source,target
 This depends on the present value of the cosmological density parameter (cf., This depends on the present value of the cosmological density parameter (cf.
" ©, = 1 for the de Sitter universe).", $\Omega_o$ = 1 for the Einstein-de Sitter universe).
" For LRAS galaxies. A5,~401005 Ape. therefore comparing this with the one for the LATSS sample. suggests a dependence between the maximum effective depth of the sample and the convergence radius. ic."," For IRAS galaxies, $R_{conv} \sim 40-100 h^{-1} Mpc$ , therefore comparing this with the one for the EMSS sample, suggests a dependence between the maximum effective depth of the sample and the convergence radius, ie."
 the deeper the sample (in distances). the larger the value of Reaves," the deeper the sample (in distances), the larger the value of $R_{conv}$."
 Jo further compare the dipole moments of the EEMSS AGNs with that of the IRAS 1.2 Jy. galaxies. we have selected: a sample of 352 LRAS galaxies with the same selection Function as the IE£MSS sample (ie.," To further compare the dipole moments of the EMSS AGNs with that of the IRAS 1.2 Jy galaxies, we have selected a sample of 352 IRAS galaxies with the same selection function as the EMSS sample (ie."
 the same redshift distribution) and. plotted. the cumulative dipole. growth curves for both saniples. as shown in figure 5.," the same redshift distribution) and plotted the cumulative dipole growth curves for both samples, as shown in figure 5."
 In these analvsis. we have plotted both curves with bias parameter of 1.0.," In these analysis, we have plotted both curves with bias parameter of 1.0."
 As can be seen at almost all distances. the dipole moment of INS. galaxies. dominates that of the IE2MSS.," As can be seen at almost all distances, the dipole moment of IRAS galaxies dominates that of the EMSS."
 H0 appears that LRAS galaxies have stronger contributions to the motion of the LG than the IEMSS AGNs., It appears that IRAS galaxies have stronger contributions to the motion of the LG than the EMSS AGNs.
 1n other words. LRAS ealaxics are more clustered than the EMSS AGNs at scales of <2005.+ Mpe (this is compared to the underlying mass distribution). which is consistent with the values of the bias parameter (assuming the Iinstein-de Sitter universe)," In other words, IRAS galaxies are more clustered than the EMSS AGNs at scales of $< 200 h^{-1}$ Mpc (this is compared to the underlying mass distribution), which is consistent with the values of the bias parameter (assuming the Einstein-de Sitter universe)."
Η the gas density and. total mass profiles of the galaxy can be represented. bv simple power laws. dt is straightforward to evaluate the right-hand side of equation (5).,"If the gas density and total mass profiles of the galaxy can be represented by simple power laws, it is straightforward to evaluate the right-hand side of equation (5)."
 In the case of a singular isothermal sphere. for example. where Perr)oxr7 and Mua)xor (where Alwar) is thefofaf mass within radius r). we find ος(10).=CALs(11)(287) and X07)RpUT) ," In the case of a singular isothermal sphere, for example, where $\rho_{\rm 
gas}(r) \propto r^{-2}$ and $M_{\rm gal}(r) \propto r$ (where $M_{\rm gal}(r)$ is the mass within radius $r$ ), we find $g_{\rm max}(R) = G M_{\rm gal}(R) / (2 R^2)$ and $\Sigma_{\rm gas}(R) = \pi \rho_{\rm gas}(R) R$."
his Leads to the following stripping condition For more general gas density and total mass profiles. the condition for ram pressure stripping may be expressed where à is a geometric constant of order unity which depends on the precise shape of the gas density and total mass profiles of the galaxy.," This leads to the following stripping condition For more general gas density and total mass profiles, the condition for ram pressure stripping may be expressed as where $\alpha$ is a geometric constant of order unity which depends on the precise shape of the gas density and total mass profiles of the galaxy."
 We note that equation (7) is similar to the analytic stripping conditions derived previously by Gisler (1976). and. Sarazin. (1979). (among others) for elliptical galaxies., We note that equation (7) is similar to the analytic stripping conditions derived previously by Gisler (1976) and Sarazin (1979) (among others) for elliptical galaxies.
" Equation (7) implies that all the gas beyond. the 3D radius Revi, where the ram pressure exceeds the eravitational restoring force per unit area (which we will refer to as the stripping radius) will be stripped.", Equation (7) implies that all the gas beyond the 3D radius $R_{\rm strip}$ where the ram pressure exceeds the gravitational restoring force per unit area (which we will refer to as the stripping radius) will be stripped.
 By assumption. the properties of both the gas and dark matter within the stripping radius are unmocified bv the stripping.," By assumption, the properties of both the gas and dark matter within the stripping radius are unmodified by the stripping."
 The Left-hand side of (7) makes it clear that the ram pressure is. in general. a function of time (ie.. for non-circular orbits).," The left-hand side of (7) makes it clear that the ram pressure is, in general, a function of time (i.e., for non-circular orbits)."
 Solow. we use the idealised: uniform. medium runs to test this simple analytic model.," Below, we use the idealised uniform medium runs to test this simple analytic model."
 However. before doing so it is worth briefly. discussing some of the assumptions of this simple model and their validity.," However, before doing so it is worth briefly discussing some of the assumptions of this simple model and their validity."
 Firstlv. the mocdel neglects WH and ICE instability stripping but. as we argued in 82.2. we do not expect this to be an important omission.," Firstly, the model neglects KH and RT instability stripping but, as we argued in 2.2, we do not expect this to be an important omission."
 Perhaps of more concern is that. by assuming that the properties of the system. within the stripping radius do not change with time. the model implicitly. neglects environmental. effects such as tidal stripping and gravitational shock heating.," Perhaps of more concern is that, by assuming that the properties of the system within the stripping radius do not change with time, the model implicitly neglects environmental effects such as tidal stripping and gravitational shock heating."
 In Appendix D. we show. using a simple argument. that one expects ram pressure stripping to be more ellicient. than idal stripping for cases where the mass of the galaxy is less han about of the mass of the group.," In Appendix B, we show, using a simple argument, that one expects ram pressure stripping to be more efficient than tidal stripping for cases where the mass of the galaxy is less than about of the mass of the group."
 In other words. or galaxies with masses of less than about of the group muss. tidal stripping is not expected to substantially moclify he structure of the galaxy. within its stripping radius.," In other words, for galaxies with masses of less than about of the group mass, tidal stripping is not expected to substantially modify the structure of the galaxy within its stripping radius."
 Our 2-svstem runs involve only svstems with mass ratios z 10:1., Our 2-system runs involve only systems with mass ratios $\ge$ 10:1.
 The neglect of shock heating would. naively appear o be a more serious omission. since the commonlv-held xeture of structure formation is that eas accreted by a massive system is shocked at the virial radius up to the virial temperature of the massive svstem.," The neglect of shock heating would naively appear to be a more serious omission, since the commonly-held picture of structure formation is that gas accreted by a massive system is shocked at the virial radius up to the virial temperature of the massive system."
 Thus. one might expect the hot gas halo of the galaxy to be quickly shock heated and become. unbound.," Thus, one might expect the hot gas halo of the galaxy to be quickly shock heated and become unbound."
 However. high. resolution simulations (both cosmological and idealised) do not confirm this picture.," However, high resolution simulations (both cosmological and idealised) do not confirm this picture."
" In particular. if the material being accreted is in smalldense ""Iumps? (e.g... low-mass virialised svstenis. as in the present case). it can penetrate all the way to the core of the massive svstem without being significantly. shocked (e.g. Motl et 22004: Alurray Lin 2004: Poole ct 22006: ALOT: Dekel Dirnboim 2007)."," In particular, if the material being accreted is in small dense “lumps” (e.g., low-mass virialised systems, as in the present case), it can penetrate all the way to the core of the massive system without being significantly shocked (e.g., Motl et 2004; Murray Lin 2004; Poole et 2006; M07; Dekel Birnboim 2007)."
 In fact. most of the interaction energv is thermalised. in the ambient medium of the more massive svstem (the ICM. in this case). while he accreted. gas sinks to bottom of the potential well (see ALOT For a detailed discussion).," In fact, most of the interaction energy is thermalised in the ambient medium of the more massive system (the ICM, in this case), while the accreted gas sinks to bottom of the potential well (see M07 for a detailed discussion)."
 However. MOT found that the raction of the total energy that is thermalised in the gas of he less massive svstem (the galaxy. in this case) increases almost linearly with the ratio of the mass of the less massive system to the total mass of both systems.," However, M07 found that the fraction of the total energy that is thermalised in the gas of the less massive system (the galaxy, in this case) increases almost linearly with the ratio of the mass of the less massive system to the total mass of both systems."
 Therefore. shock wating expected to become important. for cases where he mass of the galaxy is comparable to the mass of the group.," Therefore, shock heating expected to become important for cases where the mass of the galaxy is comparable to the mass of the group."
 Our 2-svstem runs. however. only involve. galaxies with masses lower than of the mass of the group.," Our 2-system runs, however, only involve galaxies with masses lower than of the mass of the group."
 We now explore the rani pressure stripping of galaxies as hey move through a uniform density gaseous medium., We now explore the ram pressure stripping of galaxies as they move through a uniform density gaseous medium.
 For he uniform medium. we select. densities that are typical of the group/cluster environment.," For the uniform medium, we select densities that are typical of the group/cluster environment."
 The temperature of the medium) is set such that its pressure equals that of the 100 halo of the galaxy at its outer edge (ic. the gaseous jio would. be static if it were not moving with respect to he uniform medium).," The temperature of the medium is set such that its pressure equals that of the hot halo of the galaxy at its outer edge (i.e., the gaseous halo would be static if it were not moving with respect to the uniform medium)."
 The galaxies are assigned velocities vpical of svstems orbiting in genuine groups and. clusters (i.c.. comparable to the circular. velocity of the group or cluster).," The galaxies are assigned velocities typical of systems orbiting in genuine groups and clusters (i.e., comparable to the circular velocity of the group or cluster)."
 In 44 we plot the bound mass of gas as a function of time for à small selection of the uniform. medium runs we have performed: ancl compare this with our. proposed analytic model., In 4 we plot the bound mass of gas as a function of time for a small selection of the uniform medium runs we have performed and compare this with our proposed analytic model.
 We focus first on the AZ(/) curves from the simulations (solid. red. curves)., We focus first on the $M(t)$ curves from the simulations (solid red curves).
 Firstly. the A(/) curves in," Firstly, the $M(t)$ curves in"
"study, which suggest absorption to be the main factor, are being published separately (Wilkes 22005).","study, which suggest absorption to be the main factor, are being published separately (Wilkes 2005)."
" Meanwhile, we report here the unusual X-ray spectrum of one AGN in the subset, 234449+1221M, a Type 1 QSO that exhibits an absorbed power law continuum together with a soft excess."," Meanwhile, we report here the unusual X-ray spectrum of one AGN in the subset, M, a Type 1 QSO that exhibits an absorbed power law continuum together with a soft excess."
 The suppression of the continuum below 1 keV allows the form of the soft excess to be resolved with unusual clarity., The suppression of the continuum below $\sim$ 1 keV allows the form of the soft excess to be resolved with unusual clarity.
 234449--1221M (hereafter 2M23) is optically classified as a Type 1 QSO at a redshift of z — 0.199 (Cutri 22003)., M (hereafter 2M23) is optically classified as a Type 1 QSO at a redshift of z = 0.199 (Cutri 2003).
 It was selected as a ‘red’ AGN from the 2 MASS catalogue (J-Ks=2.00+0.06) and found to have a linear broad band polarisation of ~1 bby Smith et al (2002)., It was selected as a `red' AGN from the 2 MASS catalogue $_{s}$ $\pm$ 0.06) and found to have a linear broad band polarisation of $\sim$ 1 by Smith et al (2002).
 It was observed by oon 2003 July 3 (rev., It was observed by on 2003 July 3 (rev.
" 653) for 7885 s on target, with X-ray data from the EPIC pn (Strüdder al.2001) and MOS1 and MOS2 (Turner 22001) cameras providing moderate resolution spectra over the energy band ~0.2-10 keV. Each camera was set in full-frame mode, with the medium thickness filter to remove any optical/UV light from the target source."," 653) for 7885 s on target, with X-ray data from the EPIC pn (Strüdder 2001) and MOS1 and MOS2 (Turner 2001) cameras providing moderate resolution spectra over the energy band $\sim$ 0.2–10 keV. Each camera was set in full-frame mode, with the medium thickness filter to remove any optical/UV light from the target source."
" The particle background was found to be high during parts of the observation, and those data have been excluded from our spectral analysis."," The particle background was found to be high during parts of the observation, and those data have been excluded from our spectral analysis."
" Using the recommended maximum background rates of 1 s! (pn camera) and 0.35 5 (MOS camera) the effective exposure times were thereby reduced to 4444 s (pn), 6321 (MOS1) and 6844 s (MOS2)."," Using the recommended maximum background rates of 1 $^{-1}$ (pn camera) and 0.35 $^{-1}$ (MOS camera) the effective exposure times were thereby reduced to 4444 s (pn), 6321 (MOS1) and 6844 s (MOS2)."
 'The X-ray data were screened with the XMM SAS v6.1 software and events corresponding to patterns 0-4 (single and double pixel events) selected for the pn data and patterns 0-12 for MOS1 and MOS2., The X-ray data were screened with the XMM SAS v6.1 software and events corresponding to patterns 0-4 (single and double pixel events) selected for the pn data and patterns 0-12 for MOS1 and MOS2.
 A low energy cut of 200 eV was applied to all X-ray data and known hot or bad pixels were removed., A low energy cut of 200 eV was applied to all X-ray data and known hot or bad pixels were removed.
" Source counts were obtained from a circular region of rradius centred on the target source, with the background being taken from a similar region offset from, but close to, the source."," Source counts were obtained from a circular region of radius centred on the target source, with the background being taken from a similar region offset from, but close to, the source."
" Individual EPIC spectra were binned to a minimum of 20 counts per bin to facilitate use of the x? minimalisation technique in spectral fitting, which was based on the Xspec package (Arnaud 1996)."," Individual EPIC spectra were binned to a minimum of 20 counts per bin to facilitate use of the $\chi^2$ minimalisation technique in spectral fitting, which was based on the Xspec package (Arnaud 1996)."
 All fits included absorption due to the line-of-sight Galactic column of Ng —4.66x107? cm~?., All fits included absorption due to the line-of-sight Galactic column of $N_{H}$ $\times 10^{20}$ $^{-2}$.
 Errors are quoted at the confidence level (Ax?—2.7 for one interesting parameter)., Errors are quoted at the confidence level $\Delta \chi^{2}=2.7$ for one interesting parameter).
 Given the limited number of background-subtracted counts (844 pn and 790 MOS) spectral fitting was carried out on the integrated data sets., Given the limited number of background-subtracted counts (844 pn and 790 MOS) spectral fitting was carried out on the integrated data sets.
" Guided by the data (figure 1) we first fitted a power law above 2 keV, with a common spectral index, but untied normalisations, for the 3 EPIC cameras, obtaining a good fit (x?=24 for 25 degrees of freedom) for a rather flat (hard) photon index of [=1.65+0.2."," Guided by the data (figure 1) we first fitted a power law above 2 keV, with a common spectral index, but untied normalisations, for the 3 EPIC cameras, obtaining a good fit $\chi^2$ =24 for 25 degrees of freedom) for a rather flat (hard) photon index of $\Gamma$ $\pm$ 0.2."
 Extrapolating this fit to 0.2 keV showed the spectrum to be complex at low energies (figure 2) with evidence of additional (intrinsic) absorption and (possibly) a soft excess yielding a very poor overall fit (y?=228/78)., Extrapolating this fit to 0.2 keV showed the spectrum to be complex at low energies (figure 2) with evidence of additional (intrinsic) absorption and (possibly) a soft excess yielding a very poor overall fit $\chi^2$ =228/78).
" To model the low energy absorption, we then added a photoionised absorber to the power law in Xspec, using a recent output (grid 18) of the XSTAR code (Kallman and Bautista 2001)."," To model the low energy absorption, we then added a photoionised absorber to the power law in Xspec, using a recent output (grid 18) of the XSTAR code (Kallman and Bautista 2001)."
" The ionisation parameter and column density were left as free parameters, but tied for the 3 data sets, while the key metal abundances of C-Fe were fixed at their solar values."," The ionisation parameter and column density were left as free parameters, but tied for the 3 data sets, while the key metal abundances of C–Fe were fixed at their solar values."
 Grid 18 includes a turbulent velocity of 100 km s!., Grid 18 includes a turbulent velocity of 100 km $^{-1}$.
" This addition yielded a much improved fit to the combined pn and MOS data (x?=89/76), with a column density Ng —1.02-0.1x10?? cm? of moderately ionised gas."," This addition yielded a much improved fit to the combined pn and MOS data $\chi^2$ =89/76), with a column density $_{H}$ $\pm$ $\times 10^{22}$ $^{-2}$ of moderately ionised gas."
" The ionisation parameter £(—L/nr?, where L is the ionising luminosity irradiating matter of density n at a distance r) = 1143 erg cm s! was primarily constrained by the spectral upturn, observed below ~0.7 keV, which corresponds mainly to the absorption of ionised OVII in the model (figure 3)."," The ionisation parameter $\xi$ $L/nr^2$, where L is the ionising luminosity irradiating matter of density n at a distance r) = $\pm$ 3 erg cm $^{-1}$ was primarily constrained by the spectral upturn, observed below $\sim$ 0.7 keV, which corresponds mainly to the absorption of ionised OVII in the model (figure 3)."
 Addition of the absorbing column resulted in a steepening of the power law index to Γ--2.05-Ε0.14., Addition of the absorbing column resulted in a steepening of the power law index to $\Gamma$ $\pm$ 0.14.
 Although the, Although the
aas à possible vounger analogue to the X-ray binary SS 433 and its associated. SNR W 50.,as a possible younger analogue to the X-ray binary SS 433 and its associated SNR W 50.
 X faint. jet-like structure oriented along the svmnmetry axis of numay correspond to the outllow itself. while breaks in the cars along this axis may represent this outflow. travelling bevond the shell.," A faint jet-like structure oriented along the symmetry axis of may correspond to the outflow itself, while breaks in the ears along this axis may represent this outflow travelling beyond the shell."
 Phe weak source iin the SNIUs interior is unlikely to be associated with the remnant., The weak source in the SNR's interior is unlikely to be associated with the remnant.
 We clo not detect any other central source in either X-rays or in racio., We do not detect any other central source in either X-rays or in radio.
 Phe former can be attributed to a lack of sensitivity in the observations and to absorption along the line of sight. while the latter may indicate a binary svsteni in a quiescent state or a pulsar with radio beams cirectec awav [rom us.," The former can be attributed to a lack of sensitivity in the observations and to absorption along the line of sight, while the latter may indicate a binary system in a quiescent state or a pulsar with radio beams directed away from us."
 To the SNIUs north is an unusual column of radio emission. which at one end may connect with the propose outflow from the SNRs centre and. at the other end. with vw rregion ROW SO.," To the SNR's north is an unusual column of radio emission, which at one end may connect with the proposed outflow from the SNR's centre and, at the other end, with the region RCW 80."
 Such an association puts the SNR at a listance 5.41.6. kpe ancl corresponds to an age of. less xui 4000 vr., Such an association puts the SNR at a distance $\pm$ 1.6 kpc and corresponds to an age of less than 4000 yr.
 The details of the physical process behind Lguch an interaction are unclear. but we note that a similar combination of outflow. distortion and. termination in a iermal region has been claimed for both €1332.400.1 (Ixes 32) and GS820401.2 (MBSII 54).," The details of the physical process behind such an interaction are unclear, but we note that a similar combination of outflow, distortion and termination in a thermal region has been claimed for both G332.4+00.1 (Kes 32) and G320.4–01.2 (MSH )."
 Further observations of SNR. wwill be required to determine whether our interpretation or its appearance is) valid., Further observations of SNR will be required to determine whether our interpretation for its appearance is valid.
 Lligher frequency racio observations can be used to provide higher resolution images of the ‘car ancl ‘jet’ regions and the interaction tween them. to better study the polarimetric properties of the SNR and. together with lower frequency data. to »etter constrain any spectral index cilferences between the different components of the remnant.," Higher frequency radio observations can be used to provide higher resolution images of the `ear' and `jet' regions and the interaction between them, to better study the polarimetric properties of the SNR and, together with lower frequency data, to better constrain any spectral index differences between the different components of the remnant."
 1 iis similar to W. 50. X-ray observations of greater sensitivity and at higher energies should be able to detect both a central source and evidence for outflow from it.," If is similar to W 50, X-ray observations of greater sensitivity and at higher energies should be able to detect both a central source and evidence for outflow from it."
 Apart from00.6... we find at least eight. other SNRs in whieh the shell may be alfected in some way by jets or oulllows from an associated compact source. and suggest G290.1O18 (MSII GLA) asa possible further example.," Apart from, we find at least eight other SNRs in which the shell may be affected in some way by jets or outflows from an associated compact source, and suggest G290.1–01.8 (MSH A) as a possible further example."
 While the characteristic morpholον associated: with such outflow mav become another means of determining which supernovae have massive star progenitors. there is good reason to believe that a significant fraction of SNRs harbour compact remnants which. for various reasons. we still have not cletected.," While the characteristic morphology associated with such outflow may become another means of determining which supernovae have massive star progenitors, there is good reason to believe that a significant fraction of SNRs harbour compact remnants which, for various reasons, we still have not detected."
 We are particularly erateful to Anerew Walker for carrving out the optical observations and reduction., We are particularly grateful to Andrew Walker for carrying out the optical observations and reduction.
 We also thank Waren Brazier. Jim Caswell. Mike. Ixesteven. Neil IWilleen. Vinee Melntyre ancl Jessica Try for useful discussions. Simon Johnston for reading the manuscript. Veta Avedisova for supplying us with information [rom her catalogueE of star formation regions.5 and the referee. ‘Yom Landecker. for helpful comments which improved. the paper.," We also thank Karen Brazier, Jim Caswell, Mike Kesteven, Neil Killeen, Vince McIntyre and Jessica Try for useful discussions, Simon Johnston for reading the manuscript, Veta Avedisova for supplying us with information from her catalogue of star formation regions, and the referee, Tom Landecker, for helpful comments which improved the paper."
 BAIG acknowledges the support of an Australian Postgraduate Aware., BMG acknowledges the support of an Australian Postgraduate Award.
 The Australia Telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO., The Australia Telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO.
 This research has made use of the NASA Astrophysics Data System. the CDS SIMDAD database. the IPAC TIRES facility and the LEASARC Online Service. provided by the NASA/Cocldarcd Space Εισαι Center.," This research has made use of the NASA Astrophysics Data System, the CDS SIMBAD database, the IPAC HIRES facility and the HEASARC Online Service, provided by the NASA/Goddard Space Flight Center."
We suppose that we are dealing with timing data from an array of Ny. pulsars.,We suppose that we are dealing with timing data from an array of $N_{\rm psr}$ pulsars.
 The data of cach pulsar is a N-point TOA serial signal., The data of each pulsar is a $N$ -point TOA serial signal.
 We denote the whole timing data set by 2). where the superscript is the pulsar index. and the subscript is the data index.," We denote the whole timing data set by $R_j^i$, where the superscript is the pulsar index, and the subscript is the data index."
 For example. the 2% is the j-th data point of the /-th pulsar POA.," For example, the $R_j^i$ is the $j$ -th data point of the $i$ -th pulsar TOA."
" The timing data 1s just a ;N,-tinies- AN dimensional vector Ro and their components £7 takes the form of equation. (10))."," The timing data is just a $N_{\rm 
psr}$ $N$ dimensional vector ${\rm \bf R}$ and their components $R_{j}^{i}$ takes the form of equation. \ref{eq:fullsig}) )."
 The signal part of Rois completely determined by the A-dimensional parameter Ay (GAY parameters plus pulsar parameters)., The signal part of $\rm \bf R$ is completely determined by the $k$ -dimensional parameter $\lambda_k$ (GW parameters plus pulsar parameters).
 “Phe noise part is a random variable Following independent. Gaussian statistics., The noise part is a random variable following independent Gaussian statistics.
 We have where the signal part s=Re| Ry. and the noise n is assumed to be an uncorrelated white Gaussian noise. Lo. ∫⊤⊔↗↓⊳∖↿↓↕⋖⋅∐↳∖↓⊾↔↓∢⊾∖⇁⋖⊾↓⇂∪↓⋅↿↓↥⋖⋅∣−⇂↓↕↓≻⊔↓⊳∖⋜⊔⋅↓↻∆∖⊔∪↓⊳∖⋖⋅⇂↓⋅∪⊔↓∪⇂↓↥⋖⊾↓⋅24 ; ⋅ ⋅∕⋅ ⇁∕⇁⊳∖ tin. .," We have where the signal part ${\rm \bf s}={\rm \bf R}_{\rm g}+{\rm \bf R}_{\rm par}$ , and the noise $\rm \bf n$ is assumed to be an un-correlated white Gaussian noise, i.e. $\langle n_j^i n_j^i\rangle=\sigma_{\rm n}^{2\;(i)}$ and $\langle 
n_{j'}^{i} n_j^{i'}\rangle=0$ for any $j'\neq j$ or $i' \neq i$."
 ⋅ . s ⋠⋅ ≼∙⋖⋟↓↕∣↓⋅↕∣⋡⇂⇂⇂↕∢≱↓↕≻⊳↾∐↥⋖⋅∫↗⊲⊽⋯⋯↿∖∕∖∕↴⊳∕∖⋤↴∃↕⊳∖↿↓↕⋖⋅↓↕↓↕↓↕↕↓↕↓⋜↧↓, The $\sigma_{\rm n}^{(i)}$ is the RMS level for the $i$-th pulsar TOA noise from other contributions.
↓≻↓⋅∪∣⋡⋜↧∣⋡∐⊲⊔∙∖⇁∪⇂⋅⊔↓⋜↧↳⊀↓⊔⋏∙≟∥⊔↓⊀↓⊳∖↿⋜↧↓⊊⋖⊾⊀↓⊔∠⇂∢⊾≼⋰⊔⇂⊀↓⊔⋏∙≟∖∖⊽↓↕⊲⊔∼↓↥↓≻⋜⊔⋅⋜⋯↓∢⊾∩⋅↓⋅⊳∖⋖⋅↿⊳↿↓↥⋖⋅∕∖∕↴∪↓⋅ ∕∖↨⋰↿∪≼∙⇂↥∪∪≱∖∢⋅⋡∖∖⊽↓↕∢⊾⊔⋏∙≟⊲↓∖⋰↓⊔⋏∙≟∠⇂∥⋯⊟↦↓⊲∖∪↓⋅↿↓↕⋖⋅≼⇍⋜↧⊳∖⋖⊾∖∖⊽↓↕∢⋅↓⋅⋖⊾∕∖⋜⋯∠⇂∕∖↙↓⋯∖⇁∢⊾⋖⋅⊏↥⊔⋜↧↓↓≻↓⋰↓∪↓⋅⊳⋜↧⊳∖⊳," The $P_{\epsilon, {\rm min}}(\lambda_{k}, \lambda_{k}')$ is the minimal probability of making a mistake in deciding which parameter set, the $\lambda_{k}$ or $\lambda_{k}'$, to choose, when giving data ${\rm \bf R}$ ."
∖↓↕∪∖∖⊽⊔∣⋡∙∖⇁⇀∙↗↦∣↓↕⋖⊾⇂⋅∪∐∪∖∖⋰↓⊔⋏∙≟↓∐∡⋖⋅↓∐↕∪⋯⇂ ratio test minimizes the probability of making mistakes. where the [Πλ) is the probability distribution function of the data R. when the parameters take value of λε.," For the case where $\rm \bf \lambda$ and $\rm \bf \lambda'$ have equal prior, as shown by \cite{Kassam88}, , the following likelihood ratio test minimizes the probability of making mistakes, where the $f({\rm \bf R}|\lambda_{k})$ is the probability distribution function of the data ${\rm \bf R}$, when the parameters take value of $\lambda_{k}$."
 Following the likelihood test in equation. (0C2)).," Following the likelihood test in equation. \ref{eq:minalg}) ),"
 one can show For the uncorrelated white Gaussian noise. the likelihood ratio (Πλ)/(R[AL) is Integrating over the random vectors »5. one derives and the P?(che«1Na) can be evaluated in very similar fashion.," one can show For the uncorrelated white Gaussian noise, the likelihood ratio $f({\rm \bf R}|\lambda_k)/f({\rm \bf R}|\lambda_k')$ is Integrating over the random vectors $n_{j}^i$, one derives and the $P\left(\left.\frac{f({\rm \bf R}|\lambda_{k})}{f({\rm \bf 
R}|\lambda_{k}')}<1\right|\lambda_{0,k} \right)$ can be evaluated in very similar fashion."
 Phe minimal error probability {αμ is then where equation. (C7))," The minimal error probability $P_{\epsilon, {\rm min}}$ is then where equation. \ref{eq:beta}) )"
" and (C6)) show that the larger difference between the signal of A,and the signal of Aj. the larger ¢ is. andthe lessprobability one will make a mistake in discriminating between the two signals."," and \ref{eq:errprobfinal}) ) show that the larger difference between the signal of $\lambda_{k}$and the signal of $\lambda_{k}'$ , the larger $\zeta$ is, andthe lessprobability one will make a mistake in discriminating between the two signals."
outer halo inverse-Compton scattering of the microwave background accounts for a larger share of the electron energy losses (han near (he Galactic plane. because the infrared. ancl optical photon fields quickly lose intensity bevond 5 kpe above the plane of the Galaxy.,"outer halo inverse-Compton scattering of the microwave background accounts for a larger share of the electron energy losses than near the Galactic plane, because the infrared and optical photon fields quickly lose intensity beyond 5 kpc above the plane of the Galaxy."
 Also. (he magnetic-fiekd strength is expected to fall off. although we do not know at what point it drops to iG. below which the svnchrotron energy losses are subdominant.," Also, the magnetic-field strength is expected to fall off, although we do not know at what point it drops to $\ {\rm \mu G}$, below which the synchrotron energy losses are subdominant."
 We will estimate ihe intensitv in the 100-MeV. band [rom galactie dark-matter decay in the outer halo in the next section. together with the extragalactic component.," We will estimate the intensity in the 100-MeV band from galactic dark-matter decay in the outer halo in the next section, together with the extragalactic component."
 The majority of dark matter is located sufficiently. far away [from galaxies (Z20 kpc) that positrons and electrons from its decay would primarily interact with the microwave background., The majority of dark matter is located sufficiently far away from galaxies $\gtrsim 20$ kpc) that positrons and electrons from its decay would primarily interact with the microwave background.
" Since all electrons sulfer the same late and the electron source rate scales linearly with the darkanