldovich effect (2.. tSZ hereafter: see ??. for reviews).," This is not the case for clusters' studies performed with the Sunyaev--Zeldovich effect \citealt{1972CoASP...4..173S}, tSZ hereafter; see \citealt{1999PhR...310...97B,2002ARA&A..40..643C} for reviews)."
 Since the tSZ signal has a weaker dependence on the local gas density. it is in principle better suited to sample the outer cluster's regions. which can be accessed by X-ray telescopes only with long exposures and a careful. characterization of the background noise.," Since the tSZ signal has a weaker dependence on the local gas density, it is in principle better suited to sample the outer cluster's regions, which can be accessed by X–ray telescopes only with long exposures and a careful characterization of the background noise."
" Clusters are currently observed through their thermal SZ (t$Z) signal and tSZ surveys of fairly large area of the sky promise to discover in the next future a large number of distant clusters out to zz,1.", Clusters are currently observed through their thermal SZ (tSZ) signal and tSZ surveys of fairly large area of the sky promise to discover in the next future a large number of distant clusters out to $z\magcir 1$.
" Thanks to the different dependence of the tSZ and X-ray emission on the electron number density »,. and temperature 1i. the combination of these two observations offers in principle an alternative. route to X-ray spectroscopy for the study of he structural properties of the ICM."," Thanks to the different dependence of the tSZ and X–ray emission on the electron number density $n_e$, and temperature $T_e$, the combination of these two observations offers in principle an alternative route to X–ray spectroscopy for the study of the structural properties of the ICM."
" Indeed. while the X-ray emissivity scales as n2ACD) (where ACL) is the cooling function). he tSZ signal is proportional to the gas pressure. n,7,.. integrated along the line-of-sight."," Indeed, while the X–ray emissivity scales as $n_e^2\Lambda(T)$ (where $\Lambda(T)$ is the cooling function), the tSZ signal is proportional to the gas pressure, $n_eT_e$, integrated along the line-of-sight."
 Recovering the temperature structure of galaxy clusters through the combination of X-ray and tSZ data ais several advantages with respect to the more traditional X—ray spectroscopy., Recovering the temperature structure of galaxy clusters through the combination of X–ray and tSZ data has several advantages with respect to the more traditional X--ray spectroscopy.
 First of all. surface brightness protiles can be recovered with a limited number (~ 10°) of photons. while emperature profiles require at least ten times more counts.," First of all, surface brightness profiles can be recovered with a limited number $\sim 10^3$ ) of photons, while temperature profiles require at least ten times more counts."
 Therefore. the combination of X-ray surface brightness and tSZ data should allow to probe more easily the regimes of low surface brightness (i.e. external cluster regions and high—redshift galaxy clusters). which are hardly accessible to spatially resolved X-ray spectroscopy.," Therefore, the combination of X–ray surface brightness and tSZ data should allow to probe more easily the regimes of low X--ray surface brightness (i.e. external cluster regions and high--redshift galaxy clusters), which are hardly accessible to spatially resolved X–ray spectroscopy."
 Furthermore. fitting X-ray spectra with a single temperature model is known to provide a temperature estimate which is generally biased low by the presence of relatively cold clumps embedded in the hot ICM atmosphere (22)..," Furthermore, fitting X–ray spectra with a single temperature model is known to provide a temperature estimate which is generally biased low by the presence of relatively cold clumps embedded in the hot ICM atmosphere \citep{2004MNRAS.354...10M,2006ApJ...640..710V}."
 On the other hand. combining X—ray and tSZ does not require any spectral fitting procedure and. therefore. yields a temperature which is basically mass—weighted.," On the other hand, combining X–ray and tSZ does not require any spectral fitting procedure and, therefore, yields a temperature which is basically mass–weighted."
 The combination of X-ray and tSZ observations is currently used to estimate the angular diameter distance of clusters (e.g..??..andreferencestherein) and to recover the gas mass fraction (ew.2).," The combination of X–ray and tSZ observations is currently used to estimate the angular diameter distance of clusters \citep[e.g., ][,
and references therein]{2006ApJ...647...25B,2006MNRAS.369.1459A} and to recover the gas mass fraction \citep[e.g.,][]{2006ApJ...652..917L}."
 Clearly. performing a spatially—resolved reconstruction the thermal structure of the ICM requires the availability of high— tSZ observations with a sub-aremin beam size. with a sensitivity of few ΚΕ on the beam.," Clearly, performing a spatially–resolved reconstruction the thermal structure of the ICM requires the availability of high--resolution tSZ observations with a sub-arcmin beam size, with a sensitivity of few $\mu$ K on the beam."
 Although observations of this type can not be easily carried out with millimetric and sub—millimetric telescopes of the present generation. they are certainly within the reach of forthcoming and planned instruments of the next generation. based both on interferometric arrays (ALMA: Atacama Large Millimeter ) and on single dishes with large bolometer arrays (Cornell-Caltech Atacama Telescope:CCAT?:: Large Millimeter Array: n.," Although observations of this type can not be easily carried out with millimetric and sub--millimetric telescopes of the present generation, they are certainly within the reach of forthcoming and planned instruments of the next generation, based both on interferometric arrays (ALMA: Atacama Large Millimeter ) and on single dishes with large bolometer arrays (Cornell–Caltech Atacama Telescope:; Large Millimeter Array: )."
 Combining X-ray and tSZ data to reconstruct the three dimensional gas density and temperature structure of galaxy clusters is not a new idea and different authors have proposed different approaches., Combining X–ray and tSZ data to reconstruct the three dimensional gas density and temperature structure of galaxy clusters is not a new idea and different authors have proposed different approaches.
 ? used a deprojection method. based on Fourier transforming tSZ. X-ray and lensing images. under the assumption of axial symmetry of the cluster.," \cite{1998ApJ...500L..87Z} used a deprojection method, based on Fourier transforming tSZ, X–ray and lensing images, under the assumption of axial symmetry of the cluster."
 After applying us method to simple analytical cluster models. they concluded jut the combination of the three maps allows one to measure independently the Hubble constant //u and the inclination angle.," After applying this method to simple analytical cluster models, they concluded that the combination of the three maps allows one to measure independently the Hubble constant $H_0$ and the inclination angle."
 This same method was then applied by ? to cosmological wdrodynamical simulations of galaxy clusters. who found that a reliable determination of the cluster baryon fraction. independent of 1ο inclination angle.," This same method was then applied by \cite{2001ApJ...561..600Z} to cosmological hydrodynamical simulations of galaxy clusters, who found that a reliable determination of the cluster baryon fraction, independent of the inclination angle."
 ? applied a method based on the Richardson—Lucy deconvolution to combined tSZ. X-ray and weak lensing data oa set of simulated clusters.," \cite{2000A&A...364..377R} applied a method based on the Richardson--Lucy deconvolution to combined tSZ, X–ray and weak lensing data to a set of simulated clusters."
 ?. used a perturbative approach to describe the three dimensional structure of the cluster. to combine SZ and lensing images.," \cite{2001A&A...375...14D} used a perturbative approach to describe the three dimensional structure of the cluster, to combine tSZ and lensing images."
 In this way. they were able to predict ye resulting X-ray surface brightness.," In this way, they were able to predict the resulting X–ray surface brightness."
 After testing their method against numerical simulations of clusters. they conclude that the DM and gas distributions can both be recovered quite precisely.," After testing their method against numerical simulations of clusters, they conclude that the DM and gas distributions can both be recovered quite precisely."
 ? proposed a method. based on assuming a polytropic equation of state for gas in hydrostatic equilibrium. which allowed them to recover the three dimensional profiles of clusters using the tSZ and the X-ray signals.," \cite{2004ApJ...601..599L} proposed a method, based on assuming a polytropic equation of state for gas in hydrostatic equilibrium, which allowed them to recover the three dimensional profiles of clusters using the tSZ and the X–ray signals."
 ? applied the same method of ? to deproject X-ray and tSZ maps. so as to recover the gas density and the temperature structure of clusters. under the assumption of axial symmetry.," \cite{2006A&A...455..791P} applied the same method of \cite{2000A&A...364..377R} to deproject X–ray and tSZ maps, so as to recover the gas density and the temperature structure of clusters, under the assumption of axial symmetry."
 ?. applied the combination of tSZ and X-ray observations to recover determine the ICM entropy profile.," \cite{2006ApJ...647L...5C}
 applied the combination of tSZ and X–ray observations to recover determine the ICM entropy profile."
 As for applications to real clusters. ? combined X-ray surface brightness and tSZ data. for a compilation of clusters. to estimate the central cluster temperature. and found it to be in reasonable agreement with the X-ray spectroscopic determination.," As for applications to real clusters, \cite{2000ApJ...545..141Z}
 combined X-ray surface brightness and tSZ data, for a compilation of clusters, to estimate the central cluster temperature, and found it to be in reasonable agreement with the X–ray spectroscopic determination."
 ? used ROSAT-HRI imaging data of a relatively distant cluster ες20.42) with tSZ observations to infer the global temperature of the system., \cite{2002A&A...387...56P} used ROSAT–HRI imaging data of a relatively distant cluster $z\simeq 0.42$ ) with tSZ observations to infer the global temperature of the system.
 ? combined X-ray and tSZ data to constrain the intrinsic shapes of a set of 25 clusters., \cite{2005ApJ...625..108D} combined X–ray and tSZ data to constrain the intrinsic shapes of a set of 25 clusters.
 By applying a deprojection method based on assuming the model (2).. they confirmed a marginal preference for the clusters to be aligned along the line-of-sight. thus concluding that X-ray selection may be affected by an orientation effect.," By applying a deprojection method based on assuming the $\beta$ –model \citep{1976A&A....49..137C}, they confirmed a marginal preference for the clusters to be aligned along the line-of-sight, thus concluding that X–ray selection may be affected by an orientation effect."
 ?. analyzed the potentiality of combining tSZ. X-ray and lensing data to constrain the 3D structure of the clusters.," \cite{2007arXiv0707.0572S} analyzed the potentiality of combining tSZ, X–ray and lensing data to constrain the 3D structure of the clusters."
 He found that these data are enough to determine the elongation along the line of sight (together with the distance). without however fully constraining shape and orientation.," He found that these data are enough to determine the elongation along the line of sight (together with the distance), without however fully constraining shape and orientation."
 Some of the detailed methods applied to numerical cluster models account for the presence of a realistic noise in the tSZ and X-ray maps., Some of the detailed methods applied to numerical cluster models account for the presence of a realistic noise in the tSZ and X–ray maps.
 However. they generally do not present any detailed assessment of how this noise determines the uncertainties in the deprojected profiles. which ultimately characterize the ICM thermodynamics.," However, they generally do not present any detailed assessment of how this noise determines the uncertainties in the deprojected profiles, which ultimately characterize the ICM thermodynamics."
 Having a good control on the errors is especially crucial in any deprojection technique. since errors af a given projected separation affect the deprojected signal in the inner regions. thereby introducing a non-negligible covariance in the reconstruction of the three-dimensional profiles.," Having a good control on the errors is especially crucial in any deprojection technique, since errors at a given projected separation affect the deprojected signal in the inner regions, thereby introducing a non–negligible covariance in the reconstruction of the three-dimensional profiles."
 In this paper we discuss a method to recover the three—resolution temperature and gas density profiles from the joint, In this paper we discuss a method to recover the three--dimensional temperature and gas density profiles from the joint
where the dot denotes a derivative with respect to E'7.,where the dot denotes a derivative with respect to $E^{1/2}$.
 The integration of Eq. (48) , The integration of Eq. \ref{Fowler}) )
"over a Maxwellian velocity distribution gives (Fowler.Caughlan. where S,g(K7) is defined by Inserting this into Eq. (27))"," over a Maxwellian velocity distribution gives \citep{fow67}
 where ${\cal S} _{\mbox{\footnotesize eff}}(kT)$ is defined by Inserting this into Eq. \ref{eq:R}) )"
 then immediately gives. in which the leading S(O) factor obviously cancels.," then immediately gives, in which the leading ${\cal S} (0)$ factor obviously cancels."
 In the astrophysical environments of most relevance for the present application one can often ignore the derivatives of S(O)., In the astrophysical environments of most relevance for the present application one can often ignore the derivatives of ${\cal S} (0)$.
 We are also mainly concerned with nuclei and environments with Q/KT.1 for which Eq. (51)), We are also mainly concerned with nuclei and environments with $Q/kT^>_\sim 1$ for which Eq. \ref{R for neutron capture}) )
 quickly converges., quickly converges.
 Hence. retaining only the first few terms in the expansion we can write a sufficiently accurate correction as Figure 5. shows the reverse rate correction factor for nonresonant neutron capture as a function of Q/KT.," Hence, retaining only the first few terms in the expansion we can write a sufficiently accurate correction as Figure \ref{fig:R} shows the reverse rate correction factor for nonresonant neutron capture as a function of $Q/kT$ ."
 The solid line is for an exact numerical integration of Eq. (14))., The solid line is for an exact numerical integration of Eq. \ref{eq:R-Formal}) ).
 The dashed line is from the analytic expression given in Eq. (52)), The dashed line is from the analytic expression given in Eq. \ref{nonrescorr}) )
 truncated after the first three terms., truncated after the first three terms.
 The first few terms in Eq. (52)), The first few terms in Eq. \ref{nonrescorr}) )
 are an adequate approximation until Q/KT.:0.2. below which one should include more terms.," are an adequate approximation until $Q/kT ^<_\sim 0.2$, below which one should include more terms."
 Often one encounters charged-particle and neutron-capture reactions in which the thermonuclear reaction rates can be dominated by single (or a few) low-lying resonances., Often one encounters charged-particle and neutron-capture reactions in which the thermonuclear reaction rates can be dominated by single (or a few) low-lying resonances.
 In such cases. 7) in Eq. (14))," In such cases, $\sigma_{12}$ in Eq. \ref{eq:R-Formal}) )"
" is replaced by the Breit-Wigner resonant capture> cross section for each resonance. where A is the de Broglie wavelength. i=ο!+6).)/(g,¢2) includes spin factors of the reaction. while D; is the particle (e.g.. proton or neutron) width. Τ. is the width for gamma decay from the resonant state. and E, is the observed resonance energy."," is replaced by the Breit-Wigner resonant capture cross section for each resonance, where $\lambdabar$ is the de Broglie wavelength, $\omega_r = g_r (1 + \delta_{1 2})/(g_1 g_2)$ includes spin factors of the reaction, while $\Gamma_i$ is the particle (e.g., proton or neutron) width, $\Gamma_\gamma$ is the width for gamma decay from the resonant state, and $E_r$ is the observed resonance energy."
 It is worthwhile to consider the limit in which the total resonance width is small and dominates the reaction rate., It is worthwhile to consider the limit in which the total resonance width is small and dominates the reaction rate.
" In that case. in the limit of Pio,20. we have Inserting this into Eq. (28))"," In that case, in the limit of $\Gamma_{\mbox{\footnotesize tot}} \rightarrow 0$, we have Inserting this into Eq. \ref{eq:rn}) )"
" for r,. the integrals are greatly simplified and reduce to After summing the series. this leads to the final correction factor for a single resonance of where. in the second equation the resonance energy and Q-value are in units of MeV. As in the above cases. this correction factor is only —1% in reactions for which QY/KT~I."," for $r_n$, the integrals are greatly simplified and reduce to After summing the series, this leads to the final correction factor for a single resonance of where, in the second equation the resonance energy and $Q$ -value are in units of MeV. As in the above cases, this correction factor is only $> 1$ in reactions for which $(E_r + Q)/kT \sim 1$ ."
 As an illustration of a resonant reaction. Figure 6. shows the reverse rate correction factor for the resonant reaction Cp. ΙΑΝ (Q=1.944 MeV) as a function of Το.," As an illustration of a resonant reaction, Figure \ref{R-C12pg} shows the reverse rate correction factor for the resonant reaction $^{12}$ $(p,\gamma)^{13}$ N $Q = 1.944$ MeV) as a function of $T_9$."
 The solid line on this plot was generated from Eg. (31)), The solid line on this plot was generated from Eq. \ref{eq:RT9}) )
 using the REACLIB compilation (Cyburtetal.2010) for [Nyfor}(To)] and the reaction Q-value. while the dashed line shows the result from an application of the simple single resonance correction in Eq. (56)).," using the REACLIB compilation \citep{REACLIB} for $[N_A \langle \sigma v\rangle(T_9)]$ and the reaction $Q$ -value, while the dashed line shows the result from an application of the simple single resonance correction in Eq. \ref{R_Resonant}) )."
" Even though this reaction has a second resonance at higher energy. most of the correction factor is accounted for by the single resonance approximation,"," Even though this reaction has a second resonance at higher energy, most of the correction factor is accounted for by the single resonance approximation."
 Having deduced the analytic corrections it is worthwhile to briefly consider some illustrations of the practical applications of the above corrections., Having deduced the analytic corrections it is worthwhile to briefly consider some illustrations of the practical applications of the above corrections.
 From the discussion above it is clear that these correction factors arise as O/AT~|., From the discussion above it is clear that these correction factors arise as $Q/kT \sim 1$.
 For practical applications in astrophysics. this implies 757.1.," For practical applications in astrophysics, this implies $T_9~ ^> _\sim 1$."
 We now consider several astrophysical environments in which these quantum corrections might appear., We now consider several astrophysical environments in which these quantum corrections might appear.
 These include the rapid neutron-capture reactions near the neutron drip line during the r-process. the rapid proton capture near the proton drip line during the rp-process. core or explosive oxygen or silicon burning in massive stars. the 7-process formation of proton-rich nuclei. and the first few moments of cosmic expansion during the epoch of big bang nucleosynthesis.," These include the rapid neutron-capture reactions near the neutron drip line during the $r$ -process, the rapid proton capture near the proton drip line during the $rp$ -process, core or explosive oxygen or silicon burning in massive stars, the $\gamma$ -process formation of proton-rich nuclei, and the first few moments of cosmic expansion during the epoch of big bang nucleosynthesis."
 The r-process involves a sequence of rapid neutron captures in an explosive environment (Burbidgeetal.1957:Mathews&Ward 1985).," The $r$-process involves a sequence of rapid neutron captures in an explosive environment \citep{B2FH,Mathews85}."
. It is responsible for the production of about half of the observed abundances of elements heavier than iron., It is responsible for the production of about half of the observed abundances of elements heavier than iron.
 Although many sites have been proposed for the -process. the neutrino energized wind above the proto-neutron star in core-collapse supernovae remains a favorite (Woosleyetal.1994).," Although many sites have been proposed for the $r$ -process, the neutrino energized wind above the proto-neutron star in core-collapse supernovae remains a favorite \citep{Woosley94}."
. Whatever the environment. however. it can be shown that the solar-system r-process abundances are well reproduced by beta-decay flow in a system that ts in approximate (7.5)= equilibrium.," Whatever the environment, however, it can be shown that the solar-system $r$ -process abundances are well reproduced by beta-decay flow in a system that is in approximate $(n,\gamma) \leftrightarrows (\gamma,n)$ equilibrium."
" Hence. the relative abundances of isotopes of a given element are determined by the revised nuclear Saha equation (24)) where Q, is the neutron-capture Q-value for isotope Z (or equivalently the neutron separation energy for thenucleus M 7) and n(A) represents the abundance of an isotope ''Z."," Hence, the relative abundances of isotopes of a given element are determined by the revised nuclear Saha equation \ref{sahaeq}) ) where $Q_n$ is the neutron-capture $Q$ -value for isotope $^{A}Z$ (or equivalently the neutron separation energy for thenucleus $^{A+1}Z$ ) and $n(A)$ represents the abundance of an isotope $^{A}Z$ ."
 This equation defines a sharp peak in abundances for one (or, This equation defines a sharp peak in abundances for one (or
Tsotopic ratios in the interstellar imedimu (ISM) of starburs (SB) galaxies provide important clues on their uncleo-chemical evolution.,Isotopic ratios in the interstellar medium (ISM) of starburst (SB) galaxies provide important clues on their nucleo-chemical evolution.
" Iu particular. the O/C isotopic ratio is believed to be a good racer of the chemical evolution of the Calaxy (sec c.g, Audouze 1985) This ratio is understood to be a direct 1ieasureimoent of the primary to secondary nuclear processing {~~)."," In particular, the $^{12}$ $^{13}$ C isotopic ratio is believed to be a good tracer of the chemical evolution of the Galaxy (see e.g. Audouze 1985) This ratio is understood to be a direct measurement of the primary to secondary nuclear processing \citep{Wilson1994}."
 While PC Is a ΥΠΑΝ xoduct. of stellar uucleosvuthesis. quickly produced: via Te burning iu massive stars that can be formed iu fist generation imetal-poor stYs. l5 TMSu secondary ποσα product fromt D 12€ seeds DT(2?7)..," While $^{12}$ C is a primary product of stellar nucleosynthesis, quickly produced via He burning in massive stars that can be formed in first generation metal-poor stars, $^{13}$ C is a secondary nuclear product from $^{12}$ C seeds \citep{Meyer1994,Wilson1992,Wilson1994}."
 So fu. only lower limits to the ο120 abuudauce ratios could be determined for some starburst galaxies.," So far, only lower limits to the $\rm ^{12}C/^{13}C$ abundance ratios could be determined for some starburst galaxies."
 A value of ο&[0 seas. derived toward the nuclei of the nearby galaxy NGC 253 based on observations of CN. CS. and TING (7). and further supported by CO. IICN. and UCO! data on M 82 and NGC 1915 (??)..," A value of $\rm ^{12}C/^{13}C\ga40$ was derived toward the nuclei of the nearby galaxy NGC 253 based on observations of CN, CS, and HNC \citep{Henkel1993} and further supported by CO, HCN, and $^+$ data on M 82 and NGC 4945 \citep{Henkel1993a,Henkel1994}."
 Additional CN data ou M 82 aud IC 312 resulted in lower limits to the ratio of >LO and 2230 respectively C2)..., Additional CN data on M 82 and IC 342 resulted in lower limits to the ratio of $>40$ and $>30$ respectively \citep{Henkel1998}.
 The CO aud MCC qmulti-hrausition non-LTE study toward M 82 by (2) excludes 2C ο ratios below 25 and point toward a ratio >50., The CO and $^{13}$ CO multi-transition non-LTE study toward M 82 by \citep{Mao2000} excludes $^{12}$ $^{13}$ C ratios below 25 and point toward a ratio $>50$.
" Apart from these iiultiauolecule studies toward the nearest SD ealaxics. and limited bv seusitivitv. oulv the 1200 /15C0 ratio is available for a stall suuple of nearby sources (222?ον,"," Apart from these multi-molecule studies toward the nearest SB galaxies, and limited by sensitivity, only the $^{12}$ $^{13}$ CO ratio is available for a small sample of nearby sources \citep{Young1986,Sage1991a,Aalto1991,Casoli1992,Paglione2001}."
 Towever. the lines frou the species used so far cau be severely affected by optically depth effects as estimated by ?..," However, the lines from the species used so far can be severely affected by optically depth effects as estimated by \citet{Henkel1993}."
 Thus optically thin species are crucial to derive accurate isotopic ratios., Thus optically thin species are crucial to derive accurate isotopic ratios.
 Etlvuvl (CCID) has the brightest line in the 2 wun spectral scans carried out toward NCC 253 aud M 82 (7.Aladroctal.in prep.).., Ethynyl (CCH) has the brightest line in the 2 mm spectral scans carried out toward NGC 253 and M 82 \citep[][Aladro et al. in prep.]{Mart'in2006a}.
 Its hyperfine structure. uiesolved in these objects. cau iclp to constrain the opacity through the observed lineshape.," Its hyperfine structure, unresolved in these objects, can help to constrain the opacity through the observed lineshape."
 Within the Galaxy. CCID emissiou appears tieltly bound to massive star formation at all evolutionary stages (?)..," Within the Galaxy, CCH emission appears tightly bound to massive star formation at all evolutionary stages \citep{Beuther2008}."
 Tn this paper. we present observations of CCID and two of its PC isotopologues. and provide a more stringent lower limit to the -C/YC isotopic ratio in the nuclear starburst ISAL of AL 82 and NOC 253.," In this paper, we present observations of CCH and two of its $^{13}$ C isotopologues, and provide a more stringent lower limit to the $^{12}$ $^{13}$ C isotopic ratio in the nuclear starburst ISM of M 82 and NGC 253."
 Additionally we present CO obscrvatious in the tO. substitution and the double isotopologue PCHO. The derived O/C ratio from CO. though mot as stringent as that from CCIL supports the idea of larger isotopic ratios in these starbursts than previously determined.," Additionally we present CO observations in the $^{18}$ O substitution and the double isotopologue $^{13}$$^{18}$ O. The derived $^{12}$ $^{13}$ C ratio from CO, though not as stringent as that from CCH, supports the idea of larger isotopic ratios in these starbursts than previously determined."
 We have observed the ./—21 eroup of hyperfiue (hf) transitions of CCIT (171.635 Πε). οΟΠ (170.191 GITz). aud PCC (168.271 GIIZ). andthe J=1.0 transition of 5ο (109.782 GIIZ) and CHO (101711. GIIZ) toward AD 52 aud NGC 253.," We have observed the $J=2-1$ group of hyperfine (hf) transitions of CCH (174.635 GHz), $^{13}$ CH (170.491 GHz), and $^{13}$ CCH (168.274 GHz), and the $J=1-0$ transition of $^{18}$ O (109.782 GHz) and $^{13}$ $^{18}$ O (104.711 GHz) toward M 82 and NGC 253."
 Observations were carried out with the IRAM 3012 telescope (Pico Veleta. Spain).," Observations were carried out with the IRAM 30m telescope (Pico Veleta, Spain)."
" In the case ofM 82. observations were almed toward the north-eastern inolecular lobe at the offset position (1137.|7.5"") from the ceuter (oy20u00OOEFF45129.855999.=605I0 L771)."," In the case of M 82, observations were aimed toward the north-eastern molecular lobe at the offset position $(+13'',+7.5'')$ from the center $\alpha_{J2000}=09^{\rm h}55^{\rm m}51\fs9,\delta_{J2000}=69^\circ40'47\farcs1$ )."
" NGC 253 observations were aimed at the central position (ag2990.=O08LP23323.42999.Oh 17/23/15) for CAO while the 0Ο observations were slightly offset at (137)4"")."," NGC 253 observations were aimed at the central position $\alpha_{J2000}=00^{\rm h}47^{\rm m}33\fs3,\delta_{J2000}=-25^\circ17'23\farcs15$ ) for $^{18}$ O while the $^{13}$ $^{18}$ O observations were slightly offset at $(+3'',-4'')$."
 The beam widths a these frequencies were ~LM and ~23”. for CCIT auc CO ines. respectively.," The beam widths at these frequencies were $\sim14''$ and $\sim23''$, for CCH and CO lines, respectively."
" We used the wobbler switches observing mode with a xvuunetrieal beam throw of 210"" in azimuth aud a wobbling fequency of 0.5 Tz.", We used the wobbler switched observing mode with a symmetrical beam throw of $240''$ in azimuth and a wobbling frequency of 0.5 Hz.
 As spectrometers we used he 256«I1 MIIz filter bauks and WILALA autocorrelator (2 MIIz) for CCII and CO. respectively.," As spectrometers we used the $256\times4$ MHz filter banks and WILMA autocorrelator (2 MHz) for CCH and CO, respectively."
 The CCT data or NGC 253 were extracted from the 2 uu lue survey x7., The CCH data for NGC 253 were extracted from the 2 mm line survey by \citet{Mart'in2006a}.
 Figs, Figs.
 d shows the observed spectra., \ref{fig.CCHandCO} shows the observed spectra.
 The hf structure of CCID is uuresolved., The hf structure of CCH is unresolved.
 We fitted a comb of Gaussian profiles at tlic positions of the hf ines and intensity ratios fixed by their spectroscopic xuneters (7).. shown as vertica LBies in Fie. l..," We fitted a comb of Gaussian profiles at the positions of the hf lines and intensity ratios fixed by their spectroscopic parameters \citep{Muller2001}, shown as vertical lines in Fig. \ref{fig.CCHandCO}."
 Iu M 82. he wing of enission at low velocities in CCID is a coutributiou of both the fainter hf components and the cuuission from the clear region. as also seen in the C50 profile.," In M 82, the wing of emission at low velocities in CCH is a contribution of both the fainter hf components and the emission from the nuclear region, as also seen in the $^{18}$ O profile."
 Though two velocity components could be fit to the CCID profile iu NGC 253 (?).. or the purposes of this paper we jus fit a suele velocity commpoucut.," Though two velocity components could be fit to the CCH profile in NGC 253 \citep{Mart'in2006a}, , for the purposes of this paper we just fit a single velocity component."
 We assuned optically thin cussion to ft the line profiles., We assumed optically thin emission to fit the line profiles.
 We show the resulting fits as ervey lines in Fig d. while, We show the resulting fits as grey lines in Fig \ref{fig.CCHandCO} while
Cataclysimic Variables (CVs) are close binary systems that cousist of an accreting white dwarf (the primary) and a secondary component that usually resembles a miait-seqtence star.,Cataclysmic Variables (CVs) are close binary systems that consist of an accreting white dwarf (the primary) and a secondary component that usually resembles a main-sequence star.
 comprehensively reviews CVs., \citet{warn} comprehensively reviews CVs.
 Dwarf novae. or U Ceminorum stars. are a subclass of CVs that ean be further subclassifiel based on their outburst behavior.," Dwarf novae, or U Geminorum stars, are a subclass of CVs that can be further subclassified based on their outburst behavior."
 The SU Ursae Majoris stars (referred to as UGS) form a subclass ofdwarf uovae that uudereo occasional superoutbursts in addition to normal outbursts., The SU Ursae Majoris stars (referred to as UGSU) form a subclass of dwarf novae that undergo occasional superoutbursts in addition to normal outbursts.
 Superoutbursts occur less frequently than normal outbursts. but are brighter aud last longer.," Superoutbursts occur less frequently than normal outbursts, but are brighter and last longer."
" During a superoutburst. characteristic oscillatious called ""superhuimps? develop in the light curves."," During a superoutburst, characteristic oscillations called “superhumps” develop in the light curves."
" The measured superhump period. £4. is usually a few percent longer than the measured orbital period. 2,4,"" "," The measured superhump period, $P_{\rm sh}$, is usually a few percent longer than the measured orbital period, $P_{\rm orb}$."
"Almost all known SU UMa stars have £4,«2 hr.", Almost all known SU UMa stars have $P_{\rm orb} < 2$ hr.
" The superlitunp period excess. e 2[(P4,—Pos Pa]. is an important quantity for these stars."," The superhump period excess, $\epsilon =$ $P_{\rm
sh}-P_{\rm orb}$ $P_{\rm orb}$ ], is an important quantity for these stars."
 demonstrated that € correlates well with the 1uass ratio g=οΔΙ. which is otherwise difficult to obtain.," \citet{patt01} demonstrated that $\epsilon$ correlates well with the mass ratio $q=M_2/M_1$, which is otherwise difficult to obtain."
"they are not self-consistent, because most of models available in literature use the same local approximation for Comptonization.","they are not self-consistent, because most of models available in literature use the same local approximation for Comptonization."
" Moreover, we amend some conclusions regarding the accuracy of local approximations, derived previously in X10."," Moreover, we amend some conclusions regarding the accuracy of local approximations, derived previously in X10."
" We find the initial solutions using the prescription for the Compton cooling rate in a slab geometry with initial photon energies of 1 eV, given in Dermer et ((1991; hereafter D91)."," We find the initial solutions using the prescription for the Compton cooling rate in a slab geometry with initial photon energies of 1 eV, given in Dermer et (1991; hereafter D91)."
" In X10, we found that it gives a reasonably good approximation for the innermost region."," In X10, we found that it gives a reasonably good approximation for the innermost region."
" For the models considered here, the slab approximation appears to be less accurate, however, our choice of the slab case allows for a direct comparison with previous studies, a number of which used the slab approximation based on D91, or its modification introduced in Esin et ((1996)."," For the models considered here, the slab approximation appears to be less accurate, however, our choice of the slab case allows for a direct comparison with previous studies, a number of which used the slab approximation based on D91, or its modification introduced in Esin et (1996)."
" Figs 1((a,c) and 2((a,c) show the heating and cooling rates in the initial solution."," Figs \ref{fig:rates}( (a,c) and \ref{fig:rates_stel}( (a,c) show the heating and cooling rates in the initial solution."
 Comptonization of synchrotron photons is the most efficient radiative cooling process., Comptonization of synchrotron photons is the most efficient radiative cooling process.
" However, the synchrotron emissivity decreases rapidly beyond its transition radius, r, (~20 for m=0.1 and «100 for m= 0.5)."," However, the synchrotron emissivity decreases rapidly beyond its transition radius, $r_{\rm s}$ $\simeq 20$ for $\dot m=0.1$ and $\simeq 100$ for $\dot
m=0.5$ )."
" Then, in the local model, the radiative cooling at r>r, is dominated by the (much weaker) bremsstrahlung and its Comptonization."," Then, in the local model, the radiative cooling at $r>r_{\rm s}$ is dominated by the (much weaker) bremsstrahlung and its Comptonization."
" Then, two regions can be distinguished in terms of the energy equation (ions are always advection dominated). ("," Then, two regions can be distinguished in terms of the energy equation (ions are always advection dominated). ("
"1) At r>r,, the flow is adiabatically compressed,which is reflected in the increase of T, with decreasing r (see Figs lee and 2ee); both the radiative cooling and the Coulomb heating are much weaker than the advective terms. (","i) At $r>r_{\rm s}$, the flow is adiabatically compressed,which is reflected in the increase of $T_{\rm e}$ with decreasing $r$ (see Figs \ref{fig:rates}e e and \ref{fig:rates_stel}e e); both the radiative cooling and the Coulomb heating are much weaker than the advective terms. ("
"ii) At r<rs, the radiative cooling becomes efficient and Τε decreases; the Coulomb heating is more efficient in this region and it exceeds the compression work in the innermost part (except for the model with a=0 and m= 0.1).","ii) At $r<r_{\rm s}$, the radiative cooling becomes efficient and $T_{\rm e}$ decreases; the Coulomb heating is more efficient in this region and it exceeds the compression work in the innermost part (except for the model with $a=0$ and $\dot m =
0.1$ )."
" In this region, the advection of the internal energy contributes also to the heating of electrons, however, this effect is rather weak."," In this region, the advection of the internal energy contributes also to the heating of electrons, however, this effect is rather weak."
" The solid curves in Figs 1((a,c) and 2((a,c) show the GR global Compton cooling rate obtained in our initial MC simulations, wwith the Τε satisfying the energy equation (3)) with the Compton cooling rate, Ocomptloc, given by the local slab (D91) prescription."," The solid curves in Figs \ref{fig:rates}( (a,c) and \ref{fig:rates_stel}( (a,c) show the GR global Compton cooling rate obtained in our initial MC simulations, with the $T_{\rm e}$ satisfying the energy equation \ref{eq:energy}) ) with the Compton cooling rate, $Q_{\rm Compt,loc}$, given by the local slab (D91) prescription."
" As we can see, there are significant deviations between the local (dotted curves) and global cooling rates, resulting from several effects."," As we can see, there are significant deviations between the local (dotted curves) and global cooling rates, resulting from several effects."
 Two of these effects should be generic to models of black-hole flows regardless of specific values of parameters of the flow., Two of these effects should be generic to models of black-hole flows regardless of specific values of parameters of the flow.
" First, the input of seed photons from the inner region strongly enhances the Compton cooling beyond r,."," First, the input of seed photons from the inner region strongly enhances the Compton cooling beyond $r_{\rm s}$ ."
 The second one involves the presence of the event horizon (neglected in the local, The second one involves the presence of the event horizon (neglected in the local
llgh-energv gamma-ray astronomy has progressed drastically after the launch of the Fermi Camma-ray Space Telescope. (F,High-energy gamma-ray astronomy has progressed drastically after the launch of the Fermi Gamma-ray Space Telescope ).
ermi) lis Large Area ‘Telescope (LAT) is currently observing the entire eanima-ray sky in the 0.02 300 GeV energy range (2).., Its Large Area Telescope (LAT) is currently observing the entire gamma-ray sky in the 0.02 – 300 GeV energy range \citep{atw09}.
 Phe majority of extragalactic sources detected. Ὃν are blazars. a subclass of active galactic nucle: (Αλ) dominated by broadband. nonthermal emission arising from relativistic jets oriented close to our line of sight (????)," The majority of extragalactic sources detected by are blazars, a subclass of active galactic nuclei (AGNs) dominated by broadband, nonthermal emission arising from relativistic jets oriented close to our line of sight \citep{abd09a,abd09b,abd10_catalog,abd10}."
 The 11 month catalog reports the detection of 600 blazars up to 2~3 at Galactic latitudes |b]7 107(?).., The 11 month catalog reports the detection of $\sim600$ blazars up to $z\sim3$ at Galactic latitudes $|b|>10^\circ$ \citep{abd10}.
 Ht is expected that.Fermi will detect. more than 1000 blazars in the near future (e.g.222)," It is expected that will detect more than 1000 blazars in the near future \citep[e.g.][]{nar06,der07,it09}."
 Before theFermi era. the Enereetic Gamma-lItay Experiment Telescope. (EGRET) on board the Compton Gamma Rav Observatory detected ~50 blazars in total up to 2~ 307)1.," Before the era, the Energetic Gamma-Ray Experiment Telescope (EGRET) on board the Compton Gamma Ray Observatory detected $\sim$ 50 blazars in total up to $z\sim3$ \citep{har99} ."
 On the other hand. by analyzing the Swiff/BAT blazar sample in the redshift range z— 0.08 4.0. 7. have recently suggested. that the density evolution of luminous blazars peak at z=4.3.," On the other hand, by analyzing the /BAT blazar sample in the redshift range $z=$ 0.03 – 4.0, \citet{aje09} have recently suggested that the density evolution of luminous blazars peak at $z= 4.3$."
 Since has an order of magnitude better sensitivity ancl positional accuracy at high Galactic latitudes compared to EGRET (οι. it is naturally expected thatFermi will see much deeper into the universe in πα.," Since has an order of magnitude better sensitivity and positional accuracy at high Galactic latitudes compared to EGRET \citep{atw09}, it is naturally expected that will see much deeper into the universe in gamma-rays."
 The purpose of this paper is to discuss expectations for the highest redshift’ blazars that may discover., The purpose of this paper is to discuss expectations for the highest redshift blazars that may discover.
 This requires reasonable knowledge of their ganima-ray luminosity function. (GLE)., This requires reasonable knowledge of their gamma-ray luminosity function (GLF).
 The blazar GLE has been discussed. from. different: perspectives in many papers so [ar (222? 7.," The blazar GLF has been discussed from different perspectives in many papers so far \citep{pad93,ste93,sal94,chi95,ste96,chi98,muc00,nar06,der07,it09}."
hereafter.[POO ancl 2.hereafterEEMIO have recently developed a new model of the blazar GLE that accounts for the blazar spectral sequence. as well as Iuminositv-dependent density evolution implied from. the AGN X-ray luminosity function. (NLP). and which is consistent with the ΓΙΟΤΕ and current data (sce £2)).," \citet[hereafter IT09]{it09} and \citet[][hereafter ITM10]{itm10} have recently developed a new model of the blazar GLF that accounts for the blazar spectral sequence, as well as luminosity-dependent density evolution implied from the AGN X-ray luminosity function (XLF), and which is consistent with the EGRET and current data (see \ref{sec:glf}) )."
 However. the PPAILO GLE is uncertain for z 3. because the current observed number of N-ray ACGNs and gamma-ray blazars above 2~3 is insullicient to strongly constrain the model.," However, the ITM10 GLF is uncertain for $z>3$ , because the current observed number of X-ray AGNs and gamma-ray blazars above $z\sim3$ is insufficient to strongly constrain the model."
 On the other hand. the optical luminosity function (OLE) of AGNs has been well," On the other hand, the optical luminosity function (OLF) of AGNs has been well"
infinite convolutious of Bernoulli measures. for which deteruuming the continuity type of a specific mcasure Whose parameter does not beloug to a known countable set of values is still an open problem.,"infinite convolutions of Bernoulli measures, for which determining the continuity type of a specific measure whose parameter does not belong to a known countable set of values is still an open problem."
"To parameterize this relationship the sample iu Figure 2 was fitted with a two-part function of the form where the parameters Ayo. Roos, aud (the Nav Iuniuositv ratio aud Rosshy uuuber at saturation. aud the power-law index) were varied to fud the best fit usine υπο technique.","To parameterize this relationship the sample in Figure \ref{allstars} was fitted with a two-part function of the form where the parameters $R_{X sat}$, $Ro_{sat}$, and $\beta$ (the X-ray luminosity ratio and Rossby number at saturation, and the power-law index) were varied to find the best fit using a $\chi^2$ -minimization technique."
 Uucertaintices on these quantities were then determined using a bootstrapping approach. iterating LOOO times and finding the standard deviation of cach parameter.," Uncertainties on these quantities were then determined using a bootstrapping approach, iterating 1000 times and finding the standard deviation of each parameter."
" The paramcters Z2y, ad Rose Will be discussed in more detail iu Section 23.2. aud were found to be Ίου yi;δι50.08 and Ro,= for the hbest-fitting model. which has an xis scatter of ~0.3 dex in Ray."," The parameters $R_{X sat}$ and $Ro_{sat}$ will be discussed in more detail in Section \ref{s-sat} and were found to be log $R_{X sat} = -3.13 \pm 0.08$ and $Ro_{sat} = 0.13 \pm 0.02$ for the best-fitting model, which has an rms scatter of $\sim$ 0.3 dex in $R_X$."
 The best-fitting slope to the unsaturated regime was found to be o= 2.]8c0.16. slightly steeper than the canonical value of.=2.," The best-fitting slope to the unsaturated regime was found to be $\beta = -2.18 \pm 0.16$, slightly steeper than the canonical value of $\beta \simeq -2$."
 This fit. as shown in Fieure 2.. over-predicts the Suus mean N-vav liunosity bv a factor of 2-3.," This fit, as shown in Figure \ref{allstars}, over-predicts the Sun's mean X-ray luminosity by a factor of 2-3."
 Au alternative approach is to fit the slope of the unsaturated reelme aud the saturation level separately., An alternative approach is to fit the slope of the unsaturated regime and the saturation level separately.
 We fitted a simple power law of the form logRy=logeC|JlogRe to all stars with Ro>0.2 using the different types of linear regression fits iu ?)..," We fitted a simple power law of the form $\mathrm{log} \, R_X = \mathrm{log} \, C + \beta \, \mathrm{log} \, Ro$ to all stars with $Ro \geq 0.2$ using the different types of linear regression fits in \citet{isob90}."
 We find a good aerecinent between the slopes derived from these different fits. sugeesting that the fits are all fairly linear in the log Ry log Ro plane.," We find a good agreement between the slopes derived from these different fits, suggesting that the fits are all fairly linear in the log $R_X$ – log $Ro$ plane."
 We favor the Ordinary Least Squares (OLS) bisector since the objective of the fit is to estimate the underlving functional relation between the variables. as reconuneuded by 7).. ancl this method also factors in the scatter of the line iu both variables.," We favor the Ordinary Least Squares (OLS) bisector since the objective of the fit is to estimate the underlying functional relation between the variables, as recommended by \citet{isob90}, and this method also factors in the scatter of the line in both variables."
 The fit gives a slope of ο=2.5540.15 (valid in the range 0.2<Ro<3. 0r 3.75>loe(Lyων 6.3). sienificautly steeper than both the canonical value aud that fouud from our two-part fit.," The fit gives a slope of $\beta = -2.55 \pm 0.15$ (valid in the range $0.2 < Ro < 3$, or $-3.75 > \mathrm{log} (L_X / L_{bol}) > -6.3$ ), significantly steeper than both the canonical value and that found from our two-part fit."
 7?)— fit a los-linear function to the RyRo distribution. with the goal of cinpirically deriving a correlation that would allow age estimates to be derived from X-ray. Iuninosities (via rotation periods).," \citet{mama08} fit a log-linear function to the $R_X - Ro$ distribution, with the goal of empirically deriving a correlation that would allow age estimates to be derived from X-ray luminosities (via rotation periods)."
 Thei fit docs not connect with the level of saturated N-rav cussion for very fast rotators but. as they note. it offers a good fit to many of the slow rotators such as the Sun.," Their fit does not connect with the level of saturated X-ray emission for very fast rotators but, as they note, it offers a good fit to many of the slow rotators such as the Sun."
 The sample used here suffers from à umuber of biases due to the selection of only sources with measured) N-ray fluxes and photometric rotation periods., The sample used here suffers from a number of biases due to the selection of only sources with measured X-ray fluxes and photometric rotation periods.
 While the biases stemming frou the detectabilitv of rotation periods are nivriad and complex. the bhunuinositv bias induced by ouly using sources with measured X-ray fluxes is clear.," While the biases stemming from the detectability of rotation periods are myriad and complex, the luminosity bias induced by only using sources with measured X-ray fluxes is clear."
 This bias will be most prominent in the unsaturated regine where X-ray luuinosity ratios may reach as low as ~10© ox lower., This bias will be most prominent in the unsaturated regime where X-ray luminosity ratios may reach as low as $\sim 10^{-7}$ or lower.
 This sample could therefore be uissine sole of the faintest sources at a given Rossby umber. possibly resulting in a larger spread in the RyRo diagram than is currently observed.," This sample could therefore be missing some of the faintest sources at a given Rossby number, possibly resulting in a larger spread in the $R_X - Ro$ diagram than is currently observed."
 Such a spread could casily be incuced by the increased auplitude of stellar coronal cvcles that has been suggested to occur as stars age (oe.2)., Such a spread could easily be induced by the increased amplitude of stellar coronal cycles that has been suggested to occur as stars age \citep[e.g.][]{mice03}.
 At the lareest Rossby uuubers it is likely that many of the faintest N-rav sources are not detected. inducing a strong bias in our sample that will affect the fits derived here.," At the largest Rossby numbers it is likely that many of the faintest X-ray sources are not detected, inducing a strong bias in our sample that will affect the fits derived here."
 To overcome the biases in our large sample we have iteiipted to compile from within our sample a smaller. N-rav unbiased sample that covers a large range in N-rav huninosity ratios and rotation periods.," To overcome the biases in our large sample we have attempted to compile from within our sample a smaller, X-ray unbiased sample that covers a large range in X-ray luminosity ratios and rotation periods."
 For this we use the list of 36 Mt. Wilson stars with rotation periods from the study by ο). all of which were detected bv ROSAT and therefore do not suffer from N-rav Inuiünositv biases.," For this we use the list of 36 Mt. Wilson stars with rotation periods from the study by \citet{dona96}, all of which were detected by ROSAT and therefore do not suffer from X-ray luminosity biases."
" These 36 stars are the subsample of their eutire sample of 1060 observed stars with nieasurable rotation periods over five or nio| seasons,", These 36 stars are the subsample of their entire sample of 100 observed stars with measurable rotation periods over five or more seasons.
 The authors discuss a number of possible biases m their sample resulting from effects such as active 1lon erowth aud decay. iuultiple active reeglons. aud latitudinal baucds.," The authors discuss a number of possible biases in their sample resulting from effects such as active region growth and decay, multiple active regions, and latitudinal bands."
 Thev couclude that the resulting biases affect only AP. not the period itself. and are either sanall or act to reduce the measured value of AP.," They conclude that the resulting biases affect only $\Delta P$ , not the period itself, and are either small or act to reduce the measured value of $\Delta P$."
 Therefore we believe tha this sample of 36Pa stars with measured rotation periods and aud X-ray dDundnosities is free from the majority of biases., Therefore we believe that this sample of 36 stars with measured rotation periods and and X-ray luminosities is free from the majority of biases.
 These stars were| jucluded in our sample as part of the compilations of 7) and 7).. and in Figure 3) woe show their distributio rin the Ry Ro diagram. all of which fall in the unsaturated regime of corona CLUISSIOL.," These stars were included in our sample as part of the compilations of \citet{pizz03} and \citet{mama08}, and in Figure \ref{unbiased} we show their distribution in the $R_X$ $Ro$ diagram, all of which fall in the unsaturated regime of coronal emission."
 We fitted a siuple single-part power law of the form. logRy=€|dlogRo to these points. using au OLS bisector (?).. though the slopes derived from all the different fitting ucthods are in good agreement.," We fitted a simple single-part power law of the form $\mathrm{log} \, R_X = \mathrm{log} \, C + \beta \, \mathrm{log} \, Ro$ to these points, using an OLS bisector \citep{isob90}, though the slopes derived from all the different fitting methods are in good agreement."
 The fit eives a slope of >=270+0.13 (valid iu the raneeO38<Ro<3. ¢Y l1log(Ly/Lig)ο 6.3). steeper than that fore from our lavecr sample. in aerecuicut with our predictions of the uncertainties iuduced by the biases of that sample.," The fit gives a slope of $\beta = -2.70 \pm 0.13$ (valid in the range$0.3 < Ro < 3$, or $-4 > \mathrm{log} (L_X / L_{bol}) > -6.3$ ), steeper than that found from our larger sample, in agreement with our predictions of the uncertainties induced by the biases of that sample."
 This slope is even steeper than the canonical value of >=—2 as well as the slope found bv ?) o fos 1940.5. though their use of projected rotational velocitics instead of rotation periods represents a differcutrelationship than that fitted here.," This slope is even steeper than the canonical value of $\beta = -2$ as well as the slope found by \citet{pall81} of $\beta = -1.9 \pm 0.5$ , though their use of projected rotational velocities instead of rotation periods represents a differentrelationship than that fitted here."
of the order of the BH mass once the BH returns to the centre.,of the order of the BH mass once the BH returns to the centre.
" Moreover, we find that the stars in the galactic disc are also perturbed by the orbiting BH, but there is no clear systematic trend with the radial distance from the centre as a function of time."," Moreover, we find that the stars in the galactic disc are also perturbed by the orbiting BH, but there is no clear systematic trend with the radial distance from the centre as a function of time."
" Interestingly, however, the high density gas in the wake of the BH follows the BH all the way to the centre, creating a large density enhancement."," Interestingly, however, the high density gas in the wake of the BH follows the BH all the way to the centre, creating a large density enhancement."
" In the right-hand panels of Figure 7,, we show density profiles for the case where BH accretion and feedback have been switched-on."," In the right-hand panels of Figure \ref{bulgeprop}, we show density profiles for the case where BH accretion and feedback have been switched-on."
" Here, as discussed above, the BH does not return to the centre, but instead describes a loop-like orbit, counter-rotating with respect to the disc."," Here, as discussed above, the BH does not return to the centre, but instead describes a loop-like orbit, counter-rotating with respect to the disc."
" The BH spends considerable amount of time away from the central regions, as indicated by the coloured symbols, and transfers kinetic energy to the stars which are not in the centre."," The BH spends considerable amount of time away from the central regions, as indicated by the coloured symbols, and transfers kinetic energy to the stars which are not in the centre."
 This causes a clear dip in the density of stars in the bulge for 0.5—3h!kpc (see bottom panel).," This causes a clear dip in the density of stars in the bulge for $0.5-3\,h^{-1} \, {\rm kpc}$ (see bottom panel)."
" Stars which are scattered-away from this region create density enhancements on both sides, towards the centre and away from it."," Stars which are scattered-away from this region create density enhancements on both sides, towards the centre and away from it."
" Thus, instead of a mass deficit the bulge mass within 1A!kpc is increased by ~0.7Mpu."," Thus, instead of a mass deficit the bulge mass within $1\,h^{-1} \, {\rm kpc}$ is increased by $\sim 0.7 \times M_{\rm
 BH}$."
 In this case there is also a systematic reduction of the xdensity of stars in the galactic disc in the region of the disc where the BH spends considerable amount of time (pink symbols)., In this case there is also a systematic reduction of the density of stars in the galactic disc in the region of the disc where the BH spends considerable amount of time (pink symbols).
" The bulge density declines more steeply than the disc density, and thus for radii >1A!kpc the BH is more likely to transfer its kinetic energy to the stars in the disc."," The bulge density declines more steeply than the disc density, and thus for radii $\ge 1\,h^{-1} \, {\rm kpc}$ the BH is more likely to transfer its kinetic energy to the stars in the disc."
" Additionally, due to the BH feedback in this region a ring of hot, low density gas creates a local perturbation in the gravitational potential, which is felt by the stars in the disc."," Additionally, due to the BH feedback in this region a ring of hot, low density gas creates a local perturbation in the gravitational potential, which is felt by the stars in the disc."
 A dip in the density distribution of the disc stars is formed., A dip in the density distribution of the disc stars is formed.
" While we have seen that the recoiling BH which returns to the centre (left-hand panels of Figure 7)) leads to a moderate mass deficit of the bulge, of the order of the BH mass, in some cases the mass deficit can be substantially bigger."," While we have seen that the recoiling BH which returns to the centre (left-hand panels of Figure \ref{bulgeprop}) ) leads to a moderate mass deficit of the bulge, of the order of the BH mass, in some cases the mass deficit can be substantially bigger."
" In the simulation where the BH is recoiled perpendicular to the galactic disc, and passes many more times close to the galactic centre, the mass deficit becomes of the order of ~3.5xΜηη when the BH finally returns to the centre."," In the simulation where the BH is recoiled perpendicular to the galactic disc, and passes many more times close to the galactic centre, the mass deficit becomes of the order of $\sim 3.5 \times
M_{\rm BH}$ when the BH finally returns to the centre."
" At present the spatial distribution of stars and gas in high redshift galaxies are still rather uncertain, yet this is the regime where BH mergers and thus gravitational recoils should be most frequent."," At present the spatial distribution of stars and gas in high redshift galaxies are still rather uncertain, yet this is the regime where BH mergers and thus gravitational recoils should be most frequent."
" Recent observational studies suggest that there is a significant population of high redshift galaxies that have gas-rich, thick and clumpy discs (?,andreferences therein)."," Recent observational studies suggest that there is a significant population of high redshift galaxies that have gas-rich, thick and clumpy discs \citep[][and references
 therein]{Forster2009}."
" To numerically explore this scenario, we now discuss cases where the galactic disc is very clumpy instead of stable and quasi-stationary."," To numerically explore this scenario, we now discuss cases where the galactic disc is very clumpy instead of stable and quasi-stationary."
" Even though in the model we consider the total galaxy mass and virial radius are the same, the clumpy disc has a deeper central potential with a central escape velocity Όρος~1980kms!6.6voo, as a result of more efficient radiative cooling in the innermost regions."," Even though in the model we consider the total galaxy mass and virial radius are the same, the clumpy disc has a deeper central potential with a central escape velocity $v_{\rm esc} \sim 1980\, {\rm km\, s^{-1}}
\sim 6.6\,v_{\rm 200}$, as a result of more efficient radiative cooling in the innermost regions."
" While in the case of a smooth disc a BH with kick velocity >0.3vese can leave the innermost regions, here a larger kick velocity of >0.5vese is needed to displace the BH from the central region at all."," While in the case of a smooth disc a BH with kick velocity $\ge 0.3\, v_{\rm esc}$ can leave the innermost regions, here a larger kick velocity of $ > 0.5\, v_{\rm esc}$ is needed to displace the BH from the central region at all."
" Also, the maximum distance reached at the first apocentre is affected by the structure of the gaseous disc: if the disc is relatively smooth, a BH recoiled with ~0.5vesc reaches ~4.6h!kpc, while if the disc is clumpy a BH with initial kick velocity of ~0.8ves does not reach a distance farther than 3h~'kpc from the centre."," Also, the maximum distance reached at the first apocentre is affected by the structure of the gaseous disc: if the disc is relatively smooth, a BH recoiled with $ \sim 0.5\, v_{\rm esc}$ reaches $\sim 4.6 \,h^{-1} \, {\rm kpc}$, while if the disc is clumpy a BH with initial kick velocity of $ \sim 0.8\, v_{\rm esc}$ does not reach a distance farther than $3\,h^{-1} \, {\rm kpc}$ from the centre."
" To the extent that clumpy discs are accompanied by elevated deposition rates of baryons in the centre, as it happens in our simulation, BHs are more likely to stay in the centre, or leave only for brief periods of time, when they experience merger kicks."," To the extent that clumpy discs are accompanied by elevated deposition rates of baryons in the centre, as it happens in our simulation, BHs are more likely to stay in the centre, or leave only for brief periods of time, when they experience merger kicks."
 This may contribute to explain the very scarce observational evidence for off-centred quasars (?).., This may contribute to explain the very scarce observational evidence for off-centred quasars \citep{Bonning2007}.
 An example of a gravitationally recoiled BH with Ukick=1600kms! (c0.8 vesc) in the plane of the clumpy disc is shown in Figure 8..," An example of a gravitationally recoiled BH with $v_{\rm kick} = 1600 \,{\rm
 km\,s^{-1}}$ $ \sim 0.8\, v_{\rm esc}$ ) in the plane of the clumpy disc is shown in Figure \ref{isogal_eos0.05}."
" The BH orbit (denoted with a white line) is plotted on top of the projected density map, where the clumpy nature of the disc can be clearly seen."," The BH orbit (denoted with a white line) is plotted on top of the projected density map, where the clumpy nature of the disc can be clearly seen."
" Regardless of gas accretion and feedback processes, the BH returns to the minimum of the potential in 3x10? yrs."," Regardless of gas accretion and feedback processes, the BH returns to the minimum of the potential in $3 \times 10^8\,$ yrs."
" 'The BH trajectory is completely contained in the disc, with ||<100!pc, and soon after reaching the first apocentre the BH starts co-rotating with the galactic disc."," The BH trajectory is completely contained in the disc, with $|z| < 100 \,h^{-1} \,
{\rm pc}$, and soon after reaching the first apocentre the BH starts co-rotating with the galactic disc."
" During its orbit through the clumpy disc, the BH accretes a relatively small amount of gas."," During its orbit through the clumpy disc, the BH accretes a relatively small amount of gas."
" By the time the BH returns to the centre, the BH mass has increased by ~3.6x10*h!Ms."," By the time the BH returns to the centre, the BH mass has increased by $\sim 3.6 \times 10^7 \,h^{-1}{\rm
 M}_\odot$."
" Most of the mass gain happens when the BH is on its way back to the innermost regions, passing through a dense central lump of gas."," Most of the mass gain happens when the BH is on its way back to the innermost regions, passing through a dense central lump of gas."
" The bolometric luminosity of the BH moving through a clumpy disc is on average lower than that of the BH passing though a more uniform gas distribution: in fact, the bolometric luminosity is reduced by at least one order of magnitude with respect to the values shown in Figure 6.."," The bolometric luminosity of the BH moving through a clumpy disc is on average lower than that of the BH passing though a more uniform gas distribution: in fact, the bolometric luminosity is reduced by at least one order of magnitude with respect to the values shown in Figure \ref{mbh_iso}."
" During most of the 3x105 yrs while displaced from the centre, the BH should be in the radiatively inefficient accretion regime with only a few brief bursts of typical duration «10"" yrs when passing through a dense gas lump."," During most of the $3 \times 10^8\,$ yrs while displaced from the centre, the BH should be in the radiatively inefficient accretion regime with only a few brief bursts of typical duration $< 10^7\,$ yrs when passing through a dense gas lump."
mmap).,map).
 For comparison. the dwarf irregular galaxy 2009 has a very extended desk (Warren et al.," For comparison, the dwarf irregular galaxy ESO215-G?009 has a very extended disk (Warren et al."
 2004) but no signs of significant. star formation in the outer disk: its ccolumn density reaches above 1075 atoms > in only a few locations., 2004) but no signs of significant star formation in the outer disk; its column density reaches above $10^{21}$ atoms $^{-2}$ in only a few locations.
" Deep GALEN images of nearby. galaxies show that the UV profiles of many spiral galaxies extend bevond their - or Bo, optical radius (Vhilker et al.", Deep GALEX images of nearby galaxies show that the $UV$ profiles of many spiral galaxies extend beyond their - or $B_{\rm 25}$ optical radius (Thilker et al.
 2005: Gil de Paz ct al., 2005; Gil de Paz et al.
 2005. 2007b).," 2005, 2007b)."
 In fact. Zaritsky Christlein (2007) suggest that IXCV -disks exist in 730 of the local spiral galaxy population.," In fact, Zaritsky Christlein (2007) suggest that $XUV$ -disks exist in $\sim$ of the local spiral galaxy population."
 We contend that these spectacular (XCY-disks must be located within even larger eenvelopes. here called: 2. deisks. which provide the fuel for continued star formation.," We contend that these spectacular $XUV$ -disks must be located within even larger envelopes, here called $2X$ disks, which provide the fuel for continued star formation."
 Ultimatelv. it may just be a question of sensitivity that limits our observations of the outer edges of stellar ancl gaseous disks.," Ultimately, it may just be a question of sensitivity that limits our observations of the outer edges of stellar and gaseous disks."
 We note that Irwin et al. (, We note that Irwin et al. (
2009) detect σσας out to column clensities of 310i atoms cm (assuming. the gas fills⋅ the bbeani),2009) detect gas out to column densities of $3 \times 10^{17}$ atoms $^{-2}$ (assuming the gas fills the beam).
 We use the GALEN £FUV. and NOV images to estimate the ages of the CY -rieh star elusters in the NGC 1512/1510 system., We use the GALEX $FUV$ and $NUV$ images to estimate the ages of the $UV$ -rich star clusters in the NGC 1512/1510 system.
 ‘This is done by integrating the counts per second (CDS) in ~200 selected regions (> 100 aresec?. average size = 320 aresec?) using the same polygon for. both images and applving m=2.5log(CPS)|ay (Morrissey et al.," This is done by integrating the counts per second (CPS) in $\sim$ 200 selected regions $>$ 100 $^2$, average size = 320 $^2$ ) using the same polygon for both images and applying $m_{\lambda} = -2.5\log (CPS) + a_{\lambda}$ (Morrissey et al."
 2005). where αν = 18.82 mag and eviv = 20.08 mag (all magnitudes are expressed in the AB system)," 2005), where $a_{FUV}$ = 18.82 mag and $a_{NUV}$ = 20.08 mag (all magnitudes are expressed in the AB system)."
 We did. not correct for extinction which is negligible when computing the REVNCM color: ApeyOLEIBV)— 0.0011.," We did not correct for extinction which is negligible when computing the $FUV-NUV$ color: $A_{\rm FUV}-A_{\rm NUV} = 
-0.1~E(B-V) = -0.0011$ ."
 Figure 13 shows the spatial distribution and color of the analysed star clusters., Figure 13 shows the spatial distribution and color of the analysed star clusters.
 We use dillerent symbols to identify live distinct areas within the svstem: the ring. the internal arm. the bridge to NGC 1510. the western debris and Arm 1 (sce Fig.," We use different symbols to identify five distinct areas within the system: the ring, the internal arm, the bridge to NGC 1510, the western debris and Arm 1 (see Fig."
 1)., 1).
 The FUVNEV colors (blue to red) range [rom 0.06 (voungest stellar population) at the southern end. of the bridge to |0.68 (oldest stellar population) for the farthest cluster in the NW region., The $FUV-NUV$ colors (blue to red) range from –0.06 (youngest stellar population) at the southern end of the bridge to +0.68 (oldest stellar population) for the farthest cluster in the NW region.
 Uncertainties in the color estimates strongly depend on the brightness of the star clusters (70.06 for the brightest and ~0.50 for the weakest objects)., Uncertainties in the color estimates strongly depend on the brightness of the star clusters $\sim$ 0.06 for the brightest and $\sim$ 0.50 for the weakest objects).
 For the analysed clusters in the NGC 1512/1510 system we adopt an uncertainty of —0.20., For the analysed clusters in the NGC 1512/1510 system we adopt an uncertainty of $\pm$ 0.20.
 As extinction is negligible when computing the £V.NEV colors (see above). higher values correspond to older ages For the last star-forming burst hosted by the CY -rich clusters.," As extinction is negligible when computing the $FUV-NUV$ colors (see above), higher values correspond to older ages for the last star-forming burst hosted by the $UV$ -rich clusters."
 We have used the same procedure as. described in Bianchi ct al. (, We have used the same procedure as described in Bianchi et al. (
2005) and LHibbard et al. (,2005) and Hibbard et al. (
2005) to estimate the age of the last star-forming event. assuming an instantaneous burst. and evolutionary synthesis moclels provided by Bruzual Charlot (2003).,"2005) to estimate the age of the last star-forming event, assuming an instantaneous burst, and evolutionary synthesis models provided by Bruzual Charlot (2003)."
 Fable 4. lists the results obtained for distinct areas., Table \ref{tab:galex} lists the results obtained for distinct areas.
 While the CV. colors suggest that the average stellar population in the core of NGC 1512 (red circle) is about twice as old as that of NGC 1510 (ereen circle). the high comission in both galaxies also indicates significant recent star formation.," While the $UV$ colors suggest that the average stellar population in the core of NGC 1512 (red circle) is about twice as old as that of NGC 1510 (green circle), the high emission in both galaxies also indicates significant recent star formation."
 We conclude that NGC 1512 and NGC 1510 contain both a voung stellar population and an older. more evolved stellar population.," We conclude that NGC 1512 and NGC 1510 contain both a young stellar population and an older, more evolved stellar population."
 As shown in Fig., As shown in Fig.
 13. there are definite color gradients along the spiral arms and other regions within the NGC 1512/1510 system.," 13, there are definite color gradients along the spiral arms and other regions within the NGC 1512/1510 system."
 For example. while regions within the inner star-forming ring of NGC 1512 generally. have similar colors. (ν΄NOVying=0.28£0.06 (age NO Myr). slightly vounger ages are found towards both ends of the bar. Le. at the start of the inner arms.," For example, while regions within the inner star-forming ring of NGC 1512 generally have similar colors, $(FUV-NUV)_{\rm ring} = 0.28 \pm 0.06$ (age $\sim$ 180 Myr), slightly younger ages are found towards both ends of the bar, i.e. at the start of the inner arms."
 Regions located within the bridge between NCC 1512 and NGC 1510 are On average even vounger. (£UMVNUMJudae0.2140.12 (age ~120 Myr). with ages of ~10 Myr. (the voungest regions in the whole svstem) near NGC 1512. and ~270 Myr near NGC 1510.," Regions located within the bridge between NGC 1512 and NGC 1510 are – on average – even younger, $(FUV-NUV)_{\rm bridge} = 0.21 \pm 0.12$ (age $\sim$ 120 Myr), with ages of $\sim$ 10 Myr (the youngest regions in the whole system) near NGC 1512, and $\sim$ 270 Myr near NGC 1510."
 As shown in Fig., As shown in Fig.
 12. CV- bright regions close to NGC 1512 coincide well with the ccolumn density maxima: their voung clerived age is consistent with the cemission found in these knots.," 12, $UV$ -bright regions close to NGC 1512 coincide well with the column density maxima; their young derived age is consistent with the emission found in these knots."
 A CY -color gradient is also observed. along the prominent eastern arm (Arm 1)., A $UV$ -color gradient is also observed along the prominent eastern arm (Arm 1).
 In the eastern-most regions. which also show some eenmission. we measure £1.NEV colors around. 0.05 (age 10. Myr).," In the eastern-most regions, which also show some emission, we measure $FUV-NUV$ colors around –0.05 (age $\sim$ 10 Myr)."
 As the arm curves towards the south. the CY -rieh elusters appear to get older. reaching £'UVNEVον0.66 (age —380 Myr) within the two streams of the Ooutermost regions.," As the arm curves towards the south, the $UV$ -rich clusters appear to get older, reaching $FUV-NUV \sim 0.66$ (age $\sim$ 380 Myr) within the two streams of the outermost regions."
 Within the debris in the NW area. stellar clusters near NGC 1510 tend to have vounger ages (FLUVNUM.—0.2. 0.3. ages of LOO200 Myr) than those located towards the north of NGC 1512 (REVNEV—0.5.0.7. ages of 300400 Myr).," Within the debris in the NW area, stellar clusters near NGC 1510 tend to have younger ages $FUV-NUV \sim 0.2-0.3$ , ages of 100–200 Myr) than those located towards the north of NGC 1512 $FUV-NUV \sim 0.5-0.7$, ages of 300–400 Myr)."
 The broadening of the sspiral arm at the position of the NW debris suggests that something has dispersed both the neutral gas and the stellar component in this region., The broadening of the spiral arm at the position of the NW debris suggests that something has dispersed both the neutral gas and the stellar component in this region.
 The age gradient found. in the stellar clusters indicates that it. probably. is due to the gravitational interaction with the BCD ealaxy NGC 1510., The age gradient found in the stellar clusters indicates that it probably is due to the gravitational interaction with the BCD galaxy NGC 1510.
 The overall gas distribution together with the star formation history of the svstem provides some hints as to the eravitational interaction between the large spiral NGC 1512 and the BCD galaxy NGC 1510 and. its effects. on the, The overall gas distribution together with the star formation history of the system provides some hints as to the gravitational interaction between the large spiral NGC 1512 and the BCD galaxy NGC 1510 and its effects on the
Note that. this reduces to the ? expression ouly in the case of nearly free expansion aud deviates as the shell decelerates.,"Note that, this reduces to the \cite{1997ApJ...476..232M} expression only in the case of nearly free expansion and deviates as the shell decelerates."
" In the rest of the work we use f to indicate the time £,4; iu the observers frame.", In the rest of the work we use $t$ to indicate the time $t_{obs}$ in the observer's frame.
 Iuvertiug this equation and choosing the plysically relevantbranch... gives us the analytical time evolution of the liue of sight Dlastwave radius. as in the ultra-relativistic regimüue.," Inverting this equation and choosing the physically relevant, gives us the analytical time evolution of the line of sight blastwave radius, as in the ultra-relativistic regime."
 This cau now be substituted iuto Equations (5 aud 6)) to ect the time evolution of the Lorentz factor 5 aud the thermal energy E (see Appendix}., This can now be substituted into Equations \ref{gammaR} and \ref{ER}) ) to get the time evolution of the Lorentz factor $\gamma$ and the thermal energy $E$ (see Appendix).
 This gives us a complete solution for the blastwave time evolution. parametrized by the values for 29. ο aud A.," This gives us a complete solution for the blastwave time evolution, parametrized by the values for $\gamma_0$, $M_0$ and $A$."
" Even though au analytical solution is at παπα, it is instructive to look at the Tavlor expansions iu time for the relevant blastwave parameters of radius and thermal energy Equation (12)) imauediately tells us that the blastwave of a CEDEN starts out in a nearly free expansion phase. but slows down significantly by the time ty... when the first negative term in the Taylor expansion for 5 becoues equal to 59. where ⊺↕∐↴∖↴↴∖↴↕∶↴⋁∐⋜↧↕↴∖↴↑↕∐∖↸∖∐≼↧∪↕⋟↑↕∐∖∐↸∖⋜∐⋅↕⋅↖↽↕⋟↥⋅↸∖↸∖↸∖⊼↻⋜⋯↴∖↴↕∪∐↻∐⋜↧↴∖↴↸∖ ⋜⋯≼↧↑↕∐∖↴∖↴∪↕∏↑↕∪∐↸∖∐↑↸∖↥⋅↴∖↴⋜↧↕≧↕⋜⋯≼∐≯∪↥⋅≼↧⋀∖↕↸⊳↕↘⊽↸∖↸∖↕∐↘↽↸∖≺↴∖↴↸∖↸∖ ⊀≚⋯⋉∖∐≼∐⊼↕≧⊔∪↥⋅≋↸∖≺↧∪↖↽↕∐↘↽↸∖↻∐⋜↧↴∖↴↸∖∙≼↸∖↻↸∖∐≼∐∐∶↴∙⊾↿∏⋯∐↑∐↸∖ Loreutz factor at that time."," Even though an analytical solution is at hand, it is instructive to look at the Taylor expansions in time for the relevant blastwave parameters of radius Lorentz factor and thermal energy Equation \ref{GtS}) ) immediately tells us that the blastwave of a CEDEX starts out in a nearly free expansion phase, but slows down significantly by the time $t_{dec}$, when the first negative term in the Taylor expansion for $\gamma$ becomes equal to $\gamma_0$, where This signals the end of the nearly free expansion phase and the solution enters a Blandford McKee like (see Appendix \ref{ultra}) ) or Sedov like phase, depending upon the Lorentz factor at that time."
 We shall now use the blastwave solution developed iu the previous section to predict the radio evolution of a CEDEN with a relativistic blastwave slowing down due to circumstellar interaction., We shall now use the blastwave solution developed in the previous section to predict the radio evolution of a CEDEX with a relativistic blastwave slowing down due to circumstellar interaction.
 For the prototypical SN 2009Dh. the blastwave was ouly mildly relativistic at the time of the observed radio afterglow.," For the prototypical SN 2009bb, the blastwave was only mildly relativistic at the time of the observed radio afterglow."
" Iu the absence of a significant relativistic beaming. the observer would receive enuission from the eutire shell of apparent lateral extent Rie at a time toa, given by which is valid even in the mildly relativistic regime."," In the absence of a significant relativistic beaming, the observer would receive emission from the entire shell of apparent lateral extent $R_{lat}$ at a time $t_{obs}$ given by which is valid even in the mildly relativistic regime."
 Because of its muldly relativistic outflow. all expressions derived for SN 2009bb. use the above Equation rather than Equation ὃ which is applicable in the ultra-relativistic case.," Because of its mildly relativistic outflow, all expressions derived for SN 2009bb, use the above Equation rather than Equation \ref{dtobs} which is applicable in the ultra-relativistic case."
 In either case radio observations of SN 2009bb measure esscutially the trausverse τε uot the line of sight A., In either case radio observations of SN 2009bb measure essentially the transverse $R_{lat}$ not the line of sight $R$.
" DIutegratiug term by term gives us the time evolution of the lateral radius as The thermal energy available when the shell has 110ved out to a radius δὲ is given exactly by Equation (6)). however it is again couvenicut to look at its Taylor expalision. ? eive the ΙΙ Loreutz factor +,, of the shock accelerated electrous as At the iuidlv relativistic velocities secu in SN 2009bb. the peak svuchrotron frequency of the lowest enerev electrons are likely to be below the svuchrotrou self absorption frequeney."," Integrating term by term gives us the time evolution of the lateral radius as The thermal energy available when the shell has moved out to a radius $R$ is given exactly by Equation \ref{ER}) ), however it is again convenient to look at its Taylor expansion, \citet{1998ApJ...497L..17S} give the minimum Lorentz factor $\gamma_m$ of the shock accelerated electrons as At the mildly relativistic velocities seen in SN 2009bb, the peak synchrotron frequency of the lowest energy electrons are likely to be below the synchrotron self absorption frequency."
 This explains the i77 low frequency behavior of the spectrmu., This explains the $\nu^{5/2}$ low frequency behavior of the spectrum.
" Tence. considering a. electron distribution with an energv spectrum NgQE""dE. which we assune for simplicity. to be extending frou 5,,/2,07 to infinity. filling a fraction f of the spherical volume of radius A. we need an energy If a fraction e,=E./E of the available thermal energy eoes into accelerating these clectrous. tlen for the leading order expansion of £L iu AR the normalization of the electron distribution is eiven by for p=3. as interred from the optically thin radio spectra of SN 2009bb (2)."," Hence, considering a electron distribution with an energy spectrum $N_0 E^{-p}dE$, which we assume for simplicity to be extending from $\gamma_m m_ec^2$ to infinity, filling a fraction $f$ of the spherical volume of radius $R$, we need an energy If a fraction $\epsilon_e\equiv E_e/E$ of the available thermal energy goes into accelerating these electrons, then for the leading order expansion of $E$ in $R$ the normalization of the electron distribution is given by for $p=3$, as inferred from the optically thin radio spectrum of SN 2009bb \citep{2010Natur.463..513S}."
 Iu the rest of this work we have made the simplifving asstuuption of a constaut εἰ., In the rest of this work we have made the simplifying assumption of a constant $\epsilon_e$.
 The plysics of shock acceleration is uulikelv to change during time of interest as relevant parameters such as the shock velocity docs rot change mich., The physics of shock acceleration is unlikely to change during time of interest as relevant parameters such as the shock velocity does not change much.
 Moreover. we show later iu this work. hat the light curve of a CEDEN is controlled bx he competition between a decreasing svuchrotron flux at hieh frequencics and a clecreasing optical thickuess (hence increasing fux) at low frequencies.," Moreover, we show later in this work that the light curve of a CEDEX is controlled by the competition between a decreasing synchrotron flux at high frequencies and a decreasing optical thickness (hence increasing flux) at low frequencies."
" The major ight curve features of a shifting peak frequency ancl a jiearlv constant peak flux. arise froin this effect rather han nicro-plivsical processes that may change e,"," The major light curve features of a shifting peak frequency and a nearly constant peak flux, arise from this effect rather than micro-physical processes that may change $\epsilon_e$ ."
lines have been observed with different beams and so the column densities are averaged over different areas.,lines have been observed with different beams and so the column densities are averaged over different areas.
 Also for we derived the total column density [rom the two observed lines independently (column 3 and 4 in Table 6)). and we found that the total methanol column density derived from the 4-1 4) E line is svstematically higher by a small [actor (between 1.3 and 2.5) compared to the value derived [rom the (20-150) line. even if in a few cores the two measures agree within the errors.," Also for we derived the total column density from the two observed lines independently (column 3 and 4 in Table \ref{column}) ), and we found that the total methanol column density derived from the $_{-1}$ $_{-1}$ ) E line is systematically higher by a small factor (between 1.3 and 2.5) compared to the value derived from the $_0$ $_0$ ) $^+$ line, even if in a few cores the two measures agree within the errors."
 Also in (his case this little diserepaney. could be due to opacily effects., Also in this case this little discrepancy could be due to opacity effects.
 In five out of the six cores where the NIL; (1.1) line is detected. we detect also the (2.2) transition so that we can estimate the kinetic temperature (for the sixth core we derived the upper limit).," In five out of the six cores where the $_3$ (1,1) line is detected, we detect also the (2,2) transition so that we can estimate the kinetic temperature (for the sixth core we derived the upper limit)."
 The values are reported in Table 2 and the details of the caleulation are eiven in Appendix D. For all the cores we derived kinetic temperatures between 12 and 13 Ix. These values are usually measured at the edge of the cold prestellar cores. indicating the relative vouthfulness of the observed cores.," The values are reported in Table \ref{coord} and the details of the calculation are given in Appendix B. For all the cores we derived kinetic temperatures between 12 and 13 K. These values are usually measured at the edge of the cold prestellar cores, indicating the relative youthfulness of the observed cores."
 However. high spatial resolution observations have shown that (he kinetic temperature of dense cores tvpicallv drops at or below 10 Ix ad the core centre (e.g. Tafallaetal.2004: Crapsietal. 2007)).," However, high spatial resolution observations have shown that the kinetic temperature of dense cores typically drops at or below 10 K at the core centre (e.g. \citealt{tafalla04}; \citealt{crapsi07}) )."
 On the other hand. a kinetic temperature around 12 Ix is measured in dense cores associated with protostars 2009).," On the other hand, a kinetic temperature around 12 K is measured in dense cores associated with protostars \citep{foster09}."
. Therefore. we mostly trace (he outskirts of dense cores or. alternatively the Lupus," Therefore, we mostly trace the outskirts of dense cores or, alternatively the Lupus"
An abundance of observational evidence shows that subsequent to the Recombination Ira. during which both hvdrogen and helium recombined to their neutral forms. the Universe was reionized.,"An abundance of observational evidence shows that subsequent to the Recombination Era, during which both hydrogen and helium recombined to their neutral forms, the Universe was reionized."
 “Phe best constraints on the epoch of hvdrogen reionization are derived. from. measurements of the intergalactic Lyman resonance line transitions in the spectra of high redshift Quasi-Stellar Objects (QSOs) and polarization measurements of the Cosmic Microwave Background (CAIB)., The best constraints on the epoch of hydrogen reionization are derived from measurements of the intergalactic Lyman resonance line transitions in the spectra of high redshift Quasi-Stellar Objects (QSOs) and polarization measurements of the Cosmic Microwave Background (CMB).
 Phe measured. optical depths. of intergalactic aand aabsorption in high redshift QSOs show that the Universe was reionized by z26 (??)..," The measured optical depths of intergalactic and absorption in high redshift QSOs show that the Universe was reionized by $z\gsim 6$ \citep{Becker01, 2002AJ....123.1247F}."
 This is consistent with CAIB measurements by the (WALA). which place the hycrogen reionization epoch. if a suddenprocess. at 2=11.0414 (?)..," This is consistent with CMB measurements by the ), which place the hydrogen reionization epoch, if a suddenprocess, at $z=11.0\pm1.4$ \citep{2009ApJS..180..306D}."
 The sources of hyvclrogen reionization are currently unknown. out are strongly suspected. of being νομος star-forming galaxies.," The sources of hydrogen reionization are currently unknown, but are strongly suspected of being young star-forming galaxies."
 More speculative possibilities include pockets of Population. HE stars. as may arise in isolated star clusters (??).. or miniquasars (?)..," More speculative possibilities include pockets of Population III stars, as may arise in isolated star clusters \citep{1999ApJ...514..648M, CF06}, or miniquasars \citep{Madau04}."
 Hvdrogen reionization by QSOs is untenable based on current estimates of the QSO [Iuminosity unction. unless there is a sharp rise at the faint end at high redshifts (?7)," Hydrogen reionization by QSOs is untenable based on current estimates of the QSO luminosity function, unless there is a sharp rise at the faint end at high redshifts \citep{Meiksin05, 2009ApJ...692.1476C}."
 The reionization epoch of helium. by contrast. is far ess well constrained.," The reionization epoch of helium, by contrast, is far less well constrained."
 This is primarily because of the need ο 5ο lo space to measure the intergalactic Lyman series absorption of intergalactic gas in the spectra of high redshift QSOs., This is primarily because of the need to go to space to measure the intergalactic Lyman series absorption of intergalactic gas in the spectra of high redshift QSOs.
 The current constraints place the helium retonization epoch. when helium becomes nearly fully doubly ionized. at ταολ3 (2) {ες}. ," The current constraints place the helium reionization epoch, when helium becomes nearly fully doubly ionized, at $z\gsim3$ \citep{Reimers05}. ."
3ecause of the high photoclectic threshold energy, Because of the high photoelectic threshold energy
available.,available.
 In addition. the magnitude of the core shifts that can be detected. is limited. by the resolution of the VLBI observations used.," In addition, the magnitude of the core shifts that can be detected is limited by the resolution of the VLBI observations used."
 In this paper. we discuss the opacity in the core regions of AGN and describe a new method for deriving core shifts from the frequency-dependent. time lags of Hares observed with single-dish observations.," In this paper, we discuss the opacity in the core regions of AGN and describe a new method for deriving core shifts from the frequency-dependent time lags of flares observed with single-dish observations."
 We use these time lags to derive physical parameters of the jets. such as the distance from the VLBI core to the base of the jet and the magnetic fields in the core region.," We use these time lags to derive physical parameters of the jets, such as the distance from the VLBI core to the base of the jet and the magnetic fields in the core region."
 The core is à compact feature in the VLBI map of an AGN with high brightness and a relatively lat. spectrum. which is usually interpreted as that part of the jet where the optical depth is 7=I.," The core is a compact feature in the VLBI map of an AGN with high brightness and a relatively flat spectrum, which is usually interpreted as that part of the jet where the optical depth is $\tau = 1$."
 Since the 7=1 surface has dillerent locations at cillerent frequencies (IxóniglOS1).. the absolute position of the core should depend on the observing frequeney.," Since the $\tau = 1$ surface has different locations at different frequencies \citep{Konigl_1981}, the absolute position of the core should depend on the observing frequency."
 According to the standard shoek-in-jet model. a change of electron density. and. pressure at the injection point near the base of the jet will cause a shock wave to propagate along the jet.," According to the standard shock-in-jet model, a change of electron density and pressure at the injection point near the base of the jet will cause a shock wave to propagate along the jet."
 This will cause brightening of the core region. which will be seen as a flare in the total Iux- light curves. anc will be followed by the appearance of a jet component (or components) in VLBI maps (e.g.Alarscher&Gear1985:Gomezetal. L997).," This will cause brightening of the core region, which will be seen as a flare in the total flux-density light curves, and will be followed by the appearance of a jet component (or components) in VLBI maps \citep[e.g.][]{Marscher_Gear_1985,Gomez_1997}."
. Consider a conical jot ecometry (see Figure 12) observed at a viewing angle o., Consider a conical jet geometry (see Figure \ref{jet}) ) observed at a viewing angle $\varphi$.
" A shock wave appears at the distance Ae, and then propagates along the jet.", A shock wave appears at the distance $R_{on}$ and then propagates along the jet.
 It will cross the 7=1 surface for a particular frequency i; at some time 7; and emerge out of the core region., It will cross the $\tau = 1$ surface for a particular frequency $\nu_{i}$ at some time $T_{i}$ and emerge out of the core region.
 Since the position of the 7=I surface is shifted. further from the jet base at. lower frequencies. the imes 7; will be delayed: at. lower frequencies.," Since the position of the $\tau = 1$ surface is shifted further from the jet base at lower frequencies, the times $T_{i}$ will be delayed at lower frequencies."
 Figure 1 shows how the 7; correspond. to the maxima of the total lux-densitv. Hares obtained: with single-dish observations., Figure \ref{jet} shows how the $T_{i}$ correspond to the maxima of the total flux-density flares obtained with single-dish observations.
 Crossing the 7=| surface corresponds to à maximum of the otal Hux-density outburst at the corresponding frequency. and the time of the [lare maximum thus also depends on he frequency: thus. the time lags contain information about core opacity.," Crossing the $\tau = 1$ surface corresponds to a maximum of the total flux-density outburst at the corresponding frequency, and the time of the flare maximum thus also depends on the frequency; thus, the time lags contain information about core opacity."
" According to the geometry of Figure 1. and the winciples of superluminal motion (e.g.Rees1967:Türler.2000).. the time / that has passed after the shock waves appearance at the distance Z2, in he observer's frame is where {7 is the distance along the jet axis in the rest [rame of the quasar. top), is the apparent velocity in the plane of the sky in units of e. s is the viewing angle. and zis the redshift of the source."," According to the geometry of Figure \ref{jet}
 and the principles of superluminal motion \citep[e.g.][]{Rees_1967,Tuerler_2000}, the time $t$ that has passed after the shock wave's appearance at the distance $R_{on}$ in the observer's frame is where $R$ is the distance along the jet axis in the rest frame of the quasar, $\beta_{app}$ is the apparent velocity in the plane of the sky in units of $c$, $\varphi$ is the viewing angle, and $z$ is the redshift of the source."
 In this equation. we assume that the apparent speed is the actual speed of the shock.," In this equation, we assume that the apparent speed is the actual speed of the shock."
" Observing at multiple frequencies £A, and £j. we can estimate the time laes between the maxima of the total Dux-density outburst: Assuming that the shock wave appears at the same distance. Z2, at. all. frequencies. we obtain Allan.=νοappe. Where ARea; is the distance between A at the two Lrequencics projected onto the plane of the sky."," Observing at multiple frequencies $\nu_{a}$ and $\nu_{b}$ , we can estimate the time lags between the maxima of the total flux-density outburst: Assuming that the shock wave appears at the same distance $R_{on}$ at all frequencies, we obtain $\Delta
t(\nu)_{obs} = \Delta R_{proj}/{\beta_{app} c}$ , where $\Delta R_{proj}$ is the distance between $R$ at the two frequencies projected onto the plane of the sky."
 ‘Taking expression (33) for the frequency-clependent core shift from Llirotani(2005).. we can write the dependence of the time lags on the frequency. spectral index à. magnetic Ποιά and electron density: where ap isa dimensionless variable for D and f is a function of Ny. the spectral index. and the viewing angle.," Taking expression (33) for the frequency-dependent core shift from \citet{Hirotani_2005}, we can write the dependence of the time lags on the frequency, spectral index $\alpha$, magnetic field and electron density: where $x_{B}$ is a dimensionless variable for $B$ and $f$ is a function of $N_{1}$, the spectral index, and the viewing angle."
 Defining the core-position (or time-lag) ollsct as we can obtain formulas lor the magnetic field and the distance from the VLBI core to the central engine., Defining the core-position (or time-lag) offset as we can obtain formulas for the magnetic field and the distance from the VLBI core to the central engine.
" In this formula. £2,, is measured in units of pc - Gllz. Abin wes.app in milliaresecond (mas) per vear. and 2; is the luminosity distance of the source in parsec."," In this formula, $\Omega_{r\nu}$ is measured in units of pc $\cdot$ GHz, $\Delta t$ in yrs,$\beta_{app}$ in milliarcsecond (mas) per year, and $D_{L}$ is the luminosity distance of the source in parsec."
" Formula 4 assumes that the electron. number density and magnetic field scale with distance along the jet 2 as where AN, ancl D, refer to the values of NZ and. D αἱ r= pc.", Formula \ref{eq:dt} assumes that the electron number density and magnetic field scale with distance along the jet $R$ as where $N_{1}$ and $B_{1}$ refer to the values of $N_{e}^*$ and $B$ at $r = 1$ pc.
 Following Lobanov(1998). and Lirotani(2005).. we can write the distance between the core ancl the base of the jet in terms of the frequencv-dependent time lags as where Αν ds estimated. using the [requency-dependent time lags.," Following \citet{Lobanov_1998} and \citet{Hirotani_2005}, we can write the distance between the core and the base of the jet in terms of the frequency-dependent time lags as where $k_r$ is estimated using the frequency-dependent time lags."
" We can calculate. the magnetic field at 1 pe distance for the special case when there is equipartition between the energies of the particles ancl magnetic field (A,= 1) and the spectral index is a=0.5 2009):: where 6 is the Doppler factor. 6 the jet half-opening angle. 4 the viewing angle. and ο is in Gauss."," We can calculate the magnetic field at 1 pc distance for the special case when there is equipartition between the energies of the particles and magnetic field $k_{r} = 1$ ) and the spectral index is $\alpha =
-0.5$ \citep{Osullivan_2009}: : where $\delta$ is the Doppler factor, $\theta$ the jet half-opening angle, $\varphi$ the viewing angle, and $B_{1}$ is in Gauss."
 The equipartition magnetic-field strength in the core can then be found from the relation for Boa. at a particular frequency. v., The equipartition magnetic-field strength in the core can then be found from the relation for $B_{core}$ at a particular frequency $\nu$ .
 In order tocheck the proposed. method for measuring the, In order tocheck the proposed method for measuring the
demonstrated that these features could occur simultaneously: with the formation of eccentric circumstellar rings.,demonstrated that these features could occur simultaneously with the formation of eccentric circumstellar rings.
 A simple analvsis of the perturbed. disc model was found to be in good quantitative agreement with the observations of both ju‘s dise asvnunetries anc the midplane features: for particular values of the viewing angle and epoch. and IHy-by parameters.," A simple analysis of the perturbed disc model was found to be in good quantitative agreement with the observations of both $\beta$ Pic's disc asymmetries and the midplane features; for particular values of the viewing angle and epoch, and fly-by parameters."
 In this paper we present new observations ar measurements of the length asymmetry of 3 Pic's scattered-light. disc. and then go on to simulate the dvnamies of a stellar Ηνον encounter with an initially svmmetrical cise of particles.," In this paper we present new observations and measurements of the length asymmetry of $\beta$ Pic's scattered-light disc, and then go on to simulate the dynamics of a stellar flyby encounter with an initially symmetrical disc of particles."
" Similar numerical modelling to that presented here arc in IXLSS has been considered. previously in the context. of angular momentum transfer between the perturber's orbi and a protostellar disc (Clarke Prinele 1993. Hall. Clarke Pringle 1996). the dvnamies of the Exdgeworth-Ixuiper bel (lela. Larwood Burkert 2000). and the tidal interaction of spiral galaxies Cloomre ""Toomre 1972)."," Similar numerical modelling to that presented here and in KLSS has been considered previously in the context of angular momentum transfer between the perturber's orbit and a protostellar disc (Clarke Pringle 1993, Hall, Clarke Pringle 1996), the dynamics of the Edgeworth-Kuiper belt (Ida, Larwood Burkert 2000), and the tidal interaction of spiral galaxies (Toomre Toomre 1972)."
 Here we shal consider a wider range of encounter velocities (from boum orbits through to hyperbolic trajectories) and stellar masses (from M cbwarfs to A stars. when scaled to the mass of 3 Pic) than has been studied before in any context.," Here we shall consider a wider range of encounter velocities (from bound orbits through to hyperbolic trajectories) and stellar masses (from M dwarfs to A stars, when scaled to the mass of $\beta$ Pic) than has been studied before in any context."
 We also include a discussion of the orbital dynamics of captured: particles with respect to the perturber., We also include a discussion of the orbital dynamics of captured particles with respect to the perturber.
 Εις paper can be considered as à companion to INLSS since here we also supplement their linding of circumstellar ring formation in similar simulations with an explanation of the dynamical origin of the features., This paper can be considered as a companion to KLSS since here we also supplement their finding of circumstellar ring formation in similar simulations with an explanation of the dynamical origin of the features.
 As in other works (Whitmire. Matese Tomlev. 1988. Alouillet ct al.," As in other works (Whitmire, Matese Tomley 1988, Mouillet et al."
 1997. IXLSS) we assume that the simulation particles’ distribution represents the distribution of an ünderlving disc of planetesimals. which are parent bodies whose infrequent and therefore dynamically inconsequential collisions supply the dust scattering surface that is observed in the real svstem.," 1997, KLSS) we assume that the simulation particles' distribution represents the distribution of an underlying disc of planetesimals, which are parent bodies whose infrequent and therefore dynamically inconsequential collisions supply the dust scattering surface that is observed in the real system."
 A more complete model should include consideration of erain removal ancl &eneration. processes in determining the appearence of the perturbed dise (reviewed bv Backman Paresce 1993)., A more complete model should include consideration of grain removal and generation processes in determining the appearence of the perturbed disc (reviewed by Backman Paresce 1993).
 Llowever. we defer treatment of those issues to future work. ane focus here on the first-stage problem of the dynamics.," However, we defer treatment of those issues to future work, and focus here on the first-stage problem of the dynamics."
 This stage is important in deducing the mass and orbital parameters of the postulated stellar perturber. for which it is possible to perform star catalogue searches (c.g. Ixalas. Deltorn Larwood 2000). and we proceed to do this by examining the length asvmnmetry. and other measures of the disc response. as a function. of stellar encounter parameters.," This stage is important in deducing the mass and orbital parameters of the postulated stellar perturber, for which it is possible to perform star catalogue searches (e.g. Kalas, Deltorn Larwood 2000), and we proceed to do this by examining the length asymmetry, and other measures of the disc response, as a function of stellar encounter parameters."
 However. we choose to examine the length asymmetry as the principal diagnostic measure of the disc response since it ds the most clistinet such feature both in the observations and the cdvnamical models.," However, we choose to examine the length asymmetry as the principal diagnostic measure of the disc response since it is the most distinct such feature both in the observations and the dynamical models."
 In our future work we shall also consider the subtler asvoimetrics in greater detail., In our future work we shall also consider the subtler asymmetries in greater detail.
 In Section 2 we present deep optical coronagraphic images of the disc., In Section $2$ we present deep optical coronagraphic images of the disc.
 In Section 3 we describe the results of our numerical investigations of the dynamics of tidally disrupted particle dises. ancl provide ecneral discussion of the induced asvmmeltries and particle stripping.," In Section $3$ we describe the results of our numerical investigations of the dynamics of tidally disrupted particle discs, and provide general discussion of the induced asymmetries and particle stripping."
 In Section 4 we discuss our findings and summarise the conclusions., In Section $4$ we discuss our findings and summarise the conclusions.
 New optical coronagraphic observations of the environs of 3 Pie were obtained with the University of Hawaii 22mm telescope on 2000 January 31., New optical coronagraphic observations of the environs of $\beta$ Pic were obtained with the University of Hawaii $2.2$ m telescope on 2000 January 31.
 A Κον goal was to maximize sensitivity to the outer regions of the clise., A key goal was to maximize sensitivity to the outer regions of the disc.
 The coronagraph usec has 12 interchangeable. circular. focal-plane oeculling masks. from which we selected a mask 12.5aarcsec in diameter.," The coronagraph used has 12 interchangeable, circular, focal-plane occulting masks, from which we selected a mask $12.5$ arcsec in diameter."
 This particular mask size is approximately (wo times larger than the minimum size allowable by the seeing conditions. and it partially obscures he image out to 120au projected. radius about: Pic.," This particular mask size is approximately two times larger than the minimum size allowable by the seeing conditions, and it partially obscures the image out to $120$ projected radius about $\beta$ Pic."
 llowever. it also minimizes the scattered. light in the field hat dominates the background. noise.," However, it also minimizes the scattered light in the field that dominates the background noise."
 Additionally. the occulting mask increases the cllicicney of the observations » maximizing the integration time permitted before CCD saturation occurs just beyond its edge.," Additionally, the occulting mask increases the efficiency of the observations by maximizing the integration time permitted before CCD saturation occurs just beyond its edge."
 We obtained 122 integrations of 30 seconds each hrough an /'-band filter (A70.67 sam)., We obtained 122 integrations of 30 seconds each through an $R$ -band filter $\lambda\sim$ $\mu$ m).
 Re-imaging optics oovided a pixel scale of 0.407 Lon a 20482048 CCD., Re-imaging optics provided a pixel scale of $0.407$ $^{-1}$ on a $2048\times2048$ CCD.
 Phe field was masked by the coronagraphic focal ane assembly which has a circular. clear aperture with diameter. 336aarcesec., The field was masked by the coronagraphic focal plane assembly which has a circular clear aperture with diameter $336$ arcsec.
 The airmass of observation (23.0) combined with high winds. produced image quality. varying rom 1.0 to LSaaresec.," The airmass of observation $>$ 3.0) combined with high winds, produced image quality varying from 1.0 to arcsec."
 For final data analvsis. we selected 77 frames with the image quality characterized by stellar ull-width at half-maximum (WIAD <|] 2aarcsec.," For final data analysis, we selected 77 frames with the image quality characterized by stellar full-width at half-maximum (FWHM) $\le1.2$ arcsec."
transit method. have been announced. over the last vear or so (2?2??77).. ancl one has received tentative radial velocity confirmation (?)..,"transit method have been announced over the last year or so \citep{upz+02,uzs+02,msy+03,shl+03,dhk+03}, and one has received tentative radial velocity confirmation \citep{ktj+03}."
 The plethora of eround-basecl searches currently uneerway (see ?. for a review) is expected to vield hundreds of candidate transiting giant exo-planets in the next [ew vears., The plethora of ground-based searches currently underway (see \citealt{hor02} for a review) is expected to yield hundreds of candidate transiting giant exo-planets in the next few years.
" Llowever. terrestrial planets. capable of harbouring ασια, water on their surface. are bevond the reach of the methods used so far."," However, terrestrial planets, capable of harbouring quid water on their surface, are beyond the reach of the methods used so far."
 Detecting them is the goal of a number of planned. space-missions. such as the Franco-Luropean satellite COROT (2).. NASA's (2) ancl ESA's (2)..," Detecting them is the goal of a number of planned space-missions, such as the Franco-European satellite COROT \citep{bag+03}, , NASA's \citep{bkl+03} and ESA's \citep{fav03}."
 Phese should push the numbers of known exo-planets into the thousands., These should push the numbers of known exo-planets into the thousands.
 The detection of a weak. short. periodic transit signal in noisy light curves is a challenging task.," The detection of a weak, short, periodic transit signal in noisy light curves is a challenging task."
 Vhe large number of light curves collected make the automation and optimisation of the process a necessity., The large number of light curves collected make the automation and optimisation of the process a necessity.
 This requirement is even stronger in the context of space missions. which will collect. even larger amounts of data and where telemetry limitations will require as much of the processing to be done on board. as possible.," This requirement is even stronger in the context of space missions, which will collect even larger amounts of data and where telemetry limitations will require as much of the processing to be done on board as possible."
 A number of transit detection algorithms have been implemented in the literature (22227???) and there has been some effort to compare their respective performances in a controlled Fashion (2).. but there is currently no widespread agreement on the optimal method to use.," A number of transit detection algorithms have been implemented in the literature \citep{ddk+00,ddb01,jcb02,upz+02,kzm02,af02,shl+03} and there has been some effort to compare their respective performances in a controlled fashion \citep{tin03}, but there is currently no widespread agreement on the optimal method to use."
 In a previous paper (?.. hereafter Paper ID. a dedicated Bavesian transit search algorithm was derived. based on the more general period finding method of Gregory Loreclo (??.. hereafter GL92 and €99 respectively).," In a previous paper \citealt{af02}, hereafter Paper I), a dedicated Bayesian transit search algorithm was derived, based on the more general period finding method of Gregory Loredo \citealt{gl92b,
gre99}, hereafter GL92 and G99 respectively)."
 Here we develop this algorithm further and attempt to reconcile the apparent diversity of the extant transit algorithms., Here we develop this algorithm further and attempt to reconcile the apparent diversity of the extant transit algorithms.
 Starting from the original Gregory Loredo prescription. which is based on a maximum likelihood (ML) estimation for a periodic step-function model of unspecified shape. appropriate sequential simplifications can be made.," Starting from the original Gregory Loredo prescription, which is based on a maximum likelihood (ML) estimation for a periodic step-function model of unspecified shape, appropriate sequential simplifications can be made."
 We demonstrate. that. the levels of the step-funetion bins — which define the shape of the. detected: event are not free parameters. their optimal values being fully defined. by the data.," We demonstrate that the levels of the step-function bins – which define the shape of the detected event – are not free parameters, their optimal values being fully defined by the data."
 The use of Bayesian priors can be dropped. given the lack of information currently available on the appropriate form for these priors.," The use of Bayesian priors can be dropped, given the lack of information currently available on the appropriate form for these priors."
 Finally. for detection purposes. the model can be simplified to an uncqual mark-space ratio square wave with only one out-of-transit ancl one in-transit. value.," Finally, for detection purposes, the model can be simplified to an unequal mark-space ratio square wave with only one out-of-transit and one in-transit value."
 The algorithm itself. and its implementation are presented. in Sect. 2.., The algorithm itself and its implementation are presented in Sect. \ref{sec:deri}.
 The performance has proved. better than that of he previous version. ancl the computational requirements rave been significantly reduced.," The performance has proved better than that of the previous version, and the computational requirements have been significantly reduced."
 Pursuing this simplification ias also highlighted the similarities between the previously xublished transit detection methods., Pursuing this simplification has also highlighted the similarities between the previously published transit detection methods.
 However. MLE-based. algorithms are only optimised for data containing simple transits embedded in random. noise (usually well approximated by a Gaussian. distribution)," However, ML-based algorithms are only optimised for data containing simple transits embedded in random noise (usually well approximated by a Gaussian distribution)."
 teal transit search light curves will contain instrinsic stellar variability of various amplitudes and shapes., Real transit search light curves will contain instrinsic stellar variability of various amplitudes and shapes.
 They will also suller from irregular sampling. with frequent large gaps in he coverage.," They will also suffer from irregular sampling, with frequent large gaps in the coverage."
 Combined. these effects. can pose a major hreat to our ability. to. detect. planets.," Combined, these effects can pose a major threat to our ability to detect planets."
" This problem is illustrat for the case of grouncd-based data. by recent data rom the ec.UNSW planet search project using the Automated ""atrol telescope at Siding Springs observatorv: in 5 nights of observations of the open cluster NGCG6633. nearly all of the L000 brightest. stars were found. to be variable at he millimag level (2)..."," This problem is illustrated, for the case of ground-based data, by recent data from the UNSW planet search project using the Automated Patrol telescope at Siding Springs observatory: in 5 nights of observations of the open cluster NGC6633, nearly all of the 1000 brightest stars were found to be variable at the millimag level \citep{apt03}."
 With the even higher precision xossible with upcoming space missions (~0.1 mamag). this xoblem will become even more acute due to the sensitivity o additional stellar. activitv-üinduced: variability.," With the even higher precision possible with upcoming space missions $\sim0.1$ mmag), this problem will become even more acute due to the sensitivity to additional stellar activity-induced variability."
 Worries hat this could seriously impair the detection of terrestrial xanets have lec to the development of variability filters (??7).. but these are applicable only to data with regular sampling and no gaps.," Worries that this could seriously impair the detection of terrestrial planets have led to the development of variability filters \citep{jen02, caf03}, but these are applicable only to data with regular sampling and no gaps."
 In Sect. 3..," In Sect. \ref{sec:pre},"
 we introduce more generic ilters applicable to irregularly sampled. data. or data with gaps (as expected. for space missions. due for example to clemetry drop-outs).," we introduce more generic filters applicable to irregularly sampled data, or data with gaps (as expected for space missions, due for example to telemetry drop-outs)."
 Performance estimation results are discussed. in Sect. 4..," Performance estimation results are discussed in Sect. \ref{sec:perf},"
 and their implications in Sect. 5.., and their implications in Sect. \ref{sec:discus}.
 Finally. Appendix |. contains details of how the simulated light curves used. throughout. the paper were &eeonerated.," Finally, Appendix \ref{sec:ex}
 contains details of how the simulated light curves used throughout the paper were generated."
 ‘Transit’ searches. are. generally performed. by comparing ight curves to a family of models with à common set of parameters. dillering from cach other according to the different: values used. for these parameters.," Transit searches are generally performed by comparing light curves to a family of models with a common set of parameters, differing from each other according to the different values used for these parameters."
 The best set of xwameters is identified by finding the model most likely to lave given rise to the observed data. tthe model with he highest likelihood £L.," The best set of parameters is identified by finding the model most likely to have given rise to the observed data, the model with the highest likelihood $L$."
 If the noise in cach data point d; is assumed to be Gaussian (an assumption also valid for Poisson noise in the imit of large. numbers of photons). the likelihood can be written as the product of independent Gaussian probability distribution functions: where d; is the data value at time /; and r; is the corresponding model value. Ais the total number of data points ancl a; the error associated with d;.," If the noise in each data point $d_i$ is assumed to be Gaussian (an assumption also valid for Poisson noise in the limit of large numbers of photons), the likelihood can be written as the product of independent Gaussian probability distribution functions: where $d_i$ is the data value at time $t_i$ and $r_i$ is the corresponding model value, $N$ is the total number of data points and $\sigma_i$ the error associated with $d_i$ ."
 I5q. (1)), Eq. \ref{eq:genL1}) )
 can be pewrltten as: where: so that likelihood maximisation. in the case of Gaussian noise is equivalent to. X7.2 minimisation. since the noise properties o; are assumed to be known. ffixed.," can be rewritten as: where: so that likelihood maximisation, in the case of Gaussian noise is equivalent to $\chi^2$ minimisation, since the noise properties $\sigma_i$ are assumed to be known, fixed."
 The generic method developed by Gregory Loredo (109. G99) to detectperiodic modulations in X-ray data. was used as the starting point ofthe present work.," The generic method developed by Gregory Loredo (GL92, G99) to detectperiodic modulations in X-ray data, was used as the starting point ofthe present work."
 This method is, This method is
"The spectroscopic fraction of spiral galaxies is the smallest measured so far in compact groups of galaxies: the number is well below the fraction measured for HCGs. 49%, and for SCGs. 69% (Pompei et al..","The spectroscopic fraction of spiral galaxies is the smallest measured so far in compact groups of galaxies; the number is well below the fraction measured for HCGs, $\%$, and for SCGs, $\%$ (Pompei et al.,"
 2003)., 2003).
 Such large difference might be partly caused by our use of à spectroscopic morphological criterion. while the quoted spiral fraction for nearby compact groups was derived from deep photometric studies.," Such large difference might be partly caused by our use of a spectroscopic morphological criterion, while the quoted spiral fraction for nearby compact groups was derived from deep photometric studies."
 However. if only a spectroscopic criterion is used for HCGs. the spiral fraction remains quite high. of the order of 40% (see Fig.," However, if only a spectroscopic criterion is used for HCGs, the spiral fraction remains quite high, of the order of $\%$ (see Fig."
 3 of Ribeiro et al..," 3 of Ribeiro et al.,"
 1998)., 1998).
 Hence. it seems that our confirmed compact groups have indeed a smaller fraction of late-type galaxies than HCGs.," Hence, it seems that our confirmed compact groups have indeed a smaller fraction of late-type galaxies than HCGs."
 We checked the literature to compare our results with other catalogues of groups of galaxies: since the release of the SDSS DR7. two major catalogues of galaxy groups have been published. one by MeConnachie et al. (," We checked the literature to compare our results with other catalogues of groups of galaxies: since the release of the SDSS DR7, two major catalogues of galaxy groups have been published, one by McConnachie et al. ("
2009) and another by Tago et al (2010).,2009) and another by Tago et al (2010).
 We compared our whole observed sample of 138 groups with catalogues A and B from MeConnachie and Table 2 from Tago et al., We compared our whole observed sample of 138 groups with catalogues A and B from McConnachie and Table 2 from Tago et al.
" The geometrical center of each group was used in all the catalogues and a search radius of 30"" on the sky was used. returning a total of 23 matches from MeConnachie and 5 from Tago et al."," The geometrical center of each group was used in all the catalogues and a search radius of $\arcsec$ on the sky was used, returning a total of 23 matches from McConnachie and 5 from Tago et al."
 The choice of the radius was a compromise between the two different definitions of group center of ourselves and MeConnachie. as we both used the geometrical radius. and Tago et al.," The choice of the radius was a compromise between the two different definitions of group center of ourselves and McConnachie, as we both used the geometrical radius, and Tago et al.,"
 who used a different method., who used a different method.
 When redshift measurements were available. a good agreement was found in all cases. except five (see Table 3).," When redshift measurements were available, a good agreement was found in all cases, except five (see Table 3)."
 In these cases. no more than two redshifts were available from SDSS data. while our own observations proved that the candidate compact group consisted of a couple of pairs at two different redshifts.," In these cases, no more than two redshifts were available from SDSS data, while our own observations proved that the candidate compact group consisted of a couple of pairs at two different redshifts."
 The DPOSS cluster catalogue (Lopes et al..," The DPOSS cluster catalogue (Lopes et al.,"
 2004) was also searched for possible associations between our candidate CGs and larger-scale structures from the same survey., 2004) was also searched for possible associations between our candidate CGs and larger-scale structures from the same survey.
 Here the results were somewhat mixed. because of the disagreement between the quoted photometric redshifts from the DPOSS and our spectroscopic redshifts.," Here the results were somewhat mixed, because of the disagreement between the quoted photometric redshifts from the DPOSS and our spectroscopic redshifts."
 Owing to the robustness of the spectroscopic measurements. in. particular at such low redshifts. we conclude that our redshift estimates are more reliable and reassign the same distance to the DPOSS cluster that 1s close on the sky to our candidate DPOSS compact groups and the group itself (see Table | for confirmed associations).," Owing to the robustness of the spectroscopic measurements, in particular at such low redshifts, we conclude that our redshift estimates are more reliable and reassign the same distance to the DPOSS cluster that is close on the sky to our candidate DPOSS compact groups and the group itself (see Table 1 for confirmed associations)."
 From our analysis. it becomes clear that our original sample of candidate CGs consists of a mixed bag of objects. a significant part of which is embedded in a large-scale structure.," From our analysis, it becomes clear that our original sample of candidate CGs consists of a mixed bag of objects, a significant part of which is embedded in a large-scale structure."
 Most of the rejected candidates are formed by two pairs of galaxies close together on the sky., Most of the rejected candidates are formed by two pairs of galaxies close together on the sky.
 Hence. a first result is that finding compact groups at intermediate redshift is not à trivial business. even when using search criteria based on the original Hickson's ones and modified to take into account the larger distance.," Hence, a first result is that finding compact groups at intermediate redshift is not a trivial business, even when using search criteria based on the original Hickson's ones and modified to take into account the larger distance."
 Once the candidate groups have been identified. it is of crucial importance not only to confirm spectroscopically all the candidate member galaxies. but also to study in detail the surrounding environment of the confirmed groups. to have a good understanding of what kind of objects are being observed.," Once the candidate groups have been identified, it is of crucial importance not only to confirm spectroscopically all the candidate member galaxies, but also to study in detail the surrounding environment of the confirmed groups, to have a good understanding of what kind of objects are being observed."
 This should return a reasonably clean sample of isolated compact groups., This should return a reasonably clean sample of isolated compact groups.
 Even with these precautions. our final sample represents ar upper limit to the amount of isolated compact groups. partially because of the incomplete coverage of the SDSS in the areas observed by ourselves and partially because of the limited spectroscopic coverage for objects fainter than they. —17.7.," Even with these precautions, our final sample represents an upper limit to the amount of isolated compact groups, partially because of the incomplete coverage of the SDSS in the areas observed by ourselves and partially because of the limited spectroscopic coverage for objects fainter than $_{petro}$ =17.7."
 Despite all these limitations. we have found a fraction of confirmed isolated groups of 34% of the total number of groups originally observed. which ts larger than the fraction measured for a subsample of HCGs (de Carvalho et al..," Despite all these limitations, we have found a fraction of confirmed isolated groups of $\%$ of the total number of groups originally observed, which is larger than the fraction measured for a subsample of HCGs (de Carvalho et al.,"
" 1994, 23%)."," 1994, $\%$ )."
 We wonder. however. what the real fraction for HCGs would have been if the whole 92 confirmed groups catalogue had been studied by de Carvalho et al.," We wonder, however, what the real fraction for HCGs would have been if the whole 92 confirmed groups catalogue had been studied by de Carvalho et al."
 Our confirmed isolated CGs have a median crossing time equal to about one tenth of the light travel time to us., Our confirmed isolated CGs have a median crossing time equal to about one tenth of the light travel time to us.
 Assuming the crossing time as an estimate of the group age. we conclude that we do not observe at higher redshift the same population of groups as we observe in the nearby universe: that Is we must be looking at a different population of compact groups.," Assuming the crossing time as an estimate of the group age, we conclude that we do not observe at higher redshift the same population of groups as we observe in the nearby universe; that is we must be looking at a different population of compact groups."
 If we were to assume that all these groups will continue to exist in isolation without further perturbation from the external environment. the most likely final product of such groups would be an isolated early-type galaxy.," If we were to assume that all these groups will continue to exist in isolation without further perturbation from the external environment, the most likely final product of such groups would be an isolated early-type galaxy."
 According to the model of Barnes (1989). isolated CGs are likely to evolve into a single isolated elliptical galaxies in a few crossing times. hence we expect these z=0.1 objects to be the progenitors of present-day To determine whether this conclusion is realistic. at least in qualitative terms. we compared the volume density of our confirmed CGs to the volume density of isolated early-type galaxies drawn from several literature works in the nearby universe.," According to the model of Barnes (1989), isolated CGs are likely to evolve into a single isolated elliptical galaxies in a few crossing times, hence we expect these z=0.1 objects to be the progenitors of present-day To determine whether this conclusion is realistic, at least in qualitative terms, we compared the volume density of our confirmed CGs to the volume density of isolated early-type galaxies drawn from several literature works in the nearby universe."
 We assumed that the density distribution of our compact groups in space is uniform across the surveyed area. and that our sample is complete all the way to our average redshift. we were then able to estimate an average volume density of CGs based on Eq.," We assumed that the density distribution of our compact groups in space is uniform across the surveyed area, and that our sample is complete all the way to our average redshift; we were then able to estimate an average volume density of CGs based on Eq."
 1 of Lee et al..," 1 of Lee et al.,"
 2004., 2004.
 Our isolated compact groups have a density of 1 x 10-°Mpe™*. similar to the values measured for clusters of galaxies (Bramel et al. 2000) and fossil groups (Santos et al..," Our isolated compact groups have a density of 1 x $^{-6}$ $^{-3}$, similar to the values measured for clusters of galaxies (Bramel et al, 2000) and fossil groups (Santos et al.,"
 2007; Jones et al..," 2007; Jones et al.,"
 2003)., 2003).
 Assuming that the percentage of early-type galaxies is ~ 18% of all field galaxies (starting from an estimated 826€ fraction of spirals in the field. as quoted by Nilson et al..," Assuming that the percentage of early-type galaxies is $\sim$ $\%$ of all field galaxies (starting from an estimated $\%$ fraction of spirals in the field, as quoted by Nilson et al.,"
 1973 and Gisler et al..," 1973 and Gisler et al.,"
 1980). we applied the same Eq.," 1980), we applied the same Eq."
 ] to the samples of Allam et al. 2005: Giuricin et al.," 1 to the samples of Allam et al, 2005; Giuricin et al."
 2000 and AMIGA (Verley et al..," 2000 and AMIGA (Verley et al.,"
 2007)., 2007).
 Assuming as an average redshift for, Assuming as an average redshift for
 ? suggested the B2Vn star. 1180. 4408) to be a He-rich magnetic star with a magnetosphere containing trapped gas that produces hydrogen line emission (?.. 3).," \citet{2008A&A...482..255R} suggested the B2Vn star 180, 408) to be a He-rich magnetic star with a magnetosphere containing trapped gas that produces hydrogen line emission \citealt{2005MNRAS.357..251T}, \citealt*{2007MNRAS.382..139T}) )."
 They based their suggestion on evidence derived from two FEROS echelle spectra and a Hipparcos light-curve. with a period of either single-wave dd or double-wave dd. However. a yeriod of could not be due to rotational modulation. since this would require a rotational speed well above the critical threshold.," They based their suggestion on evidence derived from two FEROS echelle spectra and a Hipparcos light-curve, with a period of either single-wave d or double-wave d. However, a period of could not be due to rotational modulation, since this would require a rotational speed well above the critical threshold."
 If contirmed. 77355 would have a unique position in he He-strong class: With esin;=320kkmss 54?) it would be the the most rapidly rotating magnetic star in the upper diagram: by a factor of about two ahead of the current record- E. which has esin;=165 lqo(1.. Op.," If confirmed, 7355 would have a unique position in the He-strong class: With $v\sin i = 320$ $^{-1}$ \citep*{2002ApJ...573..359A} it would be the the most rapidly rotating magnetic star in the upper HR-diagram; by a factor of about two ahead of the current record-holder, which has $v\sin i = 165$ $^{-1}$ \citeauthor{2002ApJ...573..359A}, op."
 cite)., cit.).
 This would make the star a show-case for the Rigidly Rotating Tagnetosphere model. that so far. though with great success. was applied to only one star. c EE (2.. op.," This would make the star a show-case for the Rigidly Rotating Magnetosphere model, that so far, though with great success, was applied to only one star, $\sigma$ E \citeauthor{2005MNRAS.357..251T}, op."
 cit.)., cit.).
 In order to test this claim. a spectropolarimetric campaign was carried out in 2008.," In order to test this claim, a spectropolarimetric campaign was carried out in 2008."
 The data described below were obtained at the VET. with the FORS|] instrument (2).. which is equipped with a super-achromatic quarter-wave retarder plate.," The data described below were obtained at the VLT with the FORS1 instrument \citep{1998Msngr..94....1A}, which is equipped with a super-achromatic quarter-wave retarder plate."
 The instrument setup used the 1200B holographie prism with a dispersion of AA//mm over a range of 366 to nnm., The instrument setup used the 1200B holographic prism with a dispersion of /mm over a range of 366 to nm.
" At a slit-width of0.3"". a (binned) pixel scale of 0.25""per pixel. and a (binned) pixel size of jim. this gives about pper pixel. which slightly oversamples the resolution element of aboutAA."," At a slit-width of, a (binned) pixel scale of per pixel, and a (binned) pixel size of $\mu$ m, this gives about per pixel, which slightly oversamples the resolution element of about."
. Each individual measurement (see Table 11) consisted of a sequence of eight exposures. taken at retarder plate position angles in the sequence 45.457.45.45..457. 45.45.45) with respect to the axis of the Wollaston prism.," Each individual measurement (see Table \ref{tab_result}) ) consisted of a sequence of eight exposures, taken at retarder plate position angles in the sequence $-45\degr,-45\degr,45\degr,45\degr,-45\degr,-45\degr,45\degr,45\degr$ ) with respect to the axis of the Wollaston prism."
 The exposure time was two seconds for the respective 8 exposures., The exposure time was two seconds for the respective 8 exposures.
 The data was taken during four nights in service mode., The data was taken during four nights in service mode.
 During two of these nights the sequence was repeated. so that we have obtained six data sets. each one reaching an approximate /;V-ratio of about 1000 per resolution element.," During two of these nights the sequence was repeated, so that we have obtained six data sets, each one reaching an approximate $/N$ -ratio of about 1000 per resolution element."
 The method for extracting the Stokes V parameter from the data is described in the FORS user manual (2) and by ?.., The method for extracting the Stokes $V$ parameter from the data is described in the FORS user manual \citep{FORS} and by \citet{2002A&A...389..191B}.
 Example Stokes V data are presented in Fig. [::, Example Stokes V data are presented in Fig. \ref{fig_FORSV};
 in this figure. and for the field strength determination (as in Fig. 29).," in this figure, and for the field strength determination (as in Fig. \ref{fig_FORSB}) ),"
 there is no rebinning from pixel space to uniform wavelength space., there is no rebinning from pixel space to uniform wavelength space.
 We calculated the wavelength for the respective data points based on the HgCd and He are line spectra taken during daytime., We calculated the wavelength for the respective data points based on the HgCd and He arc line spectra taken during daytime.
" Flat fielding is largely unnecessary for the Stokes 1 determinations. because the alternate measurement of —1/7 and Vílat./ 45"" and 45 retarder plate angles cancels out any pixel- variations in the CCD response: nevertheless. because"," Flat fielding is largely unnecessary for the Stokes $V$ determinations, because the alternate measurement of $-V/I$ and $V/I$ at $-45\degr$ and $45\degr$ retarder plate angles cancels out any pixel-to-pixel variations in the CCD response; nevertheless, because"
Toy.,$T_\mathrm{eff}$.
 Later. when the object was becoming cooler. an increasing discrepancy appears in the sense that Τω obtained using the supergiant spectra is systematically lower than that from using the giant spectra.," Later, when the object was becoming cooler, an increasing discrepancy appears in the sense that $T_\mathrm{eff}$ obtained using the supergiant spectra is systematically lower than that from using the giant spectra."
 The reason lies in the calibrations of Ty versus spectral type used in our study (Schmidt-Kaler 1982))., The reason lies in the calibrations of $T_\mathrm{eff}$ versus spectral type used in our study (Schmidt-Kaler \cite{sk}) ).
 For the same spectral type. the value of Zr for supergiants is systematically lower than that for the giants but for the G. K types the difference is small.," For the same spectral type, the value of $T_\mathrm{eff}$ for supergiants is systematically lower than that for the giants but for the G, K types the difference is small."
 For the M types the discrepancy increases and becomes as large as 530 K at MS., For the M types the discrepancy increases and becomes as large as 530 K at M5.
 This has obvious consequences for the derived effective radii and luminosities: the use of the supergiant standard spectra usually results in larger radit and luminosities., This has obvious consequences for the derived effective radii and luminosities: the use of the supergiant standard spectra usually results in larger radii and luminosities.
 Comparing our results with those obtained by MWT99.. one sees that on March 4 and 9 their Ty is systematically higher.," Comparing our results with those obtained by \cite{martini}, one sees that on March 4 and 9 their $T_\mathrm{eff}$ is systematically higher."
 This agrees with what was noted in MWT99.. namely that the value of Τω they obtained from the stellar model analysis was too high for the observed spectral type.," This agrees with what was noted in \cite{martini}, namely that the value of $T_\mathrm{eff}$ they obtained from the stellar model analysis was too high for the observed spectral type."
 MWT99 ascribed this discrepancy to the narrow observed spectral range.," \cite{martini}
 ascribed this discrepancy to the narrow observed spectral range."
 On the later dates the spectral types and 7. derived in MWTO99 are consistent and. as can be seen from Fig.," On the later dates the spectral types and $T_\mathrm{eff}$ derived in \cite{martini} are consistent and, as can be seen from Fig."
 4aa. their Των follows quite closely our values obtained using the supergiant spectra.," \ref{evol_f}a a, their $T_\mathrm{eff}$ follows quite closely our values obtained using the supergiant spectra."
 Note that. as discussed in Sect. 4.3.. ," Note that, as discussed in Sect. \ref{analys_fr}, ,"
our results obtained from the data on 5-6 June 1994 (symbols at log ¢=2.0 in Fig. 4)), our results obtained from the data on 5–6 June 1994 (symbols at log $t \simeq 2.0$ in Fig. \ref{evol_f}) )
 are subject to significant uncertainty., are subject to significant uncertainty.
 They are based on uncertain observational estimates done only in the Wien?u part of the spectrum. as well as. on the extrapolated standard spectra.," They are based on uncertain observational estimates done only in the Wien's part of the spectrum, as well as, on the extrapolated standard spectra."
 Due to the increasing discrepancy in. the effective temperature between giants and supergiants for the late M types. discussed above. the difference between our estimates of Tay is as large as 900 K. This resulted in large differences in the stellar radius and luminosity seen in Table 3. and Fig. 4.. MWT99..," Due to the increasing discrepancy in the effective temperature between giants and supergiants for the late M types, discussed above, the difference between our estimates of $T_\mathrm{eff}$ is as large as 900 K. This resulted in large differences in the stellar radius and luminosity seen in Table \ref{evol_t} and Fig. \ref{evol_f}. \cite{martini},"
 from their model atmosphere analysis. estimated that by 5-6 June the object had faded by a factor of 100 in lummosity compared to the beginning of March.," from their model atmosphere analysis, estimated that by 5–6 June the object had faded by a factor of 100 in luminosity compared to the beginning of March."
 Adopting our determinations of - Lo for the beginning of March this results in an estimate of -50 Lc and. assuming 7=2300 KK (from MWT99)). an effective radius of «44 Rc; on 5-6June.," Adopting our determinations of $\sim$ $L_{\sun}$ for the beginning of March this results in an estimate of $\sim$ $L_{\sun}$ and, assuming $T_\mathrm{eff} = 2300$ K (from \cite{martini}) ), an effective radius of $\sim$ $R_{\sun}$ on 5–6June."
 These estimates are shown with asterisks in Fig. 4 emph(b)(e).., These estimates are shown with asterisks in Fig. \ref{evol_f} .
Telescope (HST) point-spread function that did not reflect the spatial binning of the STIS CCD (this was the only one of the 12 galaxies in that paper in which this error was made).,Telescope (HST) point-spread function that did not reflect the spatial binning of the STIS CCD (this was the only one of the 12 galaxies in that paper in which this error was made).
 The revised mass is (8.5E3.5)«107M... at a distance of 24.] megaparsees. a factor of 2.3 higher than was reported previously (at the same distance).," The revised mass is $(8.5 \pm 3.5) \times
10^7 \Msun$, at a distance of 24.1 megaparsecs, a factor of 2.3 higher than was reported previously (at the same distance)."
 In order to conduct the experiment illustrated in Figure | we oversampled the grid by a factor of 2 relative to the prescription above in each dimension and then dropped out orbits at random to obtain the libraries illustrated., In order to conduct the experiment illustrated in Figure 1 we oversampled the grid by a factor of 2 relative to the prescription above in each dimension and then dropped out orbits at random to obtain the libraries illustrated.
 In Figure | we show the 4 profile as a function of BH mass (we have already marginalized over the galaxy mass-to-light ratio)., In Figure 1 we show the $\chi^2$ profile as a function of BH mass (we have already marginalized over the galaxy mass-to-light ratio).
 For small orbit libraries. Figure 1 exhibits the ragged  emphasized by VME.," For small orbit libraries, Figure 1 exhibits the ragged $\chi^2$ emphasized by VME."
" It also shows that for our nominallibrary with N,,;, =10.000 orbits. the 47 profile is smooth enough to infer BH mass estimates and uncertainties. and that that larger libraries do not alter the mass estimate."," It also shows that for our nominallibrary with $N_{orb}=$ 10,000 orbits, the $\chi^2$ profile is smooth enough to infer BH mass estimates and uncertainties, and that that larger libraries do not alter the mass estimate."
 Once the number of orbits is large enough that the 47 profile does not change as it is increased further.orbits. and the phase-space coverage be good enough.," Once the number of orbits is large enough that the $\chi^2$ profile does not change as it is increased further, and the phase-space coverage be good enough."
"by unrelated factors, we repeated this calculation for constant stars.","by unrelated factors, we repeated this calculation for constant stars."
 For that purpose we select stars below the magenta line in Figure 2 with myx22., For that purpose we select stars below the magenta line in Figure \ref{fig:qa} with $m_g\le22$.
 The result is shown in the top panel of Figure 4 (green points)., The result is shown in the top panel of Figure \ref{fig:sf} (green points).
" As expected, the SF of non-variable stars is flat over the entire range of time-scales."," As expected, the SF of non-variable stars is flat over the entire range of time-scales."
 We conclude that the observed variability of quasars is intrinsic and not caused by unrecognized measurement errors., We conclude that the observed variability of quasars is intrinsic and not caused by unrecognized measurement errors.
 The stellar structure function exceeds the noise level for the quasar sample because the stars selected for this comparison are fainter on average than the quasars., The stellar structure function exceeds the noise level for the quasar sample because the stars selected for this comparison are fainter on average than the quasars.
 The quasar SF in the top panel of Figure 4 displays several slopes and breaks., The quasar SF in the top panel of Figure \ref{fig:sf} displays several slopes and breaks.
" It starts flat at 7<2 days, then at 2€rX10 days gradually transitions to an approximate power-law increase over 10<740 days, and finally breaks to a shallower slope above 7~100."," It starts flat at $\tau\le2$ days, then at $2\le\tau\le10$ days gradually transitions to an approximate power-law increase over $10\le\tau\le40$ days, and finally breaks to a shallower slope above $\tau\simeq100$."
" The flat portion of the SF is clearly due to noise and the transition to the first power-law section is due to SFs of single quasars with different mean brightness m, reaching the level of noise at different Τ (see Equation 2)).", The flat portion of the SF is clearly due to noise and the transition to the first power-law section is due to SFs of single quasars with different mean brightness $m_g$ reaching the level of noise at different $\tau$ (see Equation \ref{eq:sf2}) ).
 The slopes seen at 10€7<40 days and 7>100 have a physical origin and are discussed further below., The slopes seen at $10\le\tau\le40$ days and $\tau\ge100$ have a physical origin and are discussed further below.
 The time interval between 40 and 100 days is poorly sampled and difficult to interpret., The time interval between 40 and 100 days is poorly sampled and difficult to interpret.
 This is a result of the SDSS scanning strategy for Stripe 82 that produces relatively few observations separated by 90-270 days in the observer frame (cf., This is a result of the SDSS scanning strategy for Stripe 82 that produces relatively few observations separated by 90–270 days in the observer frame (cf.
 Figure 3)) combined with the mean redshift of the sample ~1.5., Figure \ref{fig:qso_ex}) ) combined with the mean redshift of the sample $\sim1.5$.
 The noise contributes to the SF equally at all timescales and must be subtracted in order to expose the intrinsic quasar variability., The noise contributes to the SF equally at all timescales and must be subtracted in order to expose the intrinsic quasar variability.
 The noise-corrected SF is shown in the bottom panel of Figure 4 (blue points)., The noise-corrected SF is shown in the bottom panel of Figure \ref{fig:sf} (blue points).
" 'The shape of the quasar SF is dominated by two slopes that we estimate by fitting a broken power law model to the data We find αι=0.33, ag=0.79, το=42.3 days, and B=0.13 (solid red line)."," The shape of the quasar SF is dominated by two slopes that we estimate by fitting a broken power law model to the data We find $\alpha_1=0.33$, $\alpha_2=0.79$, $\tau_0=42.3$ days, and $\beta =
0.13$ (solid red line)."
" The reduced x? of the fit is far from unity, ie. Equation 3 does not provide a complete description of the data."," The reduced $\chi^2$ of the fit is far from unity, i.e. Equation \ref{eq:bpl} does not provide a complete description of the data."
" However, the main goal here is to detect and estimate the two slopes in the overall shape of the SF for an ensemble of quasars, and compare those coefficients with theoretical predictions."," However, the main goal here is to detect and estimate the two slopes in the overall shape of the SF for an ensemble of quasars, and compare those coefficients with theoretical predictions."
" We also estimate errors on the derived parameters using ""jackknife' resampling.", We also estimate errors on the derived parameters using 'jackknife' resampling.
" Namely, we randomly select 1/3 part of the sample, drop it, and fit ensemble SF built from the rest."," Namely, we randomly select 1/3 part of the sample, drop it, and fit ensemble SF built from the rest."
 We repeat the procedure 100 times and estimate the error on the given parameter as r.m.s., We repeat the procedure 100 times and estimate the error on the given parameter as r.m.s.
 of proper distribution., of proper distribution.
" Such estimation gives very small errors (0.01, 0.02, 3.9 days, and 0.01 for o4, a2, 7o, and B saying that the shape of ensemble SF is quite stable to correspondingly)small variations of the sample."," Such estimation gives very small errors (0.01, 0.02, 3.9 days, and 0.01 for $\alpha_1$, $\alpha_2$, $\tau_0$, and $\beta$ correspondingly) saying that the shape of ensemble SF is quite stable to small variations of the sample."
 For comparison we plot the g-band SF from Wilhite (black points in the bottom panel of," For comparison we plot the $g$ -band SF from \cite{2008MNRAS.383.1232W}
 (black points in the bottom panel of"
fIuicl. ancl the effect of the distributed mass within each protogalaxy is not mocleed at all.,"fluid, and the effect of the distributed mass within each protogalaxy is not modeled at all."
 These aspects of a more realistic model are supposed to be represented by the lreedom allowed to the peculiar motious of the mass tracers representiug the protogalaxies at high redshifS., These aspects of a more realistic model are supposed to be represented by the freedom allowed to the peculiar motions of the mass tracers representing the protogalaxies at high redshifts.
" The 12 preseut positions rtj in the four-body inodel are given: the 121, equations (9)) auc (3.2)) are to be solved for the 125, quantities aT for L€nxcUn,."," The 12 present positions $x^k_{i,n_x+1}$ in the four-body model are given; the $12n_x$ equations \ref{eq:NAM}) ) and \ref{eq:NAMi}) ) are to be solved for the $12n_x$ quantities $x^k_{i,n}$ for $1\leq n\leq n_x$."
 This is terned a πμ| actiou imetliod because the S are derivatives of the leaplrog approximation to the actior. (," This is termed a numerical action method because the $S^k_{i,n}$ are derivatives of the leapfrog approximation to the action. ("
It might be mentioned that the addition of a dyuamical drag term would remove the relation {ο an action. but the relaxation o Sry=0 with friction would still produce solutious to the discree leaplrog approximation to the equations of motion.),"It might be mentioned that the addition of a dynamical drag term would remove the relation to an action, but the relaxation to $S^k_{i,n}=0$ with friction would still produce solutions to the discrete leapfrog approximation to the equations of motion.)"
 The NA1 solution is obtaiued by iterated relaxation ol the path of each ody in turn., The NAM solution is obtained by iterated relaxation of the path of each body in turn.
" The A,14/ are adjusted to reduce tlie S7.lah to zero usineo he inverse of the 3n, by 315, —iatrix of derivatives of the Sh with respect to ther fμε,"," The $x^{k'}_{i,n'}$ are adjusted to reduce the $S^k_{i,n}$ to zero using the inverse of the $3n_x$ by $3n_x$ matrix of derivatives of the $S^k_{i,n}$ with respect to the $x^{k'}_{i,n'}$."
 There isB not a uniqueH solution at given mixed boundary couditious: the solution this procedure reaches depeids ou the starting trial paths., There is not a unique solution at given mixed boundary conditions; the solution this procedure reaches depends on the starting trial paths.
 The matrix of derivatives of tle S is written down and its use described iu more detail in Peebles (1995).," The matrix of derivatives of the $S^k_{i,n}$ is written down and its use described in more detail in Peebles (1995)."
" In the forward utunerical inteeratione of the equatious of motionthe first approximation to the initial physical position r; aud velocity v; of body 7 at the starting value a, of the expausion parameter are taken [rom the NAM solution at a chosen time step ny. n— + 2 vo—alH.— B )/2."," In the forward numerical integration of the equations of motionthe first approximation to the initial physical position $\rv_i$ and velocity $\vv_i$ of body $i$ at the starting value $a_s$ of the expansion parameter are taken from the NAM solution at a chosen time step $n_b$, = + = a_s^2 H_s + + )/2."
(011)Ry The Hubble parameter Ay at ay is given by equation (3.1))., The Hubble parameter $H_s$ at $a_s$ is given by equation \ref{eq:Friedmann}) ).
 Since the position ;rfjLg) at hieh redshift varies with time in a reasonably close approximation to Svκα} these iuterpolations are useful approxiuiations to the wanted initial couclitious.," Since the position $x^k_{i,n}$ at high redshift varies with time in a reasonably close approximation to $\delta x^k_{i,n} \propto a(t)$ these interpolations are useful approximations to the wanted initial conditions."
" The solutions presented bere use 77=2 from the,=20 NAM time steps.", The solutions presented here use $n_b=2$ from the $n_x=20$ NAM time steps.
 That is. the initial conditious are interpolated between i=2 aud av= 3. and the forward integration comaences at recshif Le," That is, the initial conditions are interpolated between $n=2$ and $n=3$ , and the forward integration commences at redshift 1+z_s = 1/a_s = 10.25."
Quiescent filaments/prominences are cool and dense magnetic and plasma structures suspended against gravity by forces thought to be of magnetic origin.,Quiescent filaments/prominences are cool and dense magnetic and plasma structures suspended against gravity by forces thought to be of magnetic origin.
 In spite of their physical properties. with temperatures and densities that are akin to those in the chromosphere. some as yet not well determined mechanisms provide the required thermal isolation from the surrounding coronal plasma and mechanical support during typical lifetimes from few days to weeks.," In spite of their physical properties, with temperatures and densities that are akin to those in the chromosphere, some as yet not well determined mechanisms provide the required thermal isolation from the surrounding coronal plasma and mechanical support during typical lifetimes from few days to weeks."
 The magnetic field that pervades these structures is believed to play a key role in the nature and the thermodynamic and mechanical stability of prommences., The magnetic field that pervades these structures is believed to play a key role in the nature and the thermodynamic and mechanical stability of prominences.
 Early observations carried out with good seeing conditions pointed out that prominences consist of fine threads (deJager.1959:Kuperus&Tandberg-Hanssen. 1967).," Early observations carried out with good seeing conditions pointed out that prominences consist of fine threads \citep{dejager59,kuperusTH67}."
". More recent high-resolution H, observations obtained with the Swedish Solar Telescope (SST) in La Palma (Linetal..2005) and the Dutch Open Telescope (DOT) in Tenerife (Heinzel&Anzer.2006) have allowed to firmly establish the filament sub-structuring and the basic geometrical and physical properties of threads (seealsoEngvold.1998;Linetal..2005.2008:Lin. 2010)."," More recent high-resolution $_\alpha$ observations obtained with the Swedish Solar Telescope (SST) in La Palma \citep{Lin05} and the Dutch Open Telescope (DOT) in Tenerife \citep{HA06} have allowed to firmly establish the filament sub-structuring and the basic geometrical and physical properties of threads \citep[see also][]{Engvold98, Lin05, Lin08, Lin10}."
. The sub-structure of quiescent prominences is often composed by a myriad of horizontal. dark and fine threads. made of cool absorbing material. believed to outline magnetic flux tubes (Engvold.1998.2008:Lin.2004:Linetal..2005.2008:Martinetal.. 2008).," The sub-structure of quiescent prominences is often composed by a myriad of horizontal, dark and fine threads, made of cool absorbing material, believed to outline magnetic flux tubes \citep{Engvold98,Engvold08, Linthesis, Lin05, Lin08,Martin08}."
. The tubes are only partially filled with cool and dense plasma and their total length is probably much larger (~ 10° km) than the threads themselves., The tubes are only partially filled with cool and dense plasma and their total length is probably much larger $\sim$ $^5$ km) than the threads themselves.
 The measured average width of resolved threads is about 0.3 aresee (~ 210 km) while their length is between 5 and 40 aresee (~ 3500 - 28 000 km)., The measured average width of resolved threads is about 0.3 arcsec $\sim$ $210$ km) while their length is between 5 and 40 arcsec $\sim$ 3500 - 28 000 km).
 The absorbing cool material is usually visible for up to 20 minutes (Linetal..2005)., The absorbing cool material is usually visible for up to 20 minutes \citep{Lin05}.
. The measured widths are close to the current resolution limit. ~ 0.16 aresee at the SST. hence thinner structures are likely to exist.," The measured widths are close to the current resolution limit, $\sim$ 0.16 arcsec at the SST, hence thinner structures are likely to exist."
 Small amplitude oscillations m prominence threads are frequently observed2010)., Small amplitude oscillations in prominence threads are frequently observed.
. Early two-dimensional observations of filaments (Yi&Engvold.199];Υetal.1991) revealed that individual threads or groups of them oscillate with periods that range between 3 and 20 minutes.," Early two-dimensional observations of filaments \citep{YiEngvold91,Yi91} revealed that individual threads or groups of them oscillate with periods that range between 3 and 20 minutes."
 Recent relevant examples are traveling waves propagating along a number of threads with average phase speed of 12 km s'. wavelength of 4 aresec. and oscillatory periods that varyfrom 3 to 9 minutes (Linetal..2007).. the both propagating and standing oscillations detected over large areas of prominences by Terradasetal.(2002) and Lin(2004).. as well as observations from instruments onboard space-crafts. such as SoHO (Blancoetal..1999;Régnier2001:Pougetetal..2006) and Hinode (Okamotoetal..2007;Terradas2008b:Ningetal.. 2009).," Recent relevant examples are traveling waves propagating along a number of threads with average phase speed of 12 km $^{-1}$, wavelength of 4 arcsec, and oscillatory periods that varyfrom 3 to 9 minutes \citep{Lin07}, the both propagating and standing oscillations detected over large areas of prominences by \citet{Terradas02} and \citet{Linthesis}, as well as observations from instruments onboard space-crafts, such as SoHO \citep{Blanco99,Regnier01,Pouget06} and Hinode \citep{Okamoto07,Terradas08hinode,Ning09}."
". The transverse oscillation nature of some of these events has been clearly established by Linetal.(2009) by combining H, filtergrams in the plane of the sky with H, Dopplergrams which allow to detect oscillations in the line-of-sight direction.", The transverse oscillation nature of some of these events has been clearly established by \citet{Lin09} by combining $_\alpha$ filtergrams in the plane of the sky with $_\alpha$ Dopplergrams which allow to detect oscillations in the line-of-sight direction.
 A recurrently observed property of prominence oscillations is their rapid temporal damping. with perturbations decaying in time-scales of only a few oscillatory periods (Landmanetal.1977:Tsubaki&Takeuchi.1986:Terradasetal..2002;Lin.2004:Ning 2009).," A recurrently observed property of prominence oscillations is their rapid temporal damping, with perturbations decaying in time-scales of only a few oscillatory periods \citep{Landman77,Tsubaki86,Tsubaki88,Wiehr89,Molowny-Horas99,Terradas02,Linthesis,Ning09}."
 Τransverse thread oscillations are commonly interpreted in terms of standing or propagating magnetohydrodynamic (MHD) kink waves., Transverse thread oscillations are commonly interpreted in terms of standing or propagating magnetohydrodynamic (MHD) kink waves.
 The measured periods are of the order of a few minutes and the wavelengths are in between 3000 - 20 000 km. although Okamotoetal.(2007) report larger wavelengths more consistent with the standing wave interpretation.," The measured periods are of the order of a few minutes and the wavelengths are in between 3000 - 20 000 km, although \citet{Okamoto07} report larger wavelengths more consistent with the standing wave interpretation."
 The measured wave quantities allow us to derive phase speeds that are consistent with the kink speed in magnetic and plasma configurations with typical properties of prominence plasmas., The measured wave quantities allow us to derive phase speeds that are consistent with the kink speed in magnetic and plasma configurations with typical properties of prominence plasmas.
 The MHD wave interpretation of thread oscillations has allowed the development of theoretical models (seeBallester. reviews).. Joarderetal.," The MHD wave interpretation of thread oscillations has allowed the development of theoretical models \citep[see][for recent reviews]{Ballester05,Ballester06}. ."
(1997);Diaz considered the MHD eigenmodes supported by a filament thread modelled in Cartesian geometry.," \citet{JNR97,diaz01,diaz03} considered the MHD eigenmodes supported by a filament thread modelled in Cartesian geometry."
 More realistic studies using cylindrical configurations have extended, More realistic studies using cylindrical configurations have extended
limited to frequencies not observable on earth (i.e. below the ionospheric cutoff).,limited to frequencies not observable on earth (i.e. below the ionospheric cutoff).
" The results of table 1 are visualized in figure 1 (for the model), figure 2 (for the model) and figure 3 (for the model)."," The results of table 1 are visualized in figure \ref{fig:radiopredictionSWmag} (for the model), figure \ref{fig:radiopredictionCMEkin} (for the model) and figure \ref{fig:radiopredictionSWkin} (for the model)."
" The predicted planetary radio emission is denoted by open triangles (two for each “potentially locked” planet, otherwise one per planet)."," The predicted planetary radio emission is denoted by open triangles (two for each “potentially locked” planet, otherwise one per planet)."
 The typical uncertainties (approx., The typical uncertainties (approx.
" one order of magnitude for the flux, and a factor of 2-3 for the maximum emission frequency) are indicated by the arrows in the upper right corner."," one order of magnitude for the flux, and a factor of 2-3 for the maximum emission frequency) are indicated by the arrows in the upper right corner."
" The sensitivity limit of previous observation attempts are shown as filled symbols and as solid lines (amoredetailedcomparisonoftheseobser-2006a;GrieBmeier, 2006)."," The sensitivity limit of previous observation attempts are shown as filled symbols and as solid lines \citep[a more detailed comparison of these observations can be found in][]{Zarka04a,Griessmeier51PEG05,GriessmeierPHD06}."
". The expected sensitivity of new and future detectors (for 1 hour integration and 4 MHz bandwidth, or any equivalent combination) is shown for comparison."," The expected sensitivity of new and future detectors (for 1 hour integration and 4 MHz bandwidth, or any equivalent combination) is shown for comparison."
" Dashed line: upgraded UTR-2, dash-dotted lines: low band and high band of LOFAR, left dotted line: LWA, right dotted line: SKA."," Dashed line: upgraded UTR-2, dash-dotted lines: low band and high band of LOFAR, left dotted line: LWA, right dotted line: SKA."
 The instruments’ sensitivities are defined by the radio sky background., The instruments' sensitivities are defined by the radio sky background.
" For a given instrument, a planet is observable if it is located either above the instrument’s symbol or above and to its right."," For a given instrument, a planet is observable if it is located either above the instrument's symbol or above and to its right."
" Again, large differences in expected flux densities are apparent between the different models."," Again, large differences in expected flux densities are apparent between the different models."
" On average, the model yields the largest flux densities, and the model yields the lowest values."," On average, the model yields the largest flux densities, and the model yields the lowest values."
" Depending on the model, between one and three planets are likely to be observable using the upgraded system of UTR-2."," Depending on the model, between one and three planets are likely to be observable using the upgraded system of UTR-2."
 Somewhat higher numbers are found for LOFAR., Somewhat higher numbers are found for LOFAR.
" Considering the uncertainties mentioned above, these numbers should not be taken literally, but should be seen as an indicator that while observation seem feasible, the number of suitable candidates is rather low."," Considering the uncertainties mentioned above, these numbers should not be taken literally, but should be seen as an indicator that while observation seem feasible, the number of suitable candidates is rather low."
" It can be seen that the maximum emission frequency of many planets lies below the ionospheric cutoff frequency, making earth-based observation of these planets impossible."," It can be seen that the maximum emission frequency of many planets lies below the ionospheric cutoff frequency, making earth-based observation of these planets impossible."
 A moon-based radio telescope however would give access to radio emission with frequencies of a few MHz 2007).., A moon-based radio telescope however would give access to radio emission with frequencies of a few MHz \citep{Zarka06PSS}. .
" As can be seen in figures 1, 2 and 3,, this frequency range includes a significant number of potential target planets with relatively high flux densities."," As can be seen in figures \ref{fig:radiopredictionSWmag}, \ref{fig:radiopredictionCMEkin} and \ref{fig:radiopredictionSWkin}, this frequency range includes a significant number of potential target planets with relatively high flux densities."
" Figures 1,, 2 and 3 also show that the relatively high frequencies of the LOFAR high band and of the SKA telescope are probably not very well suited for the search for exoplanetary radio emission."," Figures \ref{fig:radiopredictionSWmag}, \ref{fig:radiopredictionCMEkin} and \ref{fig:radiopredictionSWkin} also show that the relatively high frequencies of the LOFAR high band and of the SKA telescope are probably not very well suited for the search for exoplanetary radio emission."
" These instruments could, however, be used to search for radio emission generated by between planets and strongly magnetised stars."," These instruments could, however, be used to search for radio emission generated by between planets and strongly magnetised stars."
" According to our analysis, the best candidates are: 'To this list, one should add the planets around Ups And (b, c and d) and of HD 179949 b, whose parent stars exhibit an increase of the chromospheric emission of about (Shkolniketal.,2003,2004,2005)."," According to our analysis, the best candidates are: To this list, one should add the planets around Ups And (b, c and d) and of HD 179949 b, whose parent stars exhibit an increase of the chromospheric emission of about \citep{Shkolnik03,Shkolnik04,Shkolnik05}."
". The observations indicate one maximum per planetary orbit,a “Hot Spot"" in the stellar chromosphere which is in"," The observations indicate one maximum per planetary orbit,a “Hot Spot” in the stellar chromosphere which is in"
"serious correlator problems during the night of 17-18 July 2007 (RT9-RTA = 60 m). the final data reduction was done using 5x I2"" of observation.","serious correlator problems during the night of 17–18 July 2007 (RT9–RTA = 60 m), the final data reduction was done using $5 \times$ $^{\rm h}$ of observation."
 The total amount of flagged data was 35%., The total amount of flagged data was $\sim35$.
. The resolution at 150 MHz is 163”x181”.," The resolution at 150 MHz is $163\hbox{\arcsec}
\times 181\hbox{\arcsec}$."
 The WSRT telescopes are equipped with à pair of orthogonal feeds (XY)., The WSRT telescopes are equipped with a pair of orthogonal feeds (XY).
 All four cross correlations between the incident signals are The overall (on-axis) instrumental leakages at the WSRT. typically1%—2%.. were calibrated using an. unpolarized calibrator.," All four cross correlations between the incident signals are The overall (on-axis) instrumental leakages at the WSRT, typically, were calibrated using an unpolarized calibrator."
 The instrumental polarization. corrections. were transferred to the polarized calibrator. which was then used to phase-align the two orthogonal linear polarizations.," The instrumental polarization corrections were transferred to the polarized calibrator, which was then used to phase-align the two orthogonal linear polarizations."
 Finally. the polarization corrections Were transferred to the target source.," Finally, the polarization corrections were transferred to the target source."
 The beam pattern of the WSRT has strong instrumental off-axis polarization (e.g.??).. which changes with frequency with a dominant 17 MHz pattern.," The beam pattern of the WSRT has strong instrumental off-axis polarization \citep[e.g. ][]{2005A&A...441..931D,2008A&A...479..903P}, which changes with frequency with a dominant 17 MHz pattern."
 This instrumental polarization might be related to standing waves between the dish and the front end., This instrumental polarization might be related to standing waves between the dish and the front end.
 We did not correct for this effect. as it requires software that is not yet available.," We did not correct for this effect, as it requires software that is not yet available."
 The polarization calibration followed the standard steps described in? and ?.., The polarization calibration followed the standard steps described in \citet{1996A&AS..117..137H} and \citet{1996A&AS..117..149S}.
 Most of the calibration procedure was carried out by seripts calling NEWSTAR routines. but manual corrections had to be appliec at 85 em and 2 m because the scripts failed to find a physical solution.," Most of the calibration procedure was carried out by scripts calling NEWSTAR routines, but manual corrections had to be applied at 85 cm and 2 m because the scripts failed to find a physical solution."
 The polarized signal is described by the polarization vectorp. Whose intensity (P) and angle (y) are given by where Q. U. and V are the Stokes parameters.," The polarized signal is described by the polarization vector, whose intensity (P) and angle $\chi$ ) are given by where Q, U, and V are the Stokes parameters."
 When calibrating the data of the polarized calibrator. one must verify that rotates in the QU plane according to the known RM value of the polarized calibrator.," When calibrating the data of the polarized calibrator, one must verify that rotates in the QU plane according to the known RM value of the polarized calibrator."
 The amount of rotation A® is given by where ο is the observing wavelength., The amount of rotation $\Delta \Phi$ is given by where $\lambda$ is the observing wavelength.
 No signal in V is expected to be detected because most of the astrophysical sources only shows linear A phase difference between the X and Y channels. however. will rotate U into V. The X-Y phase difference. of the polarization calibrator is given by Equation + has two solutions: one where / is even and one where 5 is odd.," No signal in V is expected to be detected because most of the astrophysical sources only shows linear A phase difference between the X and Y channels, however, will rotate U into V. The X–Y phase difference of the polarization calibrator is given by Equation \ref{x-y} has two solutions: one where $n$ is even and one where $n$ is odd."
 The wrong solution flips the sign of the RM of the calibrator: therefore. if the sign is knownpriori. it is trivial to select the correct The polarization calibration was performed at 85 cm using DA240 as polarized calibrator.," The wrong solution flips the sign of the RM of the calibrator; therefore, if the sign is known, it is trivial to select the correct The polarization calibration was performed at 85 cm using DA240 as polarized calibrator."
 Since this source has an +3.33+0.14 rad m7 (?).. we verified that at the end of the calibration p rotates ~| rad from 381 MHz to 315 MHz and that there is no residual V signal At 150 MHz. we used as polarized calibrator.," Since this source has an ${\rm RM} =
+3.33\pm0.14$ rad $^{-2}$ \citep{2008A&A...489...69B}, we verified that at the end of the calibration $p$ rotates $\sim1$ rad from 381 MHz to 315 MHz and that there is no residual V signal At 150 MHz, we used as polarized calibrator."
 The source was observed 7 times during each observing session. in order to monitor its RM changes.," The source was observed 7 times during each observing session, in order to monitor its RM changes."
 This pulsar has an RM of +8.19 + 0.08 rad m (see Sect. 2.6)), This pulsar has an RM of +8.19 $\pm$ 0.08 rad $^{-2}$ (see Sect. \ref{ionosphericfaradayrotation}) )
 and a polarized intensity of ~1.5 Jy at 146 The results of the procedure are shown in Fig. 1..," and a polarized intensity of $\sim1.5$ Jy at 146 The results of the procedure are shown in Fig. \ref{qupoints},"
 where we present the situation in one band (146 MHz) for the first observing night (RT9-RTA = 36 m) before (top panel) and after (bottom panel) the polarization calibration., where we present the situation in one band (146 MHz) for the first observing night (RT9–RTA = 36 m) before (top panel) and after (bottom panel) the polarization calibration.
 To increase the signal to noise ratio and have a better determination of the measured Q. U. and V fluxes. the data were averaged every 10 channels.," To increase the signal to noise ratio and have a better determination of the measured Q, U, and V fluxes, the data were averaged every 10 channels."
 Before the correction. the QU points lie on a circle with approximately the correct radius. but with the wrong order: going from lower frequencies to higher frequencies. the circle should be deseribed clockwise. while here we see the opposite situation.," Before the correction, the QU points lie on a circle with approximately the correct radius, but with the wrong order: going from lower frequencies to higher frequencies, the circle should be described clockwise, while here we see the opposite situation."
 Consequently. in the UV plots there are points that have a non-zero V value.," Consequently, in the UV plots there are points that have a non-zero V value."
 The signal in V should be transferred to U. The X-Y phase difference. calculated using a linear fit for the UV points. defines the correction thàt must be applied to the data.," The signal in V should be transferred to U. The X–Y phase difference, calculated using a linear fit for the UV points, defines the correction that must be applied to the data."
 This 1s determined for each time cut and averaged during the night., This is determined for each time cut and averaged during the night.
 After the correction. all the points have approximately à zero V value and describe a circle in the QU plane with the correct rotation direction.," After the correction, all the points have approximately a zero V value and describe a circle in the QU plane with the correct rotation direction."
 The signal was also corrected for the ionospheric Faraday rotation. which is relevant at low frequencies.," The signal was also corrected for the ionospheric Faraday rotation, which is relevant at low frequencies."
 This is described below., This is described below.
 The Earth’s ionosphere has density fluctuations that mostly affect low-frequency observations. introducing a direction-dependent variation in the phase of the signal received by the interferometer.," The Earth's ionosphere has density fluctuations that mostly affect low-frequency observations, introducing a direction-dependent variation in the phase of the signal received by the interferometer."
 In addition. it also affects the polarization. giving rise to time-variable Faraday rotation.," In addition, it also affects the polarization, giving rise to time-variable Faraday rotation."
 This often amounts to several turns of the polarization. vector in the QU plane at low frequency., This often amounts to several turns of the polarization vector in the QU plane at low frequency.
 This effect can significantly depolarize the signal., This effect can significantly depolarize the signal.
 The tonospherie Faraday rotation at the WSRT is typically a few tenths of rad m7? during night time., The ionospheric Faraday rotation at the WSRT is typically a few tenths of rad $^{-2}$ during night time.
 Daytime values of 5 rad m7 are also possible during the solar maximum (?).., Daytime values of 5 rad $^{-2}$ are also possible during the solar maximum \citep{2008A&A...489...69B}.
 A variation of just 0.5 rad m in ionospheric Faraday depth corresponds to a change in polarization angle of the signal of ~200° at 115 MHz. the lowest frequency of the 2 m observations.," A variation of just 0.5 rad $^{-2}$ in ionospheric Faraday depth corresponds to a change in polarization angle of the signal of $\sim200^{\circ}$ at 115 MHz, the lowest frequency of the 2 m observations."
 The correction for this effect. is important. because it could significantly affect the results of the polarization imaging.," The correction for this effect is important, because it could significantly affect the results of the polarization imaging."
 The correction for the ionospheric Faraday rotation was only applied to the 2 m dataset. which is the one most affected by the problem.," The correction for the ionospheric Faraday rotation was only applied to the 2 m dataset, which is the one most affected by the problem."
 It was computed using global GPS total ionospheric electron content (TEC) data and an analytical model for the geomagnetic field., It was computed using global GPS total ionospheric electron content (TEC) data and an analytical model for the geomagnetic field.
 The GPS-TEC data were provided by the Center for Orbit Determination in Europe (CODE) of the Astronomical Institute of the university of Bern. Switzerland.," The GPS-TEC data were provided by the Center for Orbit Determination in Europe (CODE) of the Astronomical Institute of the university of Bern, Switzerland."
 The geomagnetic field was computed using the International Geomagnetic Reference Field (IGRF). which consists of a series of mathematical models of the Earth's," The geomagnetic field was computed using the International Geomagnetic Reference Field (IGRF), which consists of a series of mathematical models of the Earth's"
most of their mass from filaments.,most of their mass from filaments.
 In contrast. a lower mass halo may be substantially less massive (han the filament it inhabits.," In contrast, a lower mass halo may be substantially less massive than the filament it inhabits."
 The growth of such a halo will appear to be dominated by mergers with the other small halos which populate the same filaanent. (and possibly the other nearby filaments)., The growth of such a halo will appear to be dominated by mergers with the other small halos which populate the same filament (and possibly the other nearby filaments).
 In this respect. our model is qualitatively consistent with observations which suggest that massive clusters grow. by aceretion. along filaments. whereas the growth of lower mass objects is less obviously anisotropic.," In this respect, our model is qualitatively consistent with observations which suggest that massive clusters grow by accretion along filaments, whereas the growth of lower mass objects is less obviously anisotropic."
 Although our approach provides a framework for discussing the morphology of the cosmic web. we have. so far. not made any statements about precisely how the sheets. filaments and halos in our formalism are to be identified in cosmic density fields.," Although our approach provides a framework for discussing the morphology of the cosmic web, we have, so far, not made any statements about precisely how the sheets, filaments and halos in our formalism are to be identified in cosmic density fields."
 Our collapse model is calibrated so that the object which forms after collapse has been completed along all three axes. Le. à halo. has the same densitv relative (to the background. as is expected in the spherical collapse model.," Our collapse model is calibrated so that the object which forms after collapse has been completed along all three axes, i.e., a halo, has the same density relative to the background as is expected in the spherical collapse model."
 Sheets in our model should be approximately this overdensity to the one-thirds power. whereas filaments are this to the two thirds power.," Sheets in our model should be approximately this overdensity to the one-thirds power, whereas filaments are this to the two thirds power."
 Although. formally. the density of a halo depends on the background cosmological model. i( is common practice to identify halos al a given epoch as objects which are 200 times denser than the critical density at that epoch.," Although, formally, the density of a halo depends on the background cosmological model, it is common practice to identify halos at a given epoch as objects which are 200 times denser than the critical density at that epoch."
 Therefore. filaments aud sheets should be approximately 36 and 6 limes denser than the critical densitv.," Therefore, filaments and sheets should be approximately 36 and 6 times denser than the critical density."
 This provides a simple rule of thumb for idlentibving sheets and filaments in the dark matter density field., This provides a simple rule of thumb for identifying sheets and filaments in the dark matter density field.
 Note that. in the context of our model. il mav be more appropriate to think of massive halos as lving at the centers of filaments. rather than defining their endpoints.," Note that, in the context of our model, it may be more appropriate to think of massive halos as lying at the centers of filaments, rather than defining their endpoints."
 It will be interesting to see how these simple estimates compare with measurements in simulations., It will be interesting to see how these simple estimates compare with measurements in simulations.
 We extend (he excursion set approach to quantify how the cosmic web is made up of sheets. filaments ancl halos.," We extend the excursion set approach to quantify how the cosmic web is made up of sheets, filaments and halos."
 Our model assumes that objects form Irom a triaxial collapse: we define sheets as objects which have collapsed along onlv one axis. lilaments as objects which have collapsed along two axes. ancl halos as objects where all three axes have collapsed.," Our model assumes that objects form from a triaxial collapse; we define sheets as objects which have collapsed along only one axis, filaments as objects which have collapsed along two axes, and halos as objects where all three axes have collapsed."
 Therefore. our model requires specification of exactly how triaxial collapse occurs.," Therefore, our model requires specification of exactly how triaxial collapse occurs."
 Appendix A discusses our preferred. collapse model. compares il with Zeldovich’s approximation. and shows how the analvlic arguments of While&Silk(1979). can be extended to provide an accurate analvlic description of our ellipsoidal collapse moclel.," Appendix A discusses our preferred collapse model, compares it with Zeldovich's approximation, and shows how the analytic arguments of \citet{W79} can be extended to provide an accurate analytic description of our ellipsoidal collapse model."
geometry.,geometry.
 Additionally. we have set the maximum level of refinement anywhere on the grid to be time-dependent: successively higher levels of refinement are dropped from the grid as the simulation proceeds.," Additionally, we have set the maximum level of refinement anywhere on the grid to be time-dependent; successively higher levels of refinement are dropped from the grid as the simulation proceeds."
 This has the effect of dramatically increasing the Courant-limited time step at late times. allowing the calculations to be completed in a relatively small amount of computer time.," This has the effect of dramatically increasing the Courant-limited time step at late times, allowing the calculations to be completed in a relatively small amount of computer time."
 Each simulation described in this paper required approximately 3000 CPU hours to cover 10? seconds of simulation time., Each simulation described in this paper required approximately 3000 CPU hours to cover $10^5$ seconds of simulation time.
 This also negated the need to re-map the simulation onto a new grid to continue the simulations to late times (e.g..22?)..," This also negated the need to re-map the simulation onto a new grid to continue the simulations to late times \citep[e.g.,][]{Couch:09, Kifonidis:03, Kifonidis:06}."
 The jets that drive the explosions are introduced as time-dependent boundary conditions at the inner boundary of the grid where we inject two identical. oppositely-directed energetic flows.," The jets that drive the explosions are introduced as time-dependent boundary conditions at the inner boundary of the grid where we inject two identical, oppositely-directed energetic flows."
 In order to facilitate this. απ essentially spherical inner hole is excised from the 2D cylindrical grid.," In order to facilitate this, an essentially spherical inner hole is excised from the 2D cylindrical grid."
 Within this hole. the hydrodynamic solution is not calculated.," Within this hole, the hydrodynamic solution is not calculated."
 A diode boundary condition was enforced at the edge of the hole (see.e.g..2).," A diode boundary condition was enforced at the edge of the hole \citep[see, e.g.,][]{Zingale:02}."
. This boundary condition is equivalent to an outflow boundary condition when the flux into the hole is positive. but the flux out of the hole is always zero.," This boundary condition is equivalent to an outflow boundary condition when the flux into the hole is positive, but the flux out of the hole is always zero."
 We include the gravitational effect of the mass initially residing within the hole as a Newtonian point-mass at the center of the grid. and compute the self-gravity of the gas on the grid.," We include the gravitational effect of the mass initially residing within the hole as a Newtonian point-mass at the center of the grid, and compute the self-gravity of the gas on the grid."
 The mass that flows into the hole is tracked and included in the caleulation of the central point-mass gravitational potential., The mass that flows into the hole is tracked and included in the calculation of the central point-mass gravitational potential.
 The radius of the hole expands during the simulation. cutting out the smallest zones where the Courant condition is most limiting and ensuring that the hole radius is always resolved by a large number of zones as the maximum allowed refinement level is reduced.," The radius of the hole expands during the simulation, cutting out the smallest zones where the Courant condition is most limiting and ensuring that the hole radius is always resolved by a large number of zones as the maximum allowed refinement level is reduced."
" The jet injection velocity. vj. varies in time according to Via)= where vi, is the maximum jet injection velocity and fj is the total jet injection time."," The jet injection velocity, $v_{\rm jet}$, varies in time according to (t) = where $v_{\rm max}$ is the maximum jet injection velocity and $t_{\rm jet}$ is the total jet injection time."
 We ran a total of six simulations., We ran a total of six simulations.
 Two of these simulations are spherical. non-jet-driven. explosions for comparison to the jet-driven cases.," Two of these simulations are spherical, non-jet-driven, explosions for comparison to the jet-driven cases."
 The spherical explosions are initiated m an identical manner to the Jet-driven cases: injection of energetic material. except that the “jet” opening half-angle is 7/2.," The spherical explosions are initiated in an identical manner to the jet-driven cases: injection of energetic material, except that the “jet"" opening half-angle is $\pi/2$."
 For the four jet simulations. the opening half-angle of the jets is about 7/12. The parameters of the jets are listed in Table I..," For the four jet simulations, the opening half-angle of the jets is about $\pi/12$ The parameters of the jets are listed in Table \ref{table:jets}."
 The model name labeling scheme is mMrR|[cold. hot]. whereM ts the progenitor mass to the nearest solar mass.R is the progenitor radius in units of 10! em. and the cold or hot designates the jet parameters used. given in Table 1..," The model name labeling scheme is [cold, hot], where is the progenitor mass to the nearest solar mass, is the progenitor radius in units of $10^{11}$ cm, and the cold or hot designates the jet parameters used, given in Table \ref{table:jets}."
 For all simulations. the maximum extent of the grid is 10 em and the initial radius of the inner hole is 2«10° cm. roughly the radius of the iron core of the progenitor models used.," For all simulations, the maximum extent of the grid is $10^{15}$ cm and the initial radius of the inner hole is $2\times10^8$ cm, roughly the radius of the iron core of the progenitor models used."
 The ambient density and temperature at this inner radius for both progenitors is about 5.2«10° & em™ and 3.3«10” K. The jets are assumed to consist entirely of ??Ni to facilitate the tracking of the injected jet material., The ambient density and temperature at this inner radius for both progenitors is about $5.2\times10^6$ g $^{-3}$ and $3.3\times10^9$ K. The jets are assumed to consist entirely of $^{56}$ Ni to facilitate the tracking of the injected jet material.
 We note. however. the jet parameters in some of our models. e.g.. m7r6cold and m7r6hot. would predominantly freeze out into lighter nuclei te.g.. He) and not into iron group elements (see. e.g.. Pruet et al.," We note, however, the jet parameters in some of our models, e.g., m7r6cold and m7r6hot, would predominantly freeze out into lighter nuclei (e.g., $^4$ He) and not into iron group elements (see, e.g., Pruet et al."
 2004)., 2004).
 Our slower. denser jets would freeze out into the iron group.," Our slower, denser jets would freeze out into the iron group."
" The true resulting “°Ni fraction will then be a strong function of the proton fraction Y, in the jet that we do not attempt to model.", The true resulting $^{56}$ Ni fraction will then be a strong function of the proton fraction $Y_e$ in the jet that we do not attempt to model.
 The parameters of the simulations were chosen so that in every case. the injected jet mass 1s about Ο.Τ... a value similar to the ??Ni mass estimated from observations of SN 2008D (???)..," The parameters of the simulations were chosen so that in every case, the injected jet mass is about $0.1 M_\odot$, a value similar to the $^{56}$ Ni mass estimated from observations of SN 2008D \citep{Soderberg:08, Mazzali:08, Modjaz:09}."
 Also. for each model. except m2rIhot and m2rIsph. the ratio of explosion energy to ejecta mass is about 0.8 (10?!ere/M..). similar to the ratio estimated from measurements of the photospheric velocity of SN 2008D at maximum light (??)..," Also, for each model, except m2r1hot and m2r1sph, the ratio of explosion energy to ejecta mass is about 0.8 $(10^{51}\ {\rm erg} / M_\sun)$, similar to the ratio estimated from measurements of the photospheric velocity of SN 2008D at maximum light \citep{Soderberg:08, Mazzali:08}."
 Model m2rlhot and m2rlIsph have slightly higher explosion energy to ejecta mass ratios of about 1.4 (10°!erg/M.)., Model m2r1hot and m2r1sph have slightly higher explosion energy to ejecta mass ratios of about 1.4 $(10^{51}\ {\rm erg} / M_\sun)$.
 The jet parameters for models m2rlcold and m2rlhot approximately correspond to the jet parameters used in? for their models v3m12 and vim12. respectively.," The jet parameters for models m2r1cold and m2r1hot approximately correspond to the jet parameters used in \citet{Couch:09} for their models v3m12 and v1m12, respectively."
 There are 25 levels of refinement at the start of each simulation and the effective angular resolution. ids 7/1024.," There are 25 levels of refinement at the start of each simulation and the effective angular resolution, $\eta N_x^{-1}$, is $\pi/1024$."
 The simulations are run until 10° seconds. long iNafter shock breakout in all cases.," The simulations are run until $^5$ seconds, long after shock breakout in all cases."
 Figures - 5. show show density plots of the four jet-driven explosion2) simulations at three epochs: when jet injection stops. initial. shock breakout. and the end of the simulation.," Figures \ref{fig:m2r1cold} - \ref{fig:m7r6hot} show show density plots of the four jet-driven explosion simulations at three epochs: when jet injection stops, initial shock breakout, and the end of the simulation."
 In each jet explosion simulation. the jets drive bipolar shocks that expand out from the jet injection sites along the cylindrical axis.," In each jet explosion simulation, the jets drive bipolar shocks that expand out from the jet injection sites along the cylindrical axis."
 The shocks cross in the equatorial plane and establish a dense. hot pancake of unbound material.," The shocks cross in the equatorial plane and establish a dense, hot pancake of unbound material."
 The shocks in all cases erupt from the surface of the progenitor stars first at the poles., The shocks in all cases erupt from the surface of the progenitor stars first at the poles.
 The shocks accelerate into the low-density wind region and sweep around the surface of the progenitor and cross again on the equatorial plane., The shocks accelerate into the low-density wind region and sweep around the surface of the progenitor and cross again on the equatorial plane.
 This happens just before the original equatorial shock structure erupts from the progenitor surface., This happens just before the original equatorial shock structure erupts from the progenitor surface.
 The prolate shock structure evolves toward sphericity in the wind region as the reverse shock. established by the outgoing shock colliding with the wind. sweeps up an unstable shell of ejecta.," The prolate shock structure evolves toward sphericity in the wind region as the reverse shock, established by the outgoing shock colliding with the wind, sweeps up an unstable shell of ejecta."
 The explosions in. the smaller. progenitor. models m2rlhot and m2rlcold. reach the surface of the progenitor approximately 50 seconds after the start of the simulations.," The explosions in the smaller progenitor, models m2r1hot and m2r1cold, reach the surface of the progenitor approximately 50 seconds after the start of the simulations."
 For explosion m2rlcold. the shocks take about 30 seconds to cross the surface of the progenitor and collide along the equatorial plane.," For explosion m2r1cold, the shocks take about 30 seconds to cross the surface of the progenitor and collide along the equatorial plane."
 The shock surface-crossing time is only 20 seconds in model m2rlhot because the shock structure is more spherical than in m2rleold., The shock surface-crossing time is only 20 seconds in model m2r1hot because the shock structure is more spherical than in m2r1cold.
 The shocks reach peak speeds of about 1.4«I0'ems! immediately following eruption from the progenitor surface and then begin to slow in the wind., The shocks reach peak speeds of about $1.4\times10^{10}\ {\rm cm\ s^{-1}}$ immediately following eruption from the progenitor surface and then begin to slow in the wind.
At the end of the simulations. around one day after,"At the end of the simulations, around one day after"
We consider a svstem consisting of /N planets and à primary star moving under their gravitational attraction.,We consider a system consisting of $N$ planets and a primary star moving under their gravitational attraction.
 As we are interested in. possible close. approaches to. or collisions with. the central star we adopt a spherical polar coordinate system (7.06.4) with origin at the stellar centre.," As we are interested in possible close approaches to, or collisions with, the central star we adopt a spherical polar coordinate system $ (r, \theta, \varphi)$ with origin at the stellar centre."
 The planets anc central star are treated: às. point. masses., The planets and central star are treated as point masses.
 Llowever. to take into account. possible losses. of orbital energv and angular momentum to the stellar material. a simple model for taking into account the tidal interaction between the star ancl a closely approaching planet is also incluced.," However, to take into account possible losses of orbital energy and angular momentum to the stellar material, a simple model for taking into account the tidal interaction between the star and a closely approaching planet is also included."
 The equations of motion are Llere AZ.A;v; and r;; denote the mass of the central star. the mass of planet ἐν the position vector of planet. ἐς and r; respectively.," The equations of motion are Here $M_*, M_i, {\bf r}_i$ and ${\bf r}_{ij}$ denote the mass of the central star, the mass of planet $i,$ the position vector of planet, $i,$ and ${\bf r}_i-{\bf r}_j$ respectively."
 Phe acceleration of the coordinate svstem based on the central star (indirect term) is and that due to tidal interaction with planet £ is Fr; 1n the situation envisaged here. tidal interactions occur when a planet has a close encounter with the star.," The acceleration of the coordinate system based on the central star (indirect term) is and that due to tidal interaction with planet $i$ is ${\bf F}_{Ti}.$ In the situation envisaged here, tidal interactions occur when a planet has a close encounter with the star."
 When this occurs. the planet approaches from large distances on an almost parabolic orbit.," When this occurs, the planet approaches from large distances on an almost parabolic orbit."
 Ehe time between a subsequent encounters will then be long compared to that for the tidal interaction itself., The time between a subsequent encounters will then be long compared to that for the tidal interaction itself.
 Accorcingly we approximate the process as a sequence of independent energy. and angular momentum ransfers that occur at cach periastron passage., Accordingly we approximate the process as a sequence of independent energy and angular momentum transfers that occur at each periastron passage.
 We utilize he results of Press Teukolsky (1977) who calculatect these ransfers in the small perturbation limit for a non rotating star modelled as a polvtrope and a perturber on a parabolic orbit., We utilize the results of Press Teukolsky (1977) who calculated these transfers in the small perturbation limit for a non rotating star modelled as a polytrope and a perturber on a parabolic orbit.
 We shall neglect. the ellects of tides acting on the planet itself., We shall neglect the effects of tides acting on the planet itself.
 Accordingly our model is simplified., Accordingly our model is simplified.
 Llowever. it does enable us to include tidal effects and demonstrate how hey start to lead to orbital cireulavization and gravitational decoupling of an inner planet [rom the others as it moves onto a close orbit.," However, it does enable us to include tidal effects and demonstrate how they start to lead to orbital circularization and gravitational decoupling of an inner planet from the others as it moves onto a close orbit."
 However. it is only applicable while the λαοί orbit has high cecentricity.," However, it is only applicable while the planet orbit has high eccentricity."
 We adopt a form for Fy; that is able to approximately give the correct angular momentum and energy. exchanges with the star on a close approach but which is negligible at larger clistances from the central star., We adopt a form for $ {\bf F}_{Ti}$ that is able to approximately give the correct angular momentum and energy exchanges with the star on a close approach but which is negligible at larger distances from the central star.
" Llere j; is the specific angular momentum of planet /. Ry is the stellar radius. Bp;=j7/(267M.) is the distance of closest approach of planet; assuming a parabolic orbit. C1—22/3. and 1,ο”. The equations of motion are here integrated. using the Aulirsch-Stoer method ( eg."," Here $j_i$ is the specific angular momentum of planet $i,$ $R_*$ is the stellar radius, $R_{pi} =j_i^2/(2GM_*)$ is the distance of closest approach of planet $i$ assuming a parabolic orbit, $C1=2\sqrt{\pi}/3,$ and $T_1= 0.6/(1+(R_{pi}/R_*)^3).$ The equations of motion are here integrated using the Bulirsch-Stoer method ( eg."
 Press et al 1993)., Press et al 1993).
 Usinge (3)) we can derive the energye lost to the star during a close encounter of planet 7. assumed on a parabolic orbit as where. because of the rapid convergence of the integral. the limits are extended to cz. This gives which gives values coinciding approximately with valucs eiven by Press Teukolskv(1977).," Using \ref{ftidal}) ) we can derive the energy lost to the star during a close encounter of planet $i$, assumed on a parabolic orbit as where, because of the rapid convergence of the integral, the limits are extended to $\pm \infty.$ This gives which gives values coinciding approximately with values given by Press Teukolsky(1977)."
" We comment that acording to (5)) à star grazing encounter on a parabolic orbit. results in a final semi-major axis e1.7/8,M./M;. For à central. solar. mass with A,=10Hem. and M;~LAL; α~10 aus"," We comment that acording to \ref{DE}) ) a star grazing encounter on a parabolic orbit results in a final semi-major axis $a \sim 1.7R_*M_*/M_i.$ For a central solar mass with $R_*=10^{11} cm.$ and $M_i \sim 1M_J,$ $a \sim 10$ au."
 Thus bound orbits with à10 au are significantly modilied if they have a close encounter with the central star., Thus bound orbits with $a\sim 10$ au are significantly modified if they have a close encounter with the central star.
 Note too that the energy exchange rates are small for the planetary mass objects considered. here giving some justification for the lincar approximation used to calculate them., Note too that the energy exchange rates are small for the planetary mass objects considered here giving some justification for the linear approximation used to calculate them.
 The simulations performed here were begun. bv. placing N planets in some specified volume in a random location chosen to give a Monte-Carlo. realization of a prescribed density. distribution., The simulations performed here were begun by placing $N$ planets in some specified volume in a random location chosen to give a Monte-Carlo realization of a prescribed density distribution.
 We considered both the case of a uniform density spherical shell with BiniSorXofa and that of a thick annulus with Roya<rcHus occupying coshd)€8<t(OL) with a density xr Fowhere r ds the spherical radius and 8 the co.latitudo.," We considered both the case of a uniform density spherical shell with $R_{min} \leq r \leq R_{max}$ and that of a thick annulus with $R_{min} \leq r \leq R_{max}$ occupying $\cos^{-1}(0.1) \leq \theta
\leq \cos^{-1}(-0.1) $ with a density $\propto r^{-2}$, where $r$ is the spherical radius and $\theta$ the co–latitude."
 For the calculations presented here. Rivi=OLRas andl 0.5River for the annulus ancl the spherical shell. respectively.," For the calculations presented here, $R_{min}= 0.1 R_{max}$ and $0.5~R_{max}$ for the annulus and the spherical shell, respectively."
 The planets were then given the local circular velocity in the azimuthal direction., The planets were then given the local circular velocity in the azimuthal direction.
 Note that. because of the spatial placements the initial orbits are not. coplanar., Note that because of the spatial placements the initial orbits are not coplanar.
" In some cases the planets were taken to have equal mass Ad, while in others cach planet was allocated a mass qM, where q was a random number between zero and one.", In some cases the planets were taken to have equal mass $M_p$ while in others each planet was allocated a mass $qM_p$ where $q$ was a random number between zero and one.
 In the latter case the mass distribution of the protoplanets does not correspond. to the specified density distribution indicating some redistribution of mass among the embryos., In the latter case the mass distribution of the protoplanets does not correspond to the specified density distribution indicating some redistribution of mass among the embryos.
 1n general the various initial conditions we have considered Iead to the same qualitative evolution., In general the various initial conditions we have considered lead to the same qualitative evolution.
 Llowever. it must be emphasized. that the svstenis are chaotic with the consequence that very. small detailed changes to the initial conditions or the integration procedure will in general lead to very dillerent. results in detail.," However, it must be emphasized that the systems are chaotic with the consequence that very small detailed changes to the initial conditions or the integration procedure will in general lead to very different results in detail."
 To deal with this issue one can adopt the notion of shadow. orbits (Quinlan “Tremaine 1992)., To deal with this issue one can adopt the notion of shadow orbits (Quinlan Tremaine 1992).
 According to this. one can expect that although inevitable small errors lead to a significant deviation of the numerical solution from the actual one. there is another solution of the real system obtained with slightly cilferent initial conditions that remains close to the numerical one.," According to this, one can expect that although inevitable small errors lead to a significant deviation of the numerical solution from the actual one, there is another solution of the real system obtained with slightly different initial conditions that remains close to the numerical one."
 Thus we should be able to identify qualitative trends in the evolution of an ensemble, Thus we should be able to identify qualitative trends in the evolution of an ensemble
A new tool is now available to probe the population of recentlv formed massive stars. while still enubedded in thei pareut clouds.,"A new tool is now available to probe the population of recently formed massive stars, while still embedded in their parent clouds."
 Such stars are surrounded by a colmpact region. with an ionizatioi frout working outwards iuto the cloud.," Such stars are surrounded by a compact region, with an ionization front working outwards into the cloud."
 Regious uuereolus niasslve star formation contain one or 1kxe ultra-compact (UCILu)) regions. aud possibly 11016 evoved regions.," Regions undergoing massive star formation contain one or more ultra-compact ) regions, and possibly more evolved regions."
 Droufinan et al. (, Bronfman et al. (
1996. DNMD completed a survey in CS(21) towards IRAS point sources xsποηre the Wood Churelawell (198598). fai-infraved (CFIR) «dour criteria for ivegions.,"1996, BNM) completed a survey in CS(2--1) towards IRAS point sources satisfying the Wood Churchwell (1989a) far-infrared (FIR) colour criteria for regions."
 The CS molecule is a tracex of high density uolecular gas: a CS(21) detection strengheus the region identification and provides snematic iufornation., The CS molecule is a tracer of high density molecular gas; a CS(2–1) detection strengthens the region identification and provides kinematic information.
 DNM detected 813 sources (hereatcr IRAS/CS «nrces). whose azinnthallv averaged σαιactic distribulon 1s xesented iu Droufuuui et al. (," BNM detected 843 sources (hereafter IRAS/CS sources), whose azimuthally averaged galactic distribution is presented in Bronfman et al. ("
"2OO, BOXIN).","2000, BCMN)."
 lu this work we construct the huuiuositv fuucion (LF) for the IRAS/CS soreos. and show that it presents sigificant variations with ealactocentiic racins.," In this work we construct the luminosity function (LF) for the IRAS/CS sources, and show that it presents significant variations with galactocentric radius."
 We interpret the shape of the IRAS/CS sources LF ane ifs variatlons 1n terms of an eusenible of massive stav formune regiois., We interpret the shape of the IRAS/CS sources LF and its variations in terms of an ensemble of massive star forming regions.
 The stellar conten of IRAS/CS sources is characterises by the uunber of stars aud their mass spcnuu which. because of the vouth of the svstenis; is taken to represent closely their initial mass fuuction (IME).," The stellar content of IRAS/CS sources is characterised by the number of stars and their mass spectrum which, because of the youth of the systems, is taken to represent closely their initial mass function (IMF)."
 The 1se of voung tracers to derive the INE miuinises he dependence on modelling. which afflicts most previous studies;," The use of young tracers to derive the IMF minimises the dependence on modelling, which afflicts most previous studies."
 The standard approach to determining the high Lass C1 of the IMF has heen tioueh ο aud D star counts in the solar neighbourlove (c.g. Miller Scalo 1979. Lecueux 1979).," The standard approach to determining the high mass end of the IMF has been through O and B star counts in the solar neighbourhood (e.g. Miller Scalo 1979, Lequeux 1979)."
 The average mass spectrum of newly onued sars is taken as a power aw. and the value of he exponent characterises the IAF.," The average mass spectrum of newly formed stars is taken as a power law, and the value of the exponent characterises the IMF."
 These ayproaches require assunptions on the star feximation history. aud iive the drawback of not probing t1e Whole galactic disk.," These approaches require assumptions on the star formation history, and have the drawback of not probing the whole galactic disk."
 Carmany et al. (, Garmany et al. (
1982) addressed tlie| question of large scale variatious in the IMPE exponent. aud thev favour a decrease with ealactoceutrie radius (althougi their result has becu reinterpreted. e.g. Massey. 1998).,"1982) addressed the question of large scale variations in the IMF exponent, and they favour a decrease with galactocentric radius (although their result has been reinterpreted, e.g. Massey 1998)."
 A different too was used bv Vázzquez, A different tool was used by Vázzquez
(or N-rav-GRBs) observed by BeppoSAX are really due to FORBs. then afterglows should be detectable.,"(or X-ray-GRBs) observed by BeppoSAX are really due to FGRBs, then afterglows should be detectable."
 We propose that this kind. of events should. be followed: rapidly aud extensively in all bands. just like what we are doing for CRBs.," We propose that this kind of events should be followed rapidly and extensively in all bands, just like what we are doing for GRBs."
 LW observed. afterglows from these anomalous events can be used to check our concept of FORBs. and even to test the fireball model uncer quite dillerent conditions (i.e. when sy« 100).," If observed, afterglows from these anomalous events can be used to check our concept of FGRBs, and even to test the fireball model under quite different conditions (i.e., when $\gamma_0 \ll 100$ )."
 Also. these FORBs can provide valuable information for our understanding of GRBs. especially on the progenitor models.," Also, these FGRBs can provide valuable information for our understanding of GRBs, especially on the progenitor models."
 Note that beamed FCRBs can also eive birth to fast X-ray transients if they are directed toward us. but afterglows [rom such a beamed FORB and an isotropic FORB can be cliserinuinated casily from the light curves (see Figure 1).," Note that beamed FGRBs can also give birth to fast X-ray transients if they are directed toward us, but afterglows from such a beamed FGRB and an isotropic FGRB can be discriminated easily from the light curves (see Figure 1)."
 Lt is very interesting to note that optical alterglows from. two N-rav-GltDs. 011130 anc 011211. have been observed (Garnavich. Jha Ixirshner 2001: Gray et al.," It is very interesting to note that optical afterglows from two X-ray-GRBs, 011130 and 011211, have been observed (Garnavich, Jha Kirshner 2001; Grav et al."
 2001)., 2001).
 Their redshilts were measured to be z= 0.5 and 2.14 respectively (Jha et al., Their redshifts were measured to be $z = $ 0.5 and 2.14 respectively (Jha et al.
 POOL: Fruchter et al., 2001; Fruchter et al.
 2001). eliminates the possibility that they were ordinary. classic GRBs residing at extremely high redshifts (22 10).," 2001), eliminates the possibility that they were ordinary classic GRBs residing at extremely high redshifts $z \geq 10$ )."
" We propose that they should be FORBs (either isotropic or beamed) or just jetted GRB ""orphan.", We propose that they should be FGRBs (either isotropic or beamed) or just jetted GRB “orphan”.
 However. the observational data currently available are still quite poor so that we could not determine their nature definitely.," However, the observational data currently available are still quite poor so that we could not determine their nature definitely."
 As for other N-rav-CGliDs without a measured redshift. the possibility that they were at redshifts of z>10 can not be excluded.," As for other X-ray-GRBs without a measured redshift, the possibility that they were at redshifts of $z \geq 10 $ can not be excluded."
 Finally. t10 concept of FORBs is based on the fact that most popular progenitor models for CRBs are barvon-rich.," Finally, the concept of FGRBs is based on the fact that most popular progenitor models for GRBs are baryon-rich."
 Jut cases are quite different for another kind of progenitor models where strange stars are involved., But cases are quite different for another kind of progenitor models where strange stars are involved.
 Strange stars. composed mainly of u. d. and s quarks. are compact objects which are quite similar to neutron stars observationally (Alcock. Farhi Olinto 198," Strange stars, composed mainly of u, d, and s quarks, are compact objects which are quite similar to neutron stars observationally (Alcock, Farhi Olinto 1986)."
" A sltypical strange star (with mass  L4A/.) can have a matter crust of less than ~22107M. (Alcock. Farhi Olinto 1986). or even as smallas 3.10 ""AJ.(πας Lu 1997a. b)."," A typical strange star (with mass $\sim 1.4 M_\odot$ ) can have a normal matter crust of less than $\sim 2 \times 10^{-5} M_{\odot}$ (Alcock, Farhi Olinto 1986), or even as small as $\sim 3 \times 10^{-6} M_{\odot}$ (Huang Lu 1997a, b)."
 Phen barvon contamination can be clirectly avoided if GRBs are due to the phase transition of neutron stars to strange stars (Cheng Dai 199€x Dai Lu 19985b) or collisions of binary strange stars., Then baryon contamination can be directly avoided if GRBs are due to the phase transition of neutron stars to strange stars (Cheng Dai 1996; Dai Lu 1998b) or collisions of binary strange stars.
 In these mocdels. there should be very few. EFCIUDs.," In these models, there should be very few FGRBs."
 We thank an anonymous referee. for valuable comments and suggestions., We thank an anonymous referee for valuable comments and suggestions.
 YI thanks L. J. Gou and NX. Y. Wang for helpful discussion., YFH thanks L. J. Gou and X. Y. Wang for helpful discussion.
" This research was supported by the Special Funds for Major State Basie Research Projects. "" Natural Science Foundation of China (grants DM10)01. National19825109. and. 19973003). ancl the National€ (NIXDISSE €C119990754)."," This research was supported by the Special Funds for Major State Basic Research Projects, the National Natural Science Foundation of China (grants 10003001, 19825109, and 19973003), and the National 973 Project (NKBRSF G19990754)."
 Note added after acceptanceversion): The optical orphan at z=0.385 reported by Vanden Berk et al. (, Note added after acceptance: The optical orphan at z=0.385 reported by Vanden Berk et al. (
2002) has recently been proved to be an unusual radio-Ioud XN (Cal-vam et al.,2002) has recently been proved to be an unusual radio-loud AGN (Gal-yam et al.
 2002. astro-ph/0202354). and N-ray CARB 011211 was found to be in fact an ordinary. classic GRB (Frontera et al.," 2002, astro-ph/0202354), and X-ray GRB 011211 was found to be in fact an ordinary classic GRB (Frontera et al.,"
 GCN 1215)., GCN 1215).
 Additionallv. the optical identification of X-ray GARB OLLISO might also be incorrect. (Frail οἱ αἱ.," Additionally, the optical identification of X-ray GRB 011130 might also be incorrect (Frail et al.,"
 GCN 1207)., GCN 1207).
 We sincerely thank Nicola Masetti for private communication., We sincerely thank Nicola Masetti for private communication.
wide band camera for the wavefront sensing and apply the corrections to the data of all cameras.,wide band camera for the wavefront sensing and apply the corrections to the data of all cameras.
 However. the additional wavefront information contained in the narrow band data Is then not used for the image restoration.," However, the additional wavefront information contained in the narrow band data is then not used for the image restoration."
 The changing beam configuration due to seeing corrections by the AO (and tip-tilt mirror) in. principle also affects data calibration. because it changes the way the optics in front of the AO are sampled.," The changing beam configuration due to seeing corrections by the AO (and tip-tilt mirror) in principle also affects data calibration, because it changes the way the optics in front of the AO are sampled."
 However. 1t does not prevent pixel-based calibrations. and since we assume the telescope matrix is constant over the FOV. the effects of the changing beam configuration are not considered here.," However, it does not prevent pixel-based calibrations, and since we assume the telescope matrix is constant over the FOV, the effects of the changing beam configuration are not considered here."
" Image restoration of the data used in this paper was performed with MOMFBD assuming isoplanatie patches of 96x96 pixels («5.7x5.7"")) and using 37 Karhunen-Loévve modes for modeling the wavefront phases.", Image restoration of the data used in this paper was performed with MOMFBD assuming isoplanatic patches of $\times$ 96 pixels $\sim$ $\times$ ) and using 37 Karhunen-Loèvve modes for modeling the wavefront phases.
 A straightforward calibration scheme typically involves the following steps., A straightforward calibration scheme typically involves the following steps.
 Due to specific instrumental properties. such as polarization-dependent flatfields and FPL inhomogeneities. polarimetric and spectral calibration problems arise in steps 2 to 4.," Due to specific instrumental properties, such as polarization-dependent flatfields and FPI inhomogeneities, polarimetric and spectral calibration problems arise in steps 2 to 4."
 These are discussed in more detail below., These are discussed in more detail below.
 For polarimetric calibration of the data it is convenient to split the calibration in two parts., For polarimetric calibration of the data it is convenient to split the calibration in two parts.
 We can describe the total conversion matrix of the system (A) as a matrix product of the Mueller matrix of the telescope 77 and the modulation matrix of the instrument At: where the transmitted and the reflected beams have their own (although related) modulation matrices., We can describe the total conversion matrix of the system ${\cal A}$ ) as a matrix product of the Mueller matrix of the telescope ${\cal T}$ and the modulation matrix of the instrument ${\cal M}$: where the transmitted and the reflected beams have their own (although related) modulation matrices.
" Because the intensity of the light during the determination of the telescope matrix and the modulation matrix is not known, an additional gain calibration is still required."," Because the intensity of the light during the determination of the telescope matrix and the modulation matrix is not known, an additional gain calibration is still required."
 The telescope matrix T(r) varies with time. so the total system response matrix A is time dependent.," The telescope matrix ${\cal{T}}(t)$ varies with time, so the total system response matrix ${\cal A}$ is time dependent."
 This means that unless the flatfield images and the data are recorded at the same time. which is not practical. an appropriate gain correction (for the modulated data) must be computed.," This means that unless the flatfield images and the data are recorded at the same time, which is not practical, an appropriate gain correction (for the modulated data) must be computed."
 To this end. the flatfield must first be transformed to a time-independent location.," To this end, the flatfield must first be transformed to a time-independent location."
 The obvious (and only) place available for this is the plane of the sky. oon the Sun. since we assume that all time variability is contained in the telescope matrix.," The obvious (and only) place available for this is the plane of the sky, on the Sun, since we assume that all time variability is contained in the telescope matrix."
 The details of this procedure are discussed in Sect. 4.., The details of this procedure are discussed in Sect. \ref{sect:cal_scheme}.
 An important calibration problem is that part of the intensity changes over the field of view are not the result of real CCD gain variations. but of variations m FPI reflectivity and cavity size (see.e.g..22)..," An important calibration problem is that part of the intensity changes over the field of view are not the result of real CCD gain variations, but of variations in FPI reflectivity and cavity size \citep[see, e.g.,][]{ibis:2008,cauzzi:2009}."
 When observing at a wavelength where o1[0A40. un the wing of aspectral line. a wavelength shift due to a cavity error results in a change in the observed intensity that is completely unrelated to the gain of that particular pixel.," When observing at a wavelength where $\delta I/\delta \lambda \neq 0$, in the wing of a spectral line, a wavelength shift due to a cavity error results in a change in the observed intensity that is completely unrelated to the gain of that particular pixel."
 Similarly. variations in the reflectivity cause changes in the integrated transmission profile.," Similarly, variations in the reflectivity cause changes in the integrated transmission profile."
 The question. however. is which flatfield correction should be applied to the data.," The question, however, is which flatfield correction should be applied to the data."
 Although the intensity variations due to cavity errors are not real gain changes. the same cavity errors also affect the science data.," Although the intensity variations due to cavity errors are not real gain changes, the same cavity errors also affect the science data."
 The line profiles in the science data can be very different. though. so the intensity changes will in general not be the same as in the flatfield data.," The line profiles in the science data can be very different, though, so the intensity changes will in general not be the same as in the flatfield data."
 A change in wavelength scale due to a cavity error Justcannot be corrected in a flatfielding procedure. which only changes the intensity. unless one knows the exact line profile.," A change in wavelength scale due to a cavity error just be corrected in a flatfielding procedure, which only changes the intensity, unless one knows the exact line profile."
 For a data calibration scheme without image restoration. one could attempt to somehow determine the real pixel gains. apply those. and account for the wavelength shifts later on in the analysis.," For a data calibration scheme without image restoration, one could attempt to somehow determine the real pixel gains, apply those, and account for the wavelength shifts later on in the analysis."
 Por image restoration. however. the intensity variations that then remain could pose a problem for the wavefront sensing and/or the deconvolution.," For image restoration, however, the intensity variations that then remain could pose a problem for the wavefront sensing and/or the deconvolution."
" The strategy that we propose is discussed in the next section,", The strategy that we propose is discussed in the next section.
 For the wavefront sensing part of the image restoration. it is Important to use images that are as monochromatic as," For the wavefront sensing part of the image restoration, it is important to use images that are as monochromatic as"
We compare the spatial distributions of the 3.294 unfrared emission feature (IEF). the 2.12 11-0 SCD eemission line. and the 2 ccontinuum emission. in the bright visual reflection nebula7023.,"We compare the spatial distributions of the 3.29 infrared emission feature (IEF), the 2.12 1–0 S(1) emission line, and the 2 continuum emission, in the bright visual reflection nebula."
. The eemission. due to UV-pumped fluorescence. arises in narrow. dense filaments at the dissociation front at the edge of the molecular cloud.," The emission, due to UV-pumped fluorescence, arises in narrow, dense filaments at the dissociation front at the edge of the molecular cloud."
 The 3.29 HEF emission is also very strong in the same filaments. but the 2 ccontinuum emission is quite weak there.," The 3.29 IEF emission is also very strong in the same filaments, but the 2 continuum emission is quite weak there."
 On the other hand. the 2 ccontinuum emission is very bright in the region between the ffilaments and the illuminating star of7023.," On the other hand, the 2 continuum emission is very bright in the region between the filaments and the illuminating star of,."
.200775.. The 2 ccontinuum emission is brightest - ((~52 προ) from200775.. roughly midway between the star and the filaments.," The 2 continuum emission is brightest $\sim$ $\sim$ 52 mpc) from, roughly midway between the star and the filaments."
" There is also a distinct ""ring-shaped spatial structure that emits weakly at 3.29 aand is located between the 2 ccontinuum emission peak and the filaments.", There is also a distinct “ring”-shaped spatial structure that emits weakly at 3.29 and is located between the 2 continuum emission peak and the filaments.
 Our observation that both the 3.294 IIEF emission and the fluorescent emission are brightest in narrow filaments. and are spatially coincident to within ~2 mpe. is in stark contrast to observations of the uonization front and of the planetary nebulae7027.," Our observation that both the 3.29 IEF emission and the fluorescent emission are brightest in narrow filaments, and are spatially coincident to within $\sim$ 2 mpc, is in stark contrast to observations of the ionization front and of the planetary nebulae."
. Both the aand sshow a clear spatial separation between the 3.29 IIEF emission and the eemission., Both the and show a clear spatial separation between the 3.29 IEF emission and the emission.
 At theBar.. the 3.29 HEF emission peak ts 22-33 mpe closer to the exciting star of the tthan Is the fluorescent ppeak. a separation at least a factor of ten larger than observed in7023.," At the, the 3.29 IEF emission peak is 22-33 mpc closer to the exciting star of the than is the fluorescent peak, a separation at least a factor of ten larger than observed in."
. Because aand the hhave similar gas density structures. the difference in the projected distance between the 3.29 HEF emission peak and ppeak between aand the iis likely to be either related to the intensity of the incident UV field. which ts ten times higher in the tthan in7023.. and/or related to the hardness of the incident UV field. as indicated by the effective temperature of each exciting star (17.000 K for aand 40.000 K for the Nebula).," Because and the have similar gas density structures, the difference in the projected distance between the 3.29 IEF emission peak and peak between and the is likely to be either related to the intensity of the incident UV field, which is ten times higher in the than in, and/or related to the hardness of the incident UV field, as indicated by the effective temperature of each exciting star (17,000 K for and 40,000 K for the )."
 We observe very dissimilar spatial distributions of the 3.294 IIEF emission and the 2 ccontinuum emission. and in particular. a clear separation between the 3.29 HEF emission peak and the 2 ccontinuum emission peak.," We observe very dissimilar spatial distributions of the 3.29 IEF emission and the 2 continuum emission, and in particular, a clear separation between the 3.29 IEF emission peak and the 2 continuum emission peak."
 This suggests three possible interpretations. any or all of which could be correct: the excitation mechanisms for the 3.29 IIEF emission and the 2 ccontinuum emission are different: the emission processes for the 3.294 IIEF emission and the 2 ccontinuum emission are distinct: or the 3.29 IIEF carriers and the 2 ccontinuum emitters are not identical.," This suggests three possible interpretations, any or all of which could be correct: the excitation mechanisms for the 3.29 IEF emission and the 2 continuum emission are different; the emission processes for the 3.29 IEF emission and the 2 continuum emission are distinct; or the 3.29 IEF carriers and the 2 continuum emitters are not identical."
 This is in contrast to previous assumptions that the 2, This is in contrast to previous assumptions that the 2
]nitiallv. erowth from mergers is slow.,"Initially, growth from mergers is slow."
" The collision cross-section is the product of the geometric cross-section and the gravitational focusing factor. where r is (he particle radius. ey, is (he orbital velocity. 0, is the escape velocity. ancl >is a coellicient that accounts for three-climensional orbits in a rotating disk (GreenzweigLissauer1900:Spauteetal.1991:"," The collision cross-section is the product of the geometric cross-section and the gravitational focusing factor, where $r$ is the particle radius, $v_K$ is the orbital velocity, $v_{esc}$ is the escape velocity, and $\beta$ is a coefficient that accounts for three-dimensional orbits in a rotating disk \citep{grz90,spa91,ws93}."
Wetherill&Stewart 1993).. Because ery8205. eravitational locusing [actors are small.," Because $e v_K \approx v_{esc}$, gravitational focusing factors are small."
 Thus. growth is slow and orderly (Salronov1969).," Thus, growth is slow and orderly \citep{saf69}."
. As larger objects form. the smaller objects elfectivelv damp the orbital eccentricitv of larger particles through dynamical friction (e.g.Wetherill&Stewart1993:Kokubo1995:IXenvon&Liu 1998).," As larger objects form, the smaller objects effectively damp the orbital eccentricity of larger particles through dynamical friction \citep[e.g.][]{ws93,kok95,kl98}."
. Viscous stirring by the large objects heats up the orbits of the small objects., Viscous stirring by the large objects heats up the orbits of the small objects.
 In the case where gas drag is negligible. Goldreich.Lithwick&Sari.(2004b) derive a simple relation for (he ratio of the eccentricities of the large CI) and the small (s) objects in terms of their surface densities X. (see2003b. 2003c).. with. »= 1/4 to 1/2.," In the case where gas drag is negligible, \citet{gol04b} derive a simple relation for the ratio of the eccentricities of the large (`l') and the small (`s') objects in terms of their surface densities $\Sigma_{l,s}$ \citep[see also][2003b, 2003c]{kok02,raf03a}, with $n =$ 1/4 to 1/2."
"i For Xj/X,4— 10a to 10»7. ej/e;22 0.1.0.25."," For $\Sigma_l / \Sigma_s \sim$ $10^{-3}$ to $10^{-2}$, $e_l/e_s \approx$ 0.1–0.25."
i Because eieyES Lese. gravitational focusing [actors are large.," Because $e_s v_K 
\lesssim$ $v_{l,esc}$, gravitational focusing factors are large."
 Runaway growth begins., Runaway growth begins.
 Runaway growth concentrates more and more mass in the largest objects., Runaway growth concentrates more and more mass in the largest objects.
 Dynamical friction produces (he largest gravitational focusing factors among the largest objects., Dynamical friction produces the largest gravitational focusing factors among the largest objects.
 These protoplanets run away from the smaller objects ancl contain an ever growing fraction of the total mass., These protoplanets run away from the smaller objects and contain an ever growing fraction of the total mass.
 At the same time. the large objects continue to stir the leftover planetesimals.," At the same time, the large objects continue to stir the leftover planetesimals."
 The leftovers have orbital velocity clispersions comparable to the escape velocities of the oligarchs., The leftovers have orbital velocity dispersions comparable to the escape velocities of the oligarchs.
 With ese0Ces equations (1) and (2) show that collision rates decline as runaway growth continues.," With $e_s v_K \sim v_{esc}$, equations (1) and (2) show that collision rates decline as runaway growth continues."
 The ensemble of protoplanets and leftover plauietesimals then enters (he oligarchic phase. where (he largest objects grow faster than the leftover planetesimals.," The ensemble of protoplanets and leftover planetesimals then enters the oligarchic phase, where the largest objects grow faster than the leftover planetesimals."
 Among the oligarchs. the smaller oligarchs grow the fastest.," Among the oligarchs, the smaller oligarchs grow the fastest."
 Each oligarch tries to accrete all of the material in an annular ‘feeding zone’ set bv balancing the gravity of neighboringoligarchs., Each oligarch tries to accrete all of the material in an annular `feeding zone' set by balancing the gravity of neighboringoligarchs.
 Within each annulus. each oligarch stirs up the remaining planetesimals along its orbit.," Within each annulus, each oligarch stirs up the remaining planetesimals along its orbit."
 Because smaller oligarchs orbit in regions with smaller M;/X.. equations (1) ancl (2) show that smaller oligarchs have larger gravitational focusing factors.," Because smaller oligarchs orbit in regions with smaller $\Sigma_l/\Sigma_s$, equations (1) and (2) show that smaller oligarchs have larger gravitational focusing factors."
 Thus smaller oligarehis erow Taster (e.g..Ikokubo&Ida1995:Gokdreich.LitwickSari 2004b)..," Thus smaller oligarchs grow faster \citep[e.g.,][]{kok98,gol04b}. ."
 During oligarchic growth. protoplanets become isolated from their surroundings," During oligarchic growth, protoplanets become isolated from their surroundings"
MC is pleased to aknowledge the organizing committee for the invitation to attend the conference2010 and for partial financial support.,MC is pleased to aknowledge the organizing committee for the invitation to attend the conference and for partial financial support.
 MC and EB would like to thank financial support from CONACyT through the grant 49231-E., MC and EB would like to thank financial support from CONACyT through the grant 49231-E.
"To illustrate this, we consider the spectrum produced by a relativistic particle that undergoes an instantaneous scattering at t=0 through an angle a.","To illustrate this, we consider the spectrum produced by a relativistic particle that undergoes an instantaneous scattering at $t=0$ through an angle $\alpha$."
" The spectrum in this case is well known to be flat, w°, at frequencies small compared to the inverse duration of the acceleration adetaileddiscussionseeSchwingeretal.1998,chapter(for 37)."," The spectrum in this case is well known to be flat, $\omega^0$, at frequencies small compared to the inverse duration of the acceleration \citep[for a detailed discussion see][chapter~37]{schwinger98}."
". The angular integrated spectrum in this frequency range can be determined analytically (e.g.Akhiezer&Shul'ga1987) η Although this example appears straightforward, it is, in fact, quite demanding numerically, the reason for this being that the instantaneous power is itself an oscillatory function."," The angular integrated spectrum in this frequency range can be determined analytically \citep[e.g.][]{akhiezershulga87}
 = ] Although this example appears straightforward, it is, in fact, quite demanding numerically, the reason for this being that the instantaneous power is itself an oscillatory function."
" The formation length at any given time t can be easily calculated, but the exact expression is cumbersome."," The formation length at any given time $t$ can be easily calculated, but the exact expression is cumbersome."
" Far from the scattering center, tQ=Amy? /w."," Far from the scattering center, $t_{\rm c}= 4\pi\gamma^2/\omega$ ."
" As the scatterer is approached, the formation length decreases, reaching a minimum at t=0, of In this example there is no intrinsic time scale, so that we are free to choose arbitrary time, distance and frequency units."," As the scatterer is approached, the formation length decreases, reaching a minimum at $t=0$, of In this example there is no intrinsic time scale, so that we are free to choose arbitrary time, distance and frequency units."
" Defining a reference time unit to, we construct dimensionless units t=t/to, =x/cto and nEωτρ."," Defining a reference time unit $t_0$, we construct dimensionless units $\hat{t}= t/t_0$, $\hat{x}= x/ct_0$ and $\hat{\omega}= \omega t_0$."
" Figures 8 and 9 show the instantaneous power as a function of time for €=0.1 and €=10, respectively."," Figures \ref{scattest1} and \ref{scattest2} show the instantaneous power as a function of time for $\xi=0.1$ and $\xi=10$, respectively."
 The power oscillates with a slowly increasing period approximately equal to the formation time and damping with distance from the scatterer., The power oscillates with a slowly increasing period approximately equal to the formation time and damping with distance from the scatterer.
" In addition, there is an unresolved discontinuity at t=0, which arises because the particle velocity is also discontinuous at this point."," In addition, there is an unresolved discontinuity at $t=0$, which arises because the particle velocity is also discontinuous at this point."
" However, after integration over t, this feature has no influence on the energy radiated."," However, after integration over $t$, this feature has no influence on the energy radiated."
" Clearly, the linear growth phase for Q(g,t) will increase with distance from the scattering event, and the number of terms in the Euler-van Wijngaarden transform should be chosen such that the scattering is included."," Clearly, the linear growth phase for $Q(g,t)$ will increase with distance from the scattering event, and the number of terms in the Euler–van Wijngaarden transform should be chosen such that the scattering is included."
" However, since the dominant contribution to the total energy radiated comes from the first few periods, the integral of the instantaneous power converges rapidly and the error incurred from taking only the first few formation lengths when calculating P(w,t) is small."," However, since the dominant contribution to the total energy radiated comes from the first few periods, the integral of the instantaneous power converges rapidly and the error incurred from taking only the first few formation lengths when calculating $P(\omega,t)$ is small."
" To demonstrate the effects of having finite trajectory, we integrate the instantaneous power overa a time interval with T=«4?/(1--4£2), corresponding to one formation length for an emitted wave with frequency w=4."," To demonstrate the effects of having a finite trajectory, we integrate the instantaneous power over a time interval with $T={\pi\gamma^2}/{(1+4\xi^2)}$, corresponding to one formation length for an emitted wave with frequency $\omega=4$."
" From figures 8 and 9, it is clear that the solution will converge only for frequencies much larger than this."," From figures \ref{scattest1} and \ref{scattest2}, it is clear that the solution will converge only for frequencies much larger than this."
" The instantaneous power is integrated using a finite time step trapezoidal integration for two different scattering angles £=0.1 and €=10, with y=10?, as above."," The instantaneous power is integrated using a finite time step trapezoidal integration for two different scattering angles $\xi=0.1$ and $\xi=10$, with $\gamma=10^3$, as above."
 The results are shown in figure 10.., The results are shown in figure \ref{scat_spec}.
 The result is in good agreement with the analytic solution above approximately w=20., The result is in good agreement with the analytic solution above approximately $\omega=20$.
" This suggests that for a given trajectory, on a time interval [-T,T], the minimum frequency that can be investigated must have at least 10 formation lengths in this time interval."," This suggests that for a given trajectory, on a time interval $[-T,T]$, the minimum frequency that can be investigated must have at least 10 formation lengths in this time interval."
" In this paper we describe an algorithm for calculating the radiation emitted by a relativistic charged particle moving in turbulent electromagnetic fields, and use it to investigate the spectra that arise in a prescribed, stochastic realization of a static, turbulent magnetic field."," In this paper we describe an algorithm for calculating the radiation emitted by a relativistic charged particle moving in turbulent electromagnetic fields, and use it to investigate the spectra that arise in a prescribed, stochastic realization of a static, turbulent magnetic field."
 We also describe how to adapt the approach, We also describe how to adapt the approach
whence Next. we solve the system 18))-(51)) as a perturbative series over the non-Caussianity kernel Ry (ie. over powers of the parameter fxL).,"whence _L = _V Next, we solve the system \ref{dSdchi}) \ref{constraintchi}) ) as a perturbative series over the non-Gaussianity kernel $\fNLd$ (i.e. over powers of the parameter $\fNL$ )."
 At order zero we recover the Gaussian sadcdle-poiut. OQ = ALC) Cela.2) = 3," At order zero we recover the Gaussian saddle-point, ) = ), = ."
"5, At first order we obtain UO) = ALCL) ία. i)| 2A00)2 \ 2Aη acc ay 552LIE where the quautity fj, is given by Eq.(30))."," At first order we obtain ) = ) + 2 _V _2 _2) _2) _1'), = -3, where the quantity $f_{q;qq}$ is given by \ref{fq3_x0}) )."
 From Equations (52))-(58)) we also obtain the radial linear density profile of the saddle-point. up to first order. — — at | or2f ]-(60) ," From Equations \ref{chi0}) \ref{lambda1}) ) we also obtain the radial linear density profile of the saddle-point, up to first order, = , = + 2 - 3 ] ."
We can check that at ο=gq dt verifies the constraint (19)). aud at order zero we recover the Cassia profile (Valageas 2009bj.," We can check that at $q'=q$ it verifies the constraint \ref{constraint}) ), and at order zero we recover the Gaussian profile (Valageas 2009b)."
" Equations (59))-(60)) eive the integrated deusity profile. that is. àp, is tho wean linear deusity contrast within the Lagraugian radius ¢’."," Equations \ref{delta0}) \ref{delta1}) ) give the integrated density profile, that is, $\delta_{Lq'}$ is the mean linear density contrast within the Lagrangian radius $q'$."
 The local linear density contrast at radius d. δε). is given by 36 MEME ay whence — ου). = tt | 2 ld) 9--- |(63) where fowl) and fiio4G7) ave given by (33))- (36)).," The local linear density contrast at radius $q'$ , $\delta_L(q')$, is given by 3 q'^3 _L(q') = (q'^3, whence = (q'), = (q') + 2 (q') - 3 ] where $f_{0;qq}(q')$ and $f_{q;0q}(q')$ are given by \ref{fabb}) \ref{fbab}) )."
 We show in Fig., We show in Fig.
 1 the incerated lincar density xofile (59))-(60)) obtained for he masses AL101 and LOMATAL... for à CDM cosinoloev.," \ref{figdeltaLq} the integrated linear density profile \ref{delta0}) \ref{delta1}) ) obtained for the masses $M=10^{11}$ and $10^{15}h^{-1}M_{\odot}$, for a $\Lambda$ CDM cosmology."
 The depeudence on nass is due to the chauge of slope of the linear )»wer spectrum with scale., The dependence on mass is due to the change of slope of the linear power spectrum with scale.
" We uot our results for the Gaussian case (fxp=0. solid lines). large positive fry (fe—2.10° and fx,=2«104. dashed lines) aud Juge negative νι (fci=ὃν10) and fxp=2«104. dotted lines). for the local model (9))."," We plot our results for the Gaussian case $\fNL=0$, solid lines), large positive $\fNL$ $\fNL=2\times 10^{3}$ and $\fNL=2\times 10^{4}$, dashed lines) and large negative $\fNL$ $\fNL=-2\times 10^{3}$ and $\fNL=-2\times 10^{4}$, dotted lines), for the local model \ref{tfNLd_local}) )."
" Thus. we can see hat a positive [νι increases the relative density (νο, with respect to t10 density at radius 4) bot vat small aud large radi."," Thus, we can see that a positive $\fNL$ increases the relative density (i.e. with respect to the density at radius $q$ ) both at small and large radii."
 The verv hueo values of fxp required to be able to distinguish he euxves in the figure muuv that for realistic cases (ντ)«100 ) the perturbation of the deusity xofile is very πια]., The very large values of $\fNL$ required to be able to distinguish the curves in the figure imply that for realistic cases $|\fNL|<100$ ) the perturbation of the density profile is very small.
 Thor'efore. the values of he upper boundary ay. which marks he onset of shell-crossine. obtained iu Valageas (20010} for the Caussian case remain vaid up to a ναν good acenuracv.," Therefore, the values of the upper boundary $\delta_+$, which marks the onset of shell-crossing, obtained in Valageas (2009b) for the Gaussian case remain valid up to a very good accuracy."
 We can note that to obtain a simular deviatioi from the Caussian profile we need a larger valuc of the parameter fp at simallerscale., We can note that to obtain a similar deviation from the Gaussian profile we need a larger value of the parameter $\fNL$ at smallerscale.
" This cau be unudoerstoo your the expression (9)). which scales as f~[NLath)Xfxy/UGO72(hy) aid grows as KA at verv Luge scaOs,"," This can be understood from the expression \ref{tfNLd_local}) ), which scales as $\tfdel \sim \fNL /\alpha(k) \propto \fNL/(k^2 T(k))$ and grows as $k^{-2}$ at very large scales."
 The same behavior (ie. à higher sensitivity to locaype non-CGaussianity at large scales) is obtained for the |das of dark matter alos. see Eq.(2)) above and section 1 below.," The same behavior (i.e. a higher sensitivity to local-type non-Gaussianity at large scales) is obtained for the bias of dark matter halos, see \ref{Dbk_Dal}) ) above and section \ref{Bias-of-halos} below."
 Next. we defi >the coustrained weight (39)) as ," Next, we define the constrained weight \ref{rareP}) ) as =. ."
at the relevaut saddle-poiut y., at the relevant saddle-point $\chi$ .
 This eives. up to first order.," This gives, up to first order,"
spatial distribution of mass (e.g.seeFort&Mellier1994;Narayan&Bartelmann 1999).,"spatial distribution of mass \citep[e.g. see][]{fort1994,narayan1999}."
". If true, there must be three fainter counter-images: one to the north-east, one to the south-west and one at the center of the cluster core."," If true, there must be three fainter counter-images: one to the north-east, one to the south-west and one at the center of the cluster core."
" To produce the features described in the previous section, the cluster core must be very massive."," To produce the features described in the previous section, the cluster core must be very massive."
" In order to reconstruct the mass distribution in the core (the region enclosed by system we used the parametric model implemented in the publiclyA), available ray-tracing code (Julloetal.2007)."," In order to reconstruct the mass distribution in the core (the region enclosed by system A), we used the parametric model implemented in the publicly available ray-tracing code \citep{jul07}."
". To model the lens, we used two clumps of different scales—a large-scale halo, representing both the matter inside the giant cD galaxy and the dark matter halo of the cluster, and four smaller-scale clumps, modeling the small-scale perturbations associated with the galaxies embedded in the cD galaxy."," To model the lens, we used two clumps of different scales—a large-scale halo, representing both the matter inside the giant cD galaxy and the dark matter halo of the cluster, and four smaller-scale clumps, modeling the small-scale perturbations associated with the galaxies embedded in the cD galaxy."
 For all components we adopt a dual Pseudo-Isothermal Elliptical Mass Distribution (dPIEMD; see Elíasdóttiretal. 2007))., For all components we adopt a dual Pseudo-Isothermal Elliptical Mass Distribution (dPIEMD; see \citealp{eliasdottir2007}) ).
" The dPIEMD can be characterized by seven parameters: the center position the ellipticity e, the position angle 0 and the parameters(X,Y), of the density profile: the velocity dispersion oo and two characteristic radii Teore and Τομ."," The dPIEMD can be characterized by seven parameters: the center position $(X,Y)$, the ellipticity $\epsilon$, the position angle $\theta$ and the parameters of the density profile: the velocity dispersion $\sigma_0$ and two characteristic radii $r_{core}$ and $r_{cut}$ ."
" For the large halo, we left most parameters free, with broad uniform priors."," For the large halo, we left most parameters free, with broad uniform priors."
 Only Τομε remained fixed at a value of 1500 h! kpc., Only $r_{cut}$ remained fixed at a value of 1500 $^{-1}$ kpc.
" In the small- clumps, the parameters of the density profiles were scaled as a function of their galaxy luminosities (seeJulloetal.2007,andreferences therin).."," In the small-scale clumps, the parameters of the density profiles were scaled as a function of their galaxy luminosities \citep[see ][ and references therin]{jul07}."
" Using as a scaling factor the luminosity L*, associated with the -magnitude of central galaxy N.3 (see Fig."," Using as a scaling factor the luminosity $L^{*}$ , associated with the -magnitude of central galaxy N.3 (see Fig."
" 1 and Table 1), we searched for the values of of and rz, that yield the best fit, fixing at 0.15h-! kpc."," 1 and Table 1), we searched for the values of $\sigma_0^{*}$ and $r_{cut}^{*}$ that yield the best fit, fixing $r_{core}^{*}$ at $^{-1}$ kpc."
" The best-fitting parameters of the modelr*,,.. are listed in Table 2.", The best-fitting parameters of the model are listed in Table 2.
" Because the ring structure shows multiple subcomponents, we selected the most reliable set of multiple images and associated them with three different background sources in order to make our fit."," Because the ring structure shows multiple subcomponents, we selected the most reliable set of multiple images and associated them with three different background sources in order to make our fit."
" Considering an uncertainty in the position of any image equal to 0""2, we found after the optimization in the image plane a = x?/DOF=69/4 ~ 17."," Considering an uncertainty in the position of any image equal to $\farcs$ 2, we found after the optimization in the image plane a $\chi_{DOF}^{2}$ = $\chi^2/DOF = 69/4$ $\sim$ 17."
" Our model reproduces X5opwell the positions of the observed subcomponents, with a mean scatter less than 08."," Our model reproduces well the positions of the observed subcomponents, with a mean scatter less than $\farcs$ 8."
" To highlight this, we show in Figure 2,, the model-predicted counter-images of the substructures in arc A.1 (green crosses), which are in agreement with the image positions for all arcs circles)."," To highlight this, we show in Figure \ref{model}, the model-predicted counter-images of the substructures in arc A.1 (green crosses), which are in agreement with the image positions for all arcs (orange circles)."
 The fit also predicts a central demagnified (orangeimage which is lost in the cD light distribution., The fit also predicts a central demagnified image which is lost in the cD light distribution.
" It is important to note that our model is oversimplified, since we are assuming spherical halos for the galaxies."," It is important to note that our model is oversimplified, since we are assuming spherical halos for the galaxies."
 A detailed model of Abell 3827 is beyond the scope of the present work., A detailed model of Abell 3827 is beyond the scope of the present work.
" Given our best model (see Table 2), we calculated the total mass inside a radius of 20""(location of the tangential arc B.1 at ~ 37 h! kpc) and found M=(2.73:0.4)x1015 Μο..."," Given our best model (see Table 2), we calculated the total mass inside a radius of (location of the tangential arc B.1 at $\sim$ 37 $^{-1}$ kpc) and found $M = (2.7\pm0.4) \times 10^{13}$ ."
 Thismass is slightly greater than that enclosed in Abell 1689 within a similar radius (see 66 in Limousinetal.2007))., Thismass is slightly greater than that enclosed in Abell 1689 within a similar radius (see 6 in \citealp{lim07}) ).
 We estimated the mass of the cD galaxy as being ~ 3096 — 50% of the total mass of the cluster within (Limousinetal.2007)., We estimated the mass of the cD galaxy as being $\sim$ $\%$ $-$ $\%$ of the total mass of the cluster within \citep{lim07}.
. This implies a cD galaxy mass between 8.1x10!? Mo and 1.3x1015 Mo., This implies a cD galaxy mass between $8.1 \times 10^{12}$ $_{\sun}$ and $1.3 \times 10^{13}$ $_{\sun}$.
" Even assuming a conservative value of 3096, this would mean that the central cD galaxy in Abell 3827 is perhaps the most massive galaxy observed in the local universe."," Even assuming a conservative value of $\%$, this would mean that the central cD galaxy in Abell 3827 is perhaps the most massive galaxy observed in the local universe."
" Using the strong-lensing model presented above, we have analyzed the mass distribution to unprecedented spatial resolution."," Using the strong-lensing model presented above, we have analyzed the mass distribution to unprecedented spatial resolution."
 The cluster core is spatially very concentrated., The cluster core is spatially very concentrated.
" Even if we assume a conservative fraction for the mass of the central cD galaxy (see above), this galaxy is very massive."," Even if we assume a conservative fraction for the mass of the central cD galaxy (see above), this galaxy is very massive."
 The cD galaxy could be an extreme example of the effects of dry mergers on the mass of BCGs; dry mergerscan produce an increase(by a factor of up to 3) in the dark-matter-to-stellar mass ratio for the most massive systems at present (Ruszkowski& , The cD galaxy could be an extreme example of the effects of dry mergers on the mass of BCGs; dry mergerscan produce an increase(by a factor of up to 3) in the dark-matter-to-stellar mass ratio for the most massive systems at present \citep{ruszkowski2009}. .
We have 2009)..compared the total mass derived from our strong-lensing analysis with that derived from the, We have compared the total mass derived from our strong-lensing analysis with that derived from the
ποον formulas Uselloe 1953. Clendrasckhar 1969. DTs?). where aud For honeoidal density distributions the potential euergv tensor compouents are given by (Roberts. 1962) where aud C=Ug|ουν,"well-known formulas (Kellog 1953, Chendrasekhar 1969, BT87), where and For homeoidal density distributions the potential energy tensor components are given by (Roberts, 1962) where and $U=U_{11}+U_{22}+U_{33}$."
 The three integrals w; are calculated by using ideutities 238.03. 238.01 aud. 238.05 from Byrd Friccinan (1971): @2 =defy. ay =anfay.= aresinv1ai.τα αγάαλ).and finally v are the Elliptic Iutegrals of the first aud second. kiud. respectively aud &?=1À.," The three integrals $\wci$ are calculated by using identities 238.03, 238.04 and 238.05 from Byrd Friedman (1971): where $\tacd =\acd/\acu$ , $\tact =\act/\acu$, $\varphi
\equiv\arcsin\sqrt{1-\tact^2}$, $k^2 \equiv (1-\tacd^2)/(1-\tact^2)$, and finally are the Elliptic Integrals of the first and second kind, respectively and $k'^2=1-k^2$."
 Also. we recall that the TF teusor is given by Tjj=PoOjO05 the explicit evaluation of this quautity bv usine eq. (," Also, we recall that the TF tensor is given by $\Tij=-\partial^2\phi/\partial\xci \partial\xcj$: the explicit evaluation of this quantity by using eq. ("
D.1) proves eq. (,B.4) proves eq. (
20).,20).
 We also evaluate the quantity 27Gpy needed there by using+ the virialm theorem. MioP=U.," We also evaluate the quantity $2\pi G\rhocz$ needed there by using the virial theorem, $\Mc\sigvd = -U$."
 From eqs. (, From eqs. (
B.2) aud (B.S) we obtain the exact expression For the deusity distribution in eq. (,B.2) and (B.8) we obtain the exact expression For the density distribution in eq. (
19) it cau be proved that the value of the integral at denominator equals M5j 1.,19) it can be proved that the value of the integral at denominator equals $\M =\pi/4$ .
 The explicit form of the potential o generated by a eeneric homeoidal deusitv distributions usually ciunot be expressed iu explicit. closed form.," The explicit form of the potential $\phi$ generated by a generic homeoidal density distributions usually cannot be expressed in explicit, closed form."
 Ou the contrary. its expression iu the Hiit of small flattenines is trivial.," On the contrary, its expression in the limit of small flattenings is trivial."
 As described iu Sect., As described in Sect.
" 3.Pa we introduce the two ellipticities with ου=1€ al as/a,=1ip obviously. in spherical nodels €=η0."," 3, we introduce the two ellipticities with $\acd/\acu = 1-\epsilon$ and $\act/\acu = 1-\eta$; obviously, in spherical models $\epsilon =\eta
=0$."
 We now expand eq. (, We now expand eq. (
15.1) for suxUl Satteniugs. retaining only linear terius.,"B.4) for small flattenings, retaining only linear terms."
" We perform tjs expansion atfired mass. 1.0. we eliminate the coefiicicn Tay(2053/3, between eqs. ("," We perform this expansion at mass, i.e, we eliminate the coefficient $\pi\acu\acd\act\rhon$ between eqs. ("
B.3) auc (D.1).,B.3) and (B.4).
" With the normalization of lengths to «4. a tedious but straightforward calculation shows that ο=(GALfayjo. where and Z,60)=NpUdr Nay."," With the normalization of lengths to $\acu$, a tedious but straightforward calculation shows that $\phi = -(GM/\acu)
\tilde{\phi}$, where and $I_n (x)\equiv \int_0^x\rhot (t)t^ndt$."
 dyuiuical properties of seneral deusitv-potential pairs obtained with this truucation procedure are preseuted elsewhere (for a full discussion of this technique see Ciotti Bertin 2001)., Many dynamical properties of general density-potential pairs obtained with this truncation procedure are presented elsewhere (for a full discussion of this technique see Ciotti Bertin 2004).
" For example. for ellipsoidal Heruquist models. Note that. at the ceuter of the ITeruquist model. the force remains finite but is not contiuuous. Ίνοι, it depends ou the approaching direction. aud this fact produces undesidercd orbital scattering due to amplification of munerical errors."," For example, for ellipsoidal Hernquist models, Note that, at the center of the Hernquist model, the force remains finite but is not continuous, i.e., it depends on the approaching direction, and this fact produces undesidered orbital scattering due to amplification of numerical errors."
 This problem is avoided when using a density such that in eq. (, This problem is avoided when using a density such that in eq. (
12). from which Note that the force now vanishes at the model center.,"12), from which Note that the force now vanishes at the model center."
 We also expand up to linear terms the three functions iu eqs. (, We also expand up to linear terms the three functions in eqs. (
D.10)-(D.12) for p.>0 and i.>th With the aid of these expansions we can finallyobtain also the linearization of the gravitational potential energv eiven in eq. (,B.10)-(B.12) for $\mu\to 0$ and $\nu\to 0$: With the aid of these expansions we can finallyobtain also the linearization of the gravitational potential energy given in eq. (
0.5) and eq. (,B.8) and eq. (
B.11):,B.14):
velocity and the magnetic field on the surface of the star mav as well be an indication for clement redistribution on (or in) the star.,velocity and the magnetic field on the surface of the star may as well be an indication for element redistribution on (or in) the star.
 Generally He and Si variable Bp stars possess. large-scale organized magnetic fields which in many cases appear ο occur essentially under the form of a single large dipole ocated close to the centre of the star., Generally He and Si variable Bp stars possess large-scale organized magnetic fields which in many cases appear to occur essentially under the form of a single large dipole located close to the centre of the star.
 The. magnetic ield is usually diagnosed. through observations of circular »obarization in spectral lines., The magnetic field is usually diagnosed through observations of circular polarization in spectral lines.
 used. the multizmode. instrument FORS11. mounted on he Som WKueven telescope of the VLT. to measure the mean longitudinal magnetic field. in the svstem AQ Vel., used the multi-mode instrument 1 mounted on the 8 m Kueyen telescope of the VLT to measure the mean longitudinal magnetic field in the system AO Vel.
" ο detection. was achieved with the single low-resolution measurement (1122000). resulting in §6,)== SOLGLGCG. We should. however. keep in mind that the observed spectropolarimetric spectrum ds à Composite spectrum consisting of four spectropolarimetric spectra belonging to A. DB. € and D components."," No detection was achieved with the single low-resolution measurement (R=2000) resulting in $\left<B_{\rm z}\right>$ $\pm$ G. We should, however, keep in mind that the observed spectropolarimetric spectrum is a composite spectrum consisting of four spectropolarimetric spectra belonging to A, B, C and D components."
 Each of the companions can yossess an individual magnetic field of clillerent geometry. strength and. polarity.," Each of the companions can possess an individual magnetic field of different geometry, strength and polarity."
 Since the inhomogeneous elemental clistribution of Si and. Mg is also observed on the surface of he component D. the presence of a large-scale organized magnetic field is quite possible in this component too.," Since the inhomogeneous elemental distribution of Si and Mg is also observed on the surface of the component B, the presence of a large-scale organized magnetic field is quite possible in this component too."
 The components € and D show the peculiarity character vpical of Lle\In stars., The components C and D show the peculiarity character typical of HgMn stars.
 showed that ongitucinal magnetic fields in Lle\In stars are rather weak. of the order of a few hundred: Gauss. ancl less. and. the structure of their fields must. be sulliciently tangled: so hat it does not produce a strong net observable. circular rolarization signature.," showed that longitudinal magnetic fields in HgMn stars are rather weak, of the order of a few hundred Gauss and less, and the structure of their fields must be sufficiently tangled so that it does not produce a strong net observable circular polarization signature."
 Thus. the non-detection of à magnetic field in the system AO Vel can be possibly explained. by the dilution of the magnetic signal due to the superposition of four dillerentIlv polarized. spectra.," Thus, the non-detection of a magnetic field in the system AO Vel can be possibly explained by the dilution of the magnetic signal due to the superposition of four differently polarized spectra."
 On the other hand. the magnetic field| of each component should. be detectable with high resolution spectropolarimeters making use of the Zeeman effect in individual metal lines.," On the other hand, the magnetic field of each component should be detectable with high resolution spectropolarimeters making use of the Zeeman effect in individual metal lines."
 The time scale for the peculiarities to be developec remain unclear since the results of studies of evolutionary status of chemically peculiar stars of dillerent. tvpe. show somewhat contradictory results., The time scale for the peculiarities to be developed remain unclear since the results of studies of evolutionary status of chemically peculiar stars of different type show somewhat contradictory results.
 The earlv work by suggested that the frequeney. of peculiar stars of Si and Lle\In groups increases with age ancl particularly here exist no peculiar star on the ZAMS., The early work by suggested that the frequency of peculiar stars of Si and HgMn groups increases with age and particularly there exist no peculiar star on the ZAMS.
 In à more recen whotometrie search for peculiar stars in five voung clusters. also concluded. tha he CP phenomenon needs at least several Myr to start being ellective.," In a more recent photometric search for peculiar stars in five young clusters, also concluded that the CP phenomenon needs at least several Myr to start being effective."
 On the other hand. some chemically peculiar stars jas been detected within very voung associations or even in star forming regions like Ori OBI1999).. Lupus 32007).. and 19552006).," On the other hand, some chemically peculiar stars has been detected within very young associations or even in star forming regions like Ori OB1, Lupus 3, and L988."
. The results of the present paper show the existence of coeval stars with chemical peculiaritics of Si and Lle\In tvpes. close to the ZAAIS indicating that the age threshold for these peculiaritics is similar for both subgroups of chemically peculiar stars.," The results of the present paper show the existence of coeval stars with chemical peculiarities of Si and HgMn types, close to the ZAMS indicating that the age threshold for these peculiarities is similar for both subgroups of chemically peculiar stars."
 Our study supports the idea that these chemical peculiarities originate quite soon after the star formation., Our study supports the idea that these chemical peculiarities originate quite soon after the star formation.
 It is noteworthy. that the subsystem. CD. the less massive binary of the Vel. shows several similarities with the eclipsing binary AAU belonging to the Aur OBI association.," It is noteworthy, that the subsystem CD, the less massive binary of the Vel, shows several similarities with the eclipsing binary Aur belonging to the Aur OB1 association."
 Both systems are formed. by stellar components very close to the ZAMS or even in the AIS stage2006).. and they have almost the same orbital period. 4.13 and 47.15 for AAur and CCD. respectively.," Both systems are formed by stellar components very close to the ZAMS or even in the pre-MS stage, and they have almost the same orbital period, $^d$ .13 and $^d$ .15 for Aur and CD, respectively."
 La both svstems the primary is a HgMn star. but while in the VVel CD system the secondary companion shares the same peculiarity. in Nur the secondary is a normal star1995).," In both systems the primary is a HgMn star, but while in the Vel CD system the secondary companion shares the same peculiarity, in Aur the secondary is a normal star."
. In fact. the primary component of AAur should be compared: with star D of the system VVel. since they have a similar elfective temperature.," In fact, the primary component of Aur should be compared with star D of the system Vel, since they have a similar effective temperature."
 This similarity in the physical and orbital properties seems to have been translated: into the development. of similar pattern of chemical abundances: notorious overabundance of Le and Pt. overabundance of Sr. Y. and Mn at the level of 1 dex. slight overabundance of Cr and Vi. and the abundance of Si ancl Mg close to the solar abundance. or slightly subsolar.," This similarity in the physical and orbital properties seems to have been translated into the development of similar pattern of chemical abundances: notorious overabundance of Hg and Pt, overabundance of Sr, Y, and Mn at the level of 1--3 dex, slight overabundance of Cr and Ti, and the abundance of Si and Mg close to the solar abundance, or slightly subsolar."
 We selected a few additional HgMn spectroscopic binaries with cllective temperatures. close to. Why: 332964. SS9822.. 1173524. and 1191110.," We selected a few additional HgMn spectroscopic binaries with effective temperatures close to K: 32964, 89822, 173524, and 191110."
 In 77 the abundances of various elements in AAur and selected binaries are compared with those of the Vel D companion., In 7 the abundances of various elements in Aur and selected binaries are compared with those of the Vel D companion.
 The abundances are presented for Lle\In stars meniber of double-Iined spectroscopic binaries with periods between 4 and 12 days ancl having elfective temperatures in the range 117700IxXlx. For 1173524. and 1191110. we plotted the abundances determined. in both components., The abundances are presented for HgMn stars member of double-lined spectroscopic binaries with periods between 4 and 12 days and having effective temperatures in the range K. For 173524 and 191110 we plotted the abundances determined in both components.
 The abundances values have been taken from(1994)...(2004)... and (2003).," The abundances values have been taken from, and ."
. It. is remarkable. how much similar the chemical composition of these stars. is.," It is remarkable, how much similar the chemical composition of these stars is."
 We note. however. that the abundance distribution on the stellar surface of Lle\In stars is probably. inhomogeneous. ancl consequently. the chemical composition derived from spectroscopic observations that do not cover the rotational evele. should be taken just as indicative values until accurate abundance values obtained using Doppler imaging technique become available.," We note, however, that the abundance distribution on the stellar surface of HgMn stars is probably inhomogeneous, and consequently, the chemical composition derived from spectroscopic observations that do not cover the rotational cycle, should be taken just as indicative values until accurate abundance values obtained using Doppler imaging technique become available."
 Phe spotted character of magnetic Bp-Ap stars is well known. but also in the case of Le\In stars the presence of chemical spots or belts on the surface is not uncommon2009).," The spotted character of magnetic Bp-Ap stars is well known, but also in the case of HgMn stars the presence of chemical spots or belts on the surface is not uncommon."
.. As already mentioned above. the atmospheric chemical composition of AAur exhibits a non-uniform surface distribution with a very interesting pattern related to the position of the companion200Ga).," As already mentioned above, the atmospheric chemical composition of Aur exhibits a non-uniform surface distribution with a very interesting pattern related to the position of the companion."
. A similar study in VVel would be worthwhile to verily whether the elemental distribution on the stellar surfaces of C and D components show a similar behavior., A similar study in Vel would be worthwhile to verify whether the elemental distribution on the stellar surfaces of C and D components show a similar behavior.
 Furthermore. an intensive spectroscopic campaign that would. allow the reconstruction of chemical maps for all four components should. provide. important information for the proper unclerstancing of the origin of chemically peculiar stars.," Furthermore, an intensive spectroscopic campaign that would allow the reconstruction of chemical maps for all four components should provide important information for the proper understanding of the origin of chemically peculiar stars."
 reftab.lines lists all the spectral lines used. for abundance determination., \\ref{tab.lines} lists all the spectral lines used for abundance determination.
 Phe lines marked with an asterisk are blends., The lines marked with an asterisk are blends.
 The abundance was determined. using the [fitting by a synthetic spectrum., The abundance was determined using the fitting by a synthetic spectrum.
" Dy DV. =AgVOL. —m)y(931) b,, =o""din (5.38) whered,, involvesVio (he energy stress-tensor inthe Li","To complete this Section let us discuss as byproduct the ""Liouville type"" representation of the conventional $D=4$ effective action in the background of constant electromagnetic field."
"ouville theory anditsderivatives. The operators andVi, ο form thelogarithmic pair oftheoperators withthe same conlormal dimension. Thenatural question concerns the inter", To start with let us remind the first quantized representation for the effective actions for the charged particle of mass $m$ Z= (-m L(C) + (C)) W(C) where $\Phi(C)$ is the so called spin factor expressed in terms of the trajectories in $CP^3$ and $W(C)$ is the Wilson loop along the contour $C$.
"pretation of the objectcreated.bv the operator Viothat is dressing ofthe surface operator, Some", The potential need for the Liouville mode to appear is the restoration of the reparametrization invariance in the summation over the contours.
 analogy comes [from(he minimal branes inthe Liouville theory- ZZ andFZZT branes |0]..ZZbranes correspond to the D-instantons, One could expect that the integral over the reparametrization of the contour appears in some form which is familiar in the stringy calculations of the Wilson loops.
 localized in theLiouville zero mode direction and getcondensed. On the interpreted, However more convenient form of the effective action involves the integral over the Schwinger parameter.
 branesis speculate tothe blowing of the instanton. pair An interestingan, In the external self-dual field the one-loop effective action reads as = where we assume that $E=\pm H$.
alogous alsoup from the Hamiltonian viewpoint. The surface operators interpretationprovide degrees emerges freedom forthe particular. Lamillonian svslem. Oneof (he equivariantthe ofin theD 4SYM t," Let us emphasize that the effective action in QED is not holomorphic object hence we would like to represent \ref{one-loop}) ) as a kind of ""correlator"" in the Liouville-type theory that is integrated product of the chiral conformal blocks over the intermediate conformal weights."
heory be identified with the Planck constantin parametersthis Hamiltonian system [25].. The interpretationbe derivedin the worldvolume theory, Therefore the question is weather the integral over the Schwinger parameter can be treated as the integral over the intermediate conformal dimensions in the Liouville theory.
 thesurface llence haveto differentiatethe surface function will operator," First note that the Schwinger parameter can be treated as the radial coordinate in the AdS space \cite{gopa,gorly}."
respectto[26]..the Planck constant. From the quantum mechanical operator viewpoint(he corresponding angular momentuminAR! plavs the roleof kind o, On the other hand the radial coordinate in AdS geometry can be considered as the zero mode of the Liouville field \cite{polyakov} that is Schwinger parameter is related with the Liouville zero mode.
fthe generator. Probably such is relate, The correspondence can be made more precise.
"dto the Parisi-Bourlas approachR-svimmetrytothe classical dnamics where picturethe effective be naturally(vpe definedin terms of auxiliaryWW2 SUSY, R-svmmetry"," To the aim let us use the observation from \cite{gorly} that the integrand can be represented in terms of the wave function of the $SL(2,R)$ 2-dimensional YM theory on the disc which yields the solutions to the $AdS_2$ gravity and depends on"
also shown in Fig. 10..,also shown in Fig. \ref{fig:Nbody}.
 The horizontal dashed line indicates the mass of the satellite alter tidal mass loss according to the classical model., The horizontal dashed line indicates the mass of the satellite after tidal mass loss according to the classical model.
" Lhe cross on this line indicates the mean dynamical time for mass loss in this model for fe=1 (note that we could always force this cross to lie on the line in the classical model by suitable choice of fe4. ,,)-", The cross on this line indicates the mean dynamical time for mass loss in this model for $f_{\tau_{\rm dyn}}=1$ (note that we could always force this cross to lie on the N-body line in the classical model by suitable choice of $f_{\tau_{\rm dyn}}$ ).
 The limitations of the classical model are clearly seen.the satellite loses mass continuously throughout the calculation. while the classical nioclel predicts a fixed mass.," The limitations of the classical model are clearly seen—the satellite loses mass continuously throughout the calculation, while the classical model predicts a fixed mass."
 Circles indicate the prediction from the mass loss nioclel described in this work., Circles indicate the prediction from the mass loss model described in this work.
 We show results for 17 mass loss iterations and chose f-dy=0.35., We show results for 17 mass loss iterations and chose $f_{\tau_{\rm dyn}}=0.35$.
 As expected. fτανα is of order unity.," As expected, $f_{\tau_{\rm dyn}}$ is of order unity."
 Note that our model is able to match the rate of mass loss quite well for about five iterations. before beginning to significantly overestimate the rate of mass loss.," Note that our model is able to match the rate of mass loss quite well for about five iterations, before beginning to significantly overestimate the rate of mass loss."
 This discrepancy will be discussed further in relsec:cliscuss., This discrepancy will be discussed further in \\ref{sec:discuss}.
 Figure 11.. shows mass loss as a function of time [ου the same satellite in tical fields of three different strengths., Figure \ref{fig:NbodyVarM} shows mass loss as a function of time for the same satellite in tidal fields of three different strengths.
 Coloured. lines indicate. the bound. mass of. the N-bocky satellite. while coloured points indicate the results from the model described in this work.," Coloured lines indicate the bound mass of the N-body satellite, while coloured points indicate the results from the model described in this work."
 Dashed lines with crosses indicate the results of the classical model as in bie. 10.., Dashed lines with crosses indicate the results of the classical model as in Fig. \ref{fig:Nbody}.
 To obtain a good [it to the mass loss rates we are forced to adopt dillerent values of f- depending on the strength of the tical field., To obtain a good fit to the mass loss rates we are forced to adopt different values of $f_\tau$ depending on the strength of the tidal field.
 The results show have f.=L4. 0.35 and 0.15 for tidal fields of μα—5:85:104.5.8. 10? and 5.8«107 respectively.," The results show have $f_\tau=1.4$, 0.35 and 0.15 for tidal fields of $f_{\rm tidal}=5.8\times 10^{-4}$, $5.8\times
10^{-3}$ and $5.8\times 10^{-2}$ respectively."
 Once again we see that our model describes the mass loss quite well for several iterations before overestimating the mass loss rate at late times. (, Once again we see that our model describes the mass loss quite well for several iterations before overestimating the mass loss rate at late times. (
Phis overestimation is not seen for the fuii=5810? calculation as the satellite loses its mass so rapidly that the second. slow mass loss regime is never seen.),"This overestimation is not seen for the $f_{\rm tidal}=5.8\times 10^{-2}$ calculation as the satellite loses its mass so rapidly that the second, slow mass loss regime is never seen.)"
 In addition to the total bound. mass of the satellite. our model is able to predict. the radial density profile of that mass.," In addition to the total bound mass of the satellite, our model is able to predict the radial density profile of that mass."
 In Fig., In Fig.
 12. we show as coloured. lines the density profile (normalized to the original density profile) of the same satellite in three dillerent. tidal fields after 15 iterations., \ref{fig:NbodyDensity} we show as coloured lines the density profile (normalized to the original density profile) of the same satellite in three different tidal fields after 1--5 iterations.
 Coloured circles show the density. profile from. he N-bods simulation at the corresponding times., Coloured circles show the density profile from the N-body simulation at the corresponding times.
 Vertical dotted lines indicate the softening length in our calculations., Vertical dotted lines indicate the softening length in our calculations.
 As expected. in the N-body simulations the density at radii ess than a few times the softening leneth drops. quickly.," As expected, in the N-body simulations the density at radii less than a few times the softening length drops quickly."
 The vertical dashed. line. indicates the tidal radius in the classic mocel (this lino cannot be seen in the upper panel as 1¢ Classical model predicts a tidal radius bevond the virial radius for this tidal field strength)., The vertical dashed line indicates the tidal radius in the classic model (this line cannot be seen in the upper panel as the classical model predicts a tidal radius beyond the virial radius for this tidal field strength).
 For the weakest tical field (upper. panel of Fig. 12)), For the weakest tidal field (upper panel of Fig. \ref{fig:NbodyDensity}) )
 ye analytic model precicts the radial density profile seen in ια N-body simulation reasonably accurately for the first --eration (red line)., the analytic model predicts the radial density profile seen in the N-body simulation reasonably accurately for the first iteration (red line).
 After this. our model underpredicts 10 mass loss rate and. as such. overpreclicts the resulting ensity profile.," After this, our model underpredicts the mass loss rate and, as such, overpredicts the resulting density profile."
 As the tidal field is increased the mocdel fairs, As the tidal field is increased the model fairs
 The distance to the Large Magellanic Cloud (LMC) is the cornerstone of the extragalactic distance scale. owing to the fact that the zero point of both the Cepheid aud Type Ta supernova distances is fied to the LMC distance.," The distance to the Large Magellanic Cloud (LMC) is the cornerstone of the extragalactic distance scale, owing to the fact that the zero point of both the Cepheid and Type Ia supernova distances is tied to the LMC distance."
 Uufortunately. existing determinations of this fundamental quantity show a large ranee of values (Benedict et al.," Unfortunately, existing determinations of this fundamental quantity show a large range of values (Benedict et al."
 2002). which can be schematically clustered around. αιAon 15.20518.35 (short distance scale) aud GuMopar~ 18.5018.60. one distance scale).," 2002), which can be schematically clustered around $\rm (m-M)_{0,LMC}\sim$ 18.25–18.35 (short distance scale) and $\rm (m-M)_{0,LMC}\sim$ 18.50–18.60 (long distance scale)."
 We recall that the 7797 extragalactic distance scale project has deteriuned a value for the IIubble coustaut fy=72τε3(randonmi)c T(svsteimiatic) by assmnuine (aMo.pare:= 18.50480.10. (ποσα et al.," We recall that the $HST$ extragalactic distance scale project has determined a value for the Hubble constant $H_0=72\pm 3(\rm random)\pm 7(\rm systematic$ ) by assuming $\rm (m-M)_{0,LMC}=18.50\pm$ 0.10 (Freedman et al."
 2001)., 2001).
 This dichotomy is best illustrated by the recent results by Walker et al. (, This dichotomy is best illustrated by the recent results by Walker et al. (
2001. hereinafter WO1). Alves et al. (,"2001, hereinafter W01), Alves et al. ("
2002) and Salavis Cürardi (2002. hereafter SC02).,"2002) and Salaris Girardi (2002, hereinafter SG02)."
" WOI have determined the distauce to the LAIC cluster NGC 1866 bv uxing the well established Main Sequence-fittine (MS-fittiug) techuique: NGC 1866 is a well populated voung chlister located about 1"" north of the center of the LAIC. in a region with low extinction."," W01 have determined the distance to the LMC cluster NGC 1866 by using the well established Main Sequence-fitting (MS-fitting) technique; NGC 1866 is a well populated young cluster located about $4^0$ north of the center of the LMC, in a region with low extinction."
 Assuming that the cluster lies in the LAIC plane the eeonietrical correction to the LALC centre is simall. anmnountius to  0.02 mae in distance modulus.," Assuming that the cluster lies in the LMC plane the geometrical correction to the LMC centre is small, amounting to $\sim -$ 0.02 mag in distance modulus."
 WoL A\[S-fitting technique was based ou theoretical isoclirones which were shown to match properly the MS of the IEvades corrected for the IBipparcos distauce modulus: a NGC 1866 distance modulus (ivM)g18.30.18.35 was obtained. a typical example of the short distance scale.," W01 MS-fitting technique was based on theoretical isochrones which were shown to match properly the MS of the Hyades corrected for the Hipparcos distance modulus; a NGC 1866 distance modulus $\rm (m-M)_{0}\sim 18.30-18.35$ was obtained, a typical example of the short distance scale."
 Ou the other haud. Alves et al. (," On the other hand, Alves et al. ("
2002) and SCGO2 have obtained GuMpLc~18.50 by using multicolor photometry of LAIC Red Chuup (RC) field stars (observed in two different fields} as standard candles. a distance iu agreement with the long distance scale and the AEST zero poit.,"2002) and SG02 have obtained $\rm (m-M)_{0,LMC}\sim 18.50$ by using multicolor photometry of LMC Red Clump (RC) field stars (observed in two different fields) as standard candles, a distance in agreement with the long distance scale and the $HST$ zero point."
 They have both used the local RC ITipparcos absolute brightuess. corrected by the appropriate population corrections for the LMC computed by Cdrardi Salaris (2001. hereinafter CSOL) aud SCU2.," They have both used the local RC Hipparcos absolute brightness, corrected by the appropriate population corrections for the LMC computed by Girardi Salaris (2001, hereinafter GS01) and SG02."
 The use of multicolor photometry allows one to derive sinultaucouslv both distance modulus aud reddeuiug of the observed population. as shown by Alves et al. (," The use of multicolor photometry allows one to derive simultaneously both distance modulus and reddening of the observed population, as shown by Alves et al. ("
2002).,2002).
 Moreover. Sarajedini et al. (," Moreover, Sarajedini et al. ("
2002) derive similar values by using IR observations of the red clump in two LAIC star clusters.,2002) derive similar values by using IR observations of the red clump in two LMC star clusters.
 The preseut investigation alls at studvius iu more detail this discrepancy between MS-fittiung aud RC distances to the LAIC., The present investigation aims at studying in more detail this discrepancy between MS-fitting and RC distances to the LMC.
 We take advantage of the fact that the NGC 1866 WE (Joluson-Cousins) data published by Wl show not onlv the well populated MS of NGC 1866. but also a clearly defined RC of the surrounding LMC field: this occurrence allows us to sinultaneouslv apply MS-fittiug and RC method to the same photometric data for the same LMC region.," We take advantage of the fact that the NGC 1866 $VI$ (Johnson-Cousins) data published by W01 show not only the well populated MS of NGC 1866, but also a clearly defined RC of the surrounding LMC field; this occurrence allows us to simultaneously apply MS-fitting and RC method to the same photometric data for the same LMC region."
 The advantage with respect to comparing MS-fitfiug aud RC distances frou different investieatious is that im this, The advantage with respect to comparing MS-fitting and RC distances from different investigations is that in this
"having defined and p,,,, as the maximum momentum achievable by (he accelerated particles.",having defined and $\px$ as the maximum momentum achievable by the accelerated particles.
 We determine the latter sell-consistentlv. using the calenlations by Blasi.Amato&Caprioli(2007). for cosnuc rav modified shocks. assuming that the particles maxinunm energy is limitecl bv the acceleration time rather than bv the size of the system.," We determine the latter self-consistently, using the calculations by \cite{bac07} for cosmic ray modified shocks, assuming that the particles' maximum energy is limited by the acceleration time rather than by the size of the system."
" The time needed (o accelerate particles up to p,,,, turns out to be bvparts Eq.", The time needed to accelerate particles up to $\px$ turns out to be Integratingby parts Eq.
" 28. it is possible to express U,(p) in terms of U(r) and Cr. p)alone:0 Eq."," \ref{Up} it is possible to express $U_p(p)$ in terms of $U(x)$ and $x_p(x,p)$alone: Then, differentiating Eq."
 29. with respect to c. we obtain d£ Cr) Apr) Finally. we need a relation which describes how the Allvénn waves are excited by the streamüng cosmic ravs ancl how (he wave energy is (ransported in the precursor.," \ref{xicr} with respect to $x$, we obtain where Finally, we need a relation which describes how the Alfvénn waves are excited by the streaming cosmic rays and how the wave energy is transported in the precursor."
 Verv eenerallv. we can assume air) to be a function of €(r) and Cr).," Very generally, we can assume $\alpha(x)$ to be a function of $\xi(x)$ and $U(x)$."
 Using the equation of momentum conservation between a point cx in the precursor and upstream infinity. it is therefore possible to write αCr) as a function of C(.r) only (see e.g. Eq.," Using the equation of momentum conservation between a point $x$ in the precursor and upstream infinity, it is therefore possible to write $\alpha(x)$ as a function of $U(x)$ only (see e.g. Eq."
 42 in the next section. where a discussion of magnetic field amplification due to resonant strezuning instability. will be presented.)," \ref{alfares} in the next section, where a discussion of magnetic field amplification due to resonant streaming instability will be presented.)"
" The nonlinear svstem defined by Eqs, 23--", The nonlinear system defined by Eqs. \ref{conv-diff}-
34 can be solved. for a given age of (he system. wilh three nested iterations.," \ref{lambda} can be solved, for a given age of the system, with three nested iterations."
" We guess a value for p,,,,. as (he starting point of the outermost cvcle."," We guess a value for $\px$, as the starting point of the outermost cycle."
" Then. we fix a value for the ratio f0,,,/H,,4. ancl derive the corresponding fy, aud Hj rom Eq. 16.."," Then, we fix a value for the ratio $\Rs/\Rt$ , and derive the corresponding $\Rs$ and $\Rt$ from Eq. \ref{rsrt}. ."
 The equation lor conservation of momentum.," The equation for conservation of momentum,"
Povuting flux. malkine the available energy for powering a GRD,"Poynting flux, making the available energy for powering a GRB."
 The power depends ou the applied maguetic field: D442(M Pore (where By;=Blo GG)., The power depends on the applied magnetic field: ^2 )^2 (where $B_{15}=B/10^{15}$ G).
 This shows that modest variations in the applied maguetic field may explain a wide range of GRB powers. aud therefore of CRB durations.," This shows that modest variations in the applied magnetic field may explain a wide range of GRB powers, and therefore of GRB durations."
 There has been some recent dispute in the literature whether this mechamisin cau indeed be efficient (Li 1999) and whether the power of the DIT is ever siguificaut relative to that from the disk (Livio. Ogiblvie. Pringle 1999).," There has been some recent dispute in the literature whether this mechanism can indeed be efficient (Li 1999) and whether the power of the BH is ever significant relative to that from the disk (Livio, Ogilvie, Pringle 1999)."
 The answer in both cases is ves. as discussed by Lee. Wijers. Brown (1999).," The answer in both cases is yes, as discussed by Lee, Wijers, Brown (1999)."
 The issue. therefore. m Πιοπιο efücieut CRB sources among black holes is to find those that spin rapidly.," The issue, therefore, in finding efficient GRB sources among black holes is to find those that spin rapidly."
" There are a varicty of reasons why a black hole wight have high iretary ολοτα,", There are a variety of reasons why a black hole might have high angular momentum.
 It mav have formed from a rapidly rotating star. so the angular momenta was there all along Coriginal spin. according to Blandford 1999): it τας also have accreted angular momentum by interaction with a disk Cveuial spin’) or have formed by coalescence of a conrpact binary Cimortal spin).," It may have formed from a rapidly rotating star, so the angular momentum was there all along (`original spin', according to Blandford 1999); it may also have accreted angular momentum by interaction with a disk (`venial spin') or have formed by coalescence of a compact binary (`mortal spin')."
 We shall review some of the specific situations that have been proposed in turn., We shall review some of the specific situations that have been proposed in turn.
 Neutron star mergers are among the oldest proposed cosmological CRD sources (Eichler et 11989. Goodman. Dir. Nussiuov 1987. Paczvüsski 1986). aud especially the neutrino flux is still actively studied as à GRD power source (sec. ce. Ruffert Janka 1998).," Neutron star mergers are among the oldest proposed cosmological GRB sources (Eichler et 1989, Goodman, Dar, Nussinov 1987, Paczyńsski 1986), and especially the neutrino flux is still actively studied as a GRB power source (see, e.g., Ruffert Janka 1998)."
 However. once the central mass has collapsed to a black hole it becomes a good source for BZ power. since it naturally spius rapidly due to imberitauce of augular momentum from the binary (Rees /Moésszürros 1992).," However, once the central mass has collapsed to a black hole it becomes a good source for BZ power, since it naturally spins rapidly due to inheritance of angular momentum from the binary (Rees Mésszárros 1992)."
 Likewise DII-NS binaries (Lattimer Schranua 1971) will rapidly trauster a large amount of mass once the NS fills its Roche lobe. eiviug a rapidly rotating DII (IkIuzuiak Lee 1998).," Likewise BH-NS binaries (Lattimer Schramm 1974) will rapidly transfer a large amount of mass once the NS fills its Roche lobe, giving a rapidly rotating BH (Kluzniak Lee 1998)."
 The NS remnant av then be tidally destroved. leading to a conmact torus arouud the DIT.," The NS remnant may then be tidally destroyed, leading to a compact torus around the BH."
 It is unlikely that this would be lone-lived enough to produce the longer CRB. but perhaps the short (f< 153) ones could be produced (ec... Fiver. Woosley Παππά 1999).," It is unlikely that this would be long-lived enough to produce the longer GRB, but perhaps the short $t\lsim1$ s) ones could be produced (e.g., Fryer, Woosley Hartmann 1999)."
 Towever. nass transfer could stabilize and lead to a widening binary in which the NS lives until its mass drops to the minimis mass of aboutAL... and then becomes a debris torus (Portegies Zwart 1998).," However, mass transfer could stabilize and lead to a widening binary in which the NS lives until its mass drops to the minimum mass of about, and then becomes a debris torus (Portegies Zwart 1998)."
 By then. it is far οποιο] away that the resulting disk life time exceeds LOOOss. allowing even the louger GRB to be made.," By then, it is far enough away that the resulting disk life time exceeds s, allowing even the longer GRB to be made."
 Thus BU-NS and NS-NS binaries are quite promising., Thus BH-NS and NS-NS binaries are quite promising.
 They have the added advantage that their euviromuent is naturally reasonably clean. since there is no stellar envelope. and iuch of the initially present barvouic material vanishes iuto the horizon.," They have the added advantage that their environment is naturally reasonably clean, since there is no stellar envelope, and much of the initially present baryonic material vanishes into the horizon."
 The formation of a black hole directly out of a massive star has been cousidered for the production of GRB. either as hivyperuovae (Paczvisskd 1998). failed superuovae (Woosley 1993) or exploding WR stars (AlacFadven Woosley 1999).," The formation of a black hole directly out of a massive star has been considered for the production of GRB, either as hypernovae (Paczyńsski 1998), failed supernovae (Woosley 1993) or exploding WR stars (MacFadyen Woosley 1999)."
 Another siguificaut source of such eveuts is the formation of a DII of about in black hole trausieuts. which is discussed by Brown. Lee. Bethe (1999).," Another significant source of such events is the formation of a BH of about in black hole transients, which is discussed by Brown, Lee, Bethe (1999)."
 These BUs form from a helium star. because spiralin of the companion has stripped the παν of its envelope.," These BHs form from a helium star, because spiral-in of the companion has stripped the primary of its envelope."
 Both the above scenarios suffer from a problem fouud w Spruit Plinney (1998) with rotation of neutron stars: maguetic Ποιά» erown bv differential rotation in the star may cficiently couple the core and envelope. prohibiting the core to ever rotate rapidly.," Both the above scenarios suffer from a problem found by Spruit Phinney (1998) with rotation of neutron stars: magnetic fields grown by differential rotation in the star may efficiently couple the core and envelope, prohibiting the core to ever rotate rapidly."
 Then the black holes formect iu he above two wavs would not coutain enough spin energy o power a GRD. leaving oulv the more limited ri energy.," Then the black holes formed in the above two ways would not contain enough spin energy to power a GRB, leaving only the more limited $\nu\bar{\nu}$ energy."
 A third variety of black hole in à WR star would come your DILWR iuergers (Ένα Woosley 1998)., A third variety of black hole in a WR star would come from BH-WR mergers (Fryer Woosley 1998).
 These ippen in the same kinds of systems that form: DIT-NS ünaries as discussed above. in cases where the initial separation is snialler. so that spiral-in leads to complete uecreer rather than formation of a binary.," These happen in the same kinds of systems that form BH-NS binaries as discussed above, in cases where the initial separation is smaller, so that spiral-in leads to complete merger rather than formation of a binary."
" In this case. he DII and WR star are both spun up duiug the spiral process (Ίο, part of the orbital angular momentum of he binary becomes spin augular momentum)."," In this case, the BH and WR star are both spun up during the spiral-in process (i.e., part of the orbital angular momentum of the binary becomes spin angular momentum)."
 Then there is enough spin iu the system to power a GRB via the Dlaudford-Zuajek process., Then there is enough spin in the system to power a GRB via the Blandford-Znajek process.
 Tn order to evaluate the birth rates of the various progenitors discussed above. we need to establish the evolutionary paths from initial binaries takeu by cach. and then compute the fraction of all ZAMS binaries that evolve iuto the desired system.," In order to evaluate the birth rates of the various progenitors discussed above, we need to establish the evolutionary paths from initial binaries taken by each, and then compute the fraction of all ZAMS binaries that evolve into the desired system."
 Such a population svuthesis calculation is often done with large Monte Carlo codes PPortegies Zwart Yuneclson 1998)., Such a population synthesis calculation is often done with large Monte Carlo codes Portegies Zwart Yungelson 1998).
 Tere we follow the treatment bv Bethe and Brown (1998). because it is analytic and thus it is relatively trauspareut how the results depeud on the initial assunuptionus.," Here we follow the treatment by Bethe and Brown (1998), because it is analytic and thus it is relatively transparent how the results depend on the initial assumptions."
 It is lanited to systems iu which at least one star is massive enough to produce a supernova., It is limited to systems in which at least one star is massive enough to produce a supernova.
 Their final numbers agree remarkably well with the Monte Carlo simulations bv Portegies Zwart Yuneclsou (1998). if the same assuniptious about stellar evolution are used in both.," Their final numbers agree remarkably well with the Monte Carlo simulations by Portegies Zwart Yungelson (1998), if the same assumptions about stellar evolution are used in both."
 To normalize them rates. Bethe Brown (1998) used a supernova rate of a —0.02/vr per galaxy. and assumed that this equaled the birth rate of stars with mass greater than 10AY...," To normalize their rates, Bethe Brown (1998) used a supernova rate of $\alpha=$ 0.02/yr per galaxy, and assumed that this equaled the birth rate of stars with mass greater than $10\msun$."
" The birth rate of stars more massive thin AM scales as AZ"".", The birth rate of stars more massive than $M$ scales as $M^{-n}$.
 Therefore. the supernova rate m mass interval CAL is L," Therefore, the supernova rate in mass interval $M$ is n"
 Therefore. the supernova rate m mass interval CAL is LI," Therefore, the supernova rate in mass interval $M$ is n"
 Therefore. the supernova rate m mass interval CAL is LIG," Therefore, the supernova rate in mass interval $M$ is n"
 Therefore. the supernova rate m mass interval CAL is LIGA," Therefore, the supernova rate in mass interval $M$ is n"
 Therefore. the supernova rate m mass interval CAL is LIGAT," Therefore, the supernova rate in mass interval $M$ is n"
 Therefore. the supernova rate m mass interval CAL is LIGAT.," Therefore, the supernova rate in mass interval $M$ is n"
 Therefore. the supernova rate m mass interval CAL is LIGAT. ," Therefore, the supernova rate in mass interval $M$ is n"
 Therefore. the supernova rate m mass interval CAL is LIGAT. Q," Therefore, the supernova rate in mass interval $M$ is n"
 Therefore. the supernova rate m mass interval CAL is LIGAT. QM," Therefore, the supernova rate in mass interval $M$ is n"
The search for an unequivocal demonstration of the existence of stellar-mass black holes has focussed. on X-rav emitting binary systems consisting of an ordinary star together with a compact object.,The search for an unequivocal demonstration of the existence of stellar-mass black holes has focussed on X-ray emitting binary systems consisting of an ordinary star together with a compact object.
 I£ the mass of the compac object. (as. determined. from. kinematical measurements) appears to be greater than the maximum possible for a neutron star τρως then the object has been acknowledge as a black hole candidate.," If the mass of the compact object (as determined from kinematical measurements) appears to be greater than the maximum possible for a neutron star $M_{max}$, then the object has been acknowledged as a black hole candidate."
 The value of Mui ds still no reliably. known. because of uncertainties in the equation of state of matter at high. densities. but it has been widely believed. that the limit of. 3:2M. derived by Ioades hullini (1974) (together. with a possible upware correction for rotation) gives a secure upper bound.," The value of $M_{max}$ is still not reliably known, because of uncertainties in the equation of state of matter at high densities, but it has been widely believed that the limit of $3.2\,M_\odot$ derived by Rhoades Ruffini (1974) (together with a possible upward correction for rotation) gives a secure upper bound."
 The best current stellar-mass black hole candidates are in soft N-rayv transients (SAPs). a sub-class of the low mass X-ray binaries (see Charles 1996).," The best current stellar-mass black hole candidates are in soft X-ray transients (SXTs), a sub-class of the low mass X-ray binaries (see Charles 1996)."
 During quiescence. the accretion disc in these svstems becomes extremely faint and it is then possible to carry out detailed. photometry and spectroscopy of the optical companion. which allows the mass of the compact object to be directly determined (van Paradijs AleClintock 1995).," During quiescence, the accretion disc in these systems becomes extremely faint and it is then possible to carry out detailed photometry and spectroscopy of the optical companion, which allows the mass of the compact object to be directly determined (van Paradijs McClintock 1995)."
 Fig., Fig.
 1 shows the presently-known masses of neutron stars ancl black-hole cancliclates., 1 shows the presently-known masses of neutron stars and black-hole candidates.
 The “neutron star” masses all lic within a small range of L4Al.. whereas the black-hole candidates seem to form a distinct grouping around 10437..," The “neutron star” masses all lie within a small range of $1.4\, M_\odot$, whereas the black-hole candidates seem to form a distinct grouping around $\sim 10\, M_\odot$."
 The most convincing of the black hole candidates are V404 €vg (Shahbaz 1994b) and Nova Sco (Orosz ανα 1996) with masses of 12ÀA/4. and 7M. respectively. well above the IthoacdesIullini limit.," The most convincing of the black hole candidates are V404 Cyg (Shahbaz 1994b) and Nova Sco (Orosz Bailyn 1996) with masses of $12\, M_\odot$ and $7\, M_\odot$ respectively, well above the Rhoades/Ruffini limit."
 Rhoades and. Rutlini derived their result in response to the problem caused. by different: high-density equations of state leacing to widely dillerent values for. Ady... the idea being to derive a firm for non-rotating models on the basis only of knowledge which could be considere as completely. secure.," Rhoades and Ruffini derived their result in response to the problem caused by different high-density equations of state leading to widely different values for $M_{max}$, the idea being to derive a firm for non-rotating models on the basis only of knowledge which could be considered as completely secure."
 However. some of the assumptions mace are. in fact. istinctIy questionable (see Hartle 1978. Friedman Ipser 1987).," However, some of the assumptions made are, in fact, distinctly questionable (see Hartle 1978, Friedman Ipser 1987)."
 In. particular: (1) it was assume that the equation of state can be taken as accurately known [or densities up to a fiducial value po which they took as 4.6 I (ii) they imposed a causality condition which would only be appropriate for a non-dispersive medium.," In particular: (i) it was assumed that the equation of state can be taken as accurately known for densities up to a fiducial value $\rho_0$ which they took as $4.6 \times 10^{14}\,{\rm g}\,{\rm cm}^{-3}$ ; (ii) they imposed a causality condition which would only be appropriate for a non-dispersive medium."
" Ifa more conservative value is taken for po (104+ecm ay. the causality condition is dropped. and. allowance is mace [or rotation. the upper bound. for M, obtained. in this wav goes up to 14.3M. (Friedman Ipser 1987). which is no longer useful in considering black bole candidates such as V404 (νο"," If a more conservative value is taken for $\rho_0$ $10^{14}\,{\rm g}\,{\rm cm}^{-3}$ ), the causality condition is dropped and allowance is made for rotation, the upper bound for $M_{max}$ obtained in this way goes up to $14.3\,M_\odot$ (Friedman Ipser 1987) which is no longer useful in considering black hole candidates such as V404 Cyg."
 Llowever. standard realistic neutron star equations of state do. in practice. give masses. satisfving," However, standard realistic neutron star equations of state do, in practice, give masses satisfying"
scheduling of these VLBA observations. is shown in Figure 1.. reproduced here [rom Paper I. The data were recorded al each antenna in dualcicular polarization in (wo 4 Mllz baseband spectral windows. each digitally sampled at the full Nyequist rate of 8 Mbps in 1-bit quantization.,"scheduling of these VLBA observations, is shown in Figure \ref{fig-aavso}, reproduced here from Paper I. The data were recorded at each antenna in dual-circular polarization in two 4 MHz baseband spectral windows, each digitally sampled at the full Nyquist rate of 8 Mbps in 1-bit quantization."
 The lower spectral window was centered at a fixed topocentric Irequency corresponding to the ve=1.J1- SiO transition. al an assumed rest [requencey vy)= GIIz and a svstemic velocity Visi;=+9 toward TX Cam. Doppler-shifted to the center of the array and the midpoint of the observations al each epoch.," The lower spectral window was centered at a fixed topocentric frequency corresponding to the $v=1,\ J=1-0$ SiO transition, at an assumed rest frequency $\nu_0=43.122027$ GHz and a systemic velocity $V_{LSR}=+9$ toward TX Cam, Doppler-shifted to the center of the array and the midpoint of the observations at each epoch."
 No further real-time Doppler corrections were applied: these were performed in post-processing., No further real-time Doppler corrections were applied; these were performed in post-processing.
 For the majority of the VLBA epochs in Table L.. the e=2.J1—0 transition was simultaneously observed. and centered in (he second spectral window: the analvsis of these data will be presented in a future paper Each VLBA observing epoch was scheduled in a comparable local sidereal time (LST) range. as permillecl by telescope operations.," For the majority of the VLBA epochs in Table \ref{tbl-vlba-epochs}, the $v=2,\ J=1-0$ transition was simultaneously observed, and centered in the second spectral window; the analysis of these data will be presented in a future paper Each VLBA observing epoch was scheduled in a comparable local sidereal time (LST) range, as permitted by telescope operations."
 Three fixed schedule formats were used over the course of these observations., Three fixed schedule formats were used over the course of these observations.
 For epochs a schedule of 6-hour duration was used. balanced between the target source. TX Cam (3.5 h). the primary continuum. calibrator. JO359+509 (1.1 h). and secondary calibrators 3C454.3..J0609-157. and. 3€286 (each 0.22 h).," For epochs a schedule of 6-hour duration was used, balanced between the target source, TX Cam (3.5 h), the primary continuum calibrator, J0359+509 (1.1 h), and secondary calibrators 3C454.3, J0609-157, and 3C286 (each 0.22 h)."
 A single scan on 3C236 was included initially to explore an alternative absolute EVPA calibration method. as discussed further below.," A single scan on 3C286 was included initially to explore an alternative absolute EVPA calibration method, as discussed further below."
 This was not successful however. and [or epochs the 3C386 scan was re-allocated to TX Cam (3.6 h). and the schedule ," This was not successful however, and for epochs the 3C386 scan was re-allocated to TX Cam (3.6 h), and the schedule re-balanced."
For epochs{ZZ-AQ}.. an 8-hour schedule format was used. but 2 hours of each run were shared with a 22 GllIz project. leaving the total 43 Gllz observing time. and its division between sources. unchanged.," For epochs, an 8-hour schedule format was used, but 2 hours of each run were shared with a 22 GHz project, leaving the total 43 GHz observing time, and its division between sources, unchanged."
" The data were correlated at the VLBA correlator in Socorro. NM. adopting a field center position for TX Cam of (Ajay=05""00""5D.186..μμ56710""5.P.341)."," The data were correlated at the VLBA correlator in Socorro, NM, adopting a field center position for TX Cam of $\alpha_{J2000}=
05^h00^m51^s.186,\ \delta_{J2000}=56^d10^m54^s.341)$."
" The correlator accumulation interval A/, was constrained by output. data rate limits in place al the correlator at that time.", The correlator accumulation interval $\Delta t_c$ was constrained by output data rate limits in place at the correlator at that time.
" A value Al.=6.03 s was used for epochsAA-G.I-IN).. and reduced to AZ,=4.98 s for epochs(HIL."," A value $\Delta
t_c=6.03$ s was used for epochs, and reduced to $\Delta
t_c=4.98$ s for epochs."
M-ABR)... All polarization correlation products (IRI.RL.LBR.LL) were formed in each correlation accumulation interval from the dual-circular data acquired at each antenna.," All polarization correlation products (RR,RL,LR,LL) were formed in each correlation accumulation interval from the dual-circular data acquired at each antenna."
" In (his spectral-line polarization mode the VLBA correlator has a channel count limit of IN4,,=128.", In this spectral-line polarization mode the VLBA correlator has a channel count limit of $N_{chan}=128$.
 This produced auto- ancl cross-power spectra in each 4 MlIz baseband with a nominal velocity spacing of ~0.2 t.., This produced auto- and cross-power spectra in each 4 MHz baseband with a nominal velocity spacing of $\sim 0.2$ .
The situation is slightly more complex when D=D(p). because one must solve simultaneously eqs.,"The situation is slightly more complex when $D = D(p)$, because one must solve simultaneously eqs."
 24. and 20.., \ref{reldisp} and \ref{Dbar}.
 We begin by considering the limit 4—0., We begin by considering the limit $k\rightarrow 0$.
 In this case. ancl assuming 2— a constant. we easily find. to leading order in A. QF=1245LD./6P): as it must. the dispersion relation allows pure pressure waves. with the particle pressure providing a correction to the (pure gas) sound speed. because for large perturbation wavelengths particles are entrained bv the perturbation.," In this case, and assuming $\Omega\rightarrow$ a constant, we easily find, to leading order in $k$, $\Omega^2 = 1+\gamma'_c P_c/(\gamma P)$: as it must, the dispersion relation allows pure pressure waves, with the particle pressure providing a correction to the (pure gas) sound speed, because for large perturbation wavelengths particles are entrained by the perturbation."
 We remark (that. in (his limit. pressure waves aresupersonic. in the sense (hat thev are faster (han pressure waves propagaling in a pure gas of the sime (hermodyvnamical state. a result already noticed by Toptvein(1999).," We remark that, in this limit, pressure waves are, in the sense that they are faster than pressure waves propagating in a pure gas of the same thermodynamical state, a result already noticed by \citet{toptygin1999}."
.. Asstuning O— a constant. we lost a solution. so we search for the third mode solution in the form 9=ak+ higher order terms in .," Assuming $\Omega\rightarrow$ a constant, we lost a solution, so we search for the third mode solution in the form $\Omega = \alpha k+ $ higher order terms in $k$."
 We find: we use the definition 2 =i?/(e—uk.)ih/(Qe.)to simplify the above to Ll whichcan be now used with eqs.," We find: Now we use the definition $z \equiv \imath
k^2/(\omega-uk_x) = \imath k/(\Omega c_s)$ to simplify the above to whichcan be now used with eqs."
 20. and 22. to obtain where of course Of/Op«0., \ref{Dbar} and \ref{aux2} to obtain where of course $\partial f/\partial p < 0$.
 As a function of real z. the right-hand side above (where il exists) is easily seen (o be a monotonically decreasing function ofz. vanishing for 2—cox.," As a function of real $z$, the right-hand side above (where it exists) is easily seen to be a monotonically decreasing function of$z$, vanishing for $z\rightarrow\pm\infty$ ."
" In anv realise physical problem the integral must extend from a minimum (p,,) to a maximum momentum pa: since D(p) is expected to be a monotonically increasing function of p. we see that the integral above always exists lor z<1/D(py)=1/Dy. and z>1/D(p,)= 1/D,. and il divergesexactly al 2=1/D4, and z= 1/D,,."," In any realistic physical problem the integral must extend from a minimum $p_m$ ) to a maximum momentum $p_M$; since $D(p)$ is expected to be a monotonically increasing function of $p$, we see that the integral above always exists for $z
< 1/D(p_M) \equiv 1/D_M$, and $z > 1/D(p_m)\equiv 1/D_m$ , and it divergesexactly at $z = 1/D_M$ and $z = 1/D_m$ ."
" Thus the integral on the right-hand side of the equation above spans (he whole range [rom 0 to —o€ as z varies between. —x: and +1/D(p,,). and the range +x to 0 as z varies between 1/D,, and 4-2x«."," Thus the integral on the right-hand side of the equation above spans the whole range from $0$ to $-\infty$ as $z$ varies between $-\infty$ and $+1/D(p_m)$, and the range $+\infty$ to $0$ as $z$ varies between $1/D_m$ and $+\infty$."
" Somewhere in the range 1/D,,«zo there is the one and only solution of the above equation.", Somewhere in the range $1/D_m < z < +\infty$ there is the one and only solution of the above equation.
 An illustration of the integral on the right-hand side of the previous equation is shown in Fig. 1..," An illustration of the integral on the right-hand side of the previous equation is shown in Fig. \ref{fig:fz},"
 for a specific distribution funetion from AmatoandBlasi(2005): the qualitative features of (his plot are generic to all distribution functions we have tried., for a specific distribution function from \citet{amatoblasi2005}: the qualitative features of this plot are generic to all distribution functions we have tried.
 Furthermore. since 2=7h?/(w— ub). andthe small perturbations were assumed to varyas €HioukM . the resultthat z>0 implies that all modes are camped by diffusion. as physical intuition obviously suggests.," Furthermore, since $z = \imath k^2/(\omega-uk_x)$ , andthe small perturbations were assumed to varyas $e^{\imath(\omega-uk_x)t}$ , the resultthat $z > 0$ implies that all modes are damped by diffusion, as physical intuition obviously suggests."
agreement between the models and the observed data can be fully appreciated in Figure 9 where the models for metallicity (M/H|-—1.3 (dashed line) and |M/H|2—1.0 (solid line) are shown.,agreement between the models and the observed data can be fully appreciated in Figure \ref{cmd} where the models for metallicity $[M/H]=-1.3$ (dashed line) and $[M/H]=-1.0$ (solid line) are shown.
 As noted by DPO7. the models of Baraffeetal.(1997) are calculated for the F606W and FS814W filters of the WFPC2. which are slightly different from those on baord the ACS.," As noted by DP07, the models of \cite{ba97} are calculated for the F606W and F814W filters of the WFPC2, which are slightly different from those on baord the ACS."
 We used the same method proposed in their work in order to translate the filter from the WPFC2 to the ACS system., We used the same method proposed in their work in order to translate the filter from the WPFC2 to the ACS system.
 Briefly. by using synthetic model atmosphere from e.g. the ATLASO library of Kurucz(1993).. it 1s possible to calculate the magnitude difference in the same filter for the two cameras as a function of the effective temperature of the star.," Briefly, by using synthetic model atmosphere from e.g. the ATLAS9 library of \cite{ku93}, it is possible to calculate the magnitude difference in the same filter for the two cameras as a function of the effective temperature of the star."
 As shown in Figure 9. the agreement of the translated model in the ACS sample (right panel) is very good., As shown in Figure \ref{cmd} the agreement of the translated model in the ACS sample (right panel) is very good.
 The best fit of the model to the fiducial line corresponds to metallicity [M/H|]2—1.0. distance modulus (547—M)=14.21 and color excess £(B—V)2 0.26.," The best fit of the model to the fiducial line corresponds to metallicity $[M/H]=-1.0$, distance modulus $(m-M)=14.21$ and color excess $E(B-V)=0.26$ ."
 These values are in excellent agreement with those of Piotto&Zoccali (1999). namely Gn-M)=14.20 and E(B—V)20.29.," These values are in excellent agreement with those of \cite{pio99}, , namely $(m-M)=14.20$ and $E(B-V)=0.29$."
 The metallicity of the best fitting model. |[M/H]|2—1.0. is fully consistent with the value measured observationally by Carretta& (1997).. namely [Fe/H]2—1.41. whereas those for deviate in color in the lower part of the CMD. as already pointed out by Pollardetal.(2005).," The metallicity of the best fitting model, $[M/H]=-1.0$, is fully consistent with the value measured observationally by \cite{cg97}, namely $[Fe/H]=-1.41$, whereas those for $[M/H]=-1.3$ deviate in color in the lower part of the CMD, as already pointed out by \cite{pol05}."
. We used an isocrone calculated for an age of 1OGyr. the only available at the moment from Baraffeetal.(1997).," We used an isocrone calculated for an age of 10Gyr, the only available at the moment from \cite{ba97}."
. It is clear from their Figure 3a that the age plays a minor when void effect in the range of masses considered 1n this work., It is clear from their Figure 3a that the age plays a minor when void effect in the range of masses considered in this work.
 In light of the good agreement between the observed ridge line and the models of Baraffeetal.(1997). we feel confident that we can use the latter to translate magnitudes into masses.," In light of the good agreement between the observed ridge line and the models of \cite{ba97}, we feel confident that we can use the latter to translate magnitudes into masses."
 A crucial step in determining an accurate LF ts the estimation of the photometric completeness of the data., A crucial step in determining an accurate LF is the estimation of the photometric completeness of the data.
 Completeness corrections were determined via artificial star tests following the method discussed by Bellazzinietal. (2002)., Completeness corrections were determined via artificial star tests following the method discussed by \cite{be02}.
.. We first generated a catalogue of simulated. stars with a V. magnitude randomly extracted from a LF modeled to reproduce the observed LF in the V band., We first generated a catalogue of simulated stars with a $V$ magnitude randomly extracted from a LF modeled to reproduce the observed LF in the $V$ band.
 Then the / magnitude was assigned at each sampled V magnitude by interpolating the mean ridge line of the cluster (see Figure 9))., Then the $I$ magnitude was assigned at each sampled $V$ magnitude by interpolating the mean ridge line of the cluster (see Figure \ref{cmd}) ).
 The coordinates of the simulated stars where calculated in the coordinate system of the reference frame and then translated to each single image using the same matching solutions found in the data reduction phase (see Section 2.1))., The coordinates of the simulated stars where calculated in the coordinate system of the reference frame and then translated to each single image using the same matching solutions found in the data reduction phase (see Section \ref{riduz}) ).
 It is crucial to avoid interference between the artificial stars. since in that case the output of the experiments would be biased by artificial crowding not present in the original frame.," It is crucial to avoid interference between the artificial stars, since in that case the output of the experiments would be biased by artificial crowding not present in the original frame."
 For this reason the frames were divided in a grid of cells of fixed width (~15 pixel. i.e. more than 5 times larger that the mean FWHM of the stars in the frames) and only one star was randomly placed in such a box in each artificial test run.," For this reason the frames were divided in a grid of cells of fixed width $\sim
15$ pixel, i.e. more than 5 times larger that the mean FWHM of the stars in the frames) and only one star was randomly placed in such a box in each artificial test run."
 The artificial stars were added to the real images using the DAOPHOT/ADDSTAR routine., The artificial stars were added to the real images using the DAOPHOT/ADDSTAR routine.
 The reduction process was repeated on the artificial images in exactly the same way as for the scientific ones and applying the same selection criteria described in Section 2.1.., The reduction process was repeated on the artificial images in exactly the same way as for the scientific ones and applying the same selection criteria described in Section \ref{riduz}.
 More than 0000 stars were eventually simulated in each chip. for a total of more that 500.000 stars in the entire data set.," More than 000 stars were eventually simulated in each chip, for a total of more that 500,000 stars in the entire data set."
" The photometric completeness (f) was then calculated as the ratio of the number of stars recovered after the photometric reduction (N,,,) and the number of simulated stars (N5,).", The photometric completeness $f$ ) was then calculated as the ratio of the number of stars recovered after the photometric reduction $N_{out}$ ) and the number of simulated stars $N_{in}$ ).
 f£ is expressed as a function of / magnitude., $f$ is expressed as a function of $I$ magnitude.
 Due to the strong gradient in stellar density from the center of the cluster outwards. there is a significant dependence of the photometrie completeness with radial distance. even though 110 is a reasonably sparse GC and the images do not suffer from dramatic crowding.," Due to the strong gradient in stellar density from the center of the cluster outwards, there is a significant dependence of the photometric completeness with radial distance, even though 10 is a reasonably sparse GC and the images do not suffer from dramatic crowding."
 Nevertheless. in. order to take this radial effect into account. we divided the entire FoV in 6 zones characterized by à similar completeness.," Nevertheless, in order to take this radial effect into account, we divided the entire FoV in 6 zones characterized by a similar completeness."
 In Figure | the black full circle show the regions numbered from | to 6., In Figure \ref{map} the black full circle show the regions numbered from 1 to 6.
 The innermost four regions are included in the ACS FOV and are concentric annuli all centered on the nominal cluster center., The innermost four regions are included in the ACS FOV and are concentric annuli all centered on the nominal cluster center.
 We notice here that the center used in this work has been determined from accurate star counts of resolved stars in the central regions of the cluster from archival ΛΕΡΟΣ imaging of 110 (Prop., We notice here that the center used in this work has been determined from accurate star counts of resolved stars in the central regions of the cluster from archival WFPC2 imaging of 10 (Prop.
 6607. ΡΙ. F. Ferraro). as explained in a forthcoming paper (Dalessandro et al.," 6607, P.I. F. Ferraro), as explained in a forthcoming paper (Dalessandro et al."
 2010: in preparation)., 2010; in preparation).
" The adopted center of gravity 15 A000=165785,92donq2—470858707. which is in full agreement with the one, of Harrisetal.(1996)."," The adopted center of gravity is $\alpha_{\rm
J2000} =16^{\rm h}\,57^{\rm m}\, 8^{\rm s}.92\,,~\delta_{J2000} =
-4^\circ\,05^\prime\, 58\farcs07$, which is in full agreement with the one of \cite{ha96}."
 Region 5 includes both the WF3 and WF4 chips of the WFPC?2. which cover and area of equal crowding condition at the same radial distance. whereas Region 6 corresponds the whole WF? chip.," Region 5 includes both the WF3 and WF4 chips of the WFPC2, which cover and area of equal crowding condition at the same radial distance, whereas Region 6 corresponds the whole WF2 chip."
 In Figure 10. we report the resulting photometric completeness of each of the six regions as a function of the /-band magnitude.," In Figure \ref{comp}
 we report the resulting photometric completeness of each of the six regions as a function of the $I$ -band magnitude."
 It is important to notice that. even in the very central region of the cluster where saturation biases the completeness. artificial star tests show that we sample the MS stellar population of the cluster down to ~5 mag below the TO (see solid line in lower panel). with à completeness in excess of In order to derive the LF. we selected from our bona-fide photometric catalogies all stars within each of the six regions mentioned above and sorted them as a function of the /-band magnitude.," It is important to notice that, even in the very central region of the cluster where saturation biases the completeness, artificial star tests show that we sample the MS stellar population of the cluster down to $\sim 5$ mag below the TO (see solid line in lower panel), with a completeness in excess of In order to derive the LF, we selected from our bona-fide photometric catalogies all stars within each of the six regions mentioned above and sorted them as a function of the $I$ -band magnitude."
 The resulting observed LFs (OLFs) are shown as full circles in Figure 11. and as filled circles after correction for photometric completeness., The resulting observed LFs (OLFs) are shown as full circles in Figure \ref{lumf} and as filled circles after correction for photometric completeness.
 The observed and completeness-corrected LFs are also provided in Table 2.., The observed and completeness-corrected LFs are also provided in Table \ref{lumcont}.
 In Figure 11. we also show. as a dashed line. the LF published by Piotto&Zoccali(1999) in the WF2 frame. which appears in excellent agreement with ours.," In Figure \ref{lumf} we also show, as a dashed line, the LF published by \cite{pio99} in the WF2 frame, which appears in excellent agreement with ours."
 The solid line shown in Figure 11. are the theoretical LFs (TLFs) obtained by multiplying a simple power-law mass function (MF) of the type dN/dixm'' by the derivative of the mass—luminosity relationship of Baraffe et al. (, The solid line shown in Figure \ref{lumf} are the theoretical LFs (TLFs) obtained by multiplying a simple power-law mass function (MF) of the type $dN/dm \propto m^\alpha$ by the derivative of the mass–luminosity relationship of Baraffe et al. (
1997) for |M/H|=-1.0.,1997) for $[M/H]=-1.0$.
 We have adopted a distance modulus Gn-M)214.21 and a color excess E(B-V)=0.26 às found in Section. 2.2.., We have adopted a distance modulus $(m-M)=14.21$ and a color excess $E(B-V)=0.26$ as found in Section \ref{sec_cmd}.
 The power-law indices that correspond to the best fitting models for the six regions. from Region | to Region 6. are respectively à=0.7.0.4.0.1.—0.3.—0.6.—0.9.," The power-law indices that correspond to the best fitting models for the six regions, from Region 1 to Region 6, are respectively $\alpha=0.7,0.4, 0.1,-0.3, -0.6,
-0.9$."
 With the notation used there. the Salpeter IMF would have a2—2.35 and a positive index implies that the number of stars is decreasing with decreasing mass.," With the notation used there, the Salpeter IMF would have $\alpha=-2.35$ and a positive index implies that the number of stars is decreasing with decreasing mass."
" The wide range of MF slope indices from the cluster core to 2.5744, indicates that stars in M110 have experienced the effects of masssegregation."," The wide range of MF slope indices from the cluster core to $2.5\,r_{\rm hm}$ indicates that stars in 10 have experienced the effects of masssegregation."
 Massive stars are much more segregated in the central regions were the index Is positive., Massive stars are much more segregated in the central regions were the index is positive.
The MFs are almost flat in the intermediate regions with an inversion of the trend outside. where the number oflow mass stars Is Increasing compared to the more massive ones.,"The MFs are almost flat in the intermediate regions with an inversion of the trend outside, where the number oflow mass stars is increasing compared to the more massive ones."
 We address this issue, We address this issue
which vields ~4.0MeV at densities of ~3.4x1013οemoE ,which yields $\sim 4.0 \mbox{ MeV}$ at densities of $\sim 3.4 \times 10^{13} \mbox{ g cm}^{-3}$.
We increase &gradually the integration5 constant in equations (16)) and (17)) and hence ihe inclination angle& 9 of the rotation axis against5 the major axis (z-axis) of a single) ervstal., We increase gradually the integration constant in equations \ref{eq:stst-int1}) ) and \ref{eq:stst-int2}) ) and hence the inclination angle $\theta$ of the rotation axis against the major axis (z-axis) of a single crystal.
 The vortex lines now should thread through many lattice planes., The vortex lines now should thread through many lattice planes.
 We find that when the inclination angle is siiall and less than 0.77. vortex lines in equilibrium configurations move from one lattice plane to the next by forming a clear kink aud (he number of kinks increases with increasing inclination angle (Fie. 4)).," We find that when the inclination angle is small and less than $0.7^{\circ}$, vortex lines in equilibrium configurations move from one lattice plane to the next by forming a clear kink and the number of kinks increases with increasing inclination angle (Fig. \ref{stpt}) )."
 The separation L. in z between the neighboring kinks varies as L.x@|., The separation $L_z$ in z between the neighboring kinks varies as $L_z \propto \theta ^{-1}$.
 The property of a kink in Fig., The property of a kink in Fig.
 4. is the same as that in Fig. 3.., \ref{stpt} is the same as that in Fig. \ref{kink}.
 A vortex line can orient its average direction to the direction of the rotation axis bv adjusting a number of kinks., A vortex line can orient its average direction to the direction of the rotation axis by adjusting a number of kinks.
 Apart [rom the kink parts. the vortex lines are straight and in parallel to (he z-axis. ancl are firmly pinned to the lattice nuclei.," Apart from the kink parts, the vortex lines are straight and in parallel to the z-axis, and are firmly pinned to the lattice nuclei."
 Even though the extra energy. is required to create kinks. (he total energy of a vortex line with kinks is much lower than that of the inclined straight vortex line without kinks since except for kink parts the vortex line lies in the bottom region of the pinning potential (Link.Epstein.&Davi.1993).," Even though the extra energy is required to create kinks, the total energy of a vortex line with kinks is much lower than that of the inclined straight vortex line without kinks since except for kink parts the vortex line lies in the bottom region of the pinning potential \citep{lin93}."
. As the average orientation of a vortex line inclines against the major axis. the separation between the neighboring kinks aud hence the portion of a vortex line available [or pinnine decrease.," As the average orientation of a vortex line inclines against the major axis, the separation between the neighboring kinks and hence the portion of a vortex line available for pinning decrease."
 As seen in Fig. 4.," As seen in Fig. \ref{stpt},"
 (he straight pinned part of the vortex line becomes shorter than the kink part when the inclination angle is above ~0.77., the straight pinned part of the vortex line becomes shorter than the kink part when the inclination angle is above $\sim 0.7^{\circ}$.
 The vertical pinned portion as well as (he kink feature becomes less prominent al 1.37., The vertical pinned portion as well as the kink feature becomes less prominent at $\sim 1.3^{\circ}$.
 When the inclination augle exceeds e»2.57. (he equilibrium configuration of a vortex line becomes almost the straight line.," When the inclination angle exceeds $\sim 2.5^{\circ}$, the equilibrium configuration of a vortex line becomes almost the straight line."
 This consequence arises from the fact that the portion of a vortex line for pinning becomes too short to compensate (he energy cost for producing kinks when (he inclination angle exceeds a certain value., This consequence arises from the fact that the portion of a vortex line for pinning becomes too short to compensate the energy cost for producing kinks when the inclination angle exceeds a certain value.
 When the average orientation of a vortex line inclines significantly against the z-axis. we need to include (he z-components for both the force aud displacement. though neglected here.," When the average orientation of a vortex line inclines significantly against the z-axis, we need to include the z-components for both the force and displacement, though neglected here."
 We expect (hat the lattice planes different [rom those considered here may become important lor pinning., We expect that the lattice planes different from those considered here may become important for pinning.
 The (three dimensional calculations are needed in order to know the equilibrium configuration of a vortex line accurately., The three dimensional calculations are needed in order to know the equilibrium configuration of a vortex line accurately.
 We now examine how the kink solutions are modified when we include (he Magnus terms in equations (16)) and (17))., We now examine how the kink solutions are modified when we include the Magnus terms in equations \ref{eq:stst-int1}) ) and \ref{eq:stst-int2}) ).
 The pinning and Magnus terms as a function of o (0) are represented by the cosine curve and the inclined straight line. respectively.," The pinning and Magnus terms as a function of $\phi$ $\psi$ ) are represented by the cosine curve and the inclined straight line, respectively."
 Hence. there exists ó. (6) al which the integration constant (the total energv) becomes equal to the," Hence, there exists $\phi_c$ $\psi_c$ ) at which the integration constant (the ""total energy"") becomes equal to the"
pulsars.,pulsars.
" predicts that innormal neutron stars toroidal magnetic fields could give rise to prolate stars with ellipticities of order where (Bis) is the volume aE)alco magnetic field in units of 10156ον also study the role of internal magneticG. [Haskellfields, both et_al](2008 poloidal and toroidal, and how this would effect the star’s ellipticity (in particular for a star with anEoS described by an n=1 polytrope)."," predicts that in neutron stars toroidal magnetic fields could give rise to prolate stars with ellipticities of order where $\langle B_{15} \rangle$ is the volume averaged magnetic field in units of $10^{15}$ G. also study the role of internal magnetic fields, both entirely poloidal and toroidal, and how this would effect the star's ellipticity (in particular for a star with an described by an $n=1$ polytrope)."
 They give which for the toroidal case is similar to that of(2002)., They give which for the toroidal case is similar to that of.
 Very similar limits for toroidal fields in superconducting stars are given by(2008)., Very similar limits for toroidal fields in superconducting stars are given by.
" These equations can be re-arranged to give limits on the magnetic fields givengravitationalwave observations of the quadrupole (see 8??) and an assumed moment of inertia, which here we will take as 1035 m? (as noted above this is probably a lower limit and could differ by up to a factor of ~ 3)."," These equations can be re-arranged to give limits on the magnetic fields given observations of the quadrupole (see ) and an assumed moment of inertia, which here we will take as $10^{38}$ $^2$ (as noted above this is probably a lower limit and could differ by up to a factor of $\sim 3$ )."
" Potential measurements of the field strength for both the poloidal and toroidal cases if signals were observed at an S/N of 5 for the ALV, ET-B and ET-C set ups are given in Fig."," Potential measurements of the field strength for both the poloidal and toroidal cases if signals were observed at an S/N of 5 for the ALV, ET-B and ET-C set ups are given in Fig."
"[I3] We can see that for the young pulsars (with frequencies X 40Hz) internal magnetic fields of greater than 10146 would be required to observe them, which is of a similar strength to theexternal fields of a magnetars at 10!*—1015 G. For the millisecond pulsars, in particular the non-GC pulsars, internal poloidal fields of a few 1013 G could provide observable signals, although if there are only toroidal fields then a couple of orders of magnitude higher would be necessary."," We can see that for the young pulsars (with frequencies $\lesssim 40$ Hz) internal magnetic fields of greater than $10^{14}$ G would be required to observe them, which is of a similar strength to the fields of a magnetars at $10^{14}-10^{15}$ G. For the millisecond pulsars, in particular the non-GC pulsars, internal poloidal fields of a few $10^{12}$ G could provide observable signals, although if there are only toroidal fields then a couple of orders of magnitude higher would be necessary."
" Of course the field geometry could be complex and a combination of toroidal and poloidal components, and the calculations above rely on a specificEoS."," Of course the field geometry could be complex and a combination of toroidal and poloidal components, and the calculations above rely on a specific."
 We have looked at our ability to detect and estimate parameters fromgravitationalwave observations for known (non-accreting) pulsars., We have looked at our ability to detect and estimate parameters from observations for known (non-accreting) pulsars.
" Using Bayesian hypothesis testing, we estimate that signals with an S/N of 5 could be detected with 95 per cent efficiency."," Using Bayesian hypothesis testing, we estimate that signals with an S/N of 5 could be detected with 95 per cent efficiency."
" This assumes that the data is Gaussian, and experience of real detector data shows that this assumption can be reasonable on short time scales and with effectively cleaned data, although there will still probably be some small degrading of detection ability."," This assumes that the data is Gaussian, and experience of real detector data shows that this assumption can be reasonable on short time scales and with effectively cleaned data, although there will still probably be some small degrading of detection ability."
" Once detected, we have shown how estimates of various parameters will be affected as signals increase in S/N, and also how the pulsar's orientation affects this."," Once detected, we have shown how estimates of various parameters will be affected as signals increase in S/N, and also how the pulsar's orientation affects this."
 We see that for strong signals in the case where the orientation is most favourable and gives a larger S/N (ie. the gravitationalwaves are circularly polarised) the uncertainty on thegravitationalwave amplitude will actually be larger than an equivalent amplitude source with a worse orientation., We see that for strong signals in the case where the orientation is most favourable and gives a larger S/N (i.e. the \gws are circularly polarised) the uncertainty on the amplitude will actually be larger than an equivalent amplitude source with a worse orientation.
" So, when detections become regular the best parameter constraints will actually be made for the linearly polarised sources."," So, when detections become regular the best parameter constraints will actually be made for the linearly polarised sources."
" However, we also see that unless the distance to these pulsars can be measured to better than ~10 per cent then the fractional error on the quadrupole calculated from thegravitationalwave amplitude will be relatively insensitive to the orientation, because the uncertainty is dominated by the distance uncertainty."," However, we also see that unless the distance to these pulsars can be measured to better than $\sim$ 10 per cent then the fractional error on the quadrupole calculated from the amplitude will be relatively insensitive to the orientation, because the uncertainty is dominated by the distance uncertainty."
" We have seen the sorts of mass quadrupoles that would be necessary to observe the set of currently known pulsars with futuregravitationalwave observatories, and compared these to maximum theoretical predictions for a variety ofEoS."," We have seen the sorts of mass quadrupoles that would be necessary to observe the set of currently known pulsars with future observatories, and compared these to maximum theoretical predictions for a variety of."
" As has previously been noted many times (e.g. for the majority of millisecond pulsars, if we are able to beat their spin-down limits and observe them, the quadrupoles (or ellipticities) they would have are sustainable by allEoS and would therefore not be able to constrain the type of matter in the star."," As has previously been noted many times (e.g. ) for the majority of millisecond pulsars, if we are able to beat their spin-down limits and observe them, the quadrupoles (or ellipticities) they would have are sustainable by all and would therefore not be able to constrain the type of matter in the star."
" However, with observations of many pulsars useful population statistics could be obtained and potential differences between different"," However, with observations of many pulsars useful population statistics could be obtained and potential differences between different"
a different choice of à the brightest cluster would have to be replaced by the actual most massive cluster in the normalisation. ie. a true. My diagram would have to be observed.,"a different choice of $\delta t$ the brightest cluster would have to be replaced by the actual most massive cluster in the normalisation, i.e. a true $M_\mathrm{max}$ -SFR diagram would have to be observed."
 One ;xossible interpretationSFER of à=10 Myr would be that it is the ypical time-seale on whic1 the inter-stellar medium rearranges itself into a coeval population of star clusters that are distributed according to the star-cluster initial mass function (cf.2).., One possible interpretation of $\delta t = 10$ Myr would be that it is the typical time-scale on which the inter-stellar medium rearranges itself into a coeval population of star clusters that are distributed according to the star-cluster initial mass function \citep[cf. ][]{weidner-etal2004}.
 Anyway. 1e comparison of the star custer results with the CMD results will give an indirect check if our normalisation is correct.," Anyway, the comparison of the star cluster results with the CMD results will give an indirect check if our normalisation is correct."
 The method of going in 10-Myr-steps through age to estimate je star formation rate only works if there are star clusters in each formation epoch., The method of going in 10-Myr-steps through age to estimate the star formation rate only works if there are star clusters in each formation epoch.
 However. an inspection of the age-mass diagram (Fig. 2))," However, an inspection of the age-mass diagram (Fig. \ref{lmc-clusters}) )"
 shows that for ages larger than | Gyr there are ong intervals without clusters., shows that for ages larger than 1 Gyr there are long intervals without clusters.
 For a formation epoch in. which no cluster is detected a direct estimate of the star formation rate is not possible., For a formation epoch in which no cluster is detected a direct estimate of the star formation rate is not possible.
 But a non-detection does one allow to estimate imits for the star formation rate., But a non-detection does one allow to estimate limits for the star formation rate.
 Tf no cluster is detected. then none has formed massive enough to be detected. which implies a ow star formation rate.," If no cluster is detected, then none has formed massive enough to be detected, which implies a low star formation rate."
" By using a star cluster evolution model the observational limiting magnitude can be translated into a mass. the ""ding limit."," By using a star cluster evolution model the observational limiting magnitude can be translated into a mass, the fading limit."
 As no star cluster is detected above the fading limit. all cluster that might have been formed in this formation epoch must 1ive had smaller masses.," As no star cluster is detected above the fading limit, all cluster that might have been formed in this formation epoch must have had smaller masses."
 Thus the fading limit can be used as an upper limit for the most massive cluster in this epoch. and with this mass an upper limit for the star formation rate can be calculated.," Thus the fading limit can be used as an upper limit for the most massive cluster in this epoch, and with this mass an upper limit for the star formation rate can be calculated."
 The lower limit for the star formation rate in an empty epoch is no star formation., The lower limit for the star formation rate in an empty epoch is no star formation.
 This treatment of empty formation epoch gives us two results or the star formation history. an upper and a lower limit.," This treatment of empty formation epoch gives us two results for the star formation history, an upper and a lower limit."
" When he upper and lower limit are identical (i.e. when only ""full"" ormation epochs are used). the most massive cluster method (using he Minaxy-SFR relation) gives an estimate of the star formation ustory. otherwise the star formation rate can only be constrained by an upper and lower limit."," When the upper and lower limit are identical (i.e. when only “full” formation epochs are used), the most massive cluster method (using the $\bar{M}_\mathrm{max}$ -SFR relation) gives an estimate of the star formation history, otherwise the star formation rate can only be constrained by an upper and lower limit."
 This is an implicit quality assessment of the method., This is an implicit quality assessment of the method.
 Further uncertainties of results are caused by the orobabilistie nature of AM. Which mainly affects younger ages. and the uncertainties in the masses.," Further uncertainties of results are caused by the probabilistic nature of $M_\mathrm{max}$, which mainly affects younger ages, and the uncertainties in the masses."
 We discuss these and their reatment after presenting the results for the Large Magellanic Cloud., We discuss these and their treatment after presenting the results for the Large Magellanic Cloud.
 Besides the availability of data there are two other sources of uncertainty for the most-massive cluster method. statistical scatter and the age/mass uncertainties.," Besides the availability of data there are two other sources of uncertainty for the most-massive cluster method, statistical scatter and the age/mass uncertainties."
 Due to the probabilistic nature of Miyyay the stochastic scatter in the recovered star formation rate is very large for young ages. as averaging occurs only over a few of. and decreases with increasing time.," Due to the probabilistic nature of $M_\mathrm{max}$ the stochastic scatter in the recovered star formation rate is very large for young ages, as averaging occurs only over a few $\delta t$, and decreases with increasing time."
 The amount of stochastic seatter has been determined from Monte-Carlo experiments by ?.theirsec.4.3.eqq.(16)and(17)..," The amount of stochastic scatter has been determined from Monte-Carlo experiments by \citet[][their sec. 4.3, eqq. (16) and (17)]{maschberger+kroupa2007}."
 The age uncertainties are accommodated for by the averaging window. which is kept constant in logarithmic time and has approximately the size of the age uncertainties (0.5 dex).," The age uncertainties are accommodated for by the averaging window, which is kept constant in logarithmic time and has approximately the size of the age uncertainties (0.5 dex)."
 The mass uncertainty is propagated to an uncertainty in the star formation rate by using the μας values plus/minus their uncertainty in mass., The mass uncertainty is propagated to an uncertainty in the star formation rate by using the $M_\mathrm{max}$ values plus/minus their uncertainty in mass.
 In Fig., In Fig.
" 3 we show in the upper panel the age-mass diagram of the star clusters. where the clusters identified as Mj, are the large dots."," \ref{sfhmmax} we show in the upper panel the age-mass diagram of the star clusters, where the clusters identified as $M_\mathrm{max}$ are the large dots."
 R136 is shown as an open circle. as it is not contained in the ? sample.," R136 is shown as an open circle, as it is not contained in the \citet{degrijs+anders2006} sample."
 The dashed line is the fading limit. the mass that a cluster with the lowest observed brightness would have (calculated with the models).," The dashed line is the fading limit, the mass that a cluster with the lowest observed brightness would have (calculated with the models)."
 The upper and lower limit for the star formation history are shown as bold lines. whieh have the same values up to zz | Gyr (calculated with /;=8 Gyr).," The upper and lower limit for the star formation history are shown as bold lines, which have the same values up to $\approx$ 1 Gyr (calculated with $t_4 = 8$ Gyr)."
 For the youngest ages the dashed branch follows by including R136 in the star cluster sample., For the youngest ages the dashed branch follows by including R136 in the star cluster sample.
 The uncertainty in the star formation rate introduced by the uncertainties in the cluster masses is visualised as a grey region., The uncertainty in the star formation rate introduced by the uncertainties in the cluster masses is visualised as a grey region.
 To assess the significance in variations of the star formation rate we show a constant star formation rate (the thick solid line at ἐν) which is embraced by the statistical 16 and 26 scatter (thin solid lines and dashed lines. see 29).," To assess the significance in variations of the star formation rate we show a constant star formation rate (the thick solid line at $\approx 0.1 \Msun/\mathrm{yr}$ ) which is embraced by the statistical $1 \sigma$ and $2 \sigma$ scatter (thin solid lines and dashed lines, see \citealp{maschberger+kroupa2007}) )."
 Generally the obtained star formation history follows the distribution of the star clusters for about one Gyr. when the number of clusters starts thinning out.," Generally the obtained star formation history follows the distribution of the star clusters for about one Gyr, when the number of clusters starts thinning out."
 Both the upper and lower limit agree for that period. so that the result of the method should be an estimate of the star formaion history until that age.," Both the upper and lower limit agree for that period, so that the result of the method should be an estimate of the star formation history until that age."
 The peaks in the star formation rate are somewhat displaced when compared to the loci of the massive οusters which is caused by the time averaging., The peaks in the star formation rate are somewhat displaced when compared to the loci of the massive clusters which is caused by the time averaging.
 For ages younger than 100 Myr it is not possible to establish whether the variations in the derived star formation rate are caused by variations in the actual star formation rate of the Large Magellanic Cloud because of the large stochastical scatter., For ages younger than 100 Myr it is not possible to establish whether the variations in the derived star formation rate are caused by variations in the actual star formation rate of the Large Magellanic Cloud because of the large stochastical scatter.
 In the age range from 100 Myr to | Gyr the derived star formation rate deviates zz26 from a constant star formation rate. which should be caused by a decrease in the actual star formation rate.," In the age range from 100 Myr to 1 Gyr the derived star formation rate deviates $\approx 2 \sigma$ from a constant star formation rate, which should be caused by a decrease in the actual star formation rate."
 We now turn to discuss the effects of the two values for /4., We now turn to discuss the effects of the two values for $t_4$.
 Figure 4. shows this. with the star formation history using /;—8 Gyr as the solid line and 44=| Gyr as the dashed line.," Figure \ref{sfhmmax_t4} shows this, with the star formation history using $t_4 = 8$ Gyr as the solid line and $t_4 = 1$ Gyr as the dashed line."
 Our results use only massive clusters. which are significantly affected by dynamical evolution only after a long time.," Our results use only massive clusters, which are significantly affected by dynamical evolution only after a long time."
 Therefore the two, Therefore the two
the turnolf point. corresponding to the oldest. age being considered.,the turnoff point corresponding to the oldest age being considered.
 Although the Hipparcos satellite produced. a catalogue having very well understood. errors ancl highly accurate magnitude ancl colour. determinations for a Large number of stars. the sample has to be reduced: through several cuts before it complies with the restrictions required bv our method.," Although the Hipparcos satellite produced a catalogue having very well understood errors and highly accurate magnitude and colour determinations for a large number of stars, the sample has to be reduced through several cuts before it complies with the restrictions required by our method."
 The Hipparcos catalogue provides an almost complete sample of stars in the solar neighbourhood., The Hipparcos catalogue provides an almost complete sample of stars in the solar neighbourhood.
 The limiting magnitude depends. both on spectral type. ancl galactic latitucle (ESA SP-1200. Volume 1. page 131).," The limiting magnitude depends both on spectral type and galactic latitude (ESA SP-1200, Volume 1, page 131)."
" For the types earlier than G5 whieh we consider here. the limiting V magnitude is given by. Yi,7.9|Llsin|ó]"," For the types earlier than G5 which we consider here, the limiting V magnitude is given by $V_{\rm lim} = 7.9 + 1.1 \sin |b|$."
 To avoid unnecessary complications. we consider cuts of the tvpe Voconst.," To avoid unnecessary complications, we consider cuts of the type $V$ =const."
 at all [atitucies with V.3.0 Figure (3) shows a graph of Ady vs. distance for all stars in the Llipparcos catalogue having distance errors smaller than 204. and an apparent magnitude my«7.9.," at all latitudes with $V<7.9$ Figure (3) shows a graph of $M_V$ vs. distance for all stars in the Hipparcos catalogue having distance errors smaller than $20 \%$ , and an apparent magnitude $m_{V}<7.9$."
 The solic lines show the inclusion. criteria for one. possible volume limited sample. complete to Ady<3.15.κ," The solid lines show the inclusion criteria for one possible volume limited sample, complete to $M_V < 3.15, m<7.25$."
 SAS i can be seen. the maximum age which can be considered wil not be very large. as the number of stars in a volunie-liniitcc sample complete to absolute magnitudes greater than 4 rapidly dwindles.," As it can be seen, the maximum age which can be considered will not be very large, as the number of stars in a volume-limited sample complete to absolute magnitudes greater than 4 rapidly dwindles."
 After experimenting with synthetic CALDs of known SFR) produced: using our isochrone ericl a constructed to have the same numbers of stars as a function of lower magnitude limit as in Figure (3). and recovering the SET) using our method. we identified 32 vr as the maximum age we can accurately treat with the data at hand.," After experimenting with synthetic CMDs of known $SFR(t)$ produced using our isochrone grid and constructed to have the same numbers of stars as a function of lower magnitude limit as in Figure (3), and recovering the $SFR(t)$ using our method, we identified 3 Gyr as the maximum age we can accurately treat with the data at hand."
" This fixes fy=0./,3 Gyr as the temporal limits in equation (2). were the use of 200 isochrones establishes the formal resolution of the method to be 15 Myr."," This fixes $t_{0}=0, t_{1}=3$ Gyr as the temporal limits in equation (2), were the use of 200 isochrones establishes the formal resolution of the method to be $15$ Myr."
 Although the absolute magnitude errors correlate tghtlv with the distance. the colour errors correlate more strongly with the apparent magnitude. and can actually represent the dominant error in inverting the CALDs.," Although the absolute magnitude errors correlate tightly with the distance, the colour errors correlate more strongly with the apparent magnitude, and can actually represent the dominant error in inverting the CMDs."
 The solid. curve shows the my-7.25 completion limit. which implies errors similar to those used in Figures (1) and (2).," The solid curve shows the $m_{V}<7.25$ completion limit, which implies errors similar to those used in Figures (1) and (2)."
 Lt will be with complete volume-limitecl samples having this apparent magnitude limit that we will be dealing., It will be with complete volume-limited samples having this apparent magnitude limit that we will be dealing.
 As the limit in Ady is moved to dimumer stars. the structure of the S£(αι older ages is better recovered by the inversion method. but the number of younger stars diminishes (see Figure 1) and the S#ARO) of the vounger period is under represented. in the recovered. SPUU).," As the limit in $M_{V}$ is moved to dimmer stars, the structure of the $SFR(t)$ at older ages is better recovered by the inversion method, but the number of younger stars diminishes (see Figure 1) and the $SFR(t)$ of the younger period is under represented in the recovered $SFR(t)$."
 We constructed a variety of somewhat independent. Hipparcos CALDs for dilferent absolute magnitude Limits in the range 3.0«My<3.5. and obtained highly compatible answers.," We constructed a variety of somewhat independent Hipparcos CMDs for different absolute magnitude limits in the range $3.0<M_{V}<3.5$, and obtained highly compatible answers."
 Also. all our samples include a certain number of contaminating stars having ages greater than the 3 Gyr limit. considered. by the inversion method. mostly in the RGB region. as their turn olf points appear at magnitudes dimmer than the minimum ones considered.," Also, all our samples include a certain number of contaminating stars having ages greater than the 3 Gyr limit considered by the inversion method, mostly in the RGB region, as their turn off points appear at magnitudes dimmer than the minimum ones considered."
 To avoid these stars. the inversion method. considers only stars bluewards of Vf=0.7. as was done in the synthetic examples of Figures (1) and (2).," To avoid these stars, the inversion method considers only stars bluewards of $V-I=0.7$, as was done in the synthetic examples of Figures (1) and (2)."
 As the fraction of stars. produced. by the SEU which live into the observed CALD diminishes with age. in inverting a well populated CALD the older regions of the SET) are under estimated by the recovery method.," As the fraction of stars produced by the $SFR(t)$ which live into the observed CMD diminishes with age, in inverting a well populated CMD the older regions of the $SFR(t)$ are under estimated by the recovery method."
 This is compensated by a correction factor given by the assumed IME. and the mass at the tip of the RGB as a function of time. as discussed in paper 1. Once the LAL. metallicity. positions of the observed stars in the CAID and observational errors in. both coordinates (also supplied by the Llipparcos catalogue) are eiven. they are used to construct the likelihood matrix C; (1). which is the only input given to the inversion methocd.," This is compensated by a correction factor given by the assumed IMF, and the mass at the tip of the RGB as a function of time, as discussed in paper I. Once the IMF, metallicity, positions of the observed stars in the CMD and observational errors in both coordinates (also supplied by the Hipparcos catalogue) are given, they are used to construct the likelihood matrix $G_{i}(t)$ , which is the only input given to the inversion method."
 The small number of stars present in any volume-limitec sample ( 450) leaves us insensitive to the existence of small features in the SLR) producing only a lew stars., The small number of stars present in any volume-limited sample $\sim 450$ ) leaves us insensitive to the existence of small features in the $SFR(t)$ producing only a few stars.
 The limited numbers of stars also reduces the resolution of the method. as a smoothing function has to be appliec to suppress instabilities in solving the integro-dilferentia uation of the problem.," The limited numbers of stars also reduces the resolution of the method, as a smoothing function has to be applied to suppress instabilities in solving the integro-differential equation of the problem."
 This final smoothing reduces the effective temporal resolution of the method to 50 Myr. stil much higher than that of any indirect. chemical evolution inference of STBIG).," This final smoothing reduces the effective temporal resolution of the method to 50 Myr, still much higher than that of any indirect chemical evolution inference of $SFR(t)$."
 Once the apparent and absolute magnitudes of the sample have been chosen. the set of stars to be studied. is Cully specified.," Once the apparent and absolute magnitudes of the sample have been chosen, the set of stars to be studied is fully specified."
 The positions of which in the CMD are comparedto the assumed. isochrones to. construct. the. likelihood matrix. which is the only input required bythe numerical," The positions of which in the CMD are comparedto the assumed isochrones to construct the likelihood matrix, which is the only input required bythe numerical"
An interferometer is limited by the minimum spacing of its antennas.,An interferometer is limited by the minimum spacing of its antennas.
 Because two antennas can not be placed closer than some minimum distance (Dj). signals on spatial scales larger than some size (ο) Dii) Will be attenuated.," Because two antennas can not be placed closer than some minimum distance $D_{\rm min}$ ), signals on spatial scales larger than some size $\propto$$\lambda/D_{\rm min}$ ) will be attenuated."
" This effect. called the ""missing flux” problem. is resolved by using"," This effect, called the “missing flux” problem, is resolved by using"
tensor.,tensor.
 Putting the values of the 2 tensor. equation (23)). into this equation we find where A7 is the size quadrupole and e is the unweighted ellipticity as given in 2..," Putting the values of the $D$ tensor, equation \ref{eq:d}) ), into this equation we find where $R^2$ is the size quadrupole and $e$ is the unweighted ellipticity as given in \citet{2007MNRAS.380..229M}."
 Note again that for circular (o.=0) objects. twist and turn have no effect.," Note again that for circular $(e=0)$ objects, twist and turn have no effect."
" ? showed that the effect of the centroid shift is to alter observable flexion estimators By|ik’ by substracting a term (Αθ,|A? Di). and the same applies here."," \citet{2007MNRAS.380..229M} showed that the effect of the centroid shift is to alter observable flexion estimators $\hat{F}_1+i\hat{F}_2$ by substracting a term $(\Delta \bar{\theta} \hat{D}_r+\Delta\bar{\theta}^*\hat{D}_l)$ , and the same applies here."
 The shift operators D are given by By dividing both sides by foo. we can therefore propose the corrected estimator If we label the term in brackets as £. we similarly find for the turns Soour corrected estimators differ from our naive estimators only by a factor of D.," The shift operators $\hat{D}$ are given by Hence we find that equation \ref{eq:a11t1}) ) becomes By dividing both sides by $f_{22}$, we can therefore propose the corrected estimator If we label the term in brackets as $B$, we similarly find for the turns Soour corrected estimators differ from our naive estimators only by a factor of $B$."
 Again. twist can be written as a superposition of turns. and vice versa.," Again, twist can be written as a superposition of turns, and vice versa."
 As in the previous section. the presence of flexion would mean that these are not pure estimators of twist: the estimators should again be interpreted as showing combined second-order systematics. or (real or systematic) twist on scales where flexion is negligible.," As in the previous section, the presence of flexion would mean that these are not pure estimators of twist; the estimators should again be interpreted as showing combined second-order systematics, or (real or systematic) twist on scales where flexion is negligible."
 We ure now in a position to measure these twist/turn estimators on real data., We are now in a position to measure these twist/turn estimators on real data.
 We use the STAGES mosaic observed with the Hubble Space Telescope (22)..," We use the STAGES mosaic observed with the Hubble Space Telescope \citep{2007AAS...21113220G, 2008MNRAS.385.1431H}."
 This isa 0.25 square degree field observed with the Advanced Camera for Surveys in the F606W band. covering 80 ACS tiles in 80 orbits.," This is a 0.25 square degree field observed with the Advanced Camera for Surveys in the F606W band, covering 80 ACS tiles in 80 orbits."
 Drizzling is used to obtain an effective pixel size of 0.037.," Drizzling is used to obtain an effective pixel size of $0.03""$."
 We use the same galaxy catalogue as ο deconvolving and decomposing all objects into shapelets using the methods developed in ???.. ," We use the same galaxy catalogue as \citet{2008MNRAS.385.1431H}, deconvolving and decomposing all objects into shapelets using the methods developed in \citet{2003MNRAS.338...35R, 2003MNRAS.338...48R, 2005MNRAS.363..197M}."
The analysis will be described in full in Bacon et al (2009): we obtain a shapelet catalogue for 56.000 galaxies. together with measures of 3 and £77 for all objects.," The analysis will be described in full in Bacon et al (2009); we obtain a shapelet catalogue for 56,000 galaxies, together with measures of $\beta$ and $R^2$ for all objects."
 The shapelets are normalised so that fou=1., The shapelets are normalised so that $f_{00}=1$.
 We measure the twist/turn estimators for objects with F606 magnitude <23.5 using equations (48)) to (49)): we find that for this sample. 2=1.59+0.01.," We measure the twist/turn estimators for objects with F606 magnitude $<23.5$ using equations \ref{eq:t1estcor}) ) to \ref{eq:c2estcor}) ); we find that for this sample, $B=-1.59\pm0.01$."
 Since the twist and turn measurements are equivalent. here we choose to present results in terms of twist.," Since the twist and turn measurements are equivalent, here we choose to present results in terms of twist."
 The histogram of twist estimators is shown in figure 8 this includes 3e cuts for outliers with 1] + and we only consider objects with 3.«1 pixel to avoid oversampling.," The histogram of twist estimators is shown in figure \ref{fig:twisthist}; this includes $3\sigma$ cuts for outliers with $|T|>6.0$ $^{-1}$, and we only consider objects with $\beta>$ 1 pixel to avoid oversampling."
 The first thing to note is that our twist estimator is more noisy than shear and flexion estimators. having a standard deviation in one component of 2.0 +: much of this noise is due to intrinsic shape variance of the objects.," The first thing to note is that our twist estimator is more noisy than shear and flexion estimators, having a standard deviation in one component of 2.0 $^{-1}$; much of this noise is due to intrinsic shape variance of the objects."
 The turn estimatorPa as defined has a larger standard deviation of 2.9 , The turn estimator as defined has a larger standard deviation of 2.9 $^{-1}$.
"We find mean values over the STAGES survey of 7,= arcsec+. 725=0.009+0.037."," We find mean values over the STAGES survey of $\bar{T}_1=-0.016\pm0.036$ $^{-1}$, $\bar{T}_2=-0.009\pm0.037$ $^{-1}$."
 These are consistent with zero. as we might hope for a systematic mode.," These are consistent with zero, as we might hope for a systematic mode."
 At present the constraint is fairly weak. as gravitational flexion signals are at the level of 0.001 to 0.01 +: however. in upcoming lensing surveys the much larger area will lead to twist/turn constraints at the 10.1 level. which will provide important checks on systematies.," At present the constraint is fairly weak, as gravitational flexion signals are at the level of 0.001 to 0.01 $^{-1}$; however, in upcoming lensing surveys the much larger area will lead to twist/turn constraints at the $10^{-4}$ level, which will provide important checks on systematics."
 We can further explore whether the twist/turn estimator is activated as a systematic in the STAGES survey by measuring its correlation functions., We can further explore whether the twist/turn estimator is activated as a systematic in the STAGES survey by measuring its correlation functions.
 As with shear correlation functions. the twists should be rotated before they are correlated: however. while shear has to be rotated by factors of e where ó is the position angle of the line joining a pair of objects. twist has to be rotated by factors of e on account of its vector nature: We can then construct correlation functions We have measured these correlation functions for twist estimators in STAGES. and display the results infigure 9..," As with shear correlation functions, the twists should be rotated before they are correlated; however, while shear has to be rotated by factors of $^{i2\phi}$ where $\phi$ is the position angle of the line joining a pair of objects, twist has to be rotated by factors of $^{i\phi}$ on account of its vector nature: We can then construct correlation functions We have measured these correlation functions for twist estimators in STAGES, and display the results infigure \ref{fig:twistcor}. ."
 Here error bars are estimated by aVoNpairs Where o is the standard deviation of twist and Ajwars is the number of galaxy pairs in a bin., Here error bars are estimated by $\sigma^2/\sqrt{N_{\rm pairs}}$ where $\sigma$ is the standard deviation of twist and $N_{\rm pairs}$ is the number of galaxy pairs in a bin.
 We tind that the correlation functions are almost all consistent with, We find that the correlation functions are almost all consistent with
Theformation.,The.
 Spectral energy distributions (SEDs).degenerate. probe the amount. temperature and overall geometry of the dust in the dises. such as dise flaring (2).. puffed-up inner rims (22).. and indications of an average grain growth in discs as young as a few Myr (2)..," Spectral energy distributions (SEDs), probe the amount, temperature and overall geometry of the dust in the discs, such as disc flaring \citep{Meeus2001}, puffed-up inner rims \citep{Dullemond2001, Acke2009}, and indications of an average grain growth in discs as young as a few Myr \citep{D'Alessio2001}."
 Most works in the past decade have focused on the analysis of SEDs of individual objects (e.g.2) or to study systematic trends in infrared colours of various types of disces. ranging from embedded young stellar objects to exposed TTTauri stars (2)..," Most works in the past decade have focused on the analysis of SEDs of individual objects \citep[e.g.][]{D'Alessio2006} or to study systematic trends in infrared colours of various types of discs, ranging from embedded young stellar objects to exposed Tauri stars \citep{Robitaille2006}."
 Some ambiguities inherent in SED analysis can be resolvedby images in scattered light (2).. in mid-infrared thermal emission or in the mm-regime (2)..," Some ambiguities inherent in SED analysis can be resolvedby images in scattered light \citep{Stapelfeldt1998}, in mid-infrared thermal emission \citep{McCabe2003} or in the mm-regime \citep{Andrews2007}."
 The Spitzer observatory has enabled detailed studies on dust mineralogy. constraining dust properties in theupper layers of the inner disk regions by using solid-state features (22)...," The Spitzer observatory has enabled detailed studies on dust mineralogy, constraining dust properties in theupper layers of the inner disk regions by using solid-state features \citep{Furlan2006, Olofsson2009}."
 Multi-technique. panchromatic approaches. combining the aforementioned observations. are now becoming possible but remain limited to a few objects with complete data sets (e.g.222).," Multi-technique, panchromatic approaches, combining the aforementioned observations, are now becoming possible but remain limited to a few objects with complete data sets \citep[e.g.][]{Wolf2003, Pinte2008,
Duchene2009}."
 However. all these observational findings are related to the dust component.I," However, all these observational findings are related to the dust component.,"
nitially. about of the disc mass can be assumed to be present in form of gas. and the progress toward a better understanding of the gas component. such as chemical composition. gas temperature structure and vertical dise extension. is hampered by acurrent lack of observational data.," about of the disc mass can be assumed to be present in form of gas, and the progress toward a better understanding of the gas component, such as chemical composition, gas temperature structure and vertical disc extension, is hampered by a lack of observational data."
 With several Recent work has focused on the prediction of far IR line emissions from individual dises (2222). or rather small parameter studies (2). ," With several Recent work has focused on the prediction of far IR line emissions from individual discs \citep{Meijerink2008,Ercolano2008,Woitke2009b,Cernicharo2009}, , or rather small parameter studies \citep{Kamp2009}. ."
?. have recently, \citet{Goicoechea2009} have recently
101012ALL.,$\sim10^{14}-10^{15}$.
 At +=2.2 in the simmlation. these 2- and 3-halo svstenis show typical maxi separations of ~0.9Las Ape 3D from their mean positions.," At $z=2.2$ in the simulation, these 2- and 3-halo systems show typical maximum separations of $\sim0.9-1.8$ Mpc 3D from their mean positions."
 Although this comparison is limited by the preliminary halo masses of the +=2.2 overdensitics. these results may sugecst there is ligh probability that two or more of the +=2.2 overdeusities will meree by +=0.," Although this comparison is limited by the preliminary halo masses of the $z=2.2$ overdensities, these results may suggest there is high probability that two or more of the $z=2.2$ overdensities will merge by $z=0$."
" If two or more of the overdeusifies are currently eravitationally bouud. we may be viewing ποπιο sub-clusters that are cach in differcut evolutionary stages. including some whose ealaxics are rapidly evolving and ouly just formine their red galaxv population (οιο,, overdensity C)."," If two or more of the overdensities are currently gravitationally bound, we may be viewing merging sub-clusters that are each in different evolutionary stages, including some whose galaxies are rapidly evolving and only just forming their red galaxy population (e.g., overdensity C)."
 Perhaps this signifies the svstem is in a transitional phase between the kuown :z2 protoclusters” (ee.2) with more diffuse distributions of blue galaxies. auc the lower-redshift galaxy clusters with prominent red sequences.," Perhaps this signifies the system is in a transitional phase between the known $z\ga2$ “protoclusters” \citep[e.g.][]{steidel_spectroscopic_2005} with more diffuse distributions of blue galaxies, and the lower-redshift galaxy clusters with prominent red sequences."
 Of course. protocluster observations have larecly been optically-based. thus deep uear-IBR observatious of such structures aud deep optical spectroscopy of our candidate cluster are needed to understand the relationship between the various structures at 21.5. The discovery of the :=2.2 system demonstrates the powerful combination of uear-IR medium-baudwidth filters aud deep imagine of the Z FOURGE survey.," Of course, protocluster observations have largely been optically-based, thus deep near-IR observations of such structures and deep optical spectroscopy of our candidate cluster are needed to understand the relationship between the various structures at $z\ga1.5$ The discovery of the $z=2.2$ system demonstrates the powerful combination of near-IR medium-bandwidth filters and deep imaging of the $Z-$ FOURGE survey."
 These systems were undetectable in earlier optical aud near-IR catalogs., These systems were undetectable in earlier optical and near-IR catalogs.
 For example. in the optically-sclected 6Gκ 25) catalog of ?.. the overdensity is completely absent in our redshift slice of interest (2=2.1]. 2.3).," For example, in the optically-selected $i<25$ ) catalog of \citet{ilbert_cosmos_2009}, the overdensity is completely absent in our redshift slice of interest $z=2.1-2.3$ )."
 The relatively bright optical limit of this catalog means evolved galaxies at these redshifts are nüssed cutirely (only 2 of our red overdcusity galaxies have /4444«25. see Fie. 5))," The relatively bright optical limit of this catalog means evolved galaxies at these redshifts are missed entirely (only 2 of our red overdensity galaxies have $i_{total}<25$, see Fig. \ref{fig_cmd}) )."
 Even with the A-baud selected NMDS catalog of ον only a weak overdeusitv is scen in Fie. 1..," Even with the $K$ -band selected NMBS catalog of \citet{whitaker_newfirm_2011}, only a weak overdensity is seen in Fig. \ref{fig_density},"
 as the majority of the +=2.2 overdensity galaxies are too faint to be detected in the 1.3 mae., as the majority of the $z=2.2$ overdensity galaxies are too faint to be detected in the 1.3 mag.
 shallower NAIBS., shallower NMBS.
 The first results of the Z FOURGE survey sugecst we are reaching a critical threshold iu our ability to study ealaxy evolution as a function of local euviromuoeut at +Z 1.5., The first results of the $Z-$ FOURGE survey suggest we are reaching a critical threshold in our ability to study galaxy evolution as a function of local environment at $z\ga1.5$ .
 By combining the spatial distribution with improved redshift information frou deep medimu-banucd filters im the near-IR. we cau start to correlate the properties of A. selected galaxies with their cuviroument. something that has so far ouly been done in detail for Lyiiuui-break ealaxies (e.g...7).," By combining the spatial distribution with improved redshift information from deep medium-band filters in the near-IR, we can start to correlate the properties of $K_s-$ selected galaxies with their environment, something that has so far only been done in detail for Lyman-break galaxies \citep[e.g., ][]{steidel_ly_2000}."
 We acknowledge the Cook's Branch Couservaucy. for the eracious hospitalitv and comfortable surroundings which permitted the discovery of this exciting svsteni., We acknowledge the Cook's Branch Conservancy for the gracious hospitality and comfortable surroundings which permitted the discovery of this exciting system.
 We are grateful to the iustruimenutation team and staff at LOCO., We are grateful to the instrumentation team and staff at LCO.
 We appreciate the useful comuncuts from the aunonviuous reviewer., We appreciate the useful comments from the anonymous reviewer.
 LRS acknowledecs funding from a Australian Research Council (Απο Discovery Program (DP) eraut DP10091370 and Access to Major Research Facilities Proerun which is supported by the Comunomvealth of Australia under the International Science Linkages prograun., LRS acknowledges funding from a Australian Research Council (ARC) Discovery Program (DP) grant DP1094370 and Access to Major Research Facilities Program which is supported by the Commonwealth of Australia under the International Science Linkages program.
 GBP acknowledges support from two ARC DP programs (DPOT?2081 and DPLOO37T38)., GBP acknowledges support from two ARC DP programs (DP0772084 and DP1093738).
 CP. KVT and VT acknowledge support from National Scieuce Foundation grant AST-1000707.," CP, KVT and VT acknowledge support from National Science Foundation grant AST-1009707."
 Australian access to the Magellan Telescopes was supported through theNational Collaborative> Research Infrastructure Strategv of the Australian Federal Covermucut., Australian access to the Magellan Telescopes was supported through theNational Collaborative Research Infrastructure Strategy of the Australian Federal Government.
of binary and multiple svstenis is not decreasing over billions of vears of the dynamical evolution.,of binary and multiple systems is not decreasing over billions of years of the dynamical evolution.
 Onlv the shape of the period distribution is changing., Only the shape of the period distribution is changing.
 Àn interpretation of the distinctions between the period distributions of the stars of different populations requires further stud., An interpretation of the distinctions between the period distributions of the stars of different populations requires further study.
 The substellar mass companions (brown dwarls and planets) staved bevoud (he scope ol our consideration., The substellar mass companions (brown dwarfs and planets) stayed beyond the scope of our consideration.
 Current studies (e.g.. Fischer&Valenti 2005)) testify to the existence ol a correlation between the metallicity of stars and the presence of orbiting planets.," Current studies (e.g., \citealt{fischer_valenti}) ) testify to the existence of a correlation between the metallicity of stars and the presence of orbiting planets."
 At the lime of writing. catalogs of stars wilh planets (http://exoplanet.eu: do not contain stars with [Fe/Il|]<—1.," At the time of writing, catalogs of stars with planets \citep{exoplanet.eu,exoplanets.org} do not contain stars with $\mathrm{[Fe/H]}<-1$."
 Some researchers claim that brown dwaarls and some verv low lass stars (ancl possibly planets?).," Some researchers claim that brown dwarfs and some very low mass stars (and possibly planets?),"
 lorm a separate population with its own multiplieitv and kinematical properties (see. e.g. Kroupaοἱal. 2003)).," form a separate population with its own multiplicity and kinematical properties (see, e.g. \citealt{kroupa_2003}) )."
 As likely as not. the low metallicity regime mav influence (he formation of this population.," As likely as not, the low metallicity regime may influence the formation of this population."
 It is quite possible that Population 1 field stars do not contain any. brown cdwarls or planets as companions al all., It is quite possible that Population II field stars do not contain any brown dwarfs or planets as companions at all.
 Another important question is whether there exist any substellar components in the halo and thick disc systems of high multiplidtyv (CN.> 2)., Another important question is whether there exist any substellar components in the halo and thick disc systems of high multiplicity $N>2$ ).
 The ratio of binary and multiple svstems among the Population I stars. found in (his studs. does not contradict the hypothesis that the chemical composition of protostellar molecular clouds makes but an insignificant impact on the star formation process.," The ratio of binary and multiple systems among the Population II stars, found in this study, does not contradict the hypothesis that the chemical composition of protostellar molecular clouds makes but an insignificant impact on the star formation process."
 This indicates that the halo stars were formed as a result of fragmentation of molecular clouds nuclei. similarly to the way the stars form today.," This indicates that the halo stars were formed as a result of fragmentation of molecular clouds' nuclei, similarly to the way the stars form today."
 However. this issue remains unclear when we consider the substellar mass regime.," However, this issue remains unclear when we consider the substellar mass regime."
 The frequency of binary and multiple metal-poor stus imposes some restrictions on (he formation of the stellar halo in our Galaxy as well., The frequency of binary and multiple metal-poor stars imposes some restrictions on the formation of the stellar halo in our Galaxy as well.
 There are (wo general scenarios of the formation of the Milkv Way's stellar halo (see Majewski1993. [or more details):, There are two general scenarios of the formation of the Milky Way's stellar halo (see \citealt{majewski} for more details):
A comparison of the results of star formation to the iclel distribution at separations <50 AU probably should » made. as this population should not normally be alfected ov dvnamical evolution.,"A comparison of the results of star formation to the field distribution at separations $<50$ AU probably should be made, as this population should not normally be affected by dynamical evolution."
 However. it is not clear if low- and high-density environments and. isolated star formation should always produce the same cdistribution(s).," However, it is not clear if low- and high-density environments and isolated star formation should always produce the same distribution(s)."
 lt appears that star. formation should [or all masses. including Meciwarfs — produce more binaries with separations in the range 107—107 AU than are observed in the field as such binaries are highly susceptible to destruction in clusters (depending on density).," It appears that star formation should – for all masses, including M-dwarfs – produce more binaries with separations in the range $10^2$ – $10^4$ AU than are observed in the field as such binaries are highly susceptible to destruction in clusters (depending on density)."
 But again. it is not clear if low- anc high-density. environments. and isolated star formation should. always: produce the same clistribution(s).," But again, it is not clear if low- and high-density environments and isolated star formation should always produce the same distribution(s)."
 Llowever. star formation in clusters need. not. produce any binaries with separations 10 AU. as such binaries although observed. in the field. just cannot. survive in clusters. even if they can form.," However, star formation in clusters need not produce any binaries with separations $> 10^4$ AU, as such binaries – although observed in the field – just cannot survive in clusters, even if they can form."
 Their origin is a major problem in star formation and star clusters as it cannot be explained if most stars form in clusters., Their origin is a major problem in star formation and star clusters as it cannot be explained if most stars form in clusters.
 , 
Qur SUPVON ολορ οσα larec volue and we have detected a sigVificant mmmber of galaxies inL.,Our survey encompasses a large volume and we have detected a significant number of galaxies in.
. We calculated Irauasses of all kuown galaxies in the observed voune using: Where Fis the toal flux of the galaxy., We calculated masses of all known galaxies in the observed volume using: Where $F$ is the total flux of the galaxy.
 Distances for galaxies iu the M81 Filament were taken from Naracheutsey&IWaisin(2007)., Distances for galaxies in the M81 Filament were taken from \citet{kar07}.
. Distances to backeroundC» Ooealasies were taken Toni NED where available: otherwise. they were calculated from tlie radial velocity. assuniüug a IIubble constant of Ty = 15 luu | |," Distances to background galaxies were taken from NED where available; otherwise, they were calculated from the radial velocity, assuming a Hubble constant of $_0$ = 75 km $^{-1}$ $^{-1}$."
 Because of the high umuber of ealaxies and contiuuuni sourees du the field. cach galaxy spectra was re-basclined using a first-order fit o the surrounding spectral region. iu order to calculae an accurate mass.," Because of the high number of galaxies and continuum sources in the field, each galaxy spectrum was re-baselined using a first-order fit to the surrounding spectral region, in order to calculate an accurate mass."
Nine= dt =(αρἄλλα) and AToe(a) is the radial distance equivalent to a SINIX temperature change.,"$\Delta_{ice}=4$ , $x=(a_{snow}-a)/\Delta T_{snow}(a)$ and $\Delta T_{snow}(a)$ is the radial distance equivalent to a K temperature change."
" To derive «,,,,L- we adopt the temperature profile of a flat. circumstellar disk. (Ixenvon&Ilartimann1987).."," To derive $a_{snow}$, we adopt the temperature profile of a flat circumstellar disk, $T \propto T_\star \left( R_\star/a \right)^{3/4}$ \citep{1987ApJ...323..714K}."
 We scale this relation to place the snow line al AAU at LAA for a 1A. mass star. as inferred [rom analvses of water-rich objects in ihe outer asteroid belt (Abeetal.2000:Rivkin2002)..," We scale this relation to place the snow line at AU at Myr for a $1\,M_{\odot}$ mass star, as inferred from analyses of water-rich objects in the outer asteroid belt \citep{2000orem.book..413A,2002aste.conf..235R}."
" To evaluate L,(/).R,(/). and T.(/). we use PAIS evolutionary tracks [rom Siessetal.(2000): other tracks Mazzitelli1994:Daraffeetal.1993). vield similar results."," To evaluate $L_{\star}(t),R_\star(t),$ and $T_\star(t)$, we use PMS evolutionary tracks from \citet{2000A&A...358..593S}; other tracks \citep{1994ApJS...90..467D,1998A&A...337..403B} yield similar results."
" With these ingredients. we derive the evolution of σ. Mj. and /;4, as the star contracts to the main sequence."," With these ingredients, we derive the evolution of $\sigma$, $M_{iso}$, and $t_{iso}$ as the star contracts to the main sequence."
 This evolution has (wo main features., This evolution has two main features.
" Initially. the snow line is at a large distance. e,~5 AAU. from the luminous PAIS star."," Initially, the snow line is at a large distance, $a_{snow} \sim
5$ AU, from the luminous PMS star."
" Inside AU. rocky oligarchs form and reach Mj, before (he star contracts significantly."," Inside AU, rocky oligarchs form and reach $M_{iso}$ before the star contracts significantly."
" Outside AAU. /;4, is long refeq:tiso)) compared to the initial contraction time."," Outside AU, $t_{iso}$ is long \\ref{eq:tiso}) ) compared to the initial contraction time."
 As the star contracts. ices condense out of the nebula and the snow line moves inward.," As the star contracts, ices condense out of the nebula and the snow line moves inward."
 For a<1 2AAU. this material coats the erowing oligarchs. leftover planetesimals. and the surrounding debris with an icy veneer (hat may extend the oligarchie growth phase and produce more massive oligarchs.," For $a \lesssim 1$ AU, this material coats the growing oligarchs, leftover planetesimals, and the surrounding debris with an icy veneer that may extend the oligarchic growth phase and produce more massive oligarchs."
" For à21 AAU. ice condensation reduces /;;, bv a factor ~ 3 releq:tiso)). which enables the rapid formation of icy oligarchs well before the central star reaches the main sequence,"," For $a
\gtrsim 1$ AU, ice condensation reduces $t_{iso}$ by a factor $\sim$ 3 \\ref{eq:tiso}) ), which enables the rapid formation of icy oligarchs well before the central star reaches the main sequence."
 To explore the consequences of this picture. we consider a disk with o~1 0.065). which lies at the upper end of the range inferred [rom (Osterloh&Beckwith1995:Nuernbergeretal.1997.1993: 2006).. ," To explore the consequences of this picture, we consider a disk with $\beta \sim
1$ $M_{disk}/M_\star = 0.065$ ), which lies at the upper end of the range inferred from \citep{1995ApJ...439..288O,1997A&A...324.1036N,1998A&A...330..549N,2000prpl.conf..559N,2006ApJ...645.1498S}. ."
Figure 1. shows the o evolution for this svstem at several distances from a 0.25A. star.," Figure \ref{fig:sigma_a_paper.ps} shows the $\sigma$ evolution for this system at several distances from a $0.25\,M_\odot$ star."
 For disks with other masses. o.x Muyja. MjxMS. πα...Ma.," For disks with other masses, $\sigma \propto M_{disk}$ , $M_{iso} \propto M_{disk}^{3/2}$, and $t_{iso}
\propto M_{disk}^{-1/2}$."
 Aside from the long-term decline in σία) from PAIS evolution. the & evolution shows clear increaseswhen (he snow line crosses specific points in space and ices condense oul of the eas.," Aside from the long-term decline in $\sigma(a)$ from PMS evolution, the $\sigma$ evolution shows clear increaseswhen the snow line crosses specific points in space and ices condense out of the gas."
 At these times. σ remains al arelativelyconstant plateau value for ~1 MMwyr before declining monotonically as (he central star approaches (he main sequence.," At these times, $\sigma$ remains at arelativelyconstant plateau value for $\sim$ Myr before declining monotonically as the central star approaches the main sequence."
ealaxy formation physics.,galaxy formation physics.
 We thank the anouvimous referee for insightful coumucuts., We thank the anonymous referee for insightful comments.
 LOB acknowledges the support of the NSF Craduate Fellowship Program., LGB acknowledges the support of the NSF Graduate Fellowship Program.
 AJB acknowledges the support of the Cordon Betty Moore Foundation., AJB acknowledges the support of the Gordon Betty Moore Foundation.
 The authors would like to thank the tea. Carlton Daugh. Richard Bower. Shaun Cole. Carlos Freuk and Cedric Lacey. for allowing us to use in this work.," The authors would like to thank the team, Carlton Baugh, Richard Bower, Shaun Cole, Carlos Frenk and Cedric Lacey, for allowing us to use in this work."
 Additionally. we thank Andreca Fout for huplementing the original calculation of rai pressure stripping in this model.," Additionally, we thank Andreea Font for implementing the original calculation of ram pressure stripping in this model."
 The accretion shock model of upon which we base our miplemieutatiou makes several assuniptious., The accretion shock model of upon which we base our implementation makes several assumptions.
 The cluster Is asstuned to be spherically svuunuetrie7? and in bydrodvuamic equilibriuu. with au effective equation of state ptis. where 224g=1.2. and with the actual equation of state of a free monatomic gas. P=Γρ)2m. where I& is a function of the specific eutropy.," The cluster is assumed to be spherically symmetric and in hydrodynamic equilibrium, with an effective equation of state $P(r) \propto [\rho(r)]^{\gamma_{\rm eff}}$ , where $\gamma_{\rm eff} = 1.2$, and with the actual equation of state of a free monatomic gas, $P = K(s) \rho^{5/3}$, where K is a function of the specific entropy."
 The cluster potential is assiuned to be of the NEW type. aud the post-shock velocity of the gas is assumed to be negligible.," The cluster potential is assumed to be of the NFW type, and the post-shock velocity of the gas is assumed to be negligible."
" With these assumptions. they obtain the following hydrostatie model of the eas within the accretion shock: Tor} =Tayler) Poe) τή Pir) = gir)= gole) | gott) = IHere. c—rfro; is the ratio of the cluster-ceutric radius to the virial radius p, aud gj are constants of integration. which can be specified by the coustraimt that the barvouic mass inside the shock radius is equal to the total baryoulc mass of the halo f,Af and the shock juup condition relating post-shock temperature to the incomine velocity. respectively."," With these assumptions, they obtain the following hydrostatic model of the gas within the accretion shock: T(x) = g(x) (x) = _g P(x) = g(x) = g_0(x) + g_1 g_0(x) = Here, $x \equiv r/r_{vir}$ is the ratio of the cluster-centric radius to the virial radius, $\rho_g$ and $g_1$ are constants of integration, which can be specified by the constraint that the baryonic mass inside the shock radius is equal to the total baryonic mass of the halo $f_b~M$ and the shock jump condition relating post-shock temperature to the incoming velocity, respectively."
 Iu our plementation of this model we relax two particularly wajustified assumptions. that the accretion shockis always strong. and that the coustaut gy Al ," In our implementation of this model we relax two particularly unjustified assumptions, that the accretion shockis always strong, and that the constant $g_1$ \ref{eqn:g} "
report no bianodality in period distribution and no dichotonw of disked slow rotators and clisk-less fast rotators.,report no bi-modality in period distribution and no dichotomy of disked slow rotators and disk-less fast rotators.
 A recent review of this literature can be found in Mathieu(2004)., A recent review of this literature can be found in \citet{mathieu04}.
". In Chis study. we use the (A,—N) color index {ο probe a region in T Tauri dust-«disks (hat extends fom a lew stellar radii through the terrestrial planet zone (0.02-1.0AU).", In this study we use the $(K_{s}-N)$ color index to probe a region in T Tauri dust-disks that extends from a few stellar radii through the terrestrial planet zone (0.02-1.0AU).
" Comparing the (A,—IN) color index of carefully selected single stars with previously measured rotation periods allows us to investigate anv ellects the disk might have on the angular momentum of the star.", Comparing the $(K_{s}-N)$ color index of carefully selected single stars with previously measured rotation periods allows us to investigate any effects the disk might have on the angular momentum of the star.
 This paper outlines an observational study that expands on (he work presented in (1997).. and hopes to further our understandingoO of the role of disks in the rotational evolution of T Tauri stars.," This paper outlines an observational study that expands on the work presented in \citet{MB97}, and hopes to further our understanding of the role of disks in the rotational evolution of T Tauri stars."
 In section 2 we present a description of our sample. the observations and the data reduction procedure.," In section 2 we present a description of our sample, the observations and the data reduction procedure."
 In section 3 we present (he relationship between the (A;—NV) color index and rotation period of single PAIS stars in Tanrius-Auriga. and (he spectral energy distributions (SEDs) of a few stars with new M anc Q-band data.," In section 3 we present the relationship between the $(K_{s}-N)$ color index and rotation period of single PMS stars in Taurus-Auriga, and the spectral energy distributions (SEDs) of a few stars with new M and Q-band data."
 In section 4 we diseuss the results in light of current theories for the rotational evolution ol T Tauri star and disk svstems., In section 4 we discuss the results in light of current theories for the rotational evolution of T Tauri star and disk systems.
" We also demonstrate that including binaries in a study of (IN,—N) vs. rotation period diminishes any observed correlation.", We also demonstrate that including binaries in a study of $(K_{s}-N)$ vs. rotation period diminishes any observed correlation.
 We conclude with a sumnuarv nn section 5., We conclude with a summary in section 5.
 We selected stars in the SFR. that have been surveved. for. but are known to be lacking companions from the multiplicity survevs of Ghezetal.(1993). Leinert(1993) and Simonetal.(1995).. that also have photometric period dala available in the literature.," We selected stars in the SFR, that have been surveyed for, but are known to be lacking companions from the multiplicity surveys of \citet{ghez93}, \citet{leinert93} and \citet{simon95}, that also have photometric period data available in the literature."
 Photometric period data for all stars were taken from Bouvier1995) and Osterlohetal.(1996).," Photometric period data for all stars were taken from \citet{bouvier93, bouvier95} and \citet{osterloh96}."
. Infrared. Ix;-band. data for all stars were taken [rom the Two-micron all skv survey (2MAÀSS). point-source catalog.," Infrared $_{s}$ -band data for all stars were taken from the Two-micron all sky survey (2MASS), point-source catalog."
 The typical magnitude uncertainties for the Ix;-band. data ranged between 24%—3% for the stars of our sample., The typical magnitude uncertainties for the $_{s}$ -band data ranged between $2\%-3\%$ for the stars of our sample.
 We obtained new N-band observations for 12 stars., We obtained new N-band observations for 12 stars.
 The details of the observations. such as filter information. exposure Ges. and flux standards are listed in Table 1.," The details of the observations, such as filter information, exposure times, and flux standards are listed in Table 1."
 We selected 15 more stars (hat satisfied the selection criterion above and also had: N-band measurements in the literature with photometric uncertainties <30%., We selected 18 more stars that satisfied the selection criterion above and also had N-band measurements in the literature with photometric uncertainties $\leq 30\%$.
 The N-band magnitudes were queried in the catalog Gezarietal.(1999). and references therein., The N-band magnitudes were queried in the catalog \citet{gezari99} and references therein.
 The original literature source of N-band magnitudes are noted in the last column of Table 2., The original literature source of N-band magnitudes are noted in the last column of Table 2.
 When multiple measurements of an object were returned from Gezarietal.(1999) we chose the most recent measurement or the measurement with the smallest magnitude uncertainty., When multiple measurements of an object were returned from \citet{gezari99} we chose the most recent measurement or the measurement with the smallest magnitude uncertainty.
 Table 2 also lists spectral (vpes. T Daun (vpes. SED classes. photometric periods. effective temperatures and huminosities for," Table 2 also lists spectral types, T Tauri types, SED classes, photometric periods, effective temperatures and luminosities for"
"settings, most severely affecting our analysis of the 1] line; by chance the spectral artifact lies right on top of the 1] line in the pipeline reduced spectra making it impossible to measure (see Fig. H(d))).","settings, most severely affecting our analysis of the ] line; by chance the spectral artifact lies right on top of the ] line in the pipeline reduced spectra making it impossible to measure (see Fig. \ref{fig:pipeline}) )."
 Therefore the data covering the 1] line had to be re-reduced., Therefore the data covering the ] line had to be re-reduced.
" We did this using the CRIRES pipeline version the flat field from the triplet setting instead, which was taken 1.f]usingclose in time."," We did this using the CRIRES pipeline version using the flat field from the triplet setting instead, which was taken close in time."
 The spectral feature from the ghost is then situated in another part of the spectra not affecting our analysis (see Fig. Μ{ε)))., The spectral feature from the ghost is then situated in another part of the spectra not affecting our analysis (see Fig. \ref{fig:rereduced}) ).
" We found that this way of rescuing the data was better than removing the ghost feature by dividing by a telluric star or by reducing the spectra without flat fields, thereby not introducing the ghost, and then dividing the spectra with a B star to remove the ""pixel-to-pixel"" variations in the detector."," We found that this way of rescuing the data was better than removing the ghost feature by dividing by a telluric star or by reducing the spectra without flat fields, thereby not introducing the ghost, and then dividing the spectra with a B star to remove the ""pixel-to-pixel"" variations in the detector."
 The latter method was used successfully by ? when analysing science-verification spectra from CRIRES without flat fields., The latter method was used successfully by \citet{Nissen2007} when analysing science-verification spectra from CRIRES without flat fields.
 Our measured S/N values (per pixel of the spectra) of the reduced spectra reveal that our method indeed produces satisfactory signal-to-noise as shown in Table]., Our measured S/N values (per pixel of the spectra) of the reduced spectra reveal that our method indeed produces satisfactory signal-to-noise as shown in Table \ref{tab:criresobs}.
 The most relevant parts of the reduced spectra can be seen in Fig. 5]., The most relevant parts of the reduced spectra can be seen in Fig. \ref{fig:allspectra}.
 We normalized the spectra and fitted the continua by using the task (?).., We normalized the spectra and fitted the continua by using the task \citep{Tody1993}.
" The equivalent widths of the 1045 nm triplet and the 1082 nm i] line were measured using the task in by fitting a Gaussian profile to the line, or, in some cases, by straight numerical integration."," The equivalent widths of the 1045 nm triplet and the 1082 nm ] line were measured using the task in by fitting a Gaussian profile to the line, or, in some cases, by straight numerical integration."
 For two stars (HD26297 and HD29574) the equivalent widths for the forbidden line were measured by de-blending due to the neighboring telluric line., For two stars (HD26297 and HD29574) the equivalent widths for the forbidden line were measured by de-blending due to the neighboring telluric line.
 The measured values are listed in Table A]., The measured values are listed in Table \ref{tab:eqw}.
 Since our spectra have high S/N the uncertainties in the measured equivalent widths are mainly due to uncertainties in the continuum setting., Since our spectra have high S/N the uncertainties in the measured equivalent widths are mainly due to uncertainties in the continuum setting.
 The quoted uncertainties have been estimated by fitting the continuum to achieve a maximum and minimum possible value for the equivalent width., The quoted uncertainties have been estimated by fitting the continuum to achieve a maximum and minimum possible value for the equivalent width.
 The uncertainties in the measured equivalent widths will in the end produce uncertainties in the [S/Fe] less than the uncertainties introduced due to uncertainties in the stellar parameters (see Sect. ??))., The uncertainties in the measured equivalent widths will in the end produce uncertainties in the $\left[\mathrm{S}/\mathrm{Fe}\right]$ less than the uncertainties introduced due to uncertainties in the stellar parameters (see Sect. \ref{stellarparams}) ).
such considerations mav in fact well be of a more general nature than the problem of slates and transitions in strong interaction physics.,Such considerations may in fact well be of a more general nature than the problem of states and transitions in strong interaction physics.
 The question of whether svnuuetry or connectivity (cluster formation) determines the different states of many-body systems has intrigued theorists in statistical physics for a long time [28].., The question of whether symmetry or connectivity (cluster formation) determines the different states of many-body systems has intrigued theorists in statistical physics for a long time \cite{F-K}.
 The lesson learned from spin svstemis appears (o be (hat cluster formation ancl (he associated critical behaviour are the more general features. which under certain conditions ean also lead to thermal criticality. i.e. singular behaviour of the partition Iunction.," The lesson learned from spin systems appears to be that cluster formation and the associated critical behaviour are the more general features, which under certain conditions can also lead to thermal criticality, i.e., singular behaviour of the partition function."
 We (hus find (hat at sufficiently high temperatures and/or densities. strongly interacting matter will be in a new state. consisting of deconfined quarks and eluons.," We thus find that at sufficiently high temperatures and/or densities, strongly interacting matter will be in a new state, consisting of deconfined quarks and gluons."
 How can we probe the properties of this state. how can we study its features as function of temperature and density?," How can we probe the properties of this state, how can we study its features as function of temperature and density?"
 We want to address this question here in the sense of Einstein. who told us to make things as simple as possible. but not simpler.," We want to address this question here in the sense of Einstein, who told us to make things as simple as possible, but not simpler."
 So let us start wilh a theorists experimental set-up. consisting of a volume of unknown strongly interacting matter ancl a Bunsen burner. to heat it up and (hus increase its energy density.," So let us start with a theorist's experimental set-up, consisting of a volume of unknown strongly interacting matter and a Bunsen burner, to heat it up and thus increase its energy density."
in comparison with the low energy spectrum (Hurleyetal.1994).,in comparison with the low energy spectrum \citep{hurley94}.
". This means that the above fluence in the GeV energy range, is only an upper limit."," This means that the above fluence in the GeV energy range, is only an upper limit."
" At first, we present comparison with five long EGRET GRBs detected simultaneously with the bright BATSE emissions."," At first, we present comparison with five long EGRET GRBs detected simultaneously with the bright BATSE sub-MeV emissions."
 Fig., Fig.
 7 summarizes the situation., \ref{fig7} summarizes the situation.
 It shows the fluence as a function of the photon energy range., It shows the fluence as a function of the photon energy range.
" Red lines represent the fluence for the Swift GRB091112 and the associated fluence in the GeV energy region obtained on the basis of the Tupi-FLUKA result, assuming straightforward extrapolation of the keV GRB spectrum."," Red lines represent the fluence for the Swift GRB091112 and the associated fluence in the GeV energy region obtained on the basis of the Tupi-FLUKA result, assuming straightforward extrapolation of the keV GRB spectrum."
" By other words, the Swift-BAT spectral index is kept constant in the higher energy region."," By other words, the Swift-BAT spectral index is kept constant in the higher energy region."
" However, if the absolute spectral index in the GeV region is smaller than the absolute spectral index in the keV region, then this result represents an upper limit."," However, if the absolute spectral index in the GeV region is smaller than the absolute spectral index in the keV region, then this result represents an upper limit."
 The results in Fig., The results in Fig.
" 7 shows a tendency, the same fluence from keV to GeV energy range."," \ref{fig7} shows a tendency, the same fluence from keV to GeV energy range."
 Black lines are the fluence of the five EGRET events BATSE counterpart) observed in the BATSE field of view (Le&Dermer, Black lines are the fluence of the five EGRET events (as BATSE counterpart) observed in the BATSE field of view \citep{li09}.
" This result is consistent with the (asEGRET/BATSE fluence ratio 0.28 in average, as well as with the upper limits 2009)..obtained from a sample of the most luminous GBM bursts with no LAT detection, whose LAT/GBM ratio was 0.45 i the GeV fluence during the first 600 seconds after the trigger (Beniaminietal.,2011)."," This result is consistent with the EGRET/BATSE fluence ratio $0.28$ in average, as well as with the upper limits obtained from a sample of the most luminous GBM bursts with no LAT detection, whose LAT/GBM ratio was $0.45$ i the GeV fluence during the first 600 seconds after the trigger \citep{beniamini11}."
. These results are in contrast with the fluence ratio obtained here (>~ 1)., These results are in contrast with the Swift-BAT/Tupi fluence ratio obtained here $>\sim 1$ ).
 We find an average upper limit of LAT/GBM fluence Swift-BAT/Tupiratio as 0.13 for the GeV fluence., We find an average upper limit of LAT/GBM fluence ratio as 0.13 for the GeV fluence.
" Second, our comparison is extended to the other ground based observations of GRB."," Second, our comparison is extended to the other ground based observations of GRB."
 The Milagrito event is considered as the TeV counterpart of the BATSE GRB 970417a (?).., The Milagrito event is considered as the TeV counterpart of the BATSE GRB 970417a \citep{atkins03}.
 The comparison includes the upper limits at 1 and 10 MeV from the EGRET TASC detector., The comparison includes the upper limits at 1 and 10 MeV from the EGRET TASC detector.
 The energy spectrum for these events and the upper limit of the Tupi events is presented in Fig. 8.., The energy spectrum for these events and the upper limit of the Tupi events is presented in Fig. \ref{fig8}.
" To observe the structure of the counting rate sec binning), we performed confidence analysis of the background fluctuations."," To observe the structure of the counting rate (10 sec binning), we performed confidence analysis of the background fluctuations."
 We choose the interval of one hour around(10 the trigger time of the Swift GRB 091112., We choose the interval of one hour around the trigger time of the Swift GRB 091112.
 In this time interval the GRB coordinates are located within the effective field of view of the Tupi vertical telescope., In this time interval the GRB coordinates are located within the effective field of view of the Tupi vertical telescope.
" Larger intervals cannot be used, since the GRB coordinates would fall outside the field of view due to the Earth rotation."," Larger intervals cannot be used, since the GRB coordinates would fall outside the field of view due to the Earth rotation."
 The significance distribution of the muon counting rate (10 sec binning) in the Tupi vertical telescope is consistent with the Gaussian distribution (see Fig. 9))., The significance distribution of the muon counting rate (10 sec binning) in the Tupi vertical telescope is consistent with the Gaussian distribution (see Fig. \ref{fig9}) ).
 The trials with a confidence of 5.40 correspond to the peak at T+224 sec., The trials with a confidence of $5.4\sigma$ correspond to the peak at T+224 sec.
 This muon peak shows some structure., This muon peak shows some structure.
 One can notice a fast rising exponential decay (FRED) like pulse., One can notice a fast rising exponential decay (FRED) like pulse.
 This behavior is hard to explain as being the background fluctuation., This behavior is hard to explain as being the background fluctuation.
 We searched for the GRB signal in the field of view of the Tupi muon telescopes., We searched for the GRB signal in the field of view of the Tupi muon telescopes.
" We found a candidate event with features of likely association with the gamma ray burst GRB091112 observed by Swift-BAT, Fermi-GBM and Suzaku-WAM."," We found a candidate event with features of likely association with the gamma ray burst GRB091112 observed by Swift-BAT, Fermi-GBM and Suzaku-WAM."
One of the open questions in cosmology today is the state of the intergalactic medium (IGM).,One of the open questions in cosmology today is the state of the intergalactic medium (IGM).
 In the preseut popular cosmological© models. a putative cosmologicalo coustant accouuts for perhaps 2/3 of the energy density of the universe. and a similarly mysterious cold dark matter component accounts for 2/3 of the remainder.," In the present popular cosmological models, a putative cosmological constant accounts for perhaps 2/3 of the energy density of the universe, and a similarly mysterious cold dark matter component accounts for 2/3 of the remainder."
 Of order of the energy deusity is supposed to be accounted for by baryous (Langeetal.2000:Tytler2000) as obtained from primordial nucleosyutliesis calculation.," Of order of the energy density is supposed to be accounted for by baryons \citep{Lange00,Tytler00} as obtained from primordial nucleosynthesis calculation."
 Surprisingly. the vast majority of tle baryons in the local universe is as of yet uucdetected.," Surprisingly, the vast majority of the baryons in the local universe is as of yet undetected."
 The directly observed known components cousistiug of stars. as well as hot and cold gas in galaxies.," The directly observed known components consisting of stars, as well as hot and cold gas in galaxies,"
in the map and SNR.,in the map and SNR.
 A more detailed description of the error analysis of the individual structure parameters is given in the corresponding sections of this paper., A more detailed description of the error analysis of the individual structure parameters is given in the corresponding sections of this paper.
 For AA* we measured the total flux density by fitting a circular Gaussian component to the edited and fully self-calibrated visibilities of each VLBI observation after having made CLEAN maps for each epoch and using the Difmap software., For A* we measured the total flux density by fitting a circular Gaussian component to the edited and fully self-calibrated visibilities of each VLBI observation after having made CLEAN maps for each epoch and using the Difmap software.
 The results of the individual model fits are shown in Table 2.., The results of the individual model fits are shown in Table \ref{tab:model}.
" Figure 3 shows the flux density of AA* (and of 5530 used as a secondary calibrator) obtained from each VLBI experiment on a daily basis at 22, 43, and GGHz."," Figure \ref{fig:lc} shows the flux density of A* (and of 530 used as a secondary calibrator) obtained from each VLBI experiment on a daily basis at 22, 43, and GHz."
" The 10 day average mean flux density is 1.334 0.04JJy at GGHz, 1.79+0.05 JJy at GGHz, and 3.35+0.16JJy at GGHz (Table 3))."," The 10 day average mean flux density is $\pm$ Jy at GHz, $\pm$ Jy at GHz, and $\pm$ Jy at GHz (Table \ref{tab:mean}) )."
" The flux density variations of AA* appear more pronounced in the beginning of the campaign, during a time that coincides with two detected NIR flares occurring on May 15 and May 17, 2007 (??).."," The flux density variations of A* appear more pronounced in the beginning of the campaign, during a time that coincides with two detected NIR flares occurring on May 15 and May 17, 2007 \citep{2008A&A...479..625E,2010A&A...517A..46K}."
 We defer the discussion of a possible relation of this variability with the variability at higher frequencies to Sect. 4.., We defer the discussion of a possible relation of this variability with the variability at higher frequencies to Sect. \ref{sec:4}.
" The flux density variations of AA* seen at 22, 43, and GGHz appear highly correlated (indicated by the similar shape of the light curves) and progressively more pronounced towards the higher frequencies."," The flux density variations of A* seen at 22, 43, and GHz appear highly correlated (indicated by the similar shape of the light curves) and progressively more pronounced towards the higher frequencies."
" We note that the measured flux densities of 5530 do not show such a pattern, reassuring us that the variations seen in AA* do not come from calibration errors (see below)."," We note that the measured flux densities of 530 do not show such a pattern, reassuring us that the variations seen in A* do not come from calibration errors (see below)."
,2002 \usepackage{epsfig} \begin{document}
redshift sample is larger that in the nearby LILL galaxies. we think that direct measurements of electron teniperatures are needed to support such claim.,"redshift sample is larger that in the nearby HII galaxies, we think that direct measurements of electron temperatures are needed to support such claim."
 Empirical methods are basec on the underlying assumption that the ionizing properties of the voung stellar populations are the same in the dilferen objects. assumption that must be checked when comparing objects over à wide range in redshifts.," Empirical methods are based on the underlying assumption that the ionizing properties of the young stellar populations are the same in the different objects, assumption that must be checked when comparing objects over a wide range in redshifts."
 We conclude tha there ds. tentative. alber contracictory. evidence that the abundances of higher redshift objects. could. be different from. those of. loca LIL galaxies.," We conclude that there is tentative, albeit contradictory, evidence that the abundances of higher redshift objects could be different from those of local HII galaxies."
 Although the data are still very sparse anc inaccurate. if real. such clleet would introduce an importan systematic bias in the estimation of distances to hieh redshift objects that must be taken into account.," Although the data are still very sparse and inaccurate, if real, such effect would introduce an important systematic bias in the estimation of distances to high redshift objects that must be taken into account."
 In order to illustrate the potential of LILLE galaxies as deep cosmological probes we have caleulated the predicted distance moduli for the objects plotted in Figure 2. using the most recent data from the literature (distances and oxvecn abundances) for the giant HEEL regions in order to re-calibrate the zero-point., In order to illustrate the potential of HII galaxies as deep cosmological probes we have calculated the predicted distance moduli for the objects plotted in Figure \ref{lsigma} using the most recent data from the literature (distances and oxygen abundances) for the giant HII regions in order to re-calibrate the zero-point.
 The new calibration of the unbiased distance indicator introduced by NEM. Mz=OHoU .ds thus given by. from which the distance modulus is obtained as: where iis the observed. flux and yyy is the total extinction.," The new calibration of the unbiased distance indicator introduced by MTM, $M_Z ={{\sigma^5}\over{O/H}}$, is thus given by, from which the distance modulus is obtained as: where is the observed flux and $A_{\hb}$ is the total extinction."
 ligure 6 presents the resulting Hubble diagram for LLL ealaxies., Figure \ref{hubble} presents the resulting Hubble diagram for HII galaxies.
 Phe lines show the Qj;=0.5 family of models from Figure 1.., The lines show the $\Omega_{M}=0.5$ family of models from Figure \ref{focus}.
 We have used. constant values of A(I1I-7)211.25 and log(O/11)—-3.9 for all galaxies at -Q.1 to compute their distance moduli., We have used constant values of 1.25 and log(O/H)=-3.9 for all galaxies at $z>0.1$ to compute their distance moduli.
 These values correspond to the mean values of the objects in our local sample that span ranges in LULL?) and σ covered by our intermediate redshift’ sample and which are closest to those of the z~3 galaxies. (cf., These values correspond to the mean values of the objects in our local sample that span ranges in $\lbeta$ and $\sigma$ covered by our intermediate redshift sample and which are closest to those of the $z\sim3$ galaxies (cf.
 Section 5)., Section 5).
 The large symbols show the average values for each sub-sample., The large symbols show the average values for each sub-sample.
 The error. bars show the mean error in distance modulus., The error bars show the mean error in distance modulus.
 Although our data-set cannot be used (nor is intended) to place significant constraints on the cosmological parameters. it is very helpful to understand he limitations of the methoct.," Although our data-set cannot be used (nor is intended) to place significant constraints on the cosmological parameters, it is very helpful to understand the limitations of the method."
 Probably the first thing one notices is the large scatter in the data., Probably the first thing one notices is the large scatter in the data.
 Phe rms dispersion in distance modulus for the ocal sample is c;N(m—M)]=0.52 magnitudes., The rms dispersion in distance modulus for the local sample is $\rm \sigma[\Delta(m-M)]=0.52$ magnitudes.
 According o MTM. typical errors for these galaxies are in velocity dispersion and. in Πας.," According to MTM, typical errors for these galaxies are in velocity dispersion and in flux."
 Adding errors of about. in extinction and about in abundance. the expected scatter clue just to observational errors is 0.35 mae in distance modulus.," Adding errors of about in extinction and about in abundance, the expected scatter due just to observational errors is 0.35 mag in distance modulus."
 Thus. there seems to be room for improvement and errors similar to those of SNla may be achievable with better quality data.," Thus, there seems to be room for improvement and errors similar to those of SNIa may be achievable with better quality data."
 The second point is that the two high-redshift: &alaxies have distance moduli that are discrepant. by more than one magnitude., The second point is that the two high-redshift galaxies have distance moduli that are discrepant by more than one magnitude.
 While the observational errors are indeed large. this could also be due to our choice of extinction and metallicity.," While the observational errors are indeed large, this could also be due to our choice of extinction and metallicity."
 These parameters enter with the same sign in 14.1 so systematic changes of 0.2 dex in O/LE and 0.2 mag in extinction (which correspond to le deviations in the local sample) translate into shifts of 0.7 mag in distance modulus., These parameters enter with the same sign in Eq.1 so systematic changes of 0.2 dex in O/H and 0.2 mag in extinction (which correspond to $1\sigma$ deviations in the local sample) translate into shifts of 0.7 mag in distance modulus.
" Notice that. since the maximum separation between Qa;=0.2 and 3,= Lat z—3 is about one magnitude (Figure 6)). it is crucial to have &ooc nmieasurements of extinction and abundance for these objects."," Notice that, since the maximum separation between $\Omega_{M}=0.2$ and $\Omega_{M}=1$ at z=3 is about one magnitude (Figure \ref{hubble}) ), it is crucial to have good measurements of extinction and abundance for these objects."
 Finally we notice that even with our new zero-point calibration. the data for ocal LIL galaxies are inconsistent with the value of that. results. from SNla.," Finally we notice that even with our new zero-point calibration, the data for local HII galaxies are inconsistent with the value of that results from SNIa."
 We believe that the cliscrepaney arises [rom systematic errors in the photometry of Ciant HIE regions which we are in the process of checking using narrow-band CCD imaging., We believe that the discrepancy arises from systematic errors in the photometry of Giant HII regions which we are in the process of checking using narrow-band CCD imaging.
 Clearly. however. provided there are no systematic iferences in the photometric calibrations between local aud istant objects. the determination of O is independent. of," Clearly, however, provided there are no systematic differences in the photometric calibrations between local and distant objects, the determination of $\Omega$ is independent of."
 We believe that using. the new optical and. Ik spectrographs that are coming on-line on Sni-class telescopes it will be possible to measure to and σ to better than at z=8., We believe that using the new optical and IR spectrographs that are coming on-line on 8m-class telescopes it will be possible to measure to and $\sigma$ to better than at z=3.
 An accurate etermination of Oi. with r.m.s.," An accurate determination of $\Omega_{M}$, with r.m.s."
 error about 0.05 seems rerclore possible with samples of 40-50 LULL galaxies at z=1-, error about 0.05 seems therefore possible with samples of 40-50 HII galaxies at z=1-3.
 Phe determination of extinction ane metallicity at this redshift. however. will remain a challenging. observational problem.," The determination of extinction and metallicity at this redshift, however, will remain a challenging observational problem."
conmmonueuts that contribute to the observed surface brightness.,components that contribute to the observed surface brightness.
 Radial profiles are the appropriate tool for this purpose and can be easily constructed with the technique of ellipse fitting., Radial profiles are the appropriate tool for this purpose and can be easily constructed with the technique of ellipse fitting.
 This is done by means of the IRAF task ELLIPSE. which computes the isophotal contours of the surface brightness nuages aud fits them to ellipses.," This is done by means of the IRAF task ELLIPSE, which computes the isophotal contours of the surface brightness images and fits them to ellipses."
 ELLIPSE uses au algorithia developed by Jedrzejewski (1087)., ELLIPSE uses an algorithm developed by Jedrzejewski (1987).
 As a result. one gets radial profiles of briebtuess. ellipticitv aud position angles along the major axis of the ellipse family.," As a result, one gets radial profiles of brightness, ellipticity and position angles along the major axis of the ellipse family."
 This is formally equivalent to first correcting or the inclination auele by deprojection of the galaxy Πμασο and then ectting those radial variations averaged over the azimuthal anele., This is formally equivalent to first correcting for the inclination angle by deprojection of the galaxy image and then getting those radial variations averaged over the azimuthal angle.
 We rave linuted the scope of hese profiles to the extent where the brigltuess of the ealaxies equals the seusitivitv figures given in table 3.., We have limited the scope of these profiles to the extent where the brightness of the galaxies equals the sensitivity figures given in table \ref{Tab:limite}.
 The xofiles. then. will provide information about the uorphological structure of the ealaxics.," The profiles, then, will provide information about the morphological structure of the galaxies."
 Outer isophotes were used for deteriuiuation of global ealactic paraueters such as ellipticity. position. anele (hereafter. PA) aud inclination angle. this latter derived frou he ellipticity.," Outer isophotes were used for determination of global galactic parameters such as ellipticity, position angle (hereafter, PA) and inclination angle, this latter derived from the ellipticity."
 Galaxies with a lower inclination angle have higher errors because of the lack of a privileged direction., Galaxies with a lower inclination angle have higher errors because of the lack of a privileged direction.
 One can casily infer the presence of the differcut structural components. discussed in the next section. frou the variation in these parameters with galactic radius (Varela ct al.," One can easily infer the presence of the different structural components, discussed in the next section, from the variation in these parameters with galactic radius (Varela et al."
 1996: Wozniak et al., 1996; Wozniak et al.
 1995)., 1995).
 Tn table Lo we have the results of the ELLIPSE task., In table \ref{Tab:parametros} we have the results of the ELLIPSE task.
 The ellipticity is defined as δα. where e aud b are the major and minor axes of the ellipses. respectively.," The ellipticity is defined as $b/a$ , where $a $ and $b$ are the major and minor axes of the ellipses, respectively."
 The PA is the anele between the major axis of the ellipses and northsouth axis in the sky. measured from north to cast.," The PA is the angle between the major axis of the ellipses and north–south axis in the sky, measured from north to east."
 The values of cach galaxy in both filters are in reasonably eood agreement. their deviatious being due mainly to απο. ln he ELLIPSE process. possibly cuhanced by the shehtly differeut scusitivities of the images in the two filters.," The values of each galaxy in both filters are in reasonably good agreement, their deviations being due mainly to errors in the ELLIPSE process, possibly enhanced by the slightly different sensitivities of the images in the two filters."
 We can compare our results for the inclination angle and PA of cach ealaxy listed in table Lo with the values quoted iu RC3., We can compare our results for the inclination angle and PA of each galaxy listed in table \ref{Tab:parametros} with the values quoted in RC3.
te The aerecment isgeucrally good., The agreement isgenerally good.
 NGC, NGC
The viscous heatiug term. is where VHgs=(/2)Xi0.,The viscous heating term is where $W_{R\phi}=(3/2)\Sigma_i \nu_{i}\Omega$.
 To evaluate the viscosity i. we have considered both MBI and GI trausport.," To evaluate the viscosity $\nu_i$, we have considered both MRI and GI transport."
 The net viscosity 1; is the sum of both. where a;—60|603; aud The MRI viscosity is assuinied to lave a fixed value of aap Whether the region iu question is thernallv or nou-thermally ionized.," The net viscosity $\nu_i$ is the sum of both, where $\alpha_i=\alpha_{Q}+\alpha_{M}$ and The MRI viscosity is assumed to have a fixed value of $\alpha_M$ whether the region in question is thermally or non-thermally ionized."
 We assimune that above some critical temperature Z4; the MBI is fully activated throughout the disk with viscosity paramcter ayy., We assume that above some critical temperature $T_{M}$ the MRI is fully activated throughout the disk with viscosity parameter $\alpha_{M}$.
" The Toonre instability parancter Q is evaluated using the disk central (midplane) temperature Ty. the total surface density (X, X). aud assmuineg I&epleriau rotation."," The Toomre instability parameter $Q$ is evaluated using the disk central (midplane) temperature $_{d}$, the total surface density $\Sigma_{a}$ $\Sigma_{d}$ ), and assuming Keplerian rotation."
 The forni of is motivated by a desire to make gravitational torques a)significant only wheu Q=LL. as ineicated bv elobal three-dimensional sinuuations (e... Boley et al 2006).," The form of $\alpha_Q$ is motivated by a desire to make gravitational torques significant only when $Q \lesssim 1.4$, as indicated by global three-dimensional simulations (e.g., Boley et al 2006)."
 There are uncertainties in adopting the above approach to transport., There are uncertainties in adopting the above approach to transport.
 GIs involve huge scale deusitv waves that cannot be captured with a local viscous treatiuent. although local treatments are adequate under some cieunistances (Lodato&Rice2001]:Cossusotal. 20093.," GIs involve large scale density waves that cannot be captured with a local viscous treatment, although local treatments are adequate under some circumstances \citep{Lodato2004,Cossins2009}."
.. As discussed in Z2009a. the esseutial properties of this treatineut are the assuniptious that disks with GI wave Q-values of order unity. and that the GI produce ocal dissipation of the accretio1 energy.," As discussed in Z2009a, the essential properties of this treatment are the assumptions that disks with GI have $Q$ -values of order unity, and that the GI produce local dissipation of the accretion energy."
 Uider these assunptious. the precise formi of ae will not affect the disks evolution. as long as a is a steeply dechuing unction of OQ near —1.5.," Under these assumptions, the precise form of $\alpha_{Q}$ will not affect the disk's evolution, as long as $\alpha$ is a steeply declining function of Q near $\sim$ 1.5."
 To mase this pon clear. we ran the same simulation for a tes case but with the ae xesceriptiou of Lin Prinele (1987.1990).," To make this point clear, we ran the same simulation for a test case but with the $\alpha_{Q}$ prescription of Lin Pringle (1987,1990)."
 As expected. he dittereut forms of ae have no effect ou the disk outbursts.," As expected, the different forms of $\alpha_{Q}$ have no effect on the disk outbursts."
 Siuilulv. whether the MRI can be fully activated in a non-thermally-ionized laver depends im part upon whether small dust erains have been suffüicieutlv depleted (e.g... Sano 2000).," Similarly, whether the MRI can be fully activated in a non-thermally-ionized layer depends in part upon whether small dust grains have been sufficiently depleted (e.g., Sano 2000)."
 This is a complicated problem with substautial observational aud theoretical uncertainties: we therefore adopt the simplest possible approach., This is a complicated problem with substantial observational and theoretical uncertainties; we therefore adopt the simplest possible approach.
" It turus out that the value of X, is ""uinmnportanut for understanding larec outbursts (Z20092). as long as the CIiu the dead zone transports niore lass than the active laver: but X, does have inportaut effects on the loug-teri disk evolution at low accretion rates. as discussed in a following paper."," It turns out that the value of $\Sigma_a$ is unimportant for understanding large outbursts (Z2009a), as long as the GI in the dead zone transports more mass than the active layer; but $\Sigma_{a}$ does have important effects on the long-term disk evolution at low accretion rates, as discussed in a following paper."
 Tt is now clear that the maeuetic fields that eive rise to ea diffuse radiallv (Lesur Lousaretti 2008. Coan (απο 2009. Fromane Stone 2009) and take time to build up and decay (¢.¢. Hirose et al.," It is now clear that the magnetic fields that give rise to $\alpha_M$ diffuse radially (Lesur Longaretti 2008, Guan Gammie 2009, Fromang Stone 2009) and take time to build up and decay (e.g. Hirose et al."
 2009)., 2009).
 To account for these effects we introduce an evolution equation for Oa: where aay is the equilibritni value for ma;.," To account for these effects we introduce an evolution equation for $\alpha_M$: where $\alpha_{M,o}$ is the equilibrium value for $\alpha_M$."
" The first term permits aay, to relax up. or down. as fa is crossed."," The first term permits $\alpha_M$ to relax up, or down, as $T_M$ is crossed."
 The secoud termi corresyonds to racial diffusion of the magnetic field., The second term corresponds to radial diffusion of the magnetic field.
 For nunerical reasons we set the dimensionless radial diffusion coefficieut to 0.5 (the radial ciffusiou coefficient is actually a fiction ofdistauce from the midplane)., For numerical reasons we set the dimensionless radial diffusion coefficient to $0.5$ (the radial diffusion coefficient is actually a function of distance from the midplane).
 Iun the protostellu phase. the disk is unlikely to transport mass steadily from 1060 AU all the way to the star at an accretion rate matching the mass imfall rate πο5toHMvrHF fom the envelope to the outer dis-," In the protostellar phase, the disk is unlikely to transport mass steadily from $\sim$ 100 AU all the way to the star at an accretion rate matching the mass infall rate $10^{-6}-10^{-4}\msunyr$ from the envelope to the outer disk."
 This ΠΕΠΠΕΕ ΠΕ to outbursts which are qualitatively similar to that found by Avimitageetal.(2001).. Book Uartinaun (2005). iud in our 2-D hydrocdvuanic simulations (Z2009b).," This mismatch leads to outbursts which are qualitatively similar to that found by \cite{armitage01}, Book Hartmann (2005), and in our 2-D hydrodynamic simulations (Z2009b)."
" Ta παν, before the outburst. mass added to the outer disk ieoves inwards due to GI. but piles up in the inner disk as GI becomes less effective. at simaller radi."," In summary, before the outburst, mass added to the outer disk moves inwards due to GI, but piles up in the inner disk as GI becomes less effective at smaller radii."
 Eveutually. the laree X aud enerev dissipation leads to enough thermal ionization to rigger the MBRI at several AU.," Eventually, the large $\Sigma$ and energy dissipation leads to enough thermal ionization to trigger the MRI at several AU."
 The MRI frout quickly moves In across the inner disk aud the iuncer disk accretes at a higher mass accretion rate. reseciubliug FU Orionisype outbursts.," The MRI front quickly moves in across the inner disk and the inner disk accretes at a higher mass accretion rate, resembling FU Orionis-type outbursts."
 This high mass accretion rate during the outburst also makes the inner disk thermally unstable., This high mass accretion rate during the outburst also makes the inner disk thermally unstable.
 After the immer disk has been drained by the outhurst aud )econies too cold to sustain the AIRT. the disk returus to he low state.," After the inner disk has been drained by the outburst and becomes too cold to sustain the MRI, the disk returns to the low state."
 With the mass continnously accreted from he outer radi (or from au iufalliue cuvelope). the disk evolves to conditious leading to another outburst.," With the mass continuously accreted from the outer radii (or from an infalling envelope), the disk evolves to conditions leading to another outburst."
 This MRI triggered) by CI outburst can also be uuderstood as the classical thermal instability. but the S-curve is formed primarily by the variation of a near Έλι rather than variations iu opacity ac asstumed Variation in a near hydrogen ionization (c.g. Dell&Liu (1991))).," This MRI triggered by GI outburst can also be understood as the classical thermal instability, but the S-curve is formed primarily by the variation of $\alpha$ near $_{M}$, rather than variations in opacity and assumed variation in $\alpha$ near hydrogen ionization (e.g. \cite{bell94}) )."
" To test how 1D2Z models s«umnuulate the outbursts compared with 2-D simulations. we set up a fest case with all the parameters adoος from our previous 2-D simulations (2200010),"," To test how 1D2Z models simulate the outbursts compared with 2-D simulations, we set up a test case with all the parameters adopted from our previous 2-D simulations (Z2009b)."
 Iu both 1-D and 2-D siuulations. we have used an updated opacity frou Z2009a and Ti;21500 FK Because Z2009b do uot consider radiation. the imadiation factor f iu equation (6)) for the 1D2Z snuulation is set to be 0.," In both 1-D and 2-D simulations, we have used an updated opacity from Z2009a and $_{M}$ =1500 K. Because Z2009b do not consider irradiation, the irradiation factor f in equation ) for the 1D2Z simulation is set to be 0."
 The inner radius iu both cases is set to 0.2 AU., The inner radius in both cases is set to 0.2 AU.
 Figure shows the mass accretion rate as a function of time for both 1-D aud 2-D sinulatious., Figure shows the mass accretion rate as a function of time for both 1-D and 2-D simulations.
 As shown. the 1-D suuulatious closely reseiible 2-D siuulatious at the equilibrimu states. such as the state before the outburst is triggered and the state during the outburst.," As shown, the 1-D simulations closely resemble 2-D simulations at the equilibrium states, such as the state before the outburst is triggered and the state during the outburst."
 For some rapid. or small scale. disk variations. such as the MBI frout propagation aud the couvective eddies in the hot inner disks. the 2-D simulations exhibit more complex behavior than the 1-D simulations. so the outbursts ciffer in detail.," For some rapid, or small scale, disk variations, such as the MRI front propagation and the convective eddies in the hot inner disks, the 2-D simulations exhibit more complex behavior than the 1-D simulations, so the outbursts differ in detail."
" Iu particularthe 1-D simulations show au initial lueh ÀJ peak at the begiuniug of the outburst that is not seen in 2-D. The 1-D simulations also show ""drop outs” in accretion that do not occur in 2-D. Tn detail. starting from the MBI activation at ~2 AU. the MRI active region moves inwards."," In particular the 1-D simulations show an initial high $\dot{M}$ peak at the beginning of the outburst that is not seen in 2-D. The 1-D simulations also show “drop outs” in accretion that do not occur in 2-D. In detail, starting from the MRI activation at $\sim$ 2 AU, the MRI active region moves inwards."
 During this process. Inass piles up at the inner boundary of the active region. because the disk is MBI active bevoud this boundary and has a higher mass accretion rate than the MRI inactive disk at simaller radius.," During this process, mass piles up at the inner boundary of the active region, because the disk is MRI active beyond this boundary and has a higher mass accretion rate than the MRI inactive disk at smaller radius."
 Ti 1-D, In 1-D
the co-rotation radius lies in the range O.la (a is the semi-major axis of the bar).,the co-rotation radius lies in the range $\pm$ 0.1a (a is the semi-major axis of the bar).
 The wy orbits also have high curvatures near their apocentres in the regions in which the shocks occur in order for the shock loci to form along the Icacding edge of the weak bar., The $x_1$ orbits also have high curvatures near their apocentres in the regions in which the shocks occur in order for the shock loci to form along the leading edge of the weak bar.
 The shape of the shocks can then be explained by a gradual shift in the orientation of the How lines from along the bar (ej orbits) to perpendicular to the bar., The shape of the shocks can then be explained by a gradual shift in the orientation of the flow lines from along the bar $x_1$ orbits) to perpendicular to the bar.
 Angular momentum is cdissipated in the shock region and the eas then quickly settles onto smaller. lower energy. am orbits. closer to the nucleus.," Angular momentum is dissipated in the shock region and the gas then quickly settles onto smaller, lower energy, $x_2$ orbits, closer to the nucleus."
 Our observations of the shocks in NGCX4151 provide compelling evidence for the presence of these two orbit. families in the bar. with eas streaming from the shock regions making the transition between the two families.," Our observations of the shocks in NGC4151 provide compelling evidence for the presence of these two orbit families in the bar, with gas streaming from the shock regions making the transition between the two families."
 In. fact. recent. optical studies (Vila-Vilaro. et ab.," In fact, recent optical studies (Vila-Vilaro, et al.,"
 1995: Asif et al..," 1995; Asif et al.,"
". 1998) have found evidence for the presence of a cireumnuclear ellipse of dust and gas (117H"" 18). elongated perpendicular. to the bar."," 1998) have found evidence for the presence of a circumnuclear ellipse of dust and gas $11'' \times 18''$ ), elongated perpendicular to the bar."
 Such. a ring is thought to form as a result of gas Howing in c» orbits (Shlosman. 1996). interior to the outer LL. and in fact; each ofthe inner ends of the inflow we observe lie close to the ends ofthe major axis of this ellipse. providing clear evidence for such a transition.," Such a ring is thought to form as a result of gas flowing in $x_2$ orbits (Shlosman, 1996), interior to the outer ILR, and in fact, each of the inner ends of the inflow we observe lie close to the ends of the major axis of this ellipse, providing clear evidence for such a transition."
 The circummuclear ellipse in NCC4151 may therefore have formed as a natural consequence of the non-linear gas dynamics in the bar and does not require the existence of an inner stellar bar., The circumnuclear ellipse in NGC4151 may therefore have formed as a natural consequence of the non-linear gas dynamics in the bar and does not require the existence of an inner stellar bar.
 This is consistent with the results of LIU studies in which no inner bar is detected down to the central 37 CXlonso-Herrero. et al.," This is consistent with the results of IR studies in which no inner bar is detected down to the central $""$ (Alonso-Herrero, et al.,"
 1998)., 1998).
 In a non-axisvmumietric barred. potential. eas Low has a complicated. structure. with regions of both outflow and inflow (Athanassoula. 1995).," In a non-axisymmetric barred potential, gas flow has a complicated structure, with regions of both outflow and inflow (Athanassoula, 1995)."
 Lf there are no shocks in the xw. the gas follows quasi-elliptical orbits and there is only a small net inflow due to viscosity.," If there are no shocks in the bar, the gas follows quasi-elliptical orbits and there is only a small net inflow due to viscosity."
 I however. shocks are oesent. the gas changes direction and moves inwards at high speeds after hitting the shock.," If, however, shocks are present, the gas changes direction and moves inwards at high speeds after hitting the shock."
 The average inflow velocity rowever is only a few kn * despite local inflow velocities as high as 100 kn + (Athanassoula. 1992b).," The average inflow velocity however is only a few km $^{-1}$ despite local inflow velocities as high as 100 km $^{-1}$ (Athanassoula, 1992b)."
 Lt is though hat it is also easier for gas to Low into the centre when no ILRs are present., It is thought that it is also easier for gas to flow into the centre when no ILRs are present.
 Simulations have also shown that two categories. of inflow occur depending on the stage of evolution of the bar: high inflow rates occur during the bar formation stage au much smaller inflow rates occur once the bar reaches a gaeady state CXthanassoula. 1994)," Simulations have also shown that two categories of inflow occur depending on the stage of evolution of the bar; high inflow rates occur during the bar formation stage and much smaller inflow rates occur once the bar reaches a quasi-steady state (Athanassoula, 1994)."
 When the bar [first beginsὃν to form. no centra 'oncentration or LLRs are present.," When the bar first begins to form, no central concentration or ILRs are present."
 Gas inflow at this early stage is very ellicicnt anc gas is pushed towards the centre., Gas inflow at this early stage is very efficient and gas is pushed towards the centre.
 As time passes. the central mass builds up and the bar pattern speed decreases leading to the formation of LLRs and 10 quasi-steady-state with smaller inflow rates.," As time passes, the central mass builds up and the bar pattern speed decreases leading to the formation of ILRs and the quasi-steady-state with smaller inflow rates."
 This type of negative feedback loop would seems rather unpromising for the prospect of fuclling an AGN., This type of negative feedback loop would seems rather unpromising for the prospect of fuelling an AGN.
 However. the presence of LLRs. central concentration. and slow pattern speed leads to the formation of leading edge shocks which in turn cause inflow. albeit at a smaller rate than the initial bar formation stage.," However, the presence of ILRs, central concentration, and slow pattern speed leads to the formation of leading edge shocks which in turn cause inflow, albeit at a smaller rate than the initial bar formation stage."
 The streaming velocities observed. in δις151 of up to 40 km  are consistent with those. predicted. by simulations (Athanassoula. 1992h).," The streaming velocities observed in NGC4151 of up to 40 km $^{-1}$ are consistent with those predicted by simulations (Athanassoula, 1992b)."
 This less dramatic twpe of fuelling mechanism may in fact be ideal for Sevferts., This less dramatic type of fuelling mechanism may in fact be ideal for Seyferts.
 Statistical evidence shows that stronglv interacting galaxies and highly clisturbed. systems do not show an excess of Sevfert activity (Bushouse. 1986).," Statistical evidence shows that strongly interacting galaxies and highly disturbed systems do not show an excess of Seyfert activity (Bushouse, 1986)."
 ‘This suggests that Sevfert activity is strongly related to the host galaxy properties and that. nuclear activity may be the result. of the galaxy. responding coherently with well-structured features to non-axisvnunetric perturbations of the potential rather than due to major clisruption (Moles. Marquez l'erez. I," This suggests that Seyfert activity is strongly related to the host galaxy properties and that nuclear activity may be the result of the galaxy responding coherently with well-structured features to non-axisymmetric perturbations of the potential rather than due to major disruption (Moles, Marquez Perez, 1995)."
 Spectral imaging of HE in NCC4151 has shown that the central oval distortion exhibits the kinematic characteristics of a weak bar. and in addition. bright regions close to the leacing edges show sharp changes in the velocity field strikingly similar to shocks in gas-cvnamical simulations by Athanassoula.," Spectral imaging of HI in NGC4151 has shown that the central oval distortion exhibits the kinematic characteristics of a weak bar, and in addition, bright regions close to the leading edges show sharp changes in the velocity field strikingly similar to shocks in gas-dynamical simulations by Athanassoula."
 This implies the presence of both the wy and we orbit Families. since the offset shocks in weak bars are due to convergence of orbital streamlines from the two families.," This implies the presence of both the $x_1$ and $x_2$ orbit families, since the offset shocks in weak bars are due to convergence of orbital streamlines from the two families."
 The residual velocity field. shows streaming consistent with a weak bar potential. but with gas inflow clearly directed. alone narrow channels originating in the shocks and Leading to the inner dusty ellipse seen optically by Vila-Vilaro a," The residual velocity field shows streaming consistent with a weak bar potential, but with gas inflow clearly directed along narrow channels originating in the shocks and leading to the inner dusty ellipse seen optically by Vila-Vilaro ."
f We identify this ellipse with the lower energy ao orbits. and suggest that it has formed as à consequence of the eas flows in the bar. without the requirement for à second. inner bar.," We identify this ellipse with the lower energy $x_2$ orbits, and suggest that it has formed as a consequence of the gas flows in the bar, without the requirement for a second, inner bar."
 The inllow along the bar may represen an early stage in the fuelling of the AGN., The inflow along the bar may represent an early stage in the fuelling of the AGN.
 These HE observations of Νας151 demonstrate tha it is now possible to study the detailed. kinematics of gas closer to the nuclear regions than has hitherto been though »ossible. and. confirm lone-stanclingeὃν theoretical predictions of gas inflow in bars.," These HI observations of NGC4151 demonstrate that it is now possible to study the detailed kinematics of gas closer to the nuclear regions than has hitherto been thought possible, and confirm long-standing theoretical predictions of gas inflow in bars."
 Further such stuclics of bars in nearby active and normal galaxies. and comparison with cetailec simulations may provide the opportunity to fully unclerstanc this potentially important stage of the nuclear fuelling chain.," Further such studies of bars in nearby active and normal galaxies, and comparison with detailed simulations may provide the opportunity to fully understand this potentially important stage of the nuclear fuelling chain."
 We thank Alan Pedlar. Lia Athanassoula ancl Elias Drinks for helpful discussions.," We thank Alan Pedlar, Lia Athanassoula and Elias Brinks for helpful discussions."
 We are grateful to the referee. Professor Ron Buta. for helpful comments which improved an earlier draft of this paper.," We are grateful to the referee, Professor Ron Buta, for helpful comments which improved an earlier draft of this paper."
 CGAL acknowledges a research stucentship and research fellowship from the U.Ix. Particle Physics and Astronomy Research Council, CGM acknowledges a research studentship and research fellowship from the U.K. Particle Physics and Astronomy Research Council
NGC |LOGS has been observed ou four occasions witli the al.2001) in direct imagine mode with the Advanced CCD Lnagine Spectrometer (ACIS: Carimire 1997) at tle focal plane of the Higl-Resolution Mirror Assembly (vanSpeybroeck1997).,NGC 1068 has been observed on four occasions with the \citep{wei01} in direct imaging mode with the Advanced CCD Imaging Spectrometer (ACIS; Garmire 1997) at the focal plane of the High-Resolution Mirror Assembly \citep{van97}.
. Results from an alaysis of the nuclear aid extended X-ray. emission associated with NGC LOGS are presented elsewhere (Young. Wilso1 Shopbell 2001. hereafter Paper I).," Results from an analysis of the nuclear and extended X-ray emission associated with NGC 1068 are presented elsewhere (Young, Wilson, Shopbell 2001, hereafter Paper I)."
 A full account of the observations is [n]giveu) in Paper I. We concern ourselves here with a study of the discrete X-ray source population in NCC LOGS. imaged within the 8/1x«821 (35.3x35.3 kpc) field of view of the $3 chip.," A full account of the observations is given in Paper I. We concern ourselves here with a study of the discrete X-ray source population in NGC 1068, imaged within the $8.\!^{\prime}4 \times
8.\!^{\prime}4$ $35.3 \times 35.3$ kpc) field of view of the S3 chip."
 The data reduction and analysis were done using the Chandra Interactive Analysis of Observatious (6190) software version 2.2.1 (released on December 13. 2001) aud CALDB 2.12 (released on February L1. 2002). aud the reprocessed (on March. 10. 2001 using CALDB 2.3 and version BRICUSUPDIL1 of the processing software) event files.," The data reduction and analysis were done using the Chandra Interactive Analysis of Observations (CIAO) software version 2.2.1 (released on December 13, 2001) and CALDB 2.12 (released on February 14, 2002), and the reprocessed (on March 10, 2001 using CALDB 2.3 and version R4CU5UPD14.4 of the processing software) event files."
 New level 2 event files were created. applying the latest telescope geometry aud detector gain corrections. aud inclucling the same grades. bit status. aud time filters as in the existing level 2 event files.," New level 2 event files were created, applying the latest telescope geometry and detector gain corrections, and including the same grades, bit status, and time filters as in the existing level 2 event files."
 Periods of high aud low background (i.e.. flares or data dropouts due to telemetry saturation) were excluded from the data.," Periods of high and low background (i.e., flares or data dropouts due to telemetry saturation) were excluded from the data."
 This was achieved by creating a light curve over the full euerey range for the whole 53 chip. exclucling the brightest sources of X-ray enission. aud removing events 3o from the mean count rate.," This was achieved by creating a light curve over the full energy range for the whole S3 chip, excluding the brightest sources of X-ray emission, and removing events $\pm 3\sigma$ from the mean count rate."
 This procedure gives an ellective exposure titje of [7.1 ks (corrected for the dead-time in the detector)., This procedure gives an effective exposure time of 47.1 ks (corrected for the dead-time in the detector).
 We have checked whether the decline in low energy quantum elliciency of the $3 chip allects our results by using the ACISABS spectral model ou a lew sources. but founcl the spectra to be tusienificantly different. presumably because our observations were takeu early in the mission (2000 Feb. 21).," We have checked whether the decline in low energy quantum efficiency of the S3 chip affects our results by using the ACISABS spectral model on a few sources, but found the spectra to be insignificantly different, presumably because our observations were taken early in the mission (2000 Feb. 21)."
 Au image from the 3.28 frame time observation of NGC LOGS (obsid 311). on the scale of the galactie disk. is shown iu Fig. l..," An image from the 3.2s frame time observation of NGC 1068 (obsid 344), on the scale of the galactic disk, is shown in Fig. \ref{fig1}."
" There is a cousklerable amount of cliffuse X-ray. emission iu this image. which extends at least 60"" (1.2 kpe) to the northeast. 50” (3.5 kpc) to the southwest. 20"" (1.1 kpc) to the northwest. and 30”+) (2.1 kpe) 10 the southeast of the nucleus."," There is a considerable amount of diffuse X-ray emission in this image, which extends at least $60^{\prime\prime}$ (4.2 kpc) to the northeast, $50^{\prime\prime}$ (3.5 kpc) to the southwest, $20^{\prime\prime}$ (1.4 kpc) to the northwest, and $30^{\prime\prime}$ (2.1 kpc) to the southeast of the nucleus."
" The dominant large-scale structures are ""spiral aris"" that curve to a lower position angle (PA. with increasing ealactocentric distance (Youngetal.2001).", The dominant large-scale structures are “spiral arms” that curve to a lower position angle (P.A.) with increasing galactocentric distance \citep{you01}.
. Many compact sourcees of N-ray eimisslol associated with NGC LOGS are also seen in this image., Many compact sources of X-ray emission associated with NGC 1068 are also seen in this image.
 The luminous X-ray soices appear to be concentrated in the starburst region. but there are also many sources located fu‘ther out [rom he center of the galaxy.," The luminous X-ray sources appear to be concentrated in the starburst region, but there are also many sources located further out from the center of the galaxy."
 linages were extracted from the reprocessed level 2 events file in soft. (0.[—1.5 seV). hard keV). aud Full (0.1-5.0 keV) energy bands.," Images were extracted from the reprocessed level 2 events file in soft (0.4–1.5 keV), hard (1.5--5.0 keV), and full (0.4–5.0 keV) energy bands."
 We have used the CLAO program to search, We have used the CIAO program to search
"with the mass of 1019AZ,<API0 ",with the mass of $10^{10} M_{\odot} \le M < 10^{11} M_{\odot}$.
Thus we conclue that there is no mass depenudeuce ATJ..of the spin piriuueter.," Thus, we conclude that there is no mass dependence of the spin parameter."
 Otherwise. it is extremely weal.," Otherwise, it is extremely weak."
 We can see that there are sinall deviations from the log-normal distributions at high spin regions as secu iu previous works for larger halos2010)., We can see that there are small deviations from the log-normal distributions at high spin regions as seen in previous works for larger halos.
. If we remove unrelaxed halos. the deviations will disappear2010).," If we remove unrelaxed halos, the deviations will disappear."
. We preseut the first scientific results of the Cosimognid sinulatiou., We present the first scientific results of the Cosmogrid simulation.
 Because of uuprecedenutedly: Ligh resolution and powerful statistics. the simulation is suitable to resolve internal properties of halos with the nass ↕⋜∐⋅∶↴∙⊾↸∖↥⋅↑∐⋜⊔≼↧↖↖↽⋜∐⋅↕≯∶↴∙⊾⋜↧↕⋜⋯⋅↖↽⋜∐∐↧↴∖↴↿∏⋝∐⋜↕↕∪↴∖↴↖↖↽∐∪↴∖↴↸∖↴∖↴↸⊳⋜↧↕↸∖↴∖↴⋜∐⋅↸∖ comparable to ultra-taint dwarf galaxies.," Because of unprecedentedly high resolution and powerful statistics, the simulation is suitable to resolve internal properties of halos with the mass larger than dwarf galaxy and subhalos whose scales are comparable to ultra-faint dwarf galaxies."
 We stuarize the main results of this paper as follows: We lave shown here a first analysis of the Cosimogrid data and we plan to extend our analysis iu future publications., We summarize the main results of this paper as follows: We have shown here a first analysis of the Cosmogrid data and we plan to extend our analysis in future publications.
 Some of the topics that we want to address are: the variation of density profiles aud its impact on the dark matter detectability. the statistics of subhalo abundance of the mass scale down to ultra faint chwart in dwarf and ealaxyv-zed halos. the assembly. histories of halos. aud the evolution of internal properties of halos which are prescuted in this paper at only 2=0.," Some of the topics that we want to address are: the variation of density profiles and its impact on the dark matter detectability, the statistics of subhalo abundance of the mass scale down to ultra faint dwarf in dwarf- and galaxy-sized halos, the assembly histories of halos, and the evolution of internal properties of halos which are presented in this paper at only $z=0$."
 Muerical computations were partially carried out ou Crav XTL at Ceouter for Computational Astrophysics. CCA. of National Astronomical Observatory of Japan. Ihivecns at the Dutch National Πιο Performance Computing and e-Scieuce Support Center. SARA (Netherlands). HECTOoR at the Ediubureh Parallel Computing Ceuter (United. Kiuedoni). aud Louhi at IT Center for Science in Expoo (Fiuland).," Numerical computations were partially carried out on Cray XT4 at Center for Computational Astrophysics, CfCA, of National Astronomical Observatory of Japan, Huygens at the Dutch National High Performance Computing and e-Science Support Center, SARA (Netherlands), HECToR at the Edinburgh Parallel Computing Center (United Kingdom), and Louhi at IT Center for Science in Espoo (Finland)."
 Τ.Ε is financially supported by Research Fellowship of the Japan Society for the Promotion of Science (JSPS) for Young Scieutists., T.I. is financially supported by Research Fellowship of the Japan Society for the Promotion of Science (JSPS) for Young Scientists.
 This rescarcl is partially supported by the Special Coordination Fund. for Promoting Science and Technology (CRAPE-DR project) Miuistrv of," This research is partially supported by the Special Coordination Fund for Promoting Science and Technology (GRAPE-DR project), Ministry of"
using the intermittent firing of a stable noise source.,using the intermittent firing of a stable noise source.
" Next we performed a bandpass calibration using the AIPS task '""BPASS' using either 3C48 or 3C286 or both.", Next we performed a bandpass calibration using the AIPS task 'BPASS' using either 3C48 or 3C286 or both.
 We applied the bandpass solution using the AIPS task “SPLAT’., We applied the bandpass solution using the AIPS task 'SPLAT'.
 After that. we performed an external absolute gain calibration using an assumed flux for 3C48 by running the AIPS tasks “SETJY° and CALIB'. “," After that, we performed an external absolute gain calibration using an assumed flux for 3C48 by running the AIPS tasks 'SETJY' and 'CALIB'. '"
SETJY° was set to use the absolute flux density calibration determined by ? ànd the latest (epoch 1999.2) polynomial coefficients. for interpolating over frequency as determined at the VLA by NRAO staff.,SETJY' was set to use the absolute flux density calibration determined by \citet{Baars} and the latest (epoch 1999.2) polynomial coefficients for interpolating over frequency as determined at the VLA by NRAO staff.
 Finally. we self-calibrated the data for time variations in the relative complex gain phase and amplitude.," Finally, we self-calibrated the data for time variations in the relative complex gain phase and amplitude."
 Polarization calibration was performed by running the AIPS task “LPCAL’ on 3C48 and “CLCOR’ to correct: for the instrumental XY phase offset., Polarization calibration was performed by running the AIPS task 'LPCAL' on 3C48 and 'CLCOR' to correct for the instrumental XY phase offset.
 Generally. we followed the scheme for data reduction of WSRT data in AIPS as outlined by Robert Braun'.. although we ran some ALPS tasks differently depending on frequency.," Generally, we followed the scheme for data reduction of WSRT data in AIPS as outlined by Robert Braun, although we ran some AIPS tasks differently depending on frequency."
 Those differences mainly involved the details of polarization calibration., Those differences mainly involved the details of polarization calibration.
" For instance. the leakage terms (7D terms"") of the WSRT IFs are channel dependent. as pointed out by ?.paragraph3.2.."," For instance, the leakage terms (""D terms"") of the WSRT IFs are channel dependent, as pointed out by \citet[][paragraph 3.2]{Brentjens2008}."
 We took account of this. by first averaging groups of 5 channels through the AIPS task “SPLAT’.," We took account of this, by first averaging groups of 5 channels through the AIPS task 'SPLAT'."
 Next. we ran 'UVCOP' to make separate datasets from the averaged channels.," Next, we ran 'UVCOP' to make separate datasets from the averaged channels."
 After that. we ran LPCAL' and “CLCOR’ on each of these separately before applying the feed and XY instrumental phase offset corrections by again running “SPLAT”.," After that, we ran 'LPCAL' and 'CLCOR' on each of these separately before applying the feed and XY instrumental phase offset corrections by again running 'SPLAT'."
" Before imaging Stokes Q and Stokes U and before merging the datasets from 5 channel averaging back together through ""DBCON'. we applied a ParselTongue script for “derotation™ to the residual data. Le. the (u. v) data where all sources except the target were removed. by running the AIPS task ""UVSUB'."," Before imaging Stokes Q and Stokes U and before merging the datasets from 5 channel averaging back together through 'DBCON', we applied a ParselTongue script for ""derotation"" to the residual data, i.e., the (u, v) data where all sources except the target were removed, by running the AIPS task 'UVSUB'."
 The original Aips++ glish script was kindly given to us by G. Berardi: we modified and translated it to a Python/ParselTongue seript on a channel by channel basis., The original Aips++ glish script was kindly given to us by G. Bernardi; we modified and translated it to a Python/ParselTongue script on a channel by channel basis.
" The ""derotation"" of the visibilities is absolutely necessary. since the rotation measure (RM) of SGR 1806-20 is large. 272 rad/ni"" (2)."," The ""derotation"" of the visibilities is absolutely necessary, since the rotation measure (RM) of SGR 1806-20 is large, 272 $\mathrm{rad}/\mathrm{m}^2$ \citep{Gaensler2005a}."
 This means that the polarized signal would vanish if all IFs were imaged simultaneously., This means that the polarized signal would vanish if all IFs were imaged simultaneously.
 For the 350 MHz data. one really needs the derotation of the visibilities to be performed on a channel per channel basis. because the imaging of even one single IF would result in à severly corrupted measurement and underestimate of the fractional ," For the 350 MHz data, one really needs the derotation of the visibilities to be performed on a channel per channel basis, because the imaging of even one single IF would result in a severly corrupted measurement and underestimate of the fractional linear polarization."
The uncertainty in this linear..seepolarization.?)istoolargeRM(10rad//m for accurate polarization angle measurements. especially at frequencies below | GHz.," The uncertainty in this RM \citep[10 $ \mathrm{rad}/ ^2$, is too large for accurate polarization angle measurements, especially at frequencies below 1 GHz."
 For this reason we determined the RM more accurately. by fitting the sin2-RM-;U. spectrum of either Stokes U or Stokes Q to its measured values at the 8 wavelengths .t corresponding to the IFs near 350 MHz and 850 MHz.," For this reason we determined the RM more accurately, by fitting the $\sin{2\cdot \mathrm{RM} \cdot\lambda^2}$ spectrum of either Stokes U or Stokes Q to its measured values at the 8 wavelengths $\lambda$ corresponding to the IFs near 350 MHz and 850 MHz."
 The contribution to this RM from the tonosphere ts naturally included in this fit. at least the part that did not vary during the observation run.," The contribution to this RM from the ionosphere is naturally included in this fit, at least the part that did not vary during the observation run."
" We checked the output of the AIPS task ""TECOR' for any significant variations 1n the ionospheric Faraday rotation during every observing run.", We checked the output of the AIPS task 'TECOR' for any significant variations in the ionospheric Faraday rotation during every observing run.
" The ionospheric Faraday rotation computed by ""TECOR' is considered accurate since it does not use a model for the tonosphere but actual data from the CDDIS archive.", The ionospheric Faraday rotation computed by 'TECOR' is considered accurate since it does not use a model for the ionosphere but actual data from the CDDIS archive.
" We did not apply the ronospheric corrections from ""TECOR' to our data because it implicitly assumes that one has recorded data from circular It should be clear from table 1. that the maximum observing time Is 7.7 h due to the low declination of the source.", We did not apply the ionospheric corrections from 'TECOR' to our data because it implicitly assumes that one has recorded data from circular It should be clear from table \ref{tab:Obs} that the maximum observing time is 7.7 h due to the low declination of the source.
 Hence. the (u.v) coverage Is sparse for all observations. since linear arrays like the WSRT ideally have 12h runs.," Hence, the (u,v) coverage is sparse for all observations, since linear arrays like the WSRT ideally have 12h runs."
 The worst coverage was at three epochs when we alternated between three frequencies., The worst coverage was at three epochs when we alternated between three frequencies.
 The 350 MHz observations were performed on January 4. 7. 10. 16. 20. 23 and 29 and April 30/May | of 2005.," The 350 MHz observations were performed on January 4, 7, 10, 16, 20, 23 and 29 and April 30/May 1 of 2005."
 The last observation was made to make an accurate subtraction of background sources possible., The last observation was made to make an accurate subtraction of background sources possible.
 This mainly concerns the subtraction of the Luminous Blue Variable discussed in Supplementary Table | of ?.., This mainly concerns the subtraction of the Luminous Blue Variable discussed in Supplementary Table 1 of \citet{Gaensler2005a}.
 The time resolution of all observations. except the first and the last was 30s.," The time resolution of all observations, except the first and the last was 30s."
 On January 4 and April 30/May 1 the sampling times of the visibilities was 60s., On January 4 and April 30/May 1 the sampling times of the visibilities was 60s.
 The bandwidth per IF was 10 MHz. separated 8.75 MHz from each other and centered on frequencies of 315.00. 323.75. 332.50. 341.25. 350.00. 358.75. 367.50 and 376.25 MHz.," The bandwidth per IF was 10 MHz, separated 8.75 MHz from each other and centered on frequencies of 315.00, 323.75, 332.50, 341.25, 350.00, 358.75, 367.50 and 376.25 MHz."
 The IFs were split into 64 channels. each 156.25 kHz wide. except for the April 30/May | observation.," The IFs were split into 64 channels, each 156.25 kHz wide, except for the April 30/May 1 observation."
 For that observation. the IFs were split into 128 channels. each 78.125 kHz wide.," For that observation, the IFs were split into 128 channels, each 78.125 kHz wide."
 We used an automated flagger for the initial editing of our data: WSRTflagger-., We used an automated flagger for the initial editing of our data: WSRT.
. 3C286 was included in the external gain calibration. along with 3C48.," 3C286 was included in the external gain calibration, along with 3C48."
 This was trivial. since 3C286 is unpolarized at this frequency.," This was trivial, since 3C286 is unpolarized at this frequency."
 The assumed fluxes for 3C48 and 3C286 in the lowest frequency IF were 43.889 and 26.106 Jy. respectively.," The assumed fluxes for 3C48 and 3C286 in the lowest frequency IF were 43.889 and 26.106 Jy, respectively."
 The April 30/May | observation has the best (u.v) coverage.," The April 30/May 1 observation has the best (u,v) coverage."
 After performing 10 iterations of self calibration οἱ this dataset the rms noise in the final image was 2.5mJy/beam., After performing 10 iterations of self calibration on this dataset the rms noise in the final image was $2.5 \mathrm{mJy/beam}$.
 Its clean components were used to solve for the gain phases and amplitudes of the other datasets using a rather sophisticatec scheme., Its clean components were used to solve for the gain phases and amplitudes of the other datasets using a rather sophisticated scheme.
" First. a deconvolution of each of the 2005 January datasets was done in order to subtract the central regio containing the radio nebula and the LBV. using the AIPS tasks ""IMAGR'. CCEDT' and ""UVSUB'."," First, a deconvolution of each of the 2005 January datasets was done in order to subtract the central region containing the radio nebula and the LBV, using the AIPS tasks 'IMAGR', 'CCEDT' and 'UVSUB'."
 The residual data were calibrated on the April 30/May |] model which had the clear components from the central region removed., The residual data were calibrated on the April 30/May 1 model which had the clean components from the central region removed.
 The gain phase and amplitude solutions were then copied and applied to the original 2005 January datasets., The gain phase and amplitude solutions were then copied and applied to the original 2005 January datasets.
 It this way we made sure that the Stokes I flux from SGR 1806-20 would not be reduced by, It this way we made sure that the Stokes I flux from SGR 1806-20 would not be reduced by
clliciently clears the galaxy of gas.,efficiently clears the galaxy of gas.
 Pwo types of outllows are assumed: a) A well-mixed one in which galaxies eject all eas present to the intergalactic medium via a galactic winel. for galaxies characterized. by. a single episode of star formation (burst galaxies) or via two galactic winds. for those showing also a secondary episode (complex. galaxies). respectively.," Two types of outflows are assumed: a) A well-mixed one in which galaxies eject all gas present to the intergalactic medium via a galactic wind, for galaxies characterized by a single episode of star formation (burst galaxies) or via two galactic winds, for those showing also a secondary episode (complex galaxies), respectively."
 b) X metal-rich one. where a fraction + of the mass of à SN (LL. Ib. or la) is ejected to the intergalactio medium without mixing with the ambient interstellar gas 3) The star formation rate. V. is proportional to that inferred by ΗΝ. The proportional constant is denoted. by v.," b) A metal-rich one, where a fraction $\gamma$ of the mass of a SN (II, Ib, or Ia) is ejected to the intergalactic medium without mixing with the ambient interstellar gas 3) The star formation rate, $\Psi$, is proportional to that inferred by HGV, The proportional constant is denoted by $\nu$ ."
 Values of v distinct from unity were explored. to test the dependence of our results with respect to uncertainties in the total luminosities and IAL of the objects. studied. which determine the normalization on S£Igea.," Values of $\nu$ distinct from unity were explored to test the dependence of our results with respect to uncertainties in the total luminosities and IMF of the objects studied, which determine the normalization on $SFR_{HGV}$."
 ) The initial mass function. d. is that of Ixroupa. Tout Gilmore (1993). between 0.08 and 120AL.," 4) The initial mass function, $\Phi$, is that of Kroupa, Tout Gilmore (1993), between 0.08 and 120."
.. Shape and mass range are identical to those adopted by HGV., Shape and mass range are identical to those adopted by HGV.
 5) We adopted metallicity dependent stellar properties in a code without any instantaneous recycling approximation. with ΤΠ) being the lifetime of stars. as à function of their mass ancl metallicityv.," 5) We adopted metallicity dependent stellar properties in a code without any instantaneous recycling approximation, with $\tau_{s}(m)$ being the lifetime of stars, as a function of their mass and metallicity."
 Specifically. vields and remnant masses are taken from Alaeder (1992). for 9—mM.<120. and from Renzini Voli (1981). for ]Xm/M.<δ with stellar winds contributing to the vields.," Specifically, yields and remnant masses are taken from Maeder (1992) for $9 \leq m/\msun \leq 120$, and from Renzini Voli (1981) for $1 \leq m/\msun \leq 8$, with stellar winds contributing to the yields."
 We assumed three types of SN: Ia. Ib. and IH.," 6) We assumed three types of SN: Ia, Ib, and II."
 The supernovae rates are computed as described in C'arigi (1994)., The supernovae rates are computed as described in Carigi (1994).
 In this work the fraction of binary systems. predecessors of SNla is assumed. as uu=0407 and SNIb produced. by binary systems are not considered (Carigi 2000)., In this work the fraction of binary systems predecessors of SNIa is assumed as $A_{bin}=0.07$ and SNIb produced by binary systems are not considered (Carigi 2000).
 We define rgegg as the thermal energy of the gas from. supernovae. where c(£) is the evolution of the thermal energy in the hot. dilute interior of the supernovae remnants.," We define $E_{THER}$ as the thermal energy of the gas from supernovae, where $\epsilon(t)$ is the evolution of the thermal energy in the hot, dilute interior of the supernovae remnants."
 where ey= erg and feo is à cooling time scale taken from Cox(1972)., where $\epsilon_0=10^{51}$ erg and $t_C$ is a cooling time scale taken from Cox (1972).
un The above timescale wasderived for solar metallicities. a more complete treatment of the cooling processes in the expanding SN shell is given in e.g. Tantalo et al. (," The above timescale was derived for solar metallicities, a more complete treatment of the cooling processes in the expanding SN shell is given in e.g. Tantalo et al. ("
1998).,1998).
 In that work the cooling timescale we used here is compared to more detailed. metallicity. dependent ones., In that work the cooling timescale we used here is compared to more detailed metallicity dependent ones.
 These cooling timescales basically give the time it. takes for the energy of the supernova to be thermalized by the surrounding inter stellar medium., These cooling timescales basically give the time it takes for the energy of the supernova to be thermalized by the surrounding inter stellar medium.
" The detailed. timescales vary from about 2104 vears for solar metallicities. to about 2«LO"" vears for metallicities in the range of what is founcl in dSph galaxies."," The detailed timescales vary from about $2 \times 10^4$ years for solar metallicities, to about $2 \times 10^5$ years for metallicities in the range of what is found in dSph galaxies."
 It is clear that since the timescales for star formation are of the order of Gyrs. whether cach supernova completes its heating processes in 21U or 2210 is irrelevant to the problem.," It is clear that since the timescales for star formation are of the order of Gyrs, whether each supernova completes its heating processes in $2 \times 10^4$ or $2 \times 10^5$ is irrelevant to the problem."
 We did in fact run a few models with the complicated metallicity dependent scheme of the above authors and found it mace no dillerence for our particular. problem., We did in fact run a few models with the complicated metallicity dependent scheme of the above authors and found it made no difference for our particular problem.
 For simplicity we used the time scale from Cox (1972) throughout., For simplicity we used the time scale from Cox (1972) throughout.
 RSND) is the supernovae rate. and. includes. SNla. SNIb. and SNIL," $RSN(T)$ is the supernovae rate, and includes SNIa, SNIb, and SNII."
 SNla originate from € cellagrations in a C-O white cwarl forming a binary svstem with a red giant star. we compute type L supernovae rates following Ciregeio v Renzini (1983): where m; is the mass of the most massive star in the main sequence from the first stellar generation. mo is the mass of secondary star. mg is the binary svstem mass and fGnas) is the binary mass distribution function. SNib originate from. W-R. stars. ancl since the lower mass limit for W-It star progenitors (frye) depends on the stellar metallicity (Maeder 1992) then. where SNIL arise from the core collapse of massive single stars between 7.5 and πω. therefore where. In -- the resulting SET of a model to match the inferences of LGV some details must. be. noted.," SNIa originate from C deflagrations in a C-O white dwarf forming a binary system with a red giant star, we compute type I supernovae rates following Greggio y Renzini (1983): where $m_t$ is the mass of the most massive star in the main sequence from the first stellar generation, $m_2$ is the mass of secondary star, $m_B$ is the binary system mass and $f(m_2)$ is the binary mass distribution function, SNIb originate from W-R stars, and since the lower mass limit for W-R star progenitors $lim_{WR}$ ) depends on the stellar metallicity (Maeder 1992) then, where SNII arise from the core collapse of massive single stars between 7.5 and $lim_{WR}$, therefore where, In forcing the resulting SFR(t) of a model to match the inferences of HGV some details must be noted."
 The method. used by these authors vields results which are subject to a time varving error. which due to the decreasing separation ofstellar isochrones with increasing age. compounded by the increasing observational errors with increasing magnitude. ( and hence towards the turnoll of," The method used by these authors yields results which are subject to a time varying error, which due to the decreasing separation ofstellar isochrones with increasing age, compounded by the increasing observational errors with increasing magnitude, ( and hence towards the turnoff of"
(Ellingson&HHampson2003.. Jeff et al.2005.. Kesteven2007.. Cornwell et al.2004)),"\cite{ellingson}, Jeff et \cite{jeff}, \cite{kesteven}, , Cornwell et \cite{corn}) )."
 Narrow-band RFI can be detected as an impulse-like outlier in the frequency domain., Narrow-band RFI can be detected as an impulse-like outlier in the frequency domain.
 The following example illustrates the application of trimming (8) in this case., The following example illustrates the application of trimming (8) in this case.
 RFI is generated as à phase-modulated sinusoidal carrier. see Fig.," RFI is generated as a phase-modulated sinusoidal carrier, see Fig."
 5., 5.
 The power spectrum of the unmodulated carrier is shown in the upper panel and in the lower panel. the power spectrum of the randomly phase-modulated signal ts represented: where rect() is a rectangular wave with Poisson’s law distributed random Jumps from -- to +1. and the parameter of Poisson distribution .t=0.01.," The power spectrum of the unmodulated carrier is shown in the upper panel and in the lower panel, the power spectrum of the randomly phase-modulated signal is represented: where $rect(i)$ is a rectangular wave with Poisson's law distributed random jumps from $-1$ to $+1$ , and the parameter of Poisson distribution $\lambda=0.01$."
 The mixture of two input signals and their power spectra are represented in Fig., The mixture of two input signals and their power spectra are represented in Fig.
 6., 6.
" The amplitudes Al,;;=A2,;;0.5 and frequencies Fl=0.3 and F2=0.4.", The amplitudes $A1_{rfi}=A2_{rfi}=0.5$ and frequencies $F1=0.3$ and $F2=0.4$.
 Therefore. RFI is not visible in the temporal domain but is easily visible in the spectral domain after FFT with 2=2048 as two bursts.," Therefore, RFI is not visible in the temporal domain but is easily visible in the spectral domain after FFT with $n=2048$ as two bursts."
 The statistics of the power spectra are analyzed following(8) and the indexes of outliers exceeding the level equal to the 1.5%—percentile are used to reject the samples of the complex spectra of signals X and Y. where (.) denotes the Fourier transform.," The statistics of the power spectra are analyzed following(8) and the indexes of outliers exceeding the level equal to the $1.5\%-$ percentile are used to reject the samples of the complex spectra of signals $\widetilde{x}$ and $\widetilde{y}$, where $\widetilde{(.)}$ denotes the Fourier transform."
 These indexes are tagged with the indicator function ind(i) taking the numbers 0 or I. i=|. and assigned to the sequence of n samples of the complexspectra X and v.," These indexes are tagged with the indicator function $ind(i)$ taking the numbers 0 or 1, $i=1..n$ and assigned to the sequence of n samples of the complexspectra $\widetilde{x}$ and $\widetilde{y}$ ."
" The 7sum-difference"" correlator (7) is used in the spectral domain (FX-correlator):", The “sum-difference” correlator (7) is used in the spectral domain (FX-correlator):
"Comparing the Offset and Toe-in stereo pairs first, one notices that, as expected, the double sphere structure appears to hover over the axes (located further away) in the former ones.","Comparing the Offset and Toe-in stereo pairs first, one notices that, as expected, the double sphere structure appears to hover over the axes (located further away) in the former ones."
" This a direct consequence of our simplistic implementation of the Offset method - it is accurate for the data points, but not for the background axes."," This a direct consequence of our simplistic implementation of the Offset method - it is accurate for the data points, but not for the background axes."
" Nonetheless, focusing on the double-sphere structure itself, it has noticeably less depth elongation in the case of the Offset method."," Nonetheless, focusing on the double-sphere structure itself, it has noticeably less depth elongation in the case of the Offset method."
" In the Toe-in stereo pairs, not only do the axes wrap around the data points nicely, but the data points themselves appear with a strong feeling of depth."," In the Toe-in stereo pairs, not only do the axes wrap around the data points nicely, but the data points themselves appear with a strong feeling of depth."
" In that sense, we believe the Toe-in method to be much more appropriate for the publication of Astrophysical data cubes, as it provides more depth structure to the data itself."," In that sense, we believe the Toe-in method to be much more appropriate for the publication of Astrophysical data cubes, as it provides more depth structure to the data itself."
" Comparing the sTi stereo pairs with their equivalent Toe-in pairs, it can be seen that depth perception within the sTi image is gradually degraded as the elevation increases."," Comparing the sTi stereo pairs with their equivalent Toe-in pairs, it can be seen that depth perception within the sTi image is gradually degraded as the elevation increases."
" As mentioned above, this is due to the fact that the LHS and RHS sTi projection viewpoints gradually move towards each other at higher elevation."," As mentioned above, this is due to the fact that the LHS and RHS sTi projection viewpoints gradually move towards each other at higher elevation."
" Nonetheless, some degree of depth perception is present, even as high as 09—80?."," Nonetheless, some degree of depth perception is present, even as high as $\theta_0=80^{\circ}$."
" The different orientation of the LHS and RHS images are also staying small, and hence do not need to be corrected by any modification of the source code."," The different orientation of the LHS and RHS images are also staying small, and hence do not need to be corrected by any modification of the source code."
" In summary, our suggested sTi plotting method, if theoretically not correct, nevertheless appears in practice to provide (very) satisfactory results, and can be directly implemented usingPYTHON,, andMPLOTSD."," In summary, our suggested sTi plotting method, if theoretically not correct, nevertheless appears in practice to provide (very) satisfactory results, and can be directly implemented using, and."
. The experienced Python user might find it easy to update his source code to create correct Toe-in stereo pairs., The experienced Python user might find it easy to update his source code to create correct Toe-in stereo pairs.
 We intend to include our code update in future releases ofMATPLOTLIB.., We intend to include our code update in future releases of.
" Until we manage to do so, we are happy to provide our source code modifications to the interested user directly (which does not require extensive knowledge of"," Until we manage to do so, we are happy to provide our source code modifications to the interested user directly (which does not require extensive knowledge of"
" perturbations asymmetry (Goldreichisothermality.&Tremaine1979;Wardanalytical1997;predictiorTanaka (Nelsoretal.m2000;LindbladD'Angeloct2002;BateSimulationsοἱposifiv2003)), planet migrates 10* 10? (10°-10/timescales 2009)) have to assume a reduction factor for Type I migration of 30-1000 in order to match the observed distribution of planetary semimajor axes."," \citealp{Goldreich,Ward,Tanaka}) \citealp{Nelson,D'Angelo,Bate}) $\ttimes{4}$ $\ttimes{5}$ $\ttimes{6}$ $\ttimes{7}$ ) have to assume a reduction factor for Type I migration of 30–1000 in order to match the observed distribution of planetary semimajor axes."
 &Mellema(2006) made a major step towardPaardekooper the solution of this , \citet{Paardekooper06} made a major step toward the solution of this problem.
"They found that when the locally isothermalproblem. approximation usually assumed in the literature was relaxed, the plancts migratedBaruteau outwards."," They found that when the locally isothermal approximation usually assumed in the literature was relaxed, the planets migrated outwards."
 This behavior was explained by &Massct(2008) and &Pa-paloizou(2008) as resulting fromPaardekooper an entropy-related exerted by material on horseshoe orbits in the corotationtorque region., This behavior was explained by \citet{Baruteau} and \citet{Paardekooper08} as resulting from an entropy-related torque exerted by material on horseshoe orbits in the corotation region.
"that This mechanism operateswradient in regions of the disk have a negative entropy g and inefficient radiative cooling, where sustenance of the some viscous and thermal diffusior (Paardekoopertorquer"," This mechanism operates in regions of the disk that have a negative entropy gradient and inefficient radiative cooling, where sustenance of the torque requires some viscous and thermal diffusion \citealp{Paardekooper08}) )."
equires& 2008). &Crida(2008) and Kleveteeal.(2009) showed Kleythat outward migration indeed occurs in disks with realistic heating and This cooling., \citet{Kley08} and \citet{Kley09} showed that outward migration indeed occurs in disks with realistic heating and cooling.
outward migration remains rapid., This outward migration remains rapid.
" Planets migrate toward the outer disk, reach an equilibrium radius of zero torque, and stay pt thereafter."," Planets migrate toward the outer disk, reach an equilibrium radius of zero torque, and stay put thereafter."
" As byPaardekoopercttal.(2010),, slow inward migratior emphasizedthen occurs as disk evolution shifts the equilibrium radius inwards."," As emphasized by \citet{Paardekooper10}, slow inward migration then occurs as disk evolution shifts the equilibrium radius inwards."
" The situation becomes similar to that of gap-opening (Type Il with the planct migrating in planetslockstep with the as migration),the accretes."," The situation becomes similar to that of gap-opening planets (Type II migration), with the planet migrating in lockstep with the gas as the gas accretes."
 This gasscenario gasposes a subtle problem that we examine in this Letter., This scenario poses a subtle problem that we examine in this Letter.
" If the planet is moving with the gas as the disk at some point in the togetherevolution the disk may reach a depletes,thermodynamic state such that inward migration resumes."," If the planet is moving together with the gas as the disk depletes, at some point in the evolution the disk may reach a thermodynamic state such that inward migration resumes."
" This brings the problem back to square one, because, if the isi to survive, the disk lifetime must be planetshorter than the Type I remainingmigration timescale in that evolutionary state."," This brings the problem back to square one, because, if the planet is to survive, the remaining disk lifetime must be shorter than the Type I migration timescale in that evolutionary state."
 We examine this possibility using onc--dimensional evolutionary models of protoplanetary disks including and, We examine this possibility using one-dimensional evolutionary models of protoplanetary disks including heating andcooling.
" We describe the model in the heatingfollowing section, cooling.present our results in 3, and give"," We describe the model in the following section, present our results in 3, and give"
Galaxy formation involves α wide range of cliverse physical processes operating on stellar το cosmological scales. including the hierarchical growth of structure. star ormation. black hole accretion. and a plethora of poorly-understood. feedback. processes. that strongly modulate galaxy growth.,"Galaxy formation involves a wide range of diverse physical processes operating on stellar to cosmological scales, including the hierarchical growth of structure, star formation, black hole accretion, and a plethora of poorly-understood feedback processes that strongly modulate galaxy growth."
 Civen this complexity. it ds. surprising hat galaxies cisplay simple and tight scaling. relations »tween many of their key constituents.," Given this complexity, it is surprising that galaxies display simple and tight scaling relations between many of their key constituents."
 These include well-established: relations between the bulge velocity dispersion and central black hole mass2011).. circular. velocity ancl luminosity1977).. star formation rate and stellar massthercin).. and metallicity and stellar mass2006).," These include well-established relations between the bulge velocity dispersion and central black hole mass, circular velocity and luminosity, star formation rate and stellar mass, and metallicity and stellar mass."
. Each has low scatter and evolves roughly independently of mass., Each has low scatter and evolves roughly independently of mass.
 The simplicity of these relations hints at an underlving uniformity in galaxy evolution that is not immediately evident from the complexity of current hierarchical galaxy formation moclels., The simplicity of these relations hints at an underlying uniformity in galaxy evolution that is not immediately evident from the complexity of current hierarchical galaxy formation models.
 In the longstandinge canonical scenario [or Ingalaxy formation. 5galaxies form as angular5 momentum-conseryine5 disks cooling from hot eas bound within dark matter halos. and these disks. subsequently. merge to form. larger and earlier-tvpe galaxies1998).," In the longstanding canonical scenario for galaxy formation, galaxies form as angular momentum-conserving disks cooling from hot gas bound within dark matter halos, and these disks subsequently merge to form larger and earlier-type galaxies."
. This scenario is well-situated within currently favored ucrarchical cosmologies. and analytic models based. on it mve been quite successful at reproducing many observed! galaxy properties2010).," This scenario is well-situated within currently favored hierarchical cosmologies, and analytic models based on it have been quite successful at reproducing many observed galaxy properties."
. However. he present generation of such models (often called: 7semi-analytic” models) are typically enormously. complex. with a host of free parameters. describing various interrelated ohvsical phenomena.," However, the present generation of such models (often called ``semi-analytic"" models) are typically enormously complex, with a host of free parameters describing various interrelated physical phenomena."
" Numerical simulations that explicitly rack eas cdvnamical processes enable a more ab initio calculation. but still require many ""sSub-grid parameters or key physical processes ancl are in practice limited. by dvnanüe range and numerical uncertainties."," Numerical simulations that explicitly track gas dynamical processes enable a more ab initio calculation, but still require many “sub-grid"" parameters for key physical processes and are in practice limited by dynamic range and numerical uncertainties."
 In either case. he complexity of such models makes it dillicult to extract simple physical intuition for what drives the evolution of xwic galaxy properties.," In either case, the complexity of such models makes it difficult to extract simple physical intuition for what drives the evolution of basic galaxy properties."
 In this paper. we present an analytic framework or understanding the evolution of the stellar. gas. and metal content of galaxies.," In this paper, we present an analytic framework for understanding the evolution of the stellar, gas, and metal content of galaxies."
 This framework is based on intuition gained from hvdrodynamic simulations of galaxy ormation., This framework is based on intuition gained from hydrodynamic simulations of galaxy formation.
 In. such models. galaxies are fed. primarily by cold (~107 IX) streams connecting to filamentary large-scale structure2009).. outllows are strong and ubiquitous2008).. and outllowing material commonly returns (o galaxies2010).," In such models, galaxies are fed primarily by cold $\sim 10^4$ K) streams connecting to filamentary large-scale structure, outflows are strong and ubiquitous, and outflowing material commonly returns to galaxies."
. Llence in this framework. galaxy evolution is," Hence in this framework, galaxy evolution is"
Observations with the satellite have shown that the phase of prompt-to-afterglow transition is characterized by a very interesting phenomenology.,Observations with the satellite have shown that the phase of prompt-to-afterglow transition is characterized by a very interesting phenomenology.
 Typically the tail of the prompt emission. described by a very steep power law segment (temporal decay index 6~3— 5). is followed hundreds to thousands of seconds later by a flat power law segment (0~ 0.5). and then around tens of thousands of seconds later by the usual afterglow power law emission (0.~ 1.3).," Typically the tail of the prompt emission, described by a very steep power law segment (temporal decay index $\delta \sim 3-5$ ), is followed hundreds to thousands of seconds later by a flat power law segment $\delta \sim~0.5$ ), and then around tens of thousands of seconds later by the usual afterglow power law emission $\delta \sim 1.3$ )."
 Sometimes there is a third break where the afterglow light curve steepens to a power law 0~2 (Nouseketal.2006:Zhangetal. 2006).," Sometimes there is a third break where the afterglow light curve steepens to a power law $\delta \sim 2$ \citep{nousek06,zhang05}."
 It has been observed that the tail of the prompt emission. as well as the flat power law phase and the third segment are characterized by the presence of flares (Chincarinietal.2007:Falcone2007).," It has been observed that the tail of the prompt emission, as well as the flat power law phase and the third segment are characterized by the presence of flares \citep{chinca07,falcone07}."
. Flares appearing hundreds of seconds after the burst were observed for the first time by BeppoSAX in a few events (e.gGRBOII121..GRBOI1211.. 2006).," Flares appearing hundreds of seconds after the burst were observed for the first time by BeppoSAX in a few events \citep[e.g \object{GRB011121}, ."
 LaterSwifr.. thanks to its fast re-pointing capabilities. found that flares are a very common phenomenon in GRBs. as they are detectable in ~30—40% of its bursts sample (O'Brienetal.2006).," Later, thanks to its fast re-pointing capabilities, found that flares are a very common phenomenon in GRBs, as they are detectable in $\sim 30-40 \%$ of its bursts sample \citep{obrien06}."
". Moreover flares are present both in long and short GRBs (e.g.GRBO50724..2005). in classical long GRB. X-ray rich (ARR) and X-ray flash (XRF) (e.g.σιXRF050406..2006). and in low redshift (e.g.""GRBO050803.. and high redshift (e.g.GRBOSO904.. events."," Moreover flares are present both in long and short GRBs \citep[e.g. \object{GRB050724}, in classical long GRB, X-ray rich (XRR) and X-ray flash (XRF) \citep[e.g. \object{XRF050406}, and in low redshift \citep[e.g. \object{GRB050803}, and high redshift \citep[e.g. \object{GRB050904}, events."
 Several bursts show multiple flares in their X-ray light curves (e.g.GRBOSO607 and while others have only one big flare (seee.g.GRBOQ60526.Chincarinietal.2006).," Several bursts show multiple flares in their X-ray light curves \citep[e.g. \object{GRB050607} and while others have only one big flare \citep[see e.g. GRB060526,][]{chincarini06}."
 The flare phenomenon is complex. and despite the large number of ideas put forward in literature to explain its origin. no model has completely interpreted the phenomenology of observed flares.," The flare phenomenon is complex, and despite the large number of ideas put forward in literature to explain its origin, no model has completely interpreted the phenomenology of observed flares."
 The most important difference between models is the duration of central engine activity: some of them require a long-lived central engine. e.g. models involving late internal shocks (LIS) (Burrowsetal.2005:Wu2006) and delayed external shocks (DES) (Piroetal.2005:Galli&Piro2006.2007) produced by a long duration and/or re-activation of the activity of the engine. while others do not require a long duration central engine activity. e.g. models involving LIS from à short duration central engine (Zhang2006).. refreshed shocks (Rees&Meszaros1998;KumarPiran.2000a).. two components jet (Meszaros&Rees2001:Lipunovetal... 2001).. patchy jet (Kumar&Piran.|2000b).. forward shock (FS)-reverse shock (RS) (Fan&Wei2005).. external shock (ES) with a clumpy medium (Dermer&Mit-man1999;Dermer2007) and delayed magnetie dissipation in strongly magnetized ejecta caused by external shock (Giannios2000).," The most important difference between models is the duration of central engine activity: some of them require a long-lived central engine, e.g. models involving late internal shocks (LIS) \citep{burrows05,wu05} and delayed external shocks (DES) \citep{piro05,galli06,galli07} produced by a long duration and/or re-activation of the activity of the engine, while others do not require a long duration central engine activity, e.g. models involving LIS from a short duration central engine \citep{zhang05,wu05}, refreshed shocks \citep{rees98,kumar00refresh}, two components jet \citep{meszaros01,lipunov01}, patchy jet \citep{kumar00}, forward shock (FS)-reverse shock (RS) \citep{fan05}, external shock (ES) with a clumpy medium \citep{dermer00,dermer07} and delayed magnetic dissipation in strongly magnetized ejecta caused by external shock \citep{giannios06}."
. A temporal and spectral analysis of the first survey of X-ray flares observed by has recently been carried out (Chinearinietal.2007:Falcone2007).," A temporal and spectral analysis of the first survey of X-ray flares observed by has recently been carried out \citep[][]{chinca07,falcone07}."
. These authors analyzed the first 110 bursts observed by and found that 33 GRBs have significant flares in their X-ray light curves. for a total of ~70 flares.," These authors analyzed the first 110 bursts observed by and found that 33 GRBs have significant flares in their X-ray light curves, for a total of $\sim 70$ flares."
 The temporal analysis revealed that there Is à positive correlation between the time of flare appearance and its duration. and that flares can be very energetic in comparison with the underlying afterglow emission.," The temporal analysis revealed that there is a positive correlation between the time of flare appearance and its duration, and that flares can be very energetic in comparison with the underlying afterglow emission."
 Chincarinietal.(2007) find that a correlation exists between the ratio of intensity of successive prompt y-ray pulses and that between successive X-ray flares in the same burst., \citet{chinca07} find that a correlation exists between the ratio of intensity of successive prompt $\gamma$ -ray pulses and that between successive X-ray flares in the same burst.
 This is an indication that they may be caused by the same mechanism., This is an indication that they may be caused by the same mechanism.
 Falconeetal.(2007) used several spectral models to fit each flare., \citet{falcone07} used several spectral models to fit each flare.
 Usually flares can be fitted both by a simple absorbed power law or by a Band model (Bandetal.1993)., Usually flares can be fitted both by a simple absorbed power law or by a Band model \citep{band93}.
. Some flares have a soft spectrum consistent with that of the afterglow emission (e.g.GRB050712.. 2006). however the majority present a hard-to-soft spectral evolution.," Some flares have a soft spectrum consistent with that of the afterglow emission \citep[e.g. \object{GRB050712}, however the majority present a hard-to-soft spectral evolution."
 A spectral evolution of the order of 0.5-1.0 (depending on the index of the electron population) can be explained in the context of the ES if the typical emission frequency is crossing the observational band. and models such as DES (Galli&Piro2006.2007).. ES on a clumpy medium (Dermer2007) or refreshed shocks (Guettaetal.2007) can be applied to some flares of the sample.," A spectral evolution of the order of 0.5-1.0 (depending on the index of the electron population) can be explained in the context of the ES if the typical emission frequency is crossing the observational band, and models such as DES \citep{galli06,galli07}, ES on a clumpy medium \citep{dermer07} or refreshed shocks \citep{guetta07} can be applied to some flares of the sample."
 However according to the studies performed by Chincarinietal.(2007) and Falconeetal.(2007).. a large fraction of flares could be explained by LIS produced by a long duration central engine.," However according to the studies performed by \citet{chinca07} and \citet{falcone07}, a large fraction of flares could be explained by LIS produced by a long duration central engine."
 In this paper we focus on the possibility that flares are produced by LIS and study the high energy emission from flares in this scenario., In this paper we focus on the possibility that flares are produced by LIS and study the high energy emission from flares in this scenario.
 We plan to extend our study to other, We plan to extend our study to other
deviations to be detected in future IR source power spectra. in particular with /SPIRE data. which will vield higher quality data than BLAST out to sualler scales with its improved angular resolution.,"deviations to be detected in future IR source power spectra, in particular with /SPIRE data, which will yield higher quality data than BLAST out to smaller scales with its improved angular resolution."
 The correlation function of resolved sub-nuni sources provides conrplenientary information to the power spectra of unresolved sources cousidered in this work., The correlation function of resolved sub-mm sources provides complementary information to the power spectra of unresolved sources considered in this work.
 Current data is lanited: measure FE with ~2. correspouding to .XsU)ὃν for low-redshitt (2< 0.5) Mersehel--ATLAS ealaxies. although their result is consistent with ours within errors.," Current data is limited; measure $\xi(r)\propto r^{-\gamma}$ with $\gamma\sim2$, corresponding to $C_{\ell}^{\rm clust}\propto\ell^{-1}$, for low-redshift $z<0.5$ ) -ATLAS galaxies, although their result is consistent with ours within errors."
 The full THerschel--ATLAS survey will cover 30 times more skv aud provide far tighter constraints., The full -ATLAS survey will cover 30 times more sky and provide far tighter constraints.
 Discrepancies between the (ποτ and £(r) or «(0) measurements would indicate differences iu clustering properties of the bright sub-nunu galaxies compared to the füuter population. aud thus both statistics are imuportant for constraining models of galaxy clusteriug aud evolution.," Discrepancies between the $C_{\ell}^{\rm clust}$ and $\xi(r)$ or $w(\theta)$ measurements would indicate differences in clustering properties of the bright sub-mm galaxies compared to the fainter population, and thus both statistics are important for constraining models of galaxy clustering and evolution."
2ex This work was supported by the U.S. National Science Foundation through awards AST-0108608. for the ACT project. and PIIY-0355328.. AST-0707731 and PIRE-0507768.," This work was supported by the U.S. National Science Foundation through awards AST-0408698 for the ACT project, and PHY-0355328, AST-0707731 and PIRE-0507768."
 GÀ is supported by an STFC studentship and funding was also provided by Princetou University aud the Universtv of Penusvivania. ROU Fellowship (JD). ERC eraut. 259505 (JD) aud NASA evant NNNOSATIBNG (ΑΠ.," GA is supported by an STFC studentship and funding was also provided by Princeton University and the University of Pennsylvania, RCUK Fellowship (JD), ERC grant 259505 (JD) and NASA grant NNX08AH30G (AH)."
 ACT. operates in the Chajuautor Science Preserve in northern Chile uncer the auspices of the Comisidun Nacional de Inuvestigacióun Cientifica y Tecnológeica (CONICYT)., ACT operates in the Chajnantor Science Preserve in northern Chile under the auspices of the Comisiónn Nacional de Investigaciónn Científfica y Tecnológgica (CONICYT).
 Data acquisition electronics were developed with assistance from the Canada Foundation for Iunovation., Data acquisition electronics were developed with assistance from the Canada Foundation for Innovation.
 We thank Matthieu Déttheruuu for discussions about the Bll IR model. Olivier Doré.. Corilaine Lagache aud Bill Jones for discussions about the data. Joaquin Vieira. for information about SPT filters. and Caclen Marsden. Druce Partridge and George Efstathiou for helpful sugecstious.," We thank Matthieu Bétthermin for discussions about the B11 IR model, Olivier Doré,, Guilaine Lagache and Bill Jones for discussions about the data, Joaquin Vieira for information about SPT filters, and Gaelen Marsden, Bruce Partridge and George Efstathiou for helpful suggestions."
2 voars bascline.,2 years baseline.
 Then the probability for such a star to nunica curve is extremely siuall., Then the probability for such a star to mimic a curve is extremely small.
 This leaves eieht candidates. four of which are discussed below.," This leaves eight candidates, four of which are discussed below."
 Of the other four events. one ds sueecstive of a binary leus and will be the subject of further analysis.," Of the other four events, one is suggestive of a binary lens and will be the subject of further analysis."
 Another shows sole asvuuuectric correlations among the residuals of the ft aud is suspected to be due to a variable star rather than a iicrolensing effect., Another shows some asymmetric correlations among the residuals of the fit and is suspected to be due to a variable star rather than a microlensing effect.
 The two remaimine events are not convincing microlensing candidates because they are too poorly sampled and/or have too noisy a baselime to allow the correlations to be studied., The two remaining events are not convincing microlensing candidates because they are too poorly sampled and/or have too noisy a baseline to allow the correlations to be studied.
 The four candidates are PA-99-N1. PA-99-N2. PA-00-83 and PA-00-SL.," The four candidates are PA-99-N1, PA-99-N2, PA-00-S3 and PA-00-S4."
 The letter N(S) indicates whether the event lies in the north(south) ENT WEC field. the first number 99(00) eives the vear m which the maxima occurs and the second nuuber is assigned sequentially in the order of detection.," The letter N(S) indicates whether the event lies in the north(south) INT WFC field, the first number 99(00) gives the year in which the maximum occurs and the second number is assigned sequentially in the order of detection."
 Candidates PÀ-99-N1 and PA-00-SI have already Όσοι. discussed by. Απο et al. (, Candidates PA-99-N1 and PA-00-S4 have already been discussed by Aurièrre et al. (
2001) aud DPaulin-Henurikssou et al. (,2001) and Paulin-Henriksson et al. (
2002).,2002).
" The statistical relevance of the candidates is estimated the total signal-to-noise ratio S/N of the biups in thei! filter: where op, is the baseline fix eiven by the Paczvuski fit.", The statistical relevance of the candidates is estimated the total signal-to-noise ratio S/N of the bumps in the$r'$ filter: where $\phi_{\rm bl}$ is the baseline flux given by the Paczynski fit.
 The stim is taken over all datapoiuts that lie more than 230 above the baseliue., The sum is taken over all datapoints that lie more than $\sigma$ above the baseline.
 The four candidates have sigual-to-noise ratios of between 60 aud ~1600. that is. hügeli compared to typical events in the database.," The four candidates have signal-to-noise ratios of between $\sim 60$ and $\sim 1600$, that is, high compared to typical events in the database."
 Table l gives the main characteristics of the four candidates. while Figure D shows their lighteurves.," Table \ref{tab:characteristics} gives the main characteristics of the four candidates, while Figure \ref{fig:lightcurves} shows their lightcurves."
 In the following. they are presented in ascending order of distance to the ceutre of ND. as illustrated in5.," In the following, they are presented in ascending order of distance to the centre of M31, as illustrated in."
. PA-00-S3 lies 17007 from the centre of MS. within ie fields observed usine the MDNI-McCiaraw-ITill clescope (Calchi Novati et al.," PA-00-S3 lies $4'00''$ from the centre of M31, within the fields observed using the MDM-McGraw-Hill telescope (Calchi Novati et al."
 2002)., 2002).
 The continuation of the liehteurve in 1998 and 1999 with data from us telescope shows no secondary bump. confirming the uicroleusiug Lypothesis.," The continuation of the lightcurve in 1998 and 1999 with data from this telescope shows no secondary bump, confirming the microlensing hypothesis."
 At this position. bulee-bulege eusius ids expected to dominate (e... Ixerims οἳ al.," At this position, bulge-bulge lensing is expected to dominate (e.g., Kerins et al."
 2001)., 2001).
 The ligh S/N of this eveut. together with the act that the wines of the lishteurve are well sampled. ias enabled a remarkably sood direct estimate of the LEiusteiu crossing time. αν».," The high S/N of this event, together with the fact that the wings of the lightcurve are well sampled, has enabled a remarkably good direct estimate of the Einstein crossing time, ."
 For comparison. we would expect inescales of ~20(AML)? days for nulec-disk leusiug. οLH? days for bulge-bulge chasing or G0(MSAL.. davs for disk-disk leusine.," For comparison, we would expect timescales of $\sim 20 \,(M/M_\odot)^{1/2}\,$ days for bulge-disk lensing, $\sim 30 \,(M/M_\odot)^{1/2}\,$ days for bulge-bulge lensing or $\sim 
60 \,(M/M_\odot)^{1/2}\,$ days for disk-disk lensing."
 The oxoxinitv of PA-00-83 to the bulge. together with its LEimstein crossing time. «ποιος sugeests that it is a low nass stellar Ίος event.," The proximity of PA-00-S3 to the bulge, together with its Einstein crossing time, strongly suggests that it is a low mass stellar lens event."
" DA-99-N1 lies 7/52"" from the centre of M31 aud occurred πι August 1999. at the beginning of the first season of observation."," PA-99-N1 lies $7'52''$ from the centre of M31 and occurred in August 1999, at the beginning of the first season of observation."
 The data wp until November 1999 have already. been preseuted by Aurierre et al. (, The data up until November 1999 have already been presented by Aurièrre et al. (
2001).,2001).
 Since then. the baseline has been extended to January 2001. vielding better constraints on the parameters of the Paczviisski fif (see 13).," Since then, the baseline has been extended to January 2001, yielding better constraints on the parameters of the Paczyǹsski fit (see )."
 This baseline shows two secondarv bunps iu December 19990 and NovemberDecember 2000 but. usine he simple nuage differeuciug procedure explained in2.2.. oue can show that these secondary bumps are separated frou the event bv about (—17). as shown in6.," This baseline shows two secondary bumps in December 1999 and November--December 2000 but, using the simple image differencing procedure explained in, one can show that these secondary bumps are separated from the event by about $\sim 1''$ ), as shown in."
. Therefore. the existence of these secondary bunips is no reason to reject PA-99-N1. and data »)uts belongiug to secoudarv bunrps are masked for further analysis.," Therefore, the existence of these secondary bumps is no reason to reject PA-99-N1, and data points belonging to secondary bumps are masked for further analysis."
 Our detailed study of this eveut (Aurierre et al., Our detailed study of this event (Aurièrre et al.
 2001) led us to conchide tha he source star is almost certainly ideutified on IIubbk Space Telescope (UIST) archival nuages and has Johusou/Cousins magnitudes:114010.," 2001) led us to conclude that the source star is almost certainly identified on Hubble Space Telescope (HST) archival images and has Johnson/Cousins magnitudes:,."
=20b5140.12.. This allows one to weak the degeneracy between the Einstein crossing ine and he mipact parameter. and so obtain direct neasureiuents of the event duration and mipact xuunmneter:davs.," This allows one to break the degeneracy between the Einstein crossing time and the impact parameter, and so obtain direct measurements of the event duration and impact parameter:,."
.L.. These values are slightlv different from those eiven iu Auricre et al. (, These values are slightly different from those given in Auriere et al. (
2001). as we wave subsequently exteuded he baselue for this event.,"2001), as we have subsequently extended the baseline for this event."
 If the halo fraction is above20%... the leus is most probably a MÁACTIIO (with equal chance to be iu the M31 or \Glky Way halo).," If the halo fraction is above, the lens is most probably a MACHO (with equal chance to be in the M31 or Milky Way halo)."
 IHowever. it is also plausible that the lens is a star. in which case the most probable mass is around AL~0.2AJ...," However, it is also plausible that the lens is a star, in which case the most probable mass is around $M\sim 0.2\,M_\odot$."
 At 22/03” frou the ceutre of M31. PA-99-N2 lies well outside the projected area of the M31 bulge aud therefore appears to be an excellent candidate for a MLACTIO lens.," At $22'03''$ from the centre of M31, PA-99-N2 lies well outside the projected area of the M31 bulge and therefore appears to be an excellent candidate for a MACHO lens."
 Precise deteriumation of all five pariuneters of the fit is possible because of very good sampling aud s1uall error bars., Precise determination of all five parameters of the fit is possible because of very good sampling and small error bars.
" We fiud a duration for this events of fg~ Ldavs and maxi macnification Aya,=13.340.7."," We find a duration for this events of $t_{\rm E}\sim 92\pm 4\,$ days and maximum magnification $A_\textrm{max} = 13.3\pm 0.7$."
 MACTIOs are expected to lave a duration centred ou te~DOCAZ/AZ.9? days," MACHOs are expected to have a duration centred on $t_{\rm E} \sim 50 \,(M/M_\odot)^{1/2}\,$ days."
" The alternative to MACIIOs is self-leusiug by an MOL disk star (Could199ΠΕ], with a typical duvation te~GO(AL/AL3/7 days,"," The alternative to MACHOs is self-lensing by an M31 disk star \cite{gould94}, with a typical duration $t_{\rm E} \sim 60 \,(M/M_\odot)^{1/2}\,$ days."
 The very high S/N allows achromatic deviations to the standard Paczvisski crave to be revealed. implvius a 4? per degree of freedom3.," The very high S/N allows achromatic deviations to the standard Paczyǹsski curve to be revealed, implying a $\chi^2$ per degree of freedom."
1.. Some evidence of this is visible in Figure L.., Some evidence of this is visible in Figure \ref{fig:lightcurves}. .
 If these deviations are not simplydue to xvsteniatic photometric errors. they are sueecstive of a parallax effec (Alcockotal.L997) aud/or a close caustic approach (Albrowetal. 2002)..," If these deviations are not simplydue to systematic photometric errors, they are suggestive of a parallax effect \cite{macho2} and/or a close caustic approach \cite{mb9947}. ."
To evaluate the fraction of hard NRB resolved by the INT ouboard we first developed a svuthesis mocel based on the staudard assumption that the XRBD is mostly made by a combination of tvpe 1 aud 2 AGN (Setti Woltjer 1989: Comastzri et al..,"To evaluate the fraction of hard XRB resolved by the HXT onboard Constellation-X, we first developed a synthesis model based on the standard assumption that the XRB is mostly made by a combination of type 1 and 2 AGN (Setti Woltjer 1989; Comastri et al.,"
 1995. aud references therein).," 1995, and references therein)."
 Details on the model can be found iu Poupilio. La Franca Matt (1999 aud this volue).," Details on the model can be found in Pompilio, La Franca Matt (1999 and this volume)."
 Tere we stuumarize the main features of the model., Here we summarize the main features of the model.
 We are now able to predict the fraction of the Cosnic NRB which cau be resolved by CoustellationX in the 10 keV energy range., We are now able to predict the fraction of the Cosmic XRB which can be resolved by Constellation–X in the 10–40 keV energy range.
 Our estimate is based on the baseline spatial resolution. ic. 1 HPD. which is a rather couservative value.," Our estimate is based on the baseline spatial resolution, i.e. 1' HPD, which is a rather conservative value."
 Àuvy inprovenenut in this resolution will of course increase the fraction of NRB resolved., Any improvement in this resolution will of course increase the fraction of XRB resolved.
 The predictions are:, The predictions are:
This article summarizes aud explores a recent project in which we found photometric metallicities within SDSS-cdiscoverecdl dSph galaxies. using novel filter and color combinatious.,"This article summarizes and explores a recent project in which we found photometric metallicities within SDSS-discovered dSph galaxies, using novel filter and color combinations."
 For more cletails. see Hughes. Wallerstein Dotter (2011: herealter. HWD) and Hughes. Wallerstein Bossi (2008: hereafter. HWB).," For more details, see Hughes, Wallerstein Dotter (2011; hereafter, HWD) and Hughes, Wallerstein Bossi (2008; hereafter, HWB)."
 The dark matter dominated (Αη> 100). ultra-faint dwarf galaxies (UFDs: Willman 2010 reviews the SDSS search methods). are the Oleast. luminous ealaxiesO. which can be as faint as 10.* times the luminosity of the Milky Way (range: 300<L.100. 000).," The dark matter dominated $M/L>100$ ), ultra-faint dwarf galaxies (UFDs; Willman 2010 reviews the SDSS search methods), are the Òleast luminous galaxiesÓ, which can be as faint as $10^{-7}$ times the luminosity of the Milky Way (range: $300<L_\odot<100,000$ )."
 We have studied the age ancl metallicity distributions in several dwarf spheroidal (452011) systems. using Bodttes I as the proving ground (AWB: HWD).," We have studied the age and metallicity distributions in several dwarf spheroidal (dSph) systems, using Boöttes I as the proving ground (HWB; HWD)."
 Frebel. Siuou kIxirby. (2011) stucliecl the chemical composition of several UFDs with bieh-resolutiou spectroscopy.," Frebel, Simon Kirby (2011) studied the chemical composition of several UFDs with high-resolution spectroscopy."
 A recent paper, A recent paper
"jumps inj,, occur.","jumps in, occur."
" When the dark matter angular momentum is expressed in terms of the spin parameter (A.= jam/W2RvirVe; ?)), we recover the typical value of A’~0.04 with fluctuations of up to a factor of ~2 around this value."," When the dark matter angular momentum is expressed in terms of the spin parameter $\lambda'=\jdm/\sqrt{2}\rvir V_{\rm c}$ , \citealt{bullock01}) ), we recover the typical value of $\lambda'\simeq 0.04$ with fluctuations of up to a factor of $\sim 2$ around this value."
 An interesting feature in Fig., An interesting feature in Fig.
" 2 is that iincreases with time (albeit at a reduced rate below z— 3), implying that late infall carries a larger amount of angular momentum."," \ref{fig:jtot_ad} is that increases with time (albeit at a reduced rate below $z=3$ ), implying that late infall carries a larger amount of angular momentum."
 This is not a completely unexpected result given that dark matter haloes are known to experience little evolution of spin parameter with time (e.g.?).., This is not a completely unexpected result given that dark matter haloes are known to experience little evolution of spin parameter with time \citep[e.g.][]{peirani04}.
" As their mass and radius grow, so must their angular momentum."," As their mass and radius grow, so must their angular momentum."
" However, it is not trivial to understand the late accretion has largerj."," However, it is not trivial to understand the late accretion has larger."
". A naive answer is that material with larger angular momentum takes more time to reach the potential well, but this does not explain it acquired such a large angular momentum in the first place."," A naive answer is that material with larger angular momentum takes more time to reach the potential well, but this does not explain it acquired such a large angular momentum in the first place."
" We discuss in detail the cosmic evolution of the angular momentum of halos (which necessarily goes beyond tidal torque theory) in a companion paper (?),, but for completeness’ sake, we briefly outline the main idea in the paragraph below."," We discuss in detail the cosmic evolution of the angular momentum of halos (which necessarily goes beyond tidal torque theory) in a companion paper \citep{pichon11}, but for completeness' sake, we briefly outline the main idea in the paragraph below."
 The dynamics of the gas and dark matter flowing along what has been dubbed the ‘cosmic web’ can be understood as the anisotropic time evolution of the initial gaussian random gravitational field., The dynamics of the gas and dark matter flowing along what has been dubbed the `cosmic web' can be understood as the anisotropic time evolution of the initial gaussian random gravitational field.
" Cosmological structures originate as peaks in the associated initial density field (?),, which are connected to other peaks through peak patches."," Cosmological structures originate as peaks in the associated initial density field \citep{bond96}, which are connected to other peaks through peak patches."
 The bulk motion of a peak patch is determined by the gradient of the large-scale potential., The bulk motion of a peak patch is determined by the gradient of the large-scale potential.
 The latter also drives the motions of filaments which exist at the intersection of at least three void patches and connect peaks., The latter also drives the motions of filaments which exist at the intersection of at least three void patches and connect peaks.
" As a consequence of the asymmetry between voids, the gas and dark matter flowing out of these voids acquire a transverse velocity when they intersect at a filament."," As a consequence of the asymmetry between voids, the gas and dark matter flowing out of these voids acquire a transverse velocity when they intersect at a filament."
 This transverse velocity is the seed of a halo's angular momentum which is then advected along the filaments all the way into the halo sitting on the peak., This transverse velocity is the seed of a halo's angular momentum which is then advected along the filaments all the way into the halo sitting on the peak.
" Since the transverse velocity along a filament is constant to zeroth order approximation, the material initially located further away from the peak will naturally contribute more angular momentum."," Since the transverse velocity along a filament is constant to zeroth order approximation, the material initially located further away from the peak will naturally contribute more angular momentum."
" Note that the infall of matter along such filaments will contribute an increasing amount of angular momentum as time goes on (shown in Fig. 2)),"," Note that the infall of matter along such filaments will contribute an increasing amount of angular momentum as time goes on (shown in Fig. \ref{fig:jtot_ad}) ),"
 since the filament preserves its orientation over longstretches of time., since the filament preserves its orientation over longstretches of time.
The theoretical vields we will adopt in the following analysis are based on a new set οἱ zero metallicitv massive stars ranging in mass between 15and30M...,The theoretical yields we will adopt in the following analysis are based on a new set of zero metallicity massive stars ranging in mass between $\rm 15~and~80~M_\odot$.
 These evolutions have been computed with the latest version of the FRANEC code 1993).. rel.," These evolutions have been computed with the latest version of the FRANEC code \citep{CLS98}, rel."
 4.84., 4.84.
 This version of (he code does not differ significantly [rom the one adopted by Limongi.Straniero&Chieffi(2000)., This version of the code does not differ significantly from the one adopted by \cite{LSC00}.
. Let us just remind that these stellar models have been evolved with a network including 179 isotopes fully coupled to the physical evolution of the stars [rom the pre main sequence until the central temperature reaches 6LO” IX. A quantity which plavs a major role in determining the final vields of most of the intermediate mass elements is (he Carbon abundance left by the central He burning as largely discussed. by. e.g.. Weaver&Wooslev.(1993) and Imbrianietal...(2001).," Let us just remind that these stellar models have been evolved with a network including 179 isotopes fully coupled to the physical evolution of the stars from the pre main sequence until the central temperature reaches $6~10^9$ K. A quantity which plays a major role in determining the final yields of most of the intermediate mass elements is the Carbon abundance left by the central He burning as largely discussed by, e.g., \cite{ww93} and \cite{ietal01}."
. This abundance is determined by the combined effects of the IC(a.5)!O reaction rate and the behavior of the convective core during the latest part of (he central 11ο burning phase (Imbrianiοἱal.2001):: however. in a classical scenario in which the border of the convective core is determined. strictly bv the Schwarzschild criterion. the final € abundance is mainly controlled by the adopted Po.5)O rate.," This abundance is determined by the combined effects of the $\rm ^{12}C(\alpha,\gamma)^{16}O$ reaction rate and the behavior of the convective core during the latest part of the central He burning phase \citep{ietal01}; however, in a classical scenario in which the border of the convective core is determined strictly by the Schwarzschild criterion, the final C abundance is mainly controlled by the adopted $\rm ^{12}C(\alpha,\gamma)^{16}O$ rate."
 In order to bracket the possible values for this rate we chose to compute two sets of models. one by adopting the rate published by Canehlanetal.(1955).. hereinalter set IL. and a second one with the rate given by Caughlan&Fowler.(1988).. hereinafter set L. For sake of completeness Table 1 lists the C mass fraction Ne left bv the Ie burning for all the masses in the (wo sets of models.," In order to bracket the possible values for this rate we chose to compute two sets of models, one by adopting the rate published by \cite{ca85}, hereinafter set H, and a second one with the rate given by \cite{cf88}, hereinafter set L. For sake of completeness Table 1 lists the C mass fraction $\rm X_C$ left by the He burning for all the masses in the two sets of models."
 The explosive nucleosvnthesis has been computed. within the fame of the radiation dominated shock approximation (Weaver&Woosley.1980;Arnett1996).," The explosive nucleosynthesis has been computed within the frame of the radiation dominated shock approximation \citep{ww80,ar96}."
. More specifically 1 is assumed (hat. as the shock wave (escaping the iron core with energy E) moves outwad in mass (hrough the massive star envelope. (he pressure inside the shock front is nearly," More specifically it is assumed that, as the shock wave (escaping the iron core with energy E) moves outward in mass through the massive star envelope, the pressure inside the shock front is nearly"
the cone. 8. that each of these two-body processes subtend within the phase space of our model. ancl determined the rate of depletion from that area as defined in equation 5.,"the cone, $\theta$, that each of these two-body processes subtend within the phase space of our model, and determined the rate of depletion from that area as defined in equation 5."
 Even in the absence of two-body relaxation and large angle scattering. orbits in a triaxial potential stream about in angular momentum as (Πεν obex different integrals of motion (see ligure 2).," Even in the absence of two-body relaxation and large angle scattering, orbits in a triaxial potential stream about in angular momentum as they obey different integrals of motion (see figure 2)."
 This reshullles phase space and systematically introduces new orbits into the loss cone., This 'reshuffles' phase space and systematically introduces new orbits into the loss cone.
 Once an orbit is inside (he loss cone. ils apocenter shrinks rapidly. so [lowout of the loss cone via (his process is much slower (han the flow in.," Once an orbit is inside the loss cone, its apocenter shrinks rapidly, so flow of the loss cone via this process is much slower than the flow in."
 An orbit has completely changed its angular momentum when «δνμα=1., An orbit has completely changed its angular momentum when $\Delta J/J_{\rm init} = 1$.
 Figure 2 shows that. in total. about 0.2% of the orbits in our model change their angular momenta by order unity in merely 1000 dynamical times. or 4.5xI0'vears at rg for à svstenmi scaled to the Milkv. Wax.," Figure 2 shows that, in total, about $0.2\%$ of the orbits in our model change their angular momenta by order unity in merely 1000 dynamical times, or $4.5 \times 10^7 {\rm years}$ at $r_{\rm inf}$ for a system scaled to the Milky Way."
 In figure 3. we demonstrate how quickly each orbit reshullles its angular momentum per dynamical time: 4/uilu for 4 regions of total energy in the model.," In figure 3, we demonstrate how quickly each orbit reshuffles its angular momentum per dynamical time: $\Delta J/J_{\rm init}\big|_{t_{\rm dyn}}$ for 4 regions of total energy in the model."
 For each particle in our simulation. we calculate the (me it would take to change angular momentum by order unity. /une.," For each particle in our simulation, we calculate the time it would take to change angular momentum by order unity, $t_{\rm reshuffle}$."
 We determine this directly [rom the change in angular momentum per dynamical time for each orbit within the frozen triaxial potential., We determine this directly from the change in angular momentum per dynamical time for each orbit within the frozen triaxial potential.
 By keeping track of the how rapidly each orbits flows through phase space. we can estimate the rate anv particular loss cone is refilled due to (his process alone: where coshutlle Is: Note that if à model had ecqual-iass particles. N(r) would be a sum over the number of particles found in a radial bin.," By keeping track of the how rapidly each orbits flows through phase space, we can estimate the rate any particular loss cone is refilled due to this process alone: where $t_{\rm reshuffle}$ is: Note that if a model had equal-mass particles, N(r) would be a sum over the number of particles found in a radial bin."
 ILowever. recall that we generated our numerical model with a qnultimass technique (see Sigurdsson οἱ al 1998: Hollev-Dockelinann et al.," However, recall that we generated our numerical model with a 'multimass' technique (see Sigurdsson et al 1998; Holley-Bockelmann et al."
 2001). assigning more particles with smaller individual masses to the center.," 2001), assigning more particles with smaller individual masses to the center."
 These different masses change (he weight of each individual particle in the rate estimate. making V(r)=354mQ)/M(r). where A(r) is the mass of the model at radius r and (7) is Che particle mass.," These different masses change the weight of each individual particle in the rate estimate, making $N(r)= \sum_{i=1}^{n} m(i)/M(r)$, where $M(r)$ is the mass of the model at radius $r$ and $m(i)$ is the particle mass."
 Since this equation simply records how long a particular orbit takes to completely scramble its angular momentum. it holds for any densitv profile. anv galaxy shape. and any tvpe of orbit.," Since this equation simply records how long a particular orbit takes to completely scramble its angular momentum, it holds for any density profile, any galaxy shape, and any type of orbit."
 In fact. in (he trivial case of one star moving in a closed orbit about a point mass. /«pnune 15 infinite.," In fact, in the trivial case of one star moving in a closed orbit about a point mass, $t_{\rm reshuffle}$ is infinite."
 Figure 4 shows the rate of flow into (he capture and inspiral loss cone for particles in the simulation under different processes., Figure 4 shows the rate of flow into the capture and inspiral loss cone for particles in the simulation under different processes.
 Note that the rate particles stream into the loss cone bv (this Giasxial scrambling process is much larger Chan the rate in which they are lost by, Note that the rate particles stream into the loss cone by this triaxial scrambling process is much larger than the rate in which they are lost by
ido DE is a Wing model. the mass profile does not have he usual core since the disk mass dominates the centre.,"halo DF is a King model, the mass profile does not have the usual core since the disk mass dominates the centre."
 The halo density profile has a mild cusp with pxrI o within 0.1 disk exponential scale lengths similar to an JW. profile., The halo density profile has a mild cusp with $\rho \propto r^{-0.7}$ to within 0.1 disk exponential scale lengths similar to an NFW profile.
 Whether or not the haloes of spiral galaxies ive à central core is still controversial but. our model ido here is consistent. with rotation curve deconipositions (c.g. Ixent. 1986)., Whether or not the haloes of spiral galaxies have a central core is still controversial but our model halo here is consistent with rotation curve decompositions (e.g. Kent 1986).
" Ehe clise is in formal equilibrium with a 'Toomre Q —1.1 measured at 752.0724 and is approximately constant in the range OQcRAR,«0 rnsng ügher values bevond these limits.", The disc is in formal equilibrium with a Toomre $Q\sim$ 1.1 measured at $R$ $R\rm _d$ and is approximately constant in the range $1.0 < R/R_d < 4.0$ rising to higher values beyond these limits.
 While the model is stable against axisvnunetric perturbations it is inherently unstable to bar formation because of the dominance of the disk in the rotation curve., While the model is stable against axisymmetric perturbations it is inherently unstable to bar formation because of the dominance of the disk in the rotation curve.
 The model is scaled. such that CHR iSO 71. and the total cise|halo mass is about 12 (disc mass of 1.08 and halo mass of 10.57).," The model is scaled such that $G$ $R_d$ $v_{max}$ =1, and the total disc+halo mass is about 12 (disc mass of 1.98 and halo mass of 10.57)."
 We realize hese models as N-body systems at. high. resolution with (20M. particles (LOM each in the dise and the halo) and ow resolution with N-500lx. particles (250). cach in the disc ancl halo)., We realize these models as N-body systems at high resolution with N=20M particles (10M each in the disc and the halo) and low resolution with N=500K particles (250K each in the disc and halo).
 Thus. all quoted simulation lengths are in erms of the exponential disc length. and all velocities are ractions of the maximum.," Thus, all quoted simulation lengths are in terms of the exponential disc length, and all velocities are fractions of the maximum."
 We also consider a IN500Ix model with a small compact bulec of mass Al=0.32 with halo and disk mass profiles essentially unchanged., We also consider a N=500K model with a small compact bulge of mass $M=0.32$ with halo and disk mass profiles essentially unchanged.
 The ‘Toomre Q also remains comparable at ~1.06., The Toomre $Q$ also remains comparable at $\sim 1.06$.
 The code and parameters for generating these models are available by request., The code and parameters for generating these models are available by request.
 Our mocels ciffer from D&SS who use a Ixuzmin-‘Toomre dise with a vertical Gaussian profile and a lowered polvtrope distribution function (DIE) for the halo., Our models differ from S who use a Kuz'min-Toomre disc with a vertical Gaussian profile and a lowered polytrope distribution function (DF) for the halo.
 Phe recent publication by Athanassoula Alisiviotis (2002) MM) contains models based on Hernaáquist's (1993) method., The recent publication by Athanassoula Misiriotis (2002) M) contains models based on Hernquist's (1993) method.
 As well as specifving the following results in the original simulation units. the appropriate lengths and times are sealed to match. the SBa galaxy NGC 4596. for. easier comparison with real galaxies.," As well as specifying the following results in the original simulation units, the appropriate lengths and times are scaled to match the SBa galaxy NGC 4596 for easier comparison with real galaxies."
 We use the scale length of 3.2kpe and rotational velocity of 120kms given by Gerssen et al. (, We use the scale length of $3.2 \rm{\ kpc}$ and rotational velocity of $120\rm{\ km\ s}^{-1}$ given by Gerssen et al. (
1999).,1999).
 Lhe sech? scale height for the cise is 0.1 simulation units or 320 pc., The $\rm{sech}^2$ scale height for the disc is 0.1 simulation units or 320 pc.
 For these scales the unit of time is 26.3 Myr., For these scales the unit of time is 26.3 Myr.
 For the runs. we use a time step of Af=0.05 (1.32 Myr) for 10.000 time steps. for a total /—500 (13.2 Cyr) or approximately the Llubble time.," For the runs, we use a time step of $\Delta t=0.05$ (1.32 Myr) for 10,000 time steps, for a total $t$ =500 (13.2 Gyr) or approximately the Hubble time."
 We soften eravitational forces using a Plummer law with softening eneth «—0.0125 (40 pe) for the halo and «=0.005 (16 pe) or the disc., We soften gravitational forces using a Plummer law with softening length $\epsilon=0.0125$ (40 pc) for the halo and $\epsilon=0.005$ (16 pc) for the disc.
 All runs are executed with a parallel tree code (Dubinski 1996) running on a PC cluster or a 32 processor Compaq 658320., All runs are executed with a parallel tree code (Dubinski 1996) running on a PC cluster or a 32 processor Compaq GS320.
 The 20M particles simulations needed. 2 minutes per step on the C320., The 20M particles simulations needed 2 minutes per step on the GS320.
 Phe total energy. drifts » no more than 1 per cent. ancl total angular momentun is conserved. to tvpically within 0.1 per cent.," The total energy drifts by no more than 1 per cent, and total angular momentum is conserved to typically within 0.1 per cent."
 The results cliscussecl below are for the high resolution simulation unless otherwise noted., The results discussed below are for the high resolution simulation unless otherwise noted.
 Although these models are formally in equilibrium they are stronely unstable., Although these models are formally in equilibrium they are strongly unstable.
 A bar develops by /=26 (686 Myr). and is sustained for the duration of the run.," A bar develops by $t$ =26 (686 Myr), and is sustained for the duration of the run."
 Visually. the bar grows to ils greatest extent at around /—50 (1.32 Gyr).," Visually, the bar grows to its greatest extent at around $t$ =50 (1.32 Gyr)."
 The bar then bends and buckles between /=70 and £290 (a period of 526 Myr) to leave a slightly slower bar of comparable Iength., The bar then bends and buckles between $t$ =70 and $t$ =90 (a period of 526 Myr) to leave a slightly slower bar of comparable length.
 There are isophotal twists seen. during the bar buckling phase. but as noted in Shaw ct al. (," There are isophotal twists seen during the bar buckling phase, but as noted in Shaw et al. ("
1993) these disappear with the increased heating of the disc seen during the bar evolution.,1993) these disappear with the increased heating of the disc seen during the bar evolution.
 After this short. phase. the bar shows elliptical isophotes with a butterllv- or dumbbell-shape when viewed face-on.," After this short phase, the bar shows elliptical isophotes with a butterfly- or dumbbell-shape when viewed face-on."
 Fig., Fig.
 3 shows the face-on views for /—50 to 500., 3 shows the face-on views for $t$ =50 to 500.
 The evolution of the bar viewed edge-on clearly reveals the buckling instability., The evolution of the bar viewed edge-on clearly reveals the buckling instability.
 Initially the disc is thin: the formation and motion of the bar heat the disc vertically and azimuthallv., Initially the disc is thin; the formation and motion of the bar heat the disc vertically and azimuthally.
 At the onset of buckling there is a very. short lived phase of about 260 Myr in which the bar bends into an are before buckling into a boxy shape object (eclec-on views are shown in Figs 4 and 5)., At the onset of buckling there is a very short lived phase of about 260 Myr in which the bar bends into an arc before buckling into a boxy shape object (edge-on views are shown in Figs 4 and 5).
 The boxy-shaped bulge remains after buckling. and slowly evolves into the familiar peanu shape. which is most prominent when the bar is viewed on. with its long side in the plane of the sky.," The boxy-shaped bulge remains after buckling, and slowly evolves into the familiar peanut shape, which is most prominent when the bar is viewed edge-on, with its long side in the plane of the sky."
 When viewer end-on. the galaxy. resembles a disc with a spherical bulge.," When viewed end-on, the galaxy resembles a disc with a spherical bulge."
 The bar remains an obvious component of the dise a shows no sign of collapsing into a spherical bulge., The bar remains an obvious component of the disc and shows no sign of collapsing into a spherical bulge.
 There is an animation of both face-on and edge-on views available a wwew.astro.utoronto.ca/ onecill., There is an animation of both face-on and edge-on views available at www.astro.utoronto.ca/ oneill.
 There is an increase in central clensitw following the initiation of the bar. which inlluences the initial slope of the rotation curve.," There is an increase in central density following the initiation of the bar, which influences the initial slope of the rotation curve."
 Fig., Fig.
 6 shows the rotation curve at /—0. 100. 200. and 400. and it shows the increased. slope and peas during the simulation.," 6 shows the rotation curve at $t$ =0, 100, 200, and 400, and it shows the increased slope and peak during the simulation."
 The surface density along the bar is flat at small & for /—50. but rapidly turns exponential Following buckling.," The surface density along the bar is flat at small $R$ for $t$ =50, but rapidly turns exponential following buckling."
 These data will be cliscussed in more detail in the following sections., These data will be discussed in more detail in the following sections.
 Even without the gaseous component. this simulad galaxy can be compared. with observations. anc some obvious features stand. out.," Even without the gaseous component, this simulated galaxy can be compared with observations, and some obvious features stand out."
 The face-on views look very much like observed. bars. and the edge-on views are similar to several studies comparing peanut-shapecl bulges and bars MAL: Merrifield Ixuijken. 1999).," The face-on views look very much like observed bars, and the edge-on views are similar to several studies comparing peanut-shaped bulges and bars M; Merrifield Kuijken 1999)."
 More. detailed comparison with the latter follows in Section 5., More detailed comparison with the latter follows in Section 5.
 Recently. MM conducted a series of tests to compare N-body simulations of dillerent mass models. which are ideally suited to comparison with our results here.," Recently, M conducted a series of tests to compare N-body simulations of different mass models, which are ideally suited to comparison with our results here."
 They simulated three different mocels: one cisc-clominated (AID). which is similar to ours here. another disc-dominated moclel with an added bulge (AIDB). and one halo-dominated (MI: all created using the LHerneuist (1993) models.," They simulated three different models: one disc-dominated (MD), which is similar to ours here, another disc-dominated model with an added bulge (MDB), and one halo-dominated (MH): all created using the Hernquist (1993) models."
 Our work agrees quite well with MM on isophote shape and rotation curve progression for the first hall of the simulations. which span approximately the same time.," Our work agrees quite well with M on isophote shape and rotation curve progression for the first half of the simulations, which span approximately the same time."
 Our evolution here disagrees to some extent with their disc dominated: model for the latter hall of the run: the mass build up at the centre of the disc causes the inner slope of the rotation curve to become more steep (albeit slightly) and the maximum velocity to increase even during the final stages: whereas. MM found little dillerence between the rotation," Our evolution here disagrees to some extent with their disc dominated model for the latter half of the run: the mass build up at the centre of the disc causes the inner slope of the rotation curve to become more steep (albeit slightly) and the maximum velocity to increase even during the final stages; whereas, M found little difference between the rotation"
proton enerey.,proton energy.
 We note that the clillractive dissociation has also been implemented in Pythia 6.1/6.2 (Sjostvandetal.2001) and in PIIOJET (see footnote 6)., We note that the diffractive dissociation has also been implemented in Pythia 6.1/6.2 \citep{Pythia62} and in PHOJET (see footnote 6).
 The particle interaction modeling of our model A is similar to that used in Pythia: in fact the total charge multiplicity distribution including the double diffraction by Pythia 6.2 with the higher order terms is similar to tha ol model A shown in Fig.3., The particle interaction modeling of our model A is similar to that used in Pythia: in fact the total charge multiplicity distribution including the double diffraction by Pythia 6.2 with the higher order terms is similar to that of model A shown in Fig.3.
 Detailed comparison on the difference between the clillractive paris of Pytbia and PIIOJET is eiven in a review by Guillaud&Sobol(2004)., Detailed comparison on the difference between the diffractive parts of Pythia and PHOJET is given in a review by \citet{Guillaud&Sobol04}.
. We note that the diffractive parts of Pythia and PIIOJIZE are optimized in combination with (heir respective non-dillractive counter parts., We note that the diffractive parts of Pythia and PHOJET are optimized in combination with their respective non-diffractive counter parts.
 Belore proceeding to calculate the gamma-ray spectra produced by protons with continuum speclra. we have sumnied (he a0 vields from the non-cilfractive ancl diffractive interactions lo compare wilh the experimental data listed in Dermer(1936).," Before proceeding to calculate the gamma-ray spectra produced by protons with continuum spectra, we have summed the $\pi^0$ yields from the non-diffractive and diffractive interactions to compare with the experimental data listed in \citet{Dermer86}."
". Fig.5 shows the inclusive x"" cross-section or. equivalently. the average multiplicity of z"" per p-p interaction multiplied bv the cross-sections for pp(pp) collisions: the solid line. labeled as model 7À AIL. is the sum of the non-diffractive and double diffractive contributions: the dashed line. labeled as model D. represents (he non-diffractive contribution without the multiple parton interaction terms."," Fig.5 shows the inclusive $\pi^0$ cross-section or, equivalently, the average multiplicity of $\pi^0$ per $p$ $p$ interaction multiplied by the cross-sections for $pp(\bar{p}p)$ collisions: the solid line, labeled as model “A All”, is the sum of the non-diffractive and double diffractive contributions; the dashed line, labeled as model B, represents the non-diffractive contribution without the multiple parton interaction terms."
 We note that contribution of the diffractive process. model A diff. is small in the multiplieitv. just as in the charged multiplicity shown in Fig.3.," We note that contribution of the diffractive process, model A diff, is small in the multiplicity, just as in the charged multiplicity shown in Fig.3."
" Model A reproduces the measured LUz multiplicity quite well above the resonance region (7,>3 GeV).", Model A reproduces the measured $\pi^0$ multiplicity quite well above the resonance region $T_p>3$ GeV).
 We also note that the sealing model of Dermer(1936). as well as our model D reproduce the data well., We also note that the scaling model of \citet{Dermer86} as well as our model B reproduce the data well.
 To the accuracy. needed. for (he present studs. continuum spectra of protons can be approximated by a sum of a series of mono-energetic proton beams.," To the accuracy needed for the present study, continuum spectra of protons can be approximated by a sum of a series of mono-energetic proton beams."
" We choose a geometrical series of T,,=1000.0x27.227? GeV where V=0—40.", We choose a geometrical series of $T_p=1000.0 \times 2^{(N-22)/2}$ GeV where $N=0-40$.
" Each proton energy bin covers from 2""T qo 2*7T.", Each proton energy bin covers from $2^{-0.25}T_p$ to $2^{0.25}T_p$.
" The gamma-ray spectra for mono-energetic protons of kinetic energies Ti, listed in Column 1 of Table 1 are weighted by the appropriate p-p cross-sections for the energy given in Columns 2-4.", The gamma-ray spectra for mono-energetic protons of kinetic energies $T_p$ listed in Column 1 of Table 1 are weighted by the appropriate $p$ $p$ cross-sections for the energy given in Columns 2-4.
 Figs.2a and 2b show such samples [or 3 15 for models A and D. and for the non-diffractive and diffractive interactions.," Figs.2a and 2b show such samples for 3 $T_p$ 's for models A and B, and for the non-diffractive and diffractive interactions."
" The cross-section-weighted. gamma-ray spectra [or mono-energetic protons of T, is then multiplied with a proton spectrum [actor of the three listed in Column 5-7.", The cross-section-weighted gamma-ray spectra for mono-energetic protons of $T_p$ is then multiplied with a proton spectrum factor of the three listed in Column 5-7.
" By sunning over all 7,5 we obtain the gamma-ray spectrum for the proton spectrum.", By summing over all $T_p$ 's we obtain the gamma-ray spectrum for the proton spectrum.
" We note here that the sum over a geometrical series of proton kinetic energies (7,) makes the gamma-ray spectrin corresponding (o a proton spectrum with power-law index 1.0.", We note here that the sum over a geometrical series of proton kinetic energies $T_p$ ) makes the gamma-ray spectrum corresponding to a proton spectrum with power-law index 1.0.
" The 3 proton spectral [actors in Table 1 are accordingly adjusted and mutually normized to 1.0 at ZT,=1 TeV: they will be normalized dillerentlv. as will be"," The 3 proton spectral factors in Table 1 are accordingly adjusted and mutually normized to 1.0 at $T_p=1$ TeV: they will be normalized differently, as will be"
50 per cent. 50 to 75 per cent. or 75 to 100 per cent of the number of g values tested. the corresponding triplet (ΑΝ. Dy. ObNha) is marked by an open circle: a small. a median-size or a large [filled circle. respectively.,"50 per cent, 50 to 75 per cent, or 75 to 100 per cent of the number of $\eta$ values tested, the corresponding triplet $N$ , $P_h$, $v(t_{em})/V_s(t_{em}$ )) is marked by an open circle, a small, a median-size or a large filled circle, respectively."
 Figure S confirms that. the probability of successful. transverse collapse fades away with decreasing external pressure and increasing number of SNelL, Figure 8 confirms that the probability of successful transverse collapse fades away with decreasing external pressure and increasing number of SNeII.
 As mentioned in Sect. 2.3.2.0," As mentioned in Sect. \ref{sub:discNPh},"
 a low external pressure and a high number of SNeLE leads to a larger radius for the shell. decreasing thereby its surface density (eq. 19))," a low external pressure and a high number of SNeII leads to a larger radius for the shell, decreasing thereby its surface density (Eq. \ref{eq:sig0_N_Ph}) )"
 and its ability to collapse., and its ability to collapse.
" At high pressure. Le. 2,c10""ddvneem >. the ability of the shell to get [ragmented is limited by too large a number of SNell."," At high pressure, i.e. $P_h \simeq 10^{-9}$ $^{-2}$, the ability of the shell to get fragmented is limited by too large a number of SNeII."
 Figure S shows however that à SN number as large as 200 does not prevent the fragmentation., Figure 8 shows however that a SN number as large as 200 does not prevent the fragmentation.
 Accordingly. the largest metallicity which can be achieved hrough sell-enrichment. is. Fe/1I]z 1.2.," Accordingly, the largest metallicity which can be achieved through self-enrichment is $\simeq -$ 1.2."
 On the other mane. at low pressure. the transverse collapse is supported o» à low number of SNelL," On the other hand, at low pressure, the transverse collapse is supported by a low number of SNeII."
 Combining a low background oessure with the lower limit on IN. Fig.," Combining a low background pressure with the lower limit on $N$, Fig."
 S shows that the owest metallicity which can be achieved is. Fe/ll]z— 2.8 woviding that the relative initial transverse velocity. is 53 per cent., 8 shows that the lowest metallicity which can be achieved is $\simeq -$ 2.8 providing that the relative initial transverse velocity is 3 per cent.
 While this lower limit in metallicity is a. bit uncertain. as it is achieved in the case of the highest intial ransverse velocity only. the examination of the three panels in Fig.," While this lower limit in metallicity is a bit uncertain, as it is achieved in the case of the highest intial transverse velocity only, the examination of the three panels in Fig."
 S clearly shows that a metallicity of ~2.5 ds actually achievable., 8 clearly shows that a metallicity of $\simeq -2.5$ is actually achievable.
 ποσο extreme values (ος 19 anc — 2.5) match. nicely. the metallicities exhibited. by the most metal-rich ancl the most metal-poor Galactic halo GCs. respectively.," These extreme values $\simeq -$ 1.2 and $-$ 2.5) match nicely the metallicities exhibited by the most metal-rich and the most metal-poor Galactic halo GCs, respectively."
 At this stage. it is worth keeping in mind that the question addressed. here above concerns the ability of the shell to form stars and not vet the ability of these stars to evolve into a stellar cluster.," At this stage, it is worth keeping in mind that the question addressed here above concerns the ability of the shell to form stars and not yet the ability of these stars to evolve into a stellar cluster."
 We will address the ability of the newly formed. stars to form a bound. cluster in a forthcoming paper and we emphasize here that. among the cases of successful fragmentation displayed by Fig.," We will address the ability of the newly formed stars to form a bound cluster in a forthcoming paper and we emphasize here that, among the cases of successful fragmentation displayed by Fig."
 S. some ofthe newly formed stars may not be able to form a boum cluster.," 8, some of the newly formed stars may not be able to form a bound cluster."
 In other words. the collapsed shells may be a source for both halo GC's and halo field stars.," In other words, the collapsed shells may be a source for both halo GCs and halo field stars."
 Section 2. has discussed. how the self-enrichmen model for GC formation can shed lisht on the metallicity istribution of the Galactic halo., Section 2.3.2 has discussed how the self-enrichment model for GC formation can shed light on the metallicity distribution of the Galactic halo.
 Because the parameters which determine the metallicitv. ie. N and P. also contro the shell surface density. there is a direct. link between the metallicity and. the probability of starLormation®.," Because the parameters which determine the metallicity, i.e. $N$ and $P_h$, also control the shell surface density, there is a direct link between the metallicity and the probability of star."
. Furthermore. the initial radius anc velocity of the seconc eencration stars being the radius and the velocity of the shell at the time of their formation. their binding depends on the shell expansion law and. therefore. again. on N aux Dy.," Furthermore, the initial radius and velocity of the second generation stars being the radius and the velocity of the shell at the time of their formation, their binding depends on the shell expansion law and, therefore, again, on $N$ and $P_h$."
 Xs a consequence. the probability of getting a boum cluster from a shell of newly formed:stars is also. relate to their metallicity.," As a consequence, the probability of getting a bound cluster from a shell of newly formedstars is also related to their metallicity."
 H£ we assume that a significant fraction, If we assume that a significant fraction
generated by its supersonic motion through the hot intracloud medium.,generated by its supersonic motion through the hot intracloud medium.
" We can estimate the mass of the absorbing clouds (Mou~107"" M4) and their total number within the central region (No~3 10°).", We can estimate the mass of the absorbing clouds $\rm M_{cloud}\sim 10^{-10}~M_{\odot}$ ) and their total number within the central region $\rm \mathcal{N_C}\sim 3~10^7$ ).
 The inferred total mass of the BLR is about 4107M. which is two orders of magnitude lower than the BLR mass inferred from photoionization models.," The inferred total mass of the BLR is about $\rm 4~10^{-3}~M_{\odot}$, which is two orders of magnitude lower than the BLR mass inferred from photoionization models."
 The discrepancy may originate from a population of large. massive BLR clouds not identified in our eclipsing studies.," The discrepancy may originate from a population of large, massive BLR clouds not identified in our eclipsing studies."
 Alternatively. photoionization models may overestimate the BLR mass.," Alternatively, photoionization models may overestimate the BLR mass."
 In particular. UV and X-ray radiation produced by the shocks generated by the supersonic motion of the clouds may provide a local source of ionizing photons. not accounted for by classical photoionization models that assume a central point-like radiation source.," In particular, UV and X-ray radiation produced by the shocks generated by the supersonic motion of the clouds may provide a local source of ionizing photons, not accounted for by classical photoionization models that assume a central point-like radiation source."
comes Irom the reprocessing of the 27.87 s signal bv (he travelling wave whose orbital period is ~740 s. While the model can satisfactorally explain the periodicities. and perhaps even (he enigmatic 15 s quasiperiodic oscillation (QPO) discovered by Ixnigge et al. (,"comes from the reprocessing of the 27.87 s signal by the travelling wave whose orbital period is $\sim$ 740 s. While the model can satisfactorally explain the periodicities, and perhaps even the enigmatic $\sim$ 15 s quasi–periodic oscillation (QPO) discovered by Knigge et al. ("
2002). no other dwarf nova shows persistent. QPOs in quiescence. requiring WZ See to be unique in this regard.,"2002), no other dwarf nova shows persistent QPOs in quiescence, requiring WZ Sge to be unique in this regard."
 Understanding the nature of the periodicities in WZ See is important not only for its own sake. but because of the implications lor accretion disk physics in general.," Understanding the nature of the periodicities in WZ Sge is important not only for its own sake, but because of the implications for accretion disk physics in general."
 Due to its extreme outburst characteristics. WZ See is believed to have à low masstransfer rate [rom its companion star (e.g. Osaki 1996).," Due to its extreme outburst characteristics, WZ Sge is believed to have a low mass–transfer rate from its companion star (e.g. Osaki 1996)."
 Yet this alone is insufficient to allow accretion disk models to match the outburst size and timescale., Yet this alone is insufficient to allow accretion disk models to match the outburst size and timescale.
" One solution requires (hat the accretion disk have a ""hole"" at iis center (Lasota et al.", One solution requires that the accretion disk have a “hole” at its center (Lasota et al.
 1995)., 1995).
 This inner disk region may be evacuated by (1) a magnetic field. as in the DQ Her stars where the white dwarl’s magnetic field truncates ihe inner disk (Warner et al.," This inner disk region may be evacuated by (i) a magnetic field, as in the DQ Her stars where the white dwarf's magnetic field truncates the inner disk (Warner et al."
 1996: Lasota et al., 1996; Lasota et al.
 1999): or (il) evaporation via a “siphon” into a hot corona (Mever MeverIofImeister 1994)., 1999); or (ii) evaporation via a “siphon” into a hot corona (Meyer Meyer–Hofmeister 1994).
 This coronal siphon mechanism has properties related to ADAF mechanisms in black-hole accreting svstems (e.g. Mineshige et al., This coronal siphon mechanism has properties related to ADAF mechanisms in black-hole accreting systems (e.g. Mineshige et al.
 1998. MeverHolmeister Mever 2001).," 1998, Meyer–Hofmeister Meyer 2001)."
 Another solution recquires the cquiescent viscosity in WZ Sge's accretion disk to be very low: avyS0.001. compared to a more typical value Ol αρo0.03 in “normal” accretion disks (e.g. Smak 1993: Osaki 1996: \leverHofmeister. Mever Liu 1998).," Another solution requires the quiescent viscosity in WZ Sge's accretion disk to be very low: $\alpha_{cold} \ltsimeq 0.001$, compared to a more typical value of $\alpha_{cold} \sim0.03$ in “normal” accretion disks (e.g. Smak 1993; Osaki 1996; Meyer–Hofmeister, Meyer Liu 1998)."
" I WZ See can be shown (o be a DQ Herlike svstem. then the ""universali"" of the viscosity parameter is preserved and no seenunely hoc low value for 444 Is necessary."," If WZ Sge can be shown to be a DQ Her–like system, then the “universality” of the viscosity parameter is preserved and no seemingly low value for $\alpha_{cold}$ is necessary."
 On the other hand. if WZ See is a white dwarf pulsator. (hen either the coronal siphon must be operating and we have a white dwarl analog of a black hole accretion disk. or an anomalously low viscosity is required.," On the other hand, if WZ Sge is a white dwarf pulsator, then either the coronal siphon must be operating and we have a white dwarf analog of a black hole accretion disk, or an anomalously low viscosity is required."
 Either wav. understanding (he nature of the oscillations in WZ See can have an important impact on our understanding of accretion disks.," Either way, understanding the nature of the oscillations in WZ Sge can have an important impact on our understanding of accretion disks."
 In 2001 July WZ See went into oulburst. 23 νους after its previous outburst (see Patterson et al.," In 2001 July WZ Sge went into outburst, 23 years after its previous outburst (see Patterson et al."
 2002 lor extensive coverage of the 2001 outburst)., 2002 for extensive coverage of the 2001 outburst).
 Sion et al. (, Sion et al. (
2003) obtained observations of WZ See on the decline from outburst and in (his paper we present a (ime series analvsis of those same data.,2003) obtained observations of WZ Sge on the decline from outburst and in this paper we present a time series analysis of those same data.
 These observations provide compelling evidence against a simple white dwarf non radialg mode pulsation interpretation ol the oscillations., These observations provide compelling evidence against a simple white dwarf non–radial $g$ –mode pulsation interpretation of the oscillations.
 As part of the Director's Discretionary time. WZ See was observed with the ASTad four epochs: 2001 September 11. October 10. November 10. and December 11.," As part of the Director's Discretionary time, WZ Sge was observed with the at four epochs: 2001 September 11, October 10, November 10, and December 11."
 Eachobservation, Eachobservation
With the centre position.ey... and Leh set to the values eiven above. we find the inclination angle to increase [rom ~30° (Grc S) to ((r> 10).,"With the centre position, and $PA$ set to the values given above, we find the inclination angle to increase from $\sim$ $r < 8\arcmin$ ) to $r > 10\arcmin$ )."
 Phe latter is consistent with the apparent change in the ellipticity. (ic. increasing major to minor axis ratio) of NGC 1512s eas distribution with radius., The latter is consistent with the apparent change in the ellipticity (i.e. increasing major to minor axis ratio) of NGC 1512's gas distribution with radius.
 The resulting rotation curve. fot(7). is shown in Fig.," The resulting rotation curve, $v_{\rm rot}(r)$, is shown in Fig."
 6., 6.
" Phe maximum rotational velocities of zz aare reached at racii between 300"" aand —5007..", The maximum rotational velocities of $\approx$ are reached at radii between $\sim$ and $\sim$.
 Bevond that rapidly decreases. reaching 110 aat r — ((55 kpc).," Beyond that rapidly decreases, reaching $\sim$ at $r$ = (55 kpc)."
 The residual velocity. field. (see Fig., The residual velocity field (see Fig.
" 7) shows deviations"" up to approximately: zE30τν, most notably near the position of NGC 1510 and in the outer spiral/tidal arms."," 7) shows deviations up to approximately $\pm$, most notably near the position of NGC 1510 and in the outer spiral/tidal arms."
 The inner disk also shows deviations along an eastern are (similar to à onc-armed spiral) which roughly agrees with the elongated: star-forming spiral arm of NGC 1512. seen in the GALEN CV. images., The inner disk also shows deviations along an eastern arc (similar to a one-armed spiral) which roughly agrees with the elongated star-forming spiral arm of NGC 1512 seen in the GALEX $UV$ images.
 The passage of the companion would have unsettled the mass distribution. possibly causing a density wave or onc-armed spiral (as seen in the residual velocity. field).," The passage of the companion would have unsettled the mass distribution, possibly causing a density wave or one-armed spiral (as seen in the residual velocity field)."
 We estimate a dynamical mass of about 3Lott Που NGC 1512. based on a galaxy radius of r = 55 kpe and a rotational velocity of —+.," We estimate a dynamical mass of about $3 \times 10^{11}$ for NGC 1512, based on a galaxy radius of $r$ = 55 kpc and a rotational velocity of =."
 ΙΕ the outer eclouds at r= 83 kpe are bound to NGC 1512. the dynamical mass increases to 4.3LottM...," If the outer clouds at $r$ = 83 kpc are bound to NGC 1512, the dynamical mass increases to $4.3 \times 10^{11}$."
 We note that the rotation velocity of NGC 1512 is comparable or higher (200 ‘yy in the nuclear ring than in the inner disk. and significantly higher than in the outer cenvelope.," We note that the rotation velocity of NGC 1512 is comparable or higher (200 – ) in the nuclear ring than in the inner disk, and significantly higher than in the outer envelope."
 The tto rratio indicates that. $2% of the mass of NGC 1512 is in the form of &eas., The to ratio indicates that $\la$ of the mass of NGC 1512 is in the form of gas.
 No estimate of the molecular gas mass in NGC 1512 or NGC 1510 is currently. available., No estimate of the molecular gas mass in NGC 1512 or NGC 1510 is currently available.
 NGC 1510 lies at a projected distance of ~5’ ((13.8 kpe) from the centre of NGC 1512., NGC 1510 lies at a projected distance of $\sim$ (13.8 kpc) from the centre of NGC 1512.
 This places it well inside NGC 1512's clclisk. which shows an enhancement of the ccolumn density at the position of NGC 1510.," This places it well inside NGC 1512's disk, which shows an enhancement of the column density at the position of NGC 1510."
 The olfset in the residual velocity field of NGC 1512 (see Fig., The offset in the residual velocity field of NGC 1512 (see Fig.
 7) also sugeests Chat NGC 1510 contains a small amount of σσας and/or left the signature of its interaction with the inner disk of NGC 1512., 7) also suggests that NGC 1510 contains a small amount of gas and/or left the signature of its interaction with the inner disk of NGC 1512.
 Gallagher ct al. (, Gallagher et al. (
2005) speculate that NGC 1510 may have captured. gas from NGC 1512. contributing to its enhanced SE activity.,"2005) speculate that NGC 1510 may have captured gas from NGC 1512, contributing to its enhanced SF activity."
 Assuming the ασκεσιος of NGC 1510 is unresolved in the Hineps shown here. we measure an flux densitv of," Assuming the distribution of NGC 1510 is unresolved in the maps shown here, we measure an flux density of"
variation of the correlation function in dillerent. volumes of space]: where b is a parameter introduced. in. Paper LLL to describe the dependence of the error on the character of the large-scale. distribution of clusters of galaxies.,variation of the correlation function in different volumes of space): where $b$ is a parameter introduced in Paper III to describe the dependence of the error on the character of the large-scale distribution of clusters of galaxies.
 Lt must be determined from mock samples., It must be determined from mock samples.
 We have done this (for details see Paper LL) ancl found that bz1.5. see also the discussion in Sect.," We have done this (for details see Paper III) and found that $b\approx 1.5$, see also the discussion in Sect."
 4., 4.
 As we see from the above equation. the width of the error corridor for the cosmic. variance is constant.," As we see from the above equation, the width of the error corridor for the cosmic variance is constant."
 We sce from Table 2 that the amplitude of oscillations increases with the increase of the minimum supercluster richness Avy., We see from Table 2 that the amplitude of oscillations increases with the increase of the minimum supercluster richness $N_{cl}$.
" This leads us to the conclusions that. for low values of Αι we actually have a mixture of populations in the high-density population. and that the proper division of populations occurs at the highest minimum richness. IN,= S."," This leads us to the conclusions that, for low values of $N_{cl}$, we actually have a mixture of populations in the high-density population, and that the proper division of populations occurs at the highest minimum richness, $N_{cl}=8$ ."
" To check this result we have calculated the correlation function separately for clusters located in superclusters of meclium richness. from IN,=4 to UIN=T."," To check this result we have calculated the correlation function separately for clusters located in superclusters of medium richness, from $N_{cl}=4$ to $N_{cl}=7$."
 The correlation function of this subpopulation shows only marginal signs of oscillations., The correlation function of this subpopulation shows only marginal signs of oscillations.
 Thus we can accept Nay=SN as the limiting richness to select. the regularly: distributed: population of clusters in rich superclusters., Thus we can accept $N_{cl}=8$ as the limiting richness to select the regularly distributed population of clusters in rich superclusters.
 This analysis confirms results found in Papers E and EHI: a smooth distribution in. voic walls leads to a non-oscillating correlation function in the case of clusters in poor superclusters: oscillations occur only in the case i£ rich superclusters are located in a quasi-regular rectangular lattice., This analysis confirms results found in Papers I and III: a smooth distribution in void walls leads to a non-oscillating correlation function in the case of clusters in poor superclusters; oscillations occur only in the case if rich superclusters are located in a quasi-regular rectangular lattice.
 In Table 2 we ogive. parameters. of the oscillatinge correlation function. for the cluster population with measured redshifts., In Table 2 we give parameters of the oscillating correlation function for the cluster population with measured redshifts.
 The sample. of all clusters was also divided. into. high- and. low-density populations. and parameters. of the correlation function. were determined.," The sample of all clusters was also divided into high- and low-density populations, and parameters of the correlation function were determined."
 Results for samples with measured. redshifts and. for all clusters are given in Figure 3., Results for samples with measured redshifts and for all clusters are given in Figure 3.
 In this case we see that. on large scales. clusters in rich superclusters have an oscillating correlation function and clusters in poor superclusters have a zero correlation.," In this case we see that, on large scales, clusters in rich superclusters have an oscillating correlation function and clusters in poor superclusters have a zero correlation."
 Parameters of the oscillations of clusters in rich. superclusters have values very close to values. [or the sample of clusters with measured. redshifts: only the amplitude of oscillations is smaller by a factor of about 1.5., Parameters of the oscillations of clusters in rich superclusters have values very close to values for the sample of clusters with measured redshifts; only the amplitude of oscillations is smaller by a factor of about 1.5.
 A smaller amplitude for the sample. of all clusters is likely clue to the [larger observational errors in the shotometric redshifts. which smooth out features slightly in the correlation function.," A smaller amplitude for the sample of all clusters is likely due to the larger observational errors in the photometric redshifts, which smooth out features slightly in the correlation function."
 Now we compare the error in the correlation function or subsamples with various limiting richness Αι, Now we compare the error in the correlation function for subsamples with various limiting richness $N_{cl}$.
 We see hat the amplitude of oscillations for the sample ACOLRLES is approximately three times larger than the error: ic... we are able to establish the presence. of oscillations at a 3aJ evel.," We see that the amplitude of oscillations for the sample ACO.R.H8 is approximately three times larger than the error; i.e., we are able to establish the presence of oscillations at a $3\sigma$ level."
 For the sample of clusters of all richness classes taken ogether (ACOWRAL) the error is approximately equal to he amplitude of oscillations., For the sample of clusters of all richness classes taken together (ACO.R.H1) the error is approximately equal to the amplitude of oscillations.
 This shows that the division of clusters into high- and low-density populations is crucialoscillations. (, This shows that the division of clusters into high- and low-density populations is crucial. (
We note. however. that the power spectrum of the cluster population in rich superclusters is almost identical in shape to the spectrum of the whole cluster population.),"We note, however, that the power spectrum of the cluster population in rich superclusters is almost identical in shape to the spectrum of the whole cluster population.)"
 Now we determine the cluster correlation function separately for the Northern ancl Southern Galactic hemispheres., Now we determine the cluster correlation function separately for the Northern and Southern Galactic hemispheres.
" To increase the number of clusters we use the sample of all clusters. and. divide this sample again into rich ancl poor superclusters using the limiting richness IN,=SN."," To increase the number of clusters we use the sample of all clusters, and divide this sample again into rich and poor superclusters using the limiting richness $N_{cl}=8$."
 Figure + shows the correlation function of clusters located. in rich superclusters separately for both Galactic hemispheres., Figure 4 shows the correlation function of clusters located in rich superclusters separately for both Galactic hemispheres.
 We see that there are some dillerences between the correlation unctions., We see that there are some differences between the correlation functions.
 The oscillatory behaviour is very clear in. both cases. and the period of oscillations is identical (see Table 2).," The oscillatory behaviour is very clear in both cases, and the period of oscillations is identical (see Table 2)."
 The xsic cillerence lies in the amplitude. which is smaller for the eorthern hemisphere.," The basic difference lies in the amplitude, which is smaller for the Northern hemisphere."
 This suggests that the supercluster-vol network is less regular in the Northern hemisphere., This suggests that the supercluster-void network is less regular in the Northern hemisphere.
 Lt is interesting to note that Laney (1996) have determined he power spectrum of galaxies in the deep Las Campanas tedshift Survey. separately for the Northern and Southern Galactic hemispheres., It is interesting to note that Landy (1996) have determined the power spectrum of galaxies in the deep Las Campanas Redshift Survey separately for the Northern and Southern Galactic hemispheres.
 The Southern samples have a strong »alk at a wavelength zz100Ape. whereas in Northern samples this feature is much weaker.," The Southern samples have a strong peak at a wavelength $\approx 100$, whereas in Northern samples this feature is much weaker."
 “Phe similarity of these independent measures of the regularity. of the structure sugeests. first of all. that both methods. (the correlation ancl spectral analyses) work and that they measure the large-scale regularitv of the structure.," The similarity of these independent measures of the regularity of the structure suggests, first of all, that both methods (the correlation and spectral analyses) work and that they measure the large-scale regularity of the structure."
 Secondly. these results indicate that there are small-but-definite differences in the large-scale distribution of high-density regions in the nearby Universe.," Secondly, these results indicate that there are small-but-definite differences in the large-scale distribution of high-density regions in the nearby Universe."
 In other words. Northern and Southern samples. taken separately. do not form fair samples of the Universe.," In other words, Northern and Southern samples, taken separately, do not form fair samples of the Universe."
 The grid size of the supercluster-voick network can. be etermined. from. data given. in Table. 2 using relations between the eric size and parameters eiven in Paper LLL., The grid size of the supercluster-void network can be determined from data given in Table 2 using relations between the grid size and parameters given in Paper III.
 All scaling parameters depend on the period P which is equal to 10 grid size of the supercluster-void network (sce Section 4.4 of Paper HL)., All scaling parameters depend on the period $P$ which is equal to the grid size of the supercluster-void network (see Section 4.4 of Paper III).
" Phe most accurate value of the period comes from the relation 2=;N,,,,,/1.01: here Nuus ds 16 mean separation between maxima and between minima.", The most accurate value of the period comes from the relation $P=\Delta_{mean}/1.01$; here $\Delta_{mean}$ is the mean separation between maxima and between minima.
 We get The variance of the mean period is given mainly by the error of positions of the last maximum and minimum., We get The variance of the mean period is given mainly by the error of positions of the last maximum and minimum.
 The error in the location of the outermost extrema is 25 wwhich contributes an error of 5 iin P., The error in the location of the outermost extrema is 25 which contributes an error of 5 in $P$.
 Phe actual error is larger as we must take into account also possible cosmic scatter of the grid size in cillerent volumes., The actual error is larger as we must take into account also possible cosmic scatter of the grid size in different volumes.
 Comparison of dilferent subsanmples vields the error, Comparison of different subsamples yields the error
forces aud with differeut dissipation streneths are carried out.,forces and with different dissipation strengths are carried out.
 Energy is dissipated via the global dissipation schemo., Energy is dissipated via the global dissipation scheme.
 In Fig., In Fig.
 11 the velocity correlations resulting from three smnmlatious with three different reeularizations are compared., \ref{kk6_1} the velocity correlations resulting from three simulations with three different regularizations are compared.
 The reeularizatious are characterized by two paralcters., The regularizations are characterized by two parameters.
 Niunclv the softeniug leneth € and the paraiucter © that determines the streneth of the repulsive force.," Namely, the softening length $\epsilon$ and the parameter $\xi$, that determines the strength of the repulsive force."
 The softeningo leugthOo aud iJ& of the three simulations. compared in Fig. 11..," The softening length and $\xi$ of the three simulations, compared in Fig. \ref{kk6_1},"
" are. (6€=O01.£ 0.0). aud (e=0.05,6 0.0). where €=0.0 means that a πα potential is applied aud &£,71/3↽ ⋯↸∖⋜⋯↴∖↴↑∐⋜↧↑↴∖↴∐∪↥⋅↑≼∐↴∖↴↑⋜⋯↸⊳↸∖↥⋅↸∖↻∏↕↴∖↴↕↖⇁↸∖↕⋟∪↥⋅↸⊳↸∖↴∖↴⋜∐⋅↸∖⋜↧↑↖↖↽∪∏↘↽ ⋖↴∖↴↸∖↸∖≋↸∖↸⊳↑"," are, $\epsilon=0.01,\xi=0.0$ ), and $\epsilon=0.05,\xi=0.0$ ), where $\xi=0.0$ means that a Plummer potential is applied and $\xi>1/3$ means that short distance repulsive forces are at work (see Sect. \ref{sece}) )."
∙∶≩∙⋅↱⊐⋝⋟∙↽∕∏∐∖≺∐↴∖↴↴∖↴∏≻⋜↧↑↕∪∐↴∖↴⊓⋅↸∖∐∶↴∙⊾↑∐↕↴∖↴↕≯∪↥⋅⋜↧∐↑↕∐⋅↸∖↸∖ ↴∖↴↕∐∐↕↕⋜↧↑↕∪∐↴∖↴↑↕∐∖↴∖↴⋜⋯∐∖∙∩∶↕∩∙⋜⋯≼⇂↑∐↸∖↸⊳∪∐⋜⋯↴∖↴↕∐∶↴∙⊾↑↕⋯↸∖↕↴∖↴ ↸⊳∪∐↴∖↴↸∖≺∣⋯∖∐↑↕⋅↖↽↑∐↸∖↴∖↴⋜∐⊔↸∖⋜↧," The dissipation strength is for all three simulations the same, $\alpha=10$, and the collapsing time is consequently the same as well (see Fig. \ref{kk6kappa}) )."
↴∖↴↖↖⇁↸∖∐⋖↴∖↴↸∖↸∖∏∶↴∙⊾∙⊔⋝⋟∙ ↕≻↿∐⋅↕∐∶↴∙⊾↑∐↸∖∐↥∷∖↴↑∣−↥↳↥↕∪∐∶↴∙⊾≓↥⋅⋜⋯∶↴⋁↸∖↸⊳∪↥⋅↥⋅↸∖↕⋜↧↑↕∪∐↴∖↴↥⋅↸∖↴∖↴∏↕↑↕∐∶↴∙⊾ ↕≯↥⋅∪⋯↑∐↸∖↑↕∐⋅, During the first $\tau_{\rm ff}$ long-range correlations resulting from the three simulations are identical.
↸∖↸∖↴∖↴↕⋯∏↕⋜↧↑↕∪∐↴∖↴⋜∐⋅↸∖↕≼∐∖∐↑↕↸⊳⋜↧↕∙⊺∐↸∖∐↑↕∐∖∩∖≺∣⋮⋟ starts to separate., Then the $\delta(r)$ starts to separate.
 Indeed. the repulsive forces cause an," Indeed, the repulsive forces cause an"
 Indeed. the repulsive forces cause anu," Indeed, the repulsive forces cause an"
 For many stars linear. polarization is produced mainly from scattering of starlight by circumstellar matter (Kruszewski 11968; Serkowski 1970: Dyck 11971; Shawl 1975), For many stars linear polarization is produced mainly from scattering of starlight by circumstellar matter (Kruszewski 1968; Serkowski 1970; Dyck 1971; Shawl 1975).
 This polarization can be used às a diagnostic of the geometry of the circumstellar envelope and of the light source(s) (e.g.. Shakhovskoi 1965: Serkowski 1970; Brown McLean 1977; Brown 11978; Rudy Kemp 1978; Simmons 1982. 1983; Friend Cassinelli 1986: Clarke MeGale 1986. 1987).," This polarization can be used as a diagnostic of the geometry of the circumstellar envelope and of the light source(s) (e.g., Shakhovskoi 1965; Serkowski 1970; Brown McLean 1977; Brown 1978; Rudy Kemp 1978; Simmons 1982, 1983; Friend Cassinelli 1986; Clarke McGale 1986, 1987)."
 In many models for circumstellar scattering polarization. the illuminating sources are treated as isotropic point sources (e.g.. Brown McLean 1977; Brown 11978; Rudy Kemp 1978: Shawl 1975: Simmons 1982).," In many models for circumstellar scattering polarization, the illuminating sources are treated as isotropic point sources (e.g., Brown McLean 1977; Brown 1978; Rudy Kemp 1978; Shawl 1975; Simmons 1982)."
 The effect of the finite size of the star as a light source has been studied (Cassinelli. Nordsieck. Murison 1987). including the effects of limb darkening (Brown 11989) and stellar occultation (Brown Fox 1989: Fox Brown 1991: Fox 1991).," The effect of the finite size of the star as a light source has been studied (Cassinelli, Nordsieck, Murison 1987), including the effects of limb darkening (Brown 1989) and stellar occultation (Brown Fox 1989; Fox Brown 1991; Fox 1991)."
 Variable polarization is also revealing about a system. as evidenced in a recent study by Elias. Koch. Pfeiffer (2008).," Variable polarization is also revealing about a system, as evidenced in a recent study by Elias, Koch, Pfeiffer (2008)."
 With recent emphasis on clumped wind flows of hot stars (e.g.. Hamann. Feldmeier. Oskinova 2008). models have been developed to interpret variable polarization from hot star winds (Richardson. Brown. Simmons 1996; Brown. Ignace. Cassinelli 2000: Li 22000: Davies 22007).," With recent emphasis on clumped wind flows of hot stars (e.g., Hamann, Feldmeier, Oskinova 2008), models have been developed to interpret variable polarization from hot star winds (Richardson, Brown, Simmons 1996; Brown, Ignace, Cassinelli 2000; Li 2000; Davies 2007)."
 Relatively little has been done to explore the anisotropy of the source illumination and its consequences for interpreting polarimetric observations., Relatively little has been done to explore the anisotropy of the source illumination and its consequences for interpreting polarimetric observations.
 There are some exceptions. such as a study of gravity-darkening effects for the polarization from Be stars by Bjorkman Bjorkman (1994). the influence of star spots for polarizations from pre-main sequence stars by Vink ((2005). and more recently calculations of source anisotropy for interpreting polarimetric behavior observed in the post-red supergiant star HD 179821 by Patel ((2008).," There are some exceptions, such as a study of gravity-darkening effects for the polarization from Be stars by Bjorkman Bjorkman (1994), the influence of star spots for polarizations from pre-main sequence stars by Vink (2005), and more recently calculations of source anisotropy for interpreting polarimetric behavior observed in the post-red supergiant star HD 179821 by Patel (2008)."
 In a previous paper (Al-Malki 11999; hereafter Paper D. we modeled the polarization arising from Thomson and Rayleigh scattering explicitly for an arbitrary anisotropic (point) light source.," In a previous paper (Al-Malki 1999; hereafter Paper I), we modeled the polarization arising from Thomson and Rayleigh scattering explicitly for an arbitrary anisotropic (point) light source."
 As a proofof concept. the circumstellar envelope was taken as spherically symmetric to explore the polarization signals that arise solely from the properties of the source.," As a proof of concept, the circumstellar envelope was taken as spherically symmetric to explore the polarization signals that arise solely from the properties of the source."
 An upper limit to the polarization of about was derived in the limiting case of a disk-like star when viewed edge-on., An upper limit to the polarization of about was derived in the limiting case of a disk-like star when viewed edge-on.
distributions.,distributions.
 We have shown that there is a large disparity between tqe shape of the NC»Sys>) produced by the models and that found in our sample., We have shown that there is a large disparity between the shape of the $N(>S_{0.5-2})$ produced by the models and that found in our sample.
 We suggest that this is for the most part due to differences between the actual £—z distribution of sources in the feld. and the XLF/evolution model that we have used.," We suggest that this is for the most part due to differences between the actual $L-z$ distribution of sources in the field, and the XLF/evolution model that we have used."
 These XLF/evolution differences will have had some etfect on the colour distributions produced by the {ΟΛ} models. and could explain the surfeit of HR3=-ἰ sources produced by all of the /6V5) models.," These XLF/evolution differences will have had some effect on the colour distributions produced by the $f(N_H)$ models, and could explain the surfeit of $HR3 = -1$ sources produced by all of the $f(N_H)$ models."
 We have seen some evidence that suggests that the spectra of a significant fraction of absorbed sources in the sample have an additional soft X-ray component., We have seen some evidence that suggests that the spectra of a significant fraction of absorbed sources in the sample have an additional soft X-ray component.
 7This feature was not included in our spectral models. and therefore contributed a large part of the disparity between the HA] distributions of models and sample.," This feature was not included in our spectral models, and therefore contributed a large part of the disparity between the $HR1$ distributions of models and sample."
 Considering this factor. together with the XLF/evolution ditferences. we conclude that the probability for the 6=8 model shows that it provides a rather good fit to the data.," Considering this factor, together with the XLF/evolution differences, we conclude that the probability for the $\beta =8$ model shows that it provides a rather good fit to the data."
 The shape of the 6=8 distribution can be broadly reproduced using a toy model for the torus in which the density falls away rapidly for viewing angles away from the plane of the torus., The shape of the $\beta = 8$ distribution can be broadly reproduced using a toy model for the torus in which the density falls away rapidly for viewing angles away from the plane of the torus.
" We have shown that AGN having logN,,>22 can be ethciently selected by choosing sources in the regions HRI—c4>0.6 and HR?—Ore> —0.3.", We have shown that AGN having $N_H > 22$ can be efficiently selected by choosing sources in the regions $HR1 - \sigma_{HR1} > 0.6$ and $HR2 - \sigma_{HR2} > -0.3$ .
 We intend to extend the methods described here to further deep fields in order to increase the sample size. and to reach to fainter X-ray fluxes.," We intend to extend the methods described here to further deep fields in order to increase the sample size, and to reach to fainter X-ray fluxes."
 Based on observations obtained with XMM-Newton. an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.," Based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA."
 TD acknowledges the support of a PPARC Studentship., TD acknowledges the support of a PPARC Studentship.
Recenth an attempt to build a self-consistent picture was presented by Ligdon.Lingenfelter.&Rothschild(2009):Lingenfelter.Higdon.&ltothschild. (2009).. who assumed that the spatial propagation of positrons. produced. via? decav of “PN HUE) and TAL ds governed by a cdillusion process with the effective dilfusion coellicient. dilferent. in the bulge ancl the disk of the Galaxy.,"Recently an attempt to build a self-consistent picture was presented by \citet{2009ApJ...698..350H,2009PhRvL.103c1301L}, who assumed that the spatial propagation of positrons, produced via $\beta^+$ decay of $^{56}$ Ni, $^{44}$ Ti and $^{26}$ Al, is governed by a diffusion process with the effective diffusion coefficient different in the bulge and the disk of the Galaxy."
 During diffusion the positrons enter the LL and. HE envelopes of molecular clouds. in particular those forming a 7Tilted (Ferriere.Cillard.&Jean2007) within 1.5 kpc of the GC.," During diffusion the positrons enter the HII and HI envelopes of molecular clouds, in particular those forming a “Tilted \citep{2007A&A...467..611F} within 1.5 kpc of the GC."
 The model of Higdon.Lingenfelter.&Rothschild(2009)... with a reasonable set of assumptions. can explain the basic ooperties of the annihilation radiation.," The model of \citet{2009ApJ...698..350H}, with a reasonable set of assumptions, can explain the basic properties of the annihilation radiation."
 Llere we take an alternative route and. consider a possibility that a significant fraction of positrons are born in he hot ISM. which is eventually able to cool via radiative osses ancl perhaps via adiabatie expansion.," Here we take an alternative route and consider a possibility that a significant fraction of positrons are born in the hot ISM, which is eventually able to cool via radiative losses and perhaps via adiabatic expansion."
 We show below hat with these assumptions the spectral properties of the 511 keV line can be casily explained., We show below that with these assumptions the spectral properties of the 511 keV line can be easily explained.
 However. to make our jicture self-consistent one needs to model the thermal state of the ISM. which is bevond the scope of the present. paper.," However, to make our picture self-consistent one needs to model the thermal state of the ISM, which is beyond the scope of the present paper."
 This paper is based. on the data accumulated over ~G6 vears of observations and ainis at placing tighter constraints on the spectral and. spatial properties of the annihilation emission.," This paper is based on the data accumulated over $\sim
6$ years of observations and aims at placing tighter constraints on the spectral and spatial properties of the annihilation emission."
 SPL is a coded mask germanium spectrometer on. board (Winkleretal.2003).. launched in October 2002 aboard a PROTON rocket.," SPI is a coded mask germanium spectrometer on board \citep{2003A&A...411L...1W}, launched in October 2002 aboard a PROTON rocket."
" ""πο instrument. consists of 19 incividual Ge detectors. has a field of view of 30 (at zero response). an effective area at 511 keV of ~70 cnr and energy resolution of ~2 keV(Vedrennectal.2003).. The good energy resolution makes SPL an appropriate instrument for studying the spectrum of ο¢ annihilation emission."," The instrument consists of 19 individual Ge detectors, has a field of view of $\sim$ (at zero response), an effective area at 511 keV of $\sim 70$ $^2$ and energy resolution of $\sim$ 2 keV\citep{2003A&A...411L..63V}. The good energy resolution makes SPI an appropriate instrument for studying the spectrum of $e^+e^-$ annihilation emission."
 For our analysis we use all data available to us by nmid-2009. including public data. some proprietary data (in particular. proposals 0420073. 0520071 and parts of 0620059).," For our analysis we use all data available to us by mid-2009, including public data, some proprietary data (in particular, proposals 0420073, 0520071 and parts of 0620059)."
 Prior to actual data analysis. all incliviclual observations were screened for periods of very high. particle background.," Prior to actual data analysis, all individual observations were screened for periods of very high particle background."
 We use the SPL anticoinciclence (ACS) shield rate as a main indicator of high background., We use the SPI anticoincidence (ACS) shield rate as a main indicator of high background.
 Several additional observations were also omitted from the analysis. e.g. those taken shortly. after. SPL annealing procedures (1toquesetal.2003)..," Several additional observations were also omitted from the analysis, e.g. those taken shortly after SPI annealing procedures \citep{2003A&A...411L..91R}."
 For our analysis we used a combination of single and. pulsc-shape-ciscriminator (PSD) events (seeRoquesctal.2003.fordetails) and treated. them in the Sahle WM., For our analysis we used a combination of single and pulse-shape-discriminator (PSD) events \citep[see][for details]{2003A&A...411L..91R} and treated them in the same way.
 For cach detector. a linear relation between the energy. and the channel number was assumed and calibrated (separately for cach orbit). using the observed energies of lines at  LOS. 438. 584. S82. 1764. 1779. 2223 and 2754 keV (seeWeiden-erouncllines)..," For each detector, a linear relation between the energy and the channel number was assumed and calibrated (separately for each orbit), using the observed energies of lines at $\sim$ 198, 438, 584, 882, 1764, 1779, 2223 and 2754 keV \citep[see][for a comprehensive list of SPI
 background lines]{2003A&A...411L.113W}."
 With this calibration the RAIS deviation of the background 511 keV line cnerey (revolution based) is 0.0066 keV while the mean energy of the line is 510.926 keV. There is thus a small deviation of the line mean energy from 1e electron rest. energy. (510.900. keV): ALO=0.07 keV: it can be attributed to the simplified linear energy/channel relation., With this calibration the RMS deviation of the background 511 keV line energy (revolution based) is 0.0066 keV while the mean energy of the line is 510.926 keV. There is thus a small deviation of the line mean energy from the electron rest energy (510.999 keV): $\Delta E=0.07$ keV; it can be attributed to the simplified linear energy/channel relation.
 ‘This deviation is comparable to the statistical uncertainty on the line energy (see relsce:spec)) and no attempt was mace to correct for this ellect., This deviation is comparable to the statistical uncertainty on the line energy (see \\ref{sec:spec}) ) and no attempt was made to correct for this effect.
" Since the background 511. keV. line (produced. by the positrons annihilating in the body of the detector) is kinematically broadened. we used the two bracketing lines (at 438 and Sst keV) to calculate the resolution at 511 keV as EFWIIMZ,=0.5«(EWIIMass| ΛΗΛ)."," Since the background 511 keV line (produced by the positrons annihilating in the body of the detector) is kinematically broadened, we used the two bracketing lines (at 438 and 584 keV) to calculate the resolution at 511 keV as $\displaystyle {\rm
 FWHM}_{511}=0.5\times({\rm FWHM}_{438}+{\rm FWHM}_{584})$ ."
 The resulting value is FWIIMz;=2.175keV. when averaged over all observations in the vicinity of the Galactic Centre., The resulting value is ${\rm FWHM}_{511}=2.175~{\rm keV}$ when averaged over all observations in the vicinity of the Galactic Centre.
 In the background. modeling we followed the scheme used in Churazovetal. (2005)..., In the background modeling we followed the scheme used in \cite{2005MNRAS.357.1377C}. .
" Namely. the background. count rate Biff) in detector 7 at energy. ids assumed. to be proportional to the detector saturated. (ic. above S MeV) event rate Ao, and time /: where /—1.19 is the detector number."," Namely, the background count rate $B(i,E)$ in detector $i$ at energy $E$ is assumed to be proportional to the detector saturated (i.e. above 8 MeV) event rate $R_{\rm sat}$ and time $t$: where $i=1,19$ is the detector number."
 The coellicients adhd?) and SG.E) of this linear relation were determine separately for each detector/energv channel using all the available SPI cata. while the constant C'(£.£7) was estimate using only the cata away from the Galactic plane au away [rom bright sources.," The coefficients $\alpha(i,E)$ and $\beta(i,E)$ of this linear relation were determined separately for each detector/energy channel using all the available SPI data, while the constant $C(i,E)$ was estimated using only the data away from the Galactic plane and away from bright sources."
 Phe whole data set was divide into 14 time intervals (defined. by the annealing periods and ie dates of individual. detector. failures*)) ancl the cocllicients a(4. 41). 3G.E) and CG.££) were determine separately for each interval.," The whole data set was divided into 14 time intervals (defined by the annealing periods and the dates of individual detector ) and the coefficients $\alpha(i,E)$ , $\beta(i,E)$ and $C(i,E)$ were determined separately for each interval."
 “Phisprocedure. although no providing a perfect description of the background. worksreasonably well at all energies and. given the small number," Thisprocedure, although not providing a perfect description of the background, worksreasonably well at all energies and, given the small number"
are likely to be of extragalactic nature. a few others identified with stars above the NGC 2516 main sequence. should be at smaller distances than NGC 2516. aud they are likely ποσο of the voung nearby stellar population present in all N-ray surveys (Favataetal. 1993)). ον. eivoen the pointing direction. members of the Cotld Belt (Coulloutetal. 1998)).,"are likely to be of extragalactic nature, a few others identified with stars above the NGC 2516 main sequence, should be at smaller distances than NGC 2516, and they are likely members of the young nearby stellar population present in all X-ray surveys \cite{FBMS93}) ), or given the pointing direction, members of the Gould Belt \cite{GSS+98}) )."
" Due to the ""fuzzv imdl-sequence definition at wut magnitudes. a fraction of the sources idenified witi red stars could be faint cluster members."," Due to the “fuzzy” main-sequence definition at faint magnitudes, a fraction of the sources identified with red stars could be faint cluster members."
 Tuchiding detections and wpper-inüts and making use of the iaxiumun-likelibood. Ikapliui-Moeier estimator of integral distribution functious iu case of censored data (c£. Schiunitt1985: Feigelsouaud.Nelson 1985), Including detections and upper-limits and making use of the maximum-likelihood Kaplan-Meier estimator of integral distribution functions in case of censored data (cf. \cite{JHS85}; \cite{FN85}) )
) we have conrputed the X-ray. Iuniuositvfunctions shown in Fie., we have computed the X-ray luminosityfunctions shown in Fig.
" 5 ‘or various eroupiugs of spectral types (B. dA. dE. dC. dl. aud aM),"," \ref{fig:XLF} for various groupings of spectral types (B, dA, dF, dG, dK, and dM)."
 Tn some cases NLFs do not reach the unity since here are upper Bits below the lowest detection so that we have no information below this value., In some cases XLFs do not reach the unity since there are upper limits below the lowest detection so that we have no information below this value.
 Iu general. the NLFs computed over the entire FOV teud o be lower than those couputed iu fjio more restricted FOV.," In general, the XLFs computed over the entire FOV tend to be lower than those computed in the more restricted FOV."
 Applying two-sample tests for censored data. we OUxd the «iference being highest in the case of dix stars (confience level above 99:4)). and less sienificaut (confidence evel ~ )) for the dF aud dM stars. while Or he D. dA. and dC stars the test is inconclusive.," Applying two-sample tests for censored data, we found the difference being highest in the case of dK stars (confidence level above ), and less significant (confidence level $\sim$ ) for the dF and dM stars, while for the B, dA, and dG stars the test is inconclusive."
 In the case of dE. dm ancl. more nareinally. dC stars the NLFs computed over the entire FOV have a lower medians than hat derived in the more restricted ΕΟΝ.," In the case of dF, dK and, more marginally, dG stars the XLFs computed over the entire FOV have a lower medians than that derived in the more restricted FOV."
 For all the cousidered spectral types the NGC 2516 NLEs derived considering only the stars iu the FOV are statistically indistineuishable frou those derived withChandra., For all the considered spectral types the NGC 2516 XLFs derived considering only the stars in the FOV are statistically indistinguishable from those derived with.
 In he case of D. dA. and dC stars we have not Τους. statisical significaut difference between the XLEs derived over the cutive FOV and those derived frou data CITarndeuetal. 20003). while we have founad aun ukication (at confidence level) of difference in the cases of dF aud (AL stars. and a clear difference (at a coufideuce level higher than 99.9%)} in the case of dIx stars. but. as we explain below. field star contamination can be a plausible explanation for these fiudiues.," In the case of B, dA, and dG stars we have not found statistical significant difference between the XLFs derived over the entire FOV and those derived from data \cite{H++00}) ), while we have found an indication (at confidence level) of difference in the cases of dF and dM stars, and a clear difference (at a confidence level higher than ) in the case of dK stars, but, as we explain below, field star contamination can be a plausible explanation for these findings."
 Iu comparing the NGC 2516 NLEs with those of the Pleiades (Micolaetal.1999)) we have found that. irrespectively of the region of the FOV we are considering. the NLFs of D. dA aud dF stars calliot be distinguished (above the confidence level). while the NLFs of diy. stars are different at a coufideuce level higher than99.," In comparing the NGC 2516 XLFs with those of the Pleiades \cite{MSH99}) ) we have found that, irrespectively of the region of the FOV we are considering, the XLFs of B, dA and dF stars cannot be distinguished (above the confidence level), while the XLFs of dK stars are different at a confidence level higher than."
9%... Consideriug the eutime FOV the NLEs of dG aud dM stars ave cliffercut at ~ level. but. when we limit the aualvsis to the ΕΟΝ. the statistical confidence reduces to ~ in the case of dCi stars; aud no difference can be fouud for the dM stars.," Considering the entire FOV the XLFs of dG and dM stars are different at $\sim$ level, but, when we limit the analysis to the FOV, the statistical confidence reduces to $\sim$ in the case of dG stars, and no difference can be found for the dM stars."
 The NGC 2516 NLFs of dC and dix we lave derived over the eutire EPIC FOV reiuforce the suggestion based ou data that NCC 2516 members are less X-ray Iuniuous than the Pleiades ucnmbers of analogous spectral type., The NGC 2516 XLFs of dG and dK we have derived over the entire EPIC FOV reinforce the suggestion based on data that NGC 2516 members are less X-ray luminous than the Pleiades members of analogous spectral type.
 This results is particularly stroug in the case of ον stars., This results is particularly strong in the case of dK stars.
 Table 3.. which compares the median loe(Lx) values for NGC 2516 and the Pleiades. indicates that ray huninuosities are highest for dF aud dC stars.," Table \ref{tab:XLF}, which compares the median $\log(L_{\rm X})$ values for NGC 2516 and the Pleiades, indicates that X-ray luminosities are highest for dF and dG stars."
" NGC 2516 was close das a calibration target in order to ""bore sight” the aliemnent of the X-raw telescope with the detectors. however this cluster is of particular scicutific mterest siuce. beige metal-poor with respect to the Suu. it allows us to explore the effect of imetallieitv ou coronal cuiission level."," NGC 2516 was chosen as a calibration target in order to “bore sight” the alignment of the X-ray telescope with the detectors, however this cluster is of particular scientific interest since, being metal-poor with respect to the Sun, it allows us to explore the effect of metallicity on coronal emission level."
" Usi 33 ks long EPIC data set obtained by sunuuiug the data. all taken wii the thick filter. of the three disinct EPIC cameras of wo distiuc co-pointed ooervations we have reached a linitine seusitivitv of ~2.35«105 Cre loan ? and have «cetected 2Ww sources,"," Using a 33 ks long EPIC data set obtained by summing the data, all taken with the thick filter, of the three distinct EPIC cameras of two distinct co-pointed observations we have reached a limiting sensitivity of $\sim 2.35\times 10^{-15}$ erg $^{-1}$ $^{-2}$ and have detected 208 sources."
 Using ouly data from a single observation and/or from the MOS or PN cameras alone we would have reached a factor 2l worst sensitivity and wotld have detected substantially less sources., Using only data from a single observation and/or from the MOS or PN cameras alone we would have reached a factor 2–4 worst sensitivity and would have detected substantially less sources.
 The attained limiting seusitivitv has allowed us to ΕΠ ficions of NGC 2516 members with a larger nmiuber of deteced members with respect to the survey (Iudei:ctal. 2000))., The attained limiting sensitivity has allowed us to derive luminosity functions of NGC 2516 members with a larger number of detected members with respect to the survey \cite{H++00}) ).
 Tosether with better photometry mace available to us, Together with better photometry made available to us
Standard star formation modes are thought to break down near a supermassive black hole (SAIBIL). raising the question of whether or not star formation near a SMDIL is possible.,"Standard star formation modes are thought to break down near a supermassive black hole (SMBH), raising the question of whether or not star formation near a SMBH is possible,"
Almost all CJF sources (285 sources. of the sample) have been detected in the optical (see Table | in ? Του magnitudes and redshifts).,"Almost all CJF sources (285 sources, of the sample) have been detected in the optical (see Table 1 in \citealt{Britzen2007a} for magnitudes and redshifts)."
 We also investigate the CJF sample for the number of sources that belong to a cluster or a group of galaxies., We also investigate the CJF sample for the number of sources that belong to a cluster or a group of galaxies.
 Because of the large redshift span of the CJF. it is not possible to have cluster information for sources at high z (z> LS. e.g.. 2: ?)).," Because of the large redshift span of the CJF, it is not possible to have cluster information for sources at high z $z > 1.5$ , e.g., \citealt{Brodwin2008}; \citealt{Blakeslee2003}) )."
 We find 54 sources of the sample) belonging to a cluster or group of galaxies (see Table 7))., We find 54 sources of the sample) belonging to a cluster or group of galaxies (see Table \ref{tab:clusters}) ).
 For z«1l. we calculate that of the QSOs έως= 0.60). of the radio galaxies (2).= 0.27). and of the BL Lac objects (Sure= 0.25) are found in clusters.," For $z < 1$, we calculate that of the QSOs $z_{avg}=0.60$ ), of the radio galaxies $z_{avg}=0.27$ ), and of the BL Lac objects $z_{avg}=0.25$ ) are found in clusters."
 We note that radio galaxies appear to be more often members of clusters., We note that radio galaxies appear to be more often members of clusters.
 ?. find a similar trend in their redshift range (e.g.. see Fig.," \citet{Hill1991} find a similar trend in their redshift range (e.g., see Fig."
 11 of ?))., 11 of \citealt{Hill1991}) ).
 Twenty- sources of the sample) show variable fluxes in the optical (intra-day variability has not been taken into account)., Twenty-two sources of the sample) show variable fluxes in the optical (intra-day variability has not been taken into account).
 Someκά of these sources have extensive enough lightcurves to calculate the timescales of thisvariability (see Table 2))., Some of these sources have extensive enough lightcurves to calculate the timescales of thisvariability (see Table \ref{tab:multivar}) ).
of the neutron stars.,of the neutron stars.
 The imagnetie field geometry of orthogonal rotators would produce a high deeree of sauuetry vetween the two magnetic poles which would ο located verv close to cach other., The magnetic field geometry of orthogonal rotators would produce a high degree of symmetry between the two magnetic poles which would be located very close to each other.
 This would jaturallv suppress the signal at he 1/2 subliiauonic. tthe spin frequency. in the fas oscillators aud allow nearly sinultaucous ieuition since the two roles are located very close Ssfayether.," This would naturally suppress the signal at the 1/2 subharmonic, the spin frequency, in the fast oscillators and allow nearly simultaneous ignition since the two poles are located very close together."
 Chenetal.(1993) estimate hat spin up from 10 s to uillisecond. periods compresses the magnetic field iuto a region with a radius of about 105ci around he spin axis.," \citet{chen93} estimate that spin up from 10 s to millisecond periods compresses the magnetic field into a region with a radius of about $10^{4} \rm \, cm$ around the spin axis."
 For a vpical neutron star radius of 10cm. the poles would then be less than 1 roni the spin axis and be autipodal within 2* as Ainoetal.(2002) couchide is required to explain he lack of harmonics and sub-liaxmonies ii burst oscillations.," For a typical neutron star radius of $10^{6} \rm \, cm$, the poles would then be less than $1\arcdeg$ from the spin axis and be antipodal within $2\arcdeg$ as \citet{muno02} conclude is required to explain the lack of harmonics and sub-harmonics in burst oscillations."
 The requirement that there be no nore than difference in the relative brightucss of the two poles iu the main aud decaxiug portions of bursts (Munoetal.2002) is more difficult o address. but the high degree of svuunctiv )etwoeen the two poles and their close location for orthogonal rotators sugeest that such wniformity uav be achieved several rotation periods after ignition of the burst.," The requirement that there be no more than difference in the relative brightness of the two poles in the main and decaying portions of bursts \citep{muno02} is more difficult to address, but the high degree of symmetry between the two poles and their close location for orthogonal rotators suggest that such uniformity may be achieved several rotation periods after ignition of the burst."
 We ereatly appreciate the assistance by the duty scieutists of the BeppoSAX Science Operations Center in the near to real-time WEC data analysis and the efforts of the RATE team. particularly Jean Swank aud Evan Suuth. in performing these target of opportunity observations," We greatly appreciate the assistance by the duty scientists of the BeppoSAX Science Operations Center in the near to real-time WFC data analysis and the efforts of the RXTE team, particularly Jean Swank and Evan Smith, in performing these target of opportunity observations."
 PIs thanks Mal Ruderman for useful discussious aid acknowledges partial support from NASA eraut NAG5-7105., PK thanks Mal Ruderman for useful discussions and acknowledges partial support from NASA grant NAG5-7405.
 JZ acknowledges finaucial support from the Netherlands Organization for Scicutifie Research (NWO)., JZ acknowledges financial support from the Netherlands Organization for Scientific Research (NWO).
 R=0.38 (32 R=0.36 (2775).,"$B-V=0.69$ , $V-R=0.38$ $''$ $B-V=0.56$, $V-R=0.36$ $''$ S)."
" and for the smallor rine: B Vc-u6)VR= ο B V-u5LV.R=0.13 (1"" E)."," and for the smaller ring: $B-V=0.69$, $V-R=0.48$ $''$ W), $B-V=0.54$, $V-R=0.43$ $''$ E)."
 Therefore. both riugs are bluer than the central galaxy (seo previous section). and its extinction and redshift corrected colors (BV20.5. Vzz 0.1) are typical for Sc-Sced ταῖς (Buta et al.," Therefore, both rings are bluer than the central galaxy (see previous section), and its extinction and redshift corrected colors $B-V\approx0.5$, $V-R\approx0.4$ ) are typical for Sc-Scd spirals (Buta et al."
 1991: Buta Williams 1995) and similar∙∙ to those of. PRC vines. (Beshetuikov. et al., 1994; Buta Williams 1995) and similar to those of PRG rings (Reshetnikov et al.
 ;1991. 1995).," 1994, 1995)."
 Both vinesc» show a color asviuietry. in the seuse that their N aud W parts are redder. which is not unusual for polar rings sce for instance the correlation found between the large-scale color asviiuietry in the rings of tle PRCs UGCT7368 ory7576 and UGCT7365 9796.," Both rings show a color asymmetry, in the sense that their N and W parts are redder, which is not unusual for polar rings – see for instance the correlation found between the large-scale color asymmetry in the rings of the PRGs UGC 7576 and UGC 9796."
QTOE Various⇁⋅ techniques⋅ ofe. image. eubhaucement have been eniploved.] to reveal fine structure within ESO [71-6326 : ⋖↴∖↴↸∖↸∖∙↕∪↥⋅↸∖⊼⋜⋯∏≻↕↸∖∙⊑∏∐⊔∐∐∖∑⊐≚↴⋝⋜⋯↴∖↴∙∖↽≼∐∖≼∐↕↖⇁↸∖∐⋅⋜⊢⊀≚↴⋝⋜⋯↴∖↴ ; ↽∙∙ L998. for a description of some techniques).," Various techniques of image enhancement have been employed to reveal fine structure within ESO 474-G26 (see, for example, Faúnndez-Abans de Oliveira-Abans 1998, for a description of some techniques)."
 In Fig., In Fig.
 7 we ]xeseut the residual imageS of the Sgalaxy., 7 we present the residual image of the galaxy.
 The smaller (east west) ring looks very mregulu.[m] with αν coucdensations.," The smaller (east – west) ring looks very irregular, with many condensations."
 The c»brightest condeusatious show Dz21 (or Mpzz 16) aud angular sizes around 2” (2 Ipc)., The brightest condensations show $B\approx21$ (or $M_B\approx-16$ ) and angular sizes around $''$ (2 kpc).
 Most probably. the condeusatious represent eiaut regions.," Most probably, the condensations represent giant regions."
 The larger outer (northsouth) rime has the southern part approaching: (PRC.4 Galletta4 et al.," The larger outer (north–south) ring has the southern part approaching (PRC, Galletta et al."
 E1997)., 1997).
= The: western part of the ring is probably the nearest to us (frou the dust lane crossing the western side of the ceutral body Fig., The western part of the ring is probably the nearest to us (from the dust lane crossing the western side of the central body – see Fig.
 D)., 1).
 ∙≓In Fig., In Fig.
 5∙ we∖ present a deep (3 |V.etR) and (1997): hedimage of ESO. 171-626., 8 we present a deep $B+V+R$ ) and smoothed image of ESO 474-G26.
 A faint (pi( V)=267) asviuuetric envelope extends to the east., A faint $\mu(V) \geq 26^m$ ) asymmetric envelope extends to the east.
 The North aud South edges of the large ring show extcusions towards the cast and west. respectively: they might be spiral aris.," The North and South edges of the large ring show extensions towards the east and west, respectively; they might be spiral arms."
 The true ecometrical structure aud the possible origiu of ESO I71-G26 are intriguing imvsteries., The true geometrical structure and the possible origin of ESO 474-G26 are intriguing mysteries.
 A nunuber of formation scenarios resonance rine. accretion on areed carly-type galaxy. aud a nünoriuaerger — can be excluded. for the following reasons:," A number of formation scenarios – resonance ring, accretion on aringed early-type galaxy, and a minor merger – can be excluded, for the following reasons:"
lis work.,this work.
 This prompted us to prudeutlv screen cach object detected close to the published positions of 5832., This prompted us to prudently screen each object detected close to the published positions of $-$ 5832.
 In particular. we note that its racdio-timing xositiou (Fie.," In particular, we note that its radio-timing position (Fig."
 1. right panel) falls close to à V—21 object (Star C). even detected in the short 15s exposures used or the image astrometry. right ou the edge of the radio error circle (~ 1722).," 1, right panel) falls close to a $V\sim 24$ object (Star C), even detected in the short 15s exposures used for the image astrometry, right on the edge of the radio error circle $\sim 1\farcs22$ )."
 Again. based on position alone we can not rule out that Star C dis associated with the pulsar.," Again, based on position alone we can not rule out that Star C is associated with the pulsar."
 However. the probability of chance coincidence with field objects of maguitude V.Z 2lis P~0.01. Le. certainly not low cnough to statistically claim an association.," However, the probability of chance coincidence with field objects of magnitude $V\ga 24$ is $P\sim 0.04$, i.e. certainly not low enough to statistically claim an association."
 Iu addition. such an association is problematic from the point of view of the pulsus cnerectics.," In addition, such an association is problematic from the point of view of the pulsar's energetics."
 As done in Sect., As done in Sect.
 3.1. we COMPALCE the brightuess of Star € with that expected for the pulsar.," 3.1, we compared the brightness of Star C with that expected for the pulsar."
 By assiuuiug an optical efficiency comparable to that of the Vela pulsar. 5832's rotational enerev loss (E2<108° ere 1) wouk then imply oulv a factor of ~3 lower optical bhuuimositv.," By assuming an optical efficiency comparable to that of the Vela pulsar, $-$ 5832's rotational energy loss $\dot{E} \sim 2 \times 10^{36}$ erg $^{-1}$ ) would then imply only a factor of $\sim 3$ lower optical luminosity."
 Following the sale analysis as for 6129 (see Sect., Following the same analysis as for $-$ 6429 (see Sectn.
" 3.1). at the 5832 distance (2.7£0.35 kpc) aud for the corresponding- interstellar- extinction- (4,5!222 Ty) derived frou the Nyy0.0tl«107 7. (Marelli et 22011). we determine an expected magnitude Doe 33.3037. accounting for both the distance and iuterstellar extinction uncertainties."," 3.1), at the $-$ 5832 distance $2.7\pm 0.35$ kpc) and for the corresponding interstellar extinction $A_V = 5^{+2.2}_{-1.1}$ ), derived from the $N_H=0.9^{+0.4}_{-0.2} \times 10^{22}$ $^{-2}$ (Marelli et 2011), we determine an expected magnitude $V\sim33.3$ –37, accounting for both the distance and interstellar extinction uncertainties."
 Similarly. assuuius more optinüsticallv an cussion efficiency comparable to that of the Crab pulsar. we derive au expected magnitude of V~25 28.7.," Similarly, assuming more optimistically an emission efficiency comparable to that of the Crab pulsar, we derive an expected magnitude of $V\sim 25$ –28.7."
 This mcaus that. if Star C were indeed the 5832 optical counterpart. the pulsar should lave an endsson efüciencev ~2 SO times larger than the Crab.," This means that, if Star C were indeed the $-$ 5832 optical counterpart, the pulsar should have an emission efficiency $\sim 2$ –80 times larger than the Crab."
 On the other hand. by using the relation between he N-vay and optical luminosity (Zharikov et 22001: 2006) as done in Sectu.," On the other hand, by using the relation between the X-ray and optical luminosity (Zharikov et 2004; 2006) as done in Sectn."
 3.1. we obtain a maenitude iu he range V— 2931.," 3.1, we obtain a magnitude in the range $V\sim$ 29–34."
 Thus. Star € cannot be the pulsar optical counterpart.," Thus, Star C cannot be the pulsar optical counterpart."
 Then. we searched for a possible counterpart at the ulsu )ositiou.," Then, we searched for a possible counterpart at the pulsar position."
 No object is detected within. or close to. the (007555) error circle apart from a faint object (Star D: V~ 26.7) visible ~176 southwest of it (Fig.3. right}.," No object is detected within, or close to, the 55) error circle apart from a faint object (Star D; $V\sim 26.7$ ) visible $\sim 1\farcs6$ southwest of it (Fig.3, right)."
 However. the offset is about 3 times the lo uncertainty ou the pulsar position.," However, the offset is about 3 times the $1	 \sigma$ uncertainty on the pulsar position."
 Thus. we decim the association unlikely both ou the basis of the loose positional coincidence aud ou statistical erounds. with a chance coincidence probability DPo008.," Thus, we deem the association unlikely both on the basis of the loose positional coincidence and on statistical grounds, with a chance coincidence probability $P\sim 0.08$."
 Aloreovor. the lack of colour information makes it inpossible to constrain the nature of this object.," Moreover, the lack of colour information makes it impossible to constrain the nature of this object."
 Therefore. we conclude that 5832 is nof detected in the inaeoe.," Therefore, we conclude that $-$ 5832 is not detected in the image."
 Following he same procedure as used in Sect., Following the same procedure as used in Sect.
 23.1. we determined the παο of counts corresponding to a 30 detection limit in a pphotometiy aperture (41 pixel) from the standard deviation of the background sampled within the cerror circle.," 3.1, we determined the number of counts corresponding to a $3 \sigma$ detection limit in a photometry aperture (4 pixel) from the standard deviation of the background sampled within the error circle."
 After applving the aperture correction. this vield to a 36 detection limit of V.— 27.6.," After applying the aperture correction, this yield to a $3\sigma$ detection limit of $V\sim 27.6$ ."
llence the Fourier transform Again. we add these estimates of c in some optimal fashion paremeterised by a: Calculating the mean square of this field and minimising with respect to e. we find that the optimal estimate of 5 ds eiven by: This provides us with the mass-mapping equations we have been seeking.,"Hence the Fourier transform Again, we add these estimates of $\tilde{\psi}$ in some optimal fashion parameterised by $a$: Calculating the mean square of this field and minimising with respect to $a$, we find that the optimal estimate of $\kappa$ is given by: This provides us with the mass-mapping equations we have been seeking."
 We can now obtain mass maps withindependent noise for 5. F and ο. and combine these with minimum variance weighting (with respect to noise) in order to obtain a best mass map.," We can now obtain mass maps withindependent noise for $\gamma$, $\flex$ and $\sflex$, and combine these with minimum variance weighting (with respect to noise) in order to obtain a best mass map."
 These mapping relations can be ellicienthy expressed and trivially derived in the complex notation of Section 3 using equation (19)): 20.ἐςHD)po0ó where the complex. part is again seen to give us the B- component which can be used as a test of systematics., These mapping relations can be efficiently expressed and trivially derived in the complex notation of Section 3 using equation \ref{eqn:dfg}) ): + i = ^* } + i = ^* ^* } where the complex part is again seen to give us the B-field component which can be used as a test of systematics.
 Comparing these two derivations of the mapping equations. we see that (67)) gives the solution in the case of no noise. while (62)) ancl (66)) show that this is still optimal in the presence of noise due to intrinsic Uexion.," Comparing these two derivations of the mapping equations, we see that \ref{complexmap}) ) gives the solution in the case of no noise, while \ref{eqn:mapf}) ) and \ref{eqn:mapg}) ) show that this is still optimal in the presence of noise due to intrinsic flexion."
 The mapping process is illustrated in Figures 7 and 8., The mapping process is illustrated in Figures 7 and 8.
" Llere we have simulated a projected surface density for a tov cluster of galaxies. using a Gaussian cluster gravitational »»tential profile with width σ=3"" and mean & within this radius of &=0.06."," Here we have simulated a projected surface density for a toy cluster of galaxies, using a Gaussian cluster gravitational potential profile with width $\sigma=3'$ and mean $\kappa$ within this radius of $\kappa=0.06$."
 We have Iaid down three substructure Gaussians containing of the mass. with width o=1’ (one at the centre of the cluster).," We have laid down three substructure Gaussians containing of the mass, with width $\sigma=1'$ (one at the centre of the cluster)."
 The associatect shear ancl lexion fields shown in Figure 7 were caleulatecl directly rom equations (17)) ancl (20))., The associated shear and flexion fields shown in Figure 7 were calculated directly from equations \ref{eqn:gamma}) ) and \ref{eqn:fg}) ).
 Note from this figure that he shear does not respond. significantly to the small-scale structure. while Ποκίο is most alfected at these scales: this is inline with our results for galaxv-galaxy Uexion. and will be explored more in the following section.," Note from this figure that the shear does not respond significantly to the small-scale structure, while flexion is most affected at these scales; this is in line with our results for galaxy-galaxy flexion, and will be explored more in the following section."
 We also note from the figure that the first Dlexion responds locally to the density eracient. whereas the second. Hexion responds: non-locally while still giving large signals near substructure.," We also note from the figure that the first flexion responds locally to the density gradient, whereas the second flexion responds non-locally while still giving large signals near substructure."
 Shot noise is added to these fields with o.=0.2. σε=ogU44 and projected. number density n=60 as appropriate Lor a space-based survey such as CEALS (c.g. Rix et al 2004).," Shot noise is added to these fields with $\sigma_\gamma=0.2$, $\sigma_{\flex}=\sigma_{\sflex}=0.04$ and projected number density $n=60$ as appropriate for a space-based survey such as GEMS (e.g. Rix et al 2004)."
 We have then used our inversion procedure (equations 62 and 66)) together with the Ixaiser-Squires inversion for shear. to obtain maps of & from these fields. which are displayed in Figure S together with a combined convergence map from all fieles accded with minimum variance weighting.," We have then used our inversion procedure (equations \ref{eqn:mapf}
 and \ref{eqn:mapg}) ) together with the Kaiser-Squires inversion for shear, to obtain maps of $\kappa$ from these fields, which are displayed in Figure 8 together with a combined convergence map from all fields added with minimum variance weighting."
 The shear field has been smoothed. with a Gaussian of radius 0.5 as it suffers from. large Ποιατος on small scales. while the Ucxion is smoothec with radius 0.1 as does not suffer (rom this problem.," The shear field has been smoothed with a Gaussian of radius 0.5' as it suffers from large fluctuations on small scales, while the flexion is smoothed with radius 0.1' as does not suffer from this problem."
 We note that the surface density is reconstructed well from. all three fields. with maximum signal-to-noise of 3.6 for the shear reconstruction and 3.5 for the two Uexion reconstructions combined.," We note that the surface density is reconstructed well from all three fields, with maximum signal-to-noise of 3.6 for the shear reconstruction and 3.5 for the two flexion reconstructions combined."
 Lt is eratifving that the signal-to-noise for the two approaches are so similar. and strongly emphasises the value of measuring Hexion as well as shear.," It is gratifying that the signal-to-noise for the two approaches are so similar, and strongly emphasises the value of measuring flexion as well as shear."
 We also note that [lexion. does indeed. measure the substructure concentrations at. the 1.4-2.60 level. whereas shear is not able to detect. these subhalos.," We also note that flexion does indeed measure the substructure concentrations at the $\sigma$ level, whereas shear is not able to detect these subhalos."
 Future lensing maps of density will therefore benefit significantly from the inclusion of the Hexion signal. especially for the purpose of charting the substructure.," Future lensing maps of density will therefore benefit significantly from the inclusion of the flexion signal, especially for the purpose of charting the substructure."
" We will now briclly note how to extend this method in order to map the density of matter in three dimensions with llexion. following the concepts of Tavlor (2001) and ζω ""Tavlor (2003)."," We will now briefly note how to extend this method in order to map the density of matter in three dimensions with flexion, following the concepts of Taylor (2001) and Bacon Taylor (2003)."
 For this. we need to know what eravitational flexion we would measure upon a galaxy at any 3-D point in the Universe.," For this, we need to know what gravitational flexion we would measure upon a galaxy at any 3-D point in the Universe."
" We will κου in the next section that the effective Hexion along a line of sight over cosmological distances is given by where 444 is the Hubble constant. ,, is the matter density at the present epoch. e is the speed. of light. «e is comoving distance. @ is the expansion factor. 6 isthe overdensity of matter anc oa is the transverse. physical distance."," We will see in the next section that the effective flexion along a line of sight over cosmological distances is given by where $H_0$ is the Hubble constant, $\Omega_m$ is the matter density at the present epoch, $c$ is the speed of light, $w$ is comoving distance, $a$ is the expansion factor, $\delta$ isthe overdensity of matter and $x$ is the transverse physical distance."
 Now for a function. 10) that can be written as the integral of a function Du.iw). we can write the rate of change of zd with respect tow as Now ν is in a suitable form for cl. with D given in equation (68)).," Now for a function $A(w)$ that can be written as the integral of a function $B(w',w)$, we can write the rate of change of $A$ with respect to $w$ as Now $\flex$ is in a suitable form for $A$ , with $B$ given in equation \ref{eqn:feff}) )."
 We can therefore use equation (70)) to invert the integral for A. and find that the transverse egraclient of the matter overdensity. 9 can be caleulated in terms of the measured 3-D. [lexion:," We can therefore use equation \ref{eqn:ab}) ) to invert the integral for $\flex$ , and find that the transverse gradient of the matter overdensity, $\delta'$ can be calculated in terms of the measured 3-D flexion:"
the thermal line width. behaviour not found iu starless cores but which could be explained by the preseuce of au eiibedded protostar.,"the thermal line width, behaviour not found in starless cores but which could be explained by the presence of an embedded protostar."
 Broad line widths of aan Hu L1151-uun led to the discovery of a protostar in that core even though it had previously been ideuti&ed as starless (Pinedaetal.2011)., Broad line widths of and in L1451-mm led to the discovery of a protostar in that core even though it had previously been identified as starless \citep{Pineda11}.
. The preseuce of redshifted and blueshifted eenission seen about from the systemic velocity of the core would also not © expected ina starless core. but could be explained. by an outflow from an embedded: protostar.," The presence of redshifted and blueshifted emission seen about from the systemic velocity of the core would also not be expected in a starless core, but could be explained by an outflow from an embedded protostar."
 SiO. emission ocated adjacent to. Per-Bolo 15. can be. explained w the interaction between the ambient material iu he molecular cloud and an outflow launched bv the core., SiO emission located adjacent to Per-Bolo 45 can be explained by the interaction between the ambient material in the molecular cloud and an outflow launched by the core.
" Finally. the 311012 contiuuun enmuüsson detected owards Per-Bolo 15 is also suggestive of a possible embedded source. eiven that 21212uui continui emission was detected with CARMA towards Per-Bolo 58 and Ll5ll-uuu. two supposedly ""starless"" cores that were subsequently fouud to be protostellar (Enochetal.2010:Dunhametal.2011:Pineda201 1)."," Finally, the mm continuum emission detected towards Per-Bolo 45 is also suggestive of a possible embedded source, given that mm continuum emission was detected with CARMA towards Per-Bolo 58 and L1541-mm, two supposedly “starless” cores that were subsequently found to be protostellar \citep{Enoch10, Dunham11, Pineda11}."
. None of the other starless cores surveved with CARM by Schuceal.(2010). exhibited 32121uu contiuuun emission., None of the other starless cores surveyed with CARMA by \citet{Schnee10} exhibited mm continuum emission.
 Given that Per-Bolo 15 is iu the NCC 1332. cluster. it is dmuportaunt to check that the outflow does not originate frou another nearby protostar.," Given that Per-Bolo 45 is in the NGC 1333 cluster, it is important to check that the outflow does not originate from another nearby protostar."
 The elongation of the SiO enissiou points back towards the III 7-11 eroup associated with SVS 13. aud even further perhaps towards IRAS L. but cach of these cores have well-known outflows eoineiu directions other than towards Pcr-Dolo 15.," The elongation of the SiO emission points back towards the HH 7-11 group associated with SVS 13, and even further perhaps towards IRAS 4, but each of these cores have well-known outflows goingin directions other than towards Per-Bolo 45."
 For example. a CO (3-2) map of NGC. 1333 shows no outflow directed towards Per-Bolo 15 from any other object (Curtisetal.2010).," For example, a CO (3-2) map of NGC 1333 shows no outflow directed towards Per-Bolo 45 from any other object \citep{Curtis11}."
. Iustead. Per-Bolo 15 seenis to be adjacent to a compact red lobe cmanating roni IRAS 7 to the northeast aud a very exteuded red obe cimanating from IRAS 2 in the southwest.," Instead, Per-Bolo 45 seems to be adjacent to a compact red lobe emanating from IRAS 7 to the northeast and a very extended red lobe emanating from IRAS 2 in the southwest."
 These redshifted lobes have velocity ranges of to aand their blueshifted lobes range from ttozus.. both outside the range of velocities associated with he redshifted aud bhieshitted eenission frou Per-Bolo 15.," These redshifted lobes have velocity ranges of to and their blueshifted lobes range from to, both outside the range of velocities associated with the redshifted and blueshifted emission from Per-Bolo 45."
 It would also be difficult to explain how au outflow from elsewhere in the NGC 1333 cluster could interact with the deuse material in Per-Bolo 15 traced by aan Hu such a way as to increase turbulence munediatelv to the south-east of the τα contimmun peak. without also affecting the area with nearly thermal line widths around it., It would also be difficult to explain how an outflow from elsewhere in the NGC 1333 cluster could interact with the dense material in Per-Bolo 45 traced by and in such a way as to increase turbulence immediately to the south-east of the mm continuum peak without also affecting the area with nearly thermal line widths around it.
 We conclude that the molecular line observations prescuted iu this paper are best explained by the presence of a protostar embedded within Per-Bolo 15., We conclude that the molecular line observations presented in this paper are best explained by the presence of a protostar embedded within Per-Bolo 45.
 A relationship between the internal hunuinositv of a voung stellar object (YSO) aud its flux is eiven by Equation 2 iu Dunhametal.(2008)., A relationship between the internal luminosity of a young stellar object (YSO) and its flux is given by Equation 2 in \citet{Dunham08}.
. Per-Bolo 15 is not detected atnicron.. but we can use a 36 upper limit to its fflux to estimate au upper lt to the internal Iuninosity of the embedded source.," Per-Bolo 45 is not detected at, but we can use a $\sigma$ upper limit to its flux to estimate an upper limit to the internal luminosity of the embedded source."
 We find that the internal luminosity of Per-Bolo 15 is less than LO?solu. simular to the upper limit for Llli5l-nuu bv Pinedaetal.(2011) aud lower bv a factor of about LO than the huninosities of the embedded: protostars observed bySpitzer with published models shown iu Table 1 of Dunhametal.(2008).," We find that the internal luminosity of Per-Bolo 45 is less than $10^{-2}$, similar to the upper limit for L1451-mm by \citet{Pineda11} and lower by a factor of about 10 than the luminosities of the embedded protostars observed by with published models shown in Table 1 of \citet{Dunham08}."
. The upper liuüt to the huninosity of the embedded source iu Per-Bolo 15 is consistent with the seusitivitv lint of the c2d survey., The upper limit to the luminosity of the embedded source in Per-Bolo 45 is consistent with the sensitivity limit of the c2d survey.
 Asstuning that Per-Bolo [5 is protostcllar. the lack of observed ffiux would make this source a VeLLO by the definition eiven in DiFrancescoetal.(2007).," Assuming that Per-Bolo 45 is protostellar, the lack of observed flux would make this source a VeLLO by the definition given in \citet{DiFrancesco07}."
. A protostellar source with a disk viewed edee-on might remain invisible at the observed seusitivitv lmits. so it is possible that the internal huninesity of Per-Bolo 15 is higher than that of a VeLLO and it appears dim because of the viewing angle.," A protostellar source with a disk viewed edge-on might remain invisible at the observed sensitivity limits, so it is possible that the internal luminosity of Per-Bolo 45 is higher than that of a VeLLO and it appears dim because of the viewing angle."
 Given its low Ihuninositv. the source eiibedded in Per-Bolo 15 is also a plausible first hydrostatie core candidate.," Given its low luminosity, the source embedded in Per-Bolo 45 is also a plausible first hydrostatic core candidate."
 Iu this paper we ideutifv Per-Bolo 15 as à core with au embedded source. changing its classification from starless core (Enochetal.2008) to VeLLO.," In this paper we identify Per-Bolo 45 as a core with an embedded source, changing its classification from starless core \citep{Enoch08}
 to VeLLO."
 Other cores in the Perseus molecular cloud. previously identified as starless due to thei lack of near- and uic-iutrared emission (e.g.Enochetal.2008:Sadavov2010a) but subsequeutlv fouud to show evidence for protostellar activity. such as loumnchiug molecular outflows. mclude Per-Bolo 58 (Enochetal.2010:Duuhaim2011) LIL IRS2E (Chenotal.2000).. and L1151-uun (Pinedaetal. 2011).," Other cores in the Perseus molecular cloud, previously identified as starless due to their lack of near- and mid-infrared emission \citep[e.g.][]{Enoch08, Sadavoy10} but subsequently found to show evidence for protostellar activity, such as launching molecular outflows, include Per-Bolo 58 \citep{Enoch10,Dunham11} , L1448 IRS2E \citep{Chen10a}, and L1451-mm \citep{Pineda11}."
". Qut of the LL ""starless cores m Perseus surveved by Schueeetal.(2010) with interferometric observations of their 21212. coutinua. the oulv two cores detected (Per-Bolo 15 aud Per-Bolo 58) have since been shown to harbour euibedded objects."," Out of the 11 “starless” cores in Perseus surveyed by \citet{Schnee10} with interferometric observations of their mm continuum, the only two cores detected (Per-Bolo 45 and Per-Bolo 58) have since been shown to harbour embedded objects."
 This fraction of misidentified starless cores tn Perseus. 2/11 or d& probably an upper lit eiven that the cores in the Schneeotal.(2010) sample were chosen to have hieh surface xiehtuesses im the Llama contin map of Enochetal. (2006).. aud the presence of a protostar would mcerease he peal flux of a dense core.," This fraction of misidentified starless cores in Perseus, 2/11 or, is probably an upper limit given that the cores in the \citet{Schnee10} sample were chosen to have high surface brightnesses in the mm continuum map of \citet{Enoch06}, and the presence of a protostar would increase the peak flux of a dense core."
 A lower limit to the umuber of cores in Perseus wisideutified as starless can be derived frou the umber of previously identified starless cores and the uuuber of 1ewly identified protostars :uid VeLLOs., A lower limit to the number of cores in Perseus misidentified as starless can be derived from the number of previously identified starless cores and the number of newly identified protostars and VeLLOs.
 This estimate xovides a lower linit becase not every core ideutified in wide-field dust continu maps of Perseus has oen followed up with (sul»nullimeter interferometric nolecular line observations o find outflows., This estimate provides a lower limit because not every core identified in wide-field dust continuum maps of Perseus has been followed up with (sub)millimeter interferometric molecular line observations to find outflows.
 Sacdavoyctal.(2010a) πια 97 starless cores and £6 protostellar cores in Perseus. using SCUBA naps to ideutifv the cores andSpitzer maps between 3.6 aud to determine the starless or protostellar status of cach," \citet{Sadavoy10} find 97 starless cores and 46 protostellar cores in Perseus, using SCUBA maps to identify the cores and maps between 3.6 and to determine the starless or protostellar status of each"
order pileup and find that the pileup fraction (defined to be the fraction of all frames that have events 72 photons during that frame) is86%.. (,order pileup and find that the pileup fraction (defined to be the fraction of all frames that have events $> 2$ photons during that frame) is. (
The average count rates are ~letss! from Oth order. and 1etss! from the total of all dispersed events.),"The average count rates are $\sim 1 \, \rm cts \,
s^{-1}$ from 0th order, and $1 \, \rm cts \, s^{-1}$ from the total of all dispersed events.)"
 Accordingly. only 0.04etss! are expected in single photon events making useful spectroscopic information difficult. to extract from zeroth order.," Accordingly, only $0.04 \, \rm cts \, s^{-1}$ are expected in single photon events making useful spectroscopic information difficult to extract from zeroth order."
 We use the software package (Houck DeNicola 2000) for the data analysis We extract PCA (Proportional Counter Array) light curves and spectra from only the top Xenon layer using the software., We use the software package (Houck DeNicola 2000) for the data analysis We extract PCA (Proportional Counter Array) light curves and spectra from only the top Xenon layer using the software.
 Data from layer | of PCUs 0. 2. and 4 are combined to improve signal-to-noise at the expense of slightly blurring the spectral resolution.," Data from layer 1 of PCUs 0, 2, and 4 are combined to improve signal-to-noise at the expense of slightly blurring the spectral resolution."
 Good time intervals were selected to exclude any earth or South Atlantic Anomaly (SAA) passage occulations. and to ensure stable pointing.," Good time intervals were selected to exclude any earth or South Atlantic Anomaly (SAA) passage occulations, and to ensure stable pointing."
 We also filter out electron contamination events., We also filter out electron contamination events.
 L7-240 background data are generated usingV4., L7-240 background data are generated using.
Oc. The PCA response matrix for the data set was created using1., The PCA response matrix for the data set was created using.
 Background models and response matrices are representative of the most up-to-date PCA calibrations., Background models and response matrices are representative of the most up-to-date PCA calibrations.
 The PCA is better suited for constraining the continuum shape as a consequence of its wide band coverage., The PCA is better suited for constraining the continuum shape as a consequence of its wide band coverage.
 From these data. we obtain the best-fit photon index T=1.93 +0.02.," From these data, we obtain the best-fit photon index $\Gamma = 1.93 \pm 0.02$ ."
 These fits were performed in with a simple Galactic (4.06«10-9 em-7) absorbed power-law using the 3.3-4.6 keV and 8.0-10 keV spectral data (\7/dof =5.96/6).," These fits were performed in with a simple Galactic $4.06
\times 10^{20}\, \rm cm^{-2}$ ) absorbed power-law using the $-$ 4.6 keV and $-$ 10 keV spectral data $\chi^2 / dof =
5.96/6$ )."
 The 4.6—8 keV energy range were excluded in order that we may obtain the best description of D with minimal bias from the red wing of the broad iron line which can extend redwards to well below 5 keV (e.g. Fig. 3..," The $4.6-8$ keV energy range were excluded in order that we may obtain the best description of $\Gamma$ with minimal bias from the red wing of the broad iron line which can extend redwards to well below 5 keV (e.g. Fig. \ref{fig-hegasca},"
 Tanaka et al., Tanaka et al.
 1995. Iwasawa et al.," 1995, Iwasawa et al."
 1996). or even farther (e.g. Wilms et al.," 1996), or even farther (e.g. Wilms et al."
 2002. Fabian et al.," 2002, Fabian et al."
 2002)., 2002).
 We next determined the power-law normalization which best describes the HETGS spectrum by fitting the MEG and HEG (respectively. medium and high energy grating) 4 keV data. with a power-law (I fixed at the best-fit value) modified by 2«107!em absorption (to accomodate the warm absorber which has ὃς3% effect at 3 keV. and no effect at <4 keV).," We next determined the power-law normalization which best describes the HETGS spectrum by fitting the MEG and HEG (respectively, medium and high energy grating) $3-4$ keV data, with a power-law $\Gamma$ fixed at the best-fit value) modified by $2 \times 10^{21} \, \rm cm^{-2}$ absorption (to accomodate the warm absorber which has $\approxlt 3$ effect at 3 keV, and no effect at $\approxgt 4$ keV)."
 This limited energy range was chosen in order to avoid contamination from the absorption features attributed to the warm absorber below 3 keV (e.g. Lee et al., This limited energy range was chosen in order to avoid contamination from the absorption features attributed to the warm absorber below 3 keV (e.g. Lee et al.
 2001. Sako et al.," 2001, Sako et al."
 2002) and the broad Fe Ka emission above + keV. The continuum is defined as the extrapolation of this fit to include energies to 8 keV. Fig., 2002) and the broad Fe $\alpha$ emission above 4 keV. The continuum is defined as the extrapolation of this fit to include energies to 8 keV. Fig.
 2. illustrates the power-law continuum. described previously over-plotted on the binned (0.055 .) HEG spectrum — notice the clear excess between 5 and 6.6 keV. The corresponding ratio plot of data-to-model in Fig., \ref{fig-cont} illustrates the power-law continuum described previously over-plotted on the binned (0.055 ) HEG spectrum $-$ notice the clear excess between 5 and 6.6 keV. The corresponding ratio plot of $-$ $-$ model in Fig.
 3. further shows that the heavily binned data," \ref{fig-hegasca}
 further shows that the heavily binned data"
Estimating the mass of a DII is relatively easy since mass has a measurable effect even al large radii. where Newtonian gravity. applies.,"Estimating the mass of a BH is relatively easy since mass has a measurable effect even at large radii, where Newtonian gravity applies."
 Spin. on the other hand. does not have any Newltonian elfect the orbit of a planet in the solar svstenm. for instance. would be the same whether (he Sun corotates or counter-rotates with the planetary orbit.," Spin, on the other hand, does not have any Newtonian effect — the orbit of a planet in the solar system, for instance, would be the same whether the Sun corotates or counter-rotates with the planetary orbit."
 Only for relativistic orbits does spin have measurable effects., Only for relativistic orbits does spin have measurable effects.
 Therefore. to measure a... we need test particles on orbits with verv small radii.," Therefore, to measure $a_*$, we need test particles on orbits with very small radii."
 Fortunately. astrophysical DIIs do have such test particles in the form of accreting gas.," Fortunately, astrophysical BHs do have such test particles in the form of accreting gas."
 When considering circular orbits in a DII spacetime (e.g.. Misner et al.," When considering circular orbits in a BH spacetime (e.g., Misner et al."
 1973: Shapiro Teukolskv 19823: ILutle 2003). a kev concept is the innermost stable circular orbit. or ISCO. with a radius designated. νου (also relerred to as the marginally stable orbit).," 1973; Shapiro Teukolsky 1983; Hartle 2003), a key concept is the innermost stable circular orbit, or ISCO, with a radius designated $R_{\rm ISCO}$ (also referred to as the marginally stable orbit)."
 Circular orbits with radii 2>νου are stable to small perturbations. whereas (hose with HocRyeo are unstable.," Circular orbits with radii $R \geq R_{\rm ISCO}$ are stable to small perturbations, whereas those with $R < R_{\rm ISCO}$ are unstable."
 Figure 2 shows the variation of κου with e., Figure 2 shows the variation of $R_{\rm ISCO}$ with $a_*$ .
" For à maximally spinning DIL. Ryeo=CMfe? if the orbit corotates with the BIL (a,=+1 in Fig."," For a maximally spinning BH, $R_{\rm ISCO} = GM/c^2$ if the orbit corotates with the BH $a_*=+1$ in Fig."
" 2) and Που=OGAL/e? if it counter-rolates (à,= —1): for a non-spinning BIL (a,=0). Riscoο"," 2) and $R_{\rm ISCO}=9GM/c^2$ if it counter-rotates $a_*=-1$ ); for a non-spinning BH $a_*=0$ ), $R_{\rm
ISCO}=6GM/c^2$."
 Corresponding to changes in Ryseo. there ave variations in the angular velocily of an orbiting particle at {μου (as measured at infinity). ancl in the binding energy of the particle.," Corresponding to changes in $R_{\rm ISCO}$ , there are variations in the angular velocity of an orbiting particle at $R_{\rm
ISCO}$ (as measured at infinity), and in the binding energy of the particle."
 These variations are shown in Figure 2., These variations are shown in Figure 2.
 The gas in an accretion disk starts [rom Large radii and spirals in through a sequence ol nearly eireular orbits as it viscously loses angular momentum., The gas in an accretion disk starts from large radii and spirals in through a sequence of nearly circular orbits as it viscously loses angular momentum.
 When the gas reaches the ISCO. no more stable circular orbits are available. so the gas accelerates racially and into the BIL," When the gas reaches the ISCO, no more stable circular orbits are available, so the gas accelerates radially and free-falls into the BH."
 Thus. the ISCO serves effectively as the inner edge of the accretion disk.," Thus, the ISCO serves effectively as the inner edge of the accretion disk."
" A variety. of observational methods have been proposed for estimating the radius fy,=fico of the disk inner edge. or one of the other quantities plotted in Figure 2. with a view to thereby estimating ας."," A variety of observational methods have been proposed for estimating the radius $R_{\rm in}=R_{\rm ISCO}$ of the disk inner edge, or one of the other quantities plotted in Figure 2, with a view to thereby estimating $a_*$."
 When a DII has a large mass accretion rate M. corresponding to an accretion luminosity L4 above a few per cent of Lig. the accreting gas tends to be optically (hick ancl to radiate approximately as à blackbody.," When a BH has a large mass accretion rate $\dot M$, corresponding to an accretion luminosity $L_{\rm acc}$ above a few per cent of $L_{\rm
Edd}$, the accreting gas tends to be optically thick and to radiate approximately as a blackbody."
" Iu this spectral state. called the ""high soft state” (McClintock Remillare 2004). one can theoretically ealeulate the flix of radiation Fi?) emitted by the accretion disk. and hence obtain the effective temperature profile Tyr?)=|F(R)/o]""/. where σ is theStefan-Boltzmann constant."," In this spectral state, called the “high soft state” (McClintock Remillard 2004), one can theoretically calculate the flux of radiation $F(R)$ emitted by the accretion disk, and hence obtain the effective temperature profile $T_{\rm eff}(R) \equiv [F(R)/\sigma]^{1/4}$, where $\sigma$ is theStefan-Boltzmann constant."
 If the disk emits as a true blackbodyat each racius. it is a simplematter to calculate the total spectral Iuminositv. {αν," If the disk emits as a true blackbodyat each radius, it is a simplematter to calculate the total spectral luminosity $L_\nu d\nu$ ."
 By comparing, By comparing
3.2 Non-supersymmetric =fe =hb=hy.Al the R-level.,"For $D_{ABC}=D_{333}$ and $D_A=D_3$ : For $D_{ABC}=D_{123}$ and $D_A=D_3$: The latter case agrees with \cite{nonsusy2}, where the horizon solutions were obtained by extremizing the entropy Note that the radial derivatives of our solutions for $\xi_A(r),\xi_0(r),\xi_T(r)$ diverge at $r=0$."
the ," The curvature, however, is regular."
In the non-supersvimmetric case (qj« 0) with! =4?bt =fy. thesoluti," The entropy formula that we use in the supersymmetric case \ref{susy_entropy}) ), is no longer valid in the non-supersymmetric case."
"on reads GET] SUUS. CC Dod c SEN Go + 25r +G0rb +30h) η... 15D(r+ hy)! Sos0 AE (-120rG4 hyn £eο e2097) 42 Ὅυα ForD Daand Dy,Da: Lr."," In the latter case, one can use either Sen's entropy function method \cite{nonsusy1,nonsusy2}, or the Wald entropy formula for the non-extremal case with $R^2$ -terms \cite{r2ne}: In fact, in our solutions $C_{0101},D$ do not contribute to the entropy to first order in $\epsilon$, and thus the formula does reduce to the supersymmetric one."
-K οί)IN, Note also that $G_N(0)\neq1$.
 Da4ge Dis DyD:," Plugging in the solution gives: as in \cite{nonsusy1,nonsusy2}."
" St"")4E (—840r(r ο In £—e e 85614 4- 216972520+ GSSrk 0+ 1504]0 15D(r+"," As discussed therein, this differs from the statistical microscopic entropy \cite{micro_nonsusy}, due to higher curvature $D$ -terms, which are not taken into account here."
 hj)! At the horizon(7 0)we £j)," Using the entropy function method with our first order solutions, one can get the entropyto second order: The central charge reads and the ADM mass takes the form:"
The new oobservatious of the 7~3.1 SATCs aand pprovide supporting evidence that they represent carly and advanced stage. gasieh major merecrs.,"The new observations of the $z$$\sim$ 3.4 SMGs and provide supporting evidence that they represent early and advanced stage, gas-rich major mergers."
 Receut. lower resolution sstudics of the —20kkpc separation lerecr JJI223707|62114 (292. 188: Ivison— et —citevearivill:: Biechers et citevearriclla) ) aay sueeest mn intermediate uecreer stage (with two separated components. but closer in projected distance and redshift than iu L700). πι between those observed in these wo tarects.," Recent, lower resolution studies of the $\sim$ kpc separation merger J123707+6214 $z$ =2.488; Ivison et \\citeyear{ivi11}; Riechers et \\citeyear{rie11a}) ) may suggest an intermediate merger stage (with two separated components, but closer in projected distance and redshift than in ), in between those observed in these two targets."
 These EVLA observations thus may be a first step toward establishing a molecular gas-based “mnerecr sequence for eas-rich starburst galaxies at veh redshift. which may crucially constrain formation nodels of SAICSs (0.5. Dave et citevemrdaviü: Tavward et citevearhavl1)).," These EVLA observations thus may be a first step toward establishing a molecular gas-based “merger sequence” for gas-rich starburst galaxies at high redshift, which may crucially constrain formation models of SMGs (e.g., Davé et \\citeyear{dav10}; ; Hayward et \\citeyear{hay11}) )."
 Tf the pproperties of the 2.3.1 systems studied. here are representativo of their parent population. SALGs in advanced merger stages exhibit substantially inore extended. broader low-7 CO line emission than in earlier merecr stages.," If the properties of the $z$$\sim$ 3.4 systems studied here are representative of their parent population, SMGs in advanced merger stages exhibit substantially more extended, broader $J$ CO line emission than in earlier merger stages."
 Observations of high-7 CO line ciission alone will underestimate the eas content and extent of the tidal structure in advanced-stage merecrs. viclding an incomplete picture of the processes that drive the eas ΠΠ m such svsteuis.," Observations of $J$ CO line emission alone will underestimate the gas content and extent of the tidal structure in advanced-stage mergers, yielding an incomplete picture of the processes that drive the gas dynamics in such systems."
 The observations preseuted here thus show the kev nuportauce of spatially and clvnamically resolved oobservatious of SAGs to understand the gas physics that drive star formation iu these luniuous. massive eas-rich lieh redshitt salaxies.," The observations presented here thus show the key importance of spatially and dynamically resolved observations of SMGs to understand the gas physics that drive star formation in these luminous, massive gas-rich high redshift galaxies."
 Iu combination with hieher-/ CO line observations with shorter waveleneth interferometers such as the upcoming Atacama Laree (sub)Milliueter Array (ALMA). this makes the EVLA a uniquely powerful tool to distinguish different hieh-: ealaxy populations based ou their molecular gas coutent.," In combination with $J$ CO line observations with shorter wavelength interferometers such as the upcoming Atacama Large (sub)Millimeter Array (ALMA), this makes the EVLA a uniquely powerful tool to distinguish different $z$ galaxy populations based on their molecular gas content."
 We thank the referee. Dy. Laura Uaiuline. for a helpful report. aud Christian Παικο for the original version of the LVG code.," We thank the referee, Dr. Laura Hainline, for a helpful report, and Christian Henkel for the original version of the LVG code."
 DR acknowledges support from NASA through a Spitzer Space Telescope eraut., DR acknowledges support from NASA through a Spitzer Space Telescope grant.
 The National Radio Astronomy Observatory is a facility ofthe National Scicuce Foundation operated under cooperative agreement by Associated Universities. Inc.," The National Radio Astronomy Observatory is a facility ofthe National Science Foundation operated under cooperative agreement by Associated Universities, Inc."
Figure 4. shows the (VB—V) CAD obtained from the ground-based FORSI VLT observations.,"Figure \ref{fig:CMD1} shows the $(V,B-V)$ CMD obtained from the ground-based FORS1 VLT observations."
 Photometric errors have been calculated for each star from the rans., Photometric errors have been calculated for each star from the r.m.s.
 scatter of repeated exposures., scatter of repeated exposures.
 La order to minimize the probability of photometric contamination bv nearby stars. only (he 14.000 stars with (he lowest photometric errors {σιcoy«0.01 mag. see Sollima et al.," In order to minimize the probability of photometric contamination by nearby stars, only the 14,000 stars with the lowest photometric errors $\sigma_V\simeq\sigma_B<$ 0.01 mag, see Sollima et al."
 2004. in preparation) have been plotted.," 2004, in preparation) have been plotted."
 The complex structure of the RGB shows beautifully. but the most striking feature in this CMD is the additional. narrow SGD sequence. which sticks out of the main SGB-TO region of the cluster.," The complex structure of the RGB shows beautifully, but the most striking feature in this CMD is the additional, narrow SGB sequence, which sticks out of the main SGB-TO region of the cluster."
 Fig., Fig.
 5 clisplavs the (2555.D145—4555) CMD obtained trom the HST/ACS sample: more than 4000000 stars with the lowest photometric errors are plotted.," \ref{fig:CMD2} displays the $(R_{625},B_{435}-R_{625})$ CMD obtained from the HST/ACS sample: more than 000 stars with the lowest photometric errors are plotted."
 All the evolutionary sequences are extremely well defined. apart [rom the brightest giants (hat are saturated even in the shortest exposures (not plotted in Fie. 5)).," All the evolutionary sequences are extremely well defined, apart from the brightest giants that are saturated even in the shortest exposures (not plotted in Fig. \ref{fig:CMD2}) )."
 The SGB-a is better defined (han in the FORS1 CAID. and the complex SGD/TO structures are more clearly distinguishable.," The SGB-a is better defined than in the FORS1 CMD, and the complex SGB/TO structures are more clearly distinguishable."
 In this CMD. the SGD-a appears as the direct continuation of the RGD-a. although the presence ol a number of stars located in between the main SGB and the SGB-a (at Hj»;=17—18) olfers room to other possible interpretations.," In this CMD, the SGB-a appears as the direct continuation of the RGB-a, although the presence of a number of stars located in between the main SGB and the SGB-a (at $R_{625}=17-18$ ) offers room to other possible interpretations."
" The 5GB-a sequence merges into the bulk of the cluster MS ad a significantly fainter magnitude (AW~ARgo,0.6 mmag) with respect to the dominant population.", The SGB-a sequence merges into the bulk of the cluster MS at a significantly fainter magnitude $\Delta V \sim \Delta R_{625} \sim 0.6$ mag) with respect to the dominant population.
 SGB-a stars in common to both the FORS1 and ACS catalogs are marked in Figure I., SGB-a stars in common to both the FORS1 and ACS catalogs are marked in Figure 1.
 Both the FORSI and ACS CMDs show that the MS-TO of the SGB-a population (δαEDB—a)=18.40+ 0.15) is significantly fainter than the MS-TO of the dominant cluster population (2120P)=17.80 £0.15)., Both the FORS1 and ACS CMDs show that the MS-TO of the SGB-a population $R_{625}^{TO}(SGB-a)=18.40 \pm0.15$ ) is significantly fainter than the MS-TO of the dominant cluster population $R_{625}^{TO}(MP)=17.80 \pm0.15$ ).
 A hint of the presence of such a feature was already noted by Anderson (2002. see his Fig.," A hint of the presence of such a feature was already noted by Anderson (2002, see his Fig."
 D). in the core of the cluster on the basis of an instrumental (ρωC444—4:5) CMD obtained from WEDPC?2/IIST observations.," 1), in the core of the cluster on the basis of an instrumental $(U_{336},U_{336}-R_{675})$ CMD obtained from WFPC2/HST observations."
 However. the hieh quality CMDs presented here provide the first clear-cut definition of tliis sequence in the CMD of w Cen.," However, the high quality CMDs presented here provide the first clear-cut definition of this sequence in the CMD of $\omega$ Cen."
 The TO and SGB regions of w Cen Censlshow uthe sameme level of complexity already observeobserved al the RGB level: a well defined and populated main SGB sequence. highly homogeneous both in terms of age and metallicity. (72)," The TO and SGB regions of $\omega$ Cen show the same level of complexity already observed at the RGB level: a well defined and populated main SGB sequence, highly homogeneous both in terms of age and metallicity. )"
) a more continuous distribution of stars toward the red. tracing a less homogeneous stellar component. with different metallicities and/or ages.," a more continuous distribution of stars toward the red, tracing a less homogeneous stellar component, with different metallicities and/or ages."
(11) a well defined narrow additional SGB. redder and fainter (han the main SGB.," a well defined narrow additional SGB, redder and fainter than the main SGB."
 The sharpness of this sequence strongly suggests a high degree of homogeneity in the age and metallicity of its stars., The sharpness of this sequence strongly suggests a high degree of homogeneity in the age and metallicity of its stars.
but no source was observed at the radio position (Johnston et al.,but no source was observed at the radio position (Johnston et al.
 1995) down to a linitiuz maguitudes of Vox21 (Mignuani. 1998) and Ro~21.5 (unpublished).," 1995) down to a limiting magnitudes of $V \sim 24$ (Mignani, 1998) and $R \sim 24.5$ (unpublished)."
 The pulsar field was observed again by Chakrabarty Ikaspi (1998) who also performed the first optical timine experiaeut but no pulsation was detected resulting m au upper Πιτ of R18.," The pulsar field was observed again by Chakrabarty Kaspi (1998) who also performed the first optical timing experiment but no pulsation was detected resulting in an upper limit of $R 
\ge 18$."
 Now observations of 11 have been performed last August as a test case for the Science Verification (SV) phase of the First. Unit (UTI) of the ESO Very Large Telescope (Leibuudgut. De Marchi aud Reuzini. 1998). aimed to assess the scieutific poteutialities of the telescope.," New observations of $-$ 44 have been performed last August as a test case for the Science Verification (SV) phase of the First Unit (UT1) of the ESO Very Large Telescope (Leibundgut, De Marchi and Renzini, 1998), aimed to assess the scientific potentialities of the telescope."
 The results of these observations are reported iu Sect., The results of these observations are reported in Sect.
 2 aud the results briefly cüsceussed m Sect.3., 2 and the results briefly discussed in Sect.3.
 The feld of LL has been observed onu the üght of Aug 17th. 1998 with the VLT-UTI at the ESO observatory in Paranal.," The field of $-$ 44 has been observed on the night of Aug 17th, 1998 with the VLT-UT1 at the ESO observatory in Paranal."
 Observation were performed in visitor mode by R. Cihuozzi aud D. Leibuugut of he SV teana., Observation were performed in visitor mode by R. Gilmozzi and B. Leibungut of the SV team.
" The UTl was equipped with a Test Camera. conumnissoned for the SV program. mounting a Tektronix, 20187 CCD with a measured conversion actor of 2.5 ¢ ‘ADU aud a readout noise of 7.9 « runs."," The UT1 was equipped with a Test Camera, commissioned for the SV program, mounting a Tektronix $2048^2$ CCD with a measured conversion factor of 2.5 $e^{-}$ /ADU and a readout noise of 7.9 $e^{-}$ r.m.s."
" The CCD pixel size is 27 jp which translates to 4,0155 arcsec at the telescope plate scale. corresponding QO an hominal ποια of view of 935 « 93 arcsec (see http:ww.eso.org/paraual/sv/ for further details)."," The CCD pixel size is 27 $\mu$ which translates to 0.0455 arcsec at the telescope plate scale, corresponding to a nominal field of view of 93 $\times$ 93 arcsec (see http://www.eso.org/paranal/sv/ for further details)."
 Ilowewer. diving the science verification all observations were taken with a 2« binning of the CCD. leading to an actual pixel size of 0.09 aresec.," However, during the science verification all observations were taken with a $2 
\times 2$ binning of the CCD, leading to an actual pixel size of 0.09 arcsec."
 A total of 6 exposures of GOO sec each has been obtained iu à Johnson V filter., A total of 6 exposures of 600 sec each has been obtained in a Johnson V filter.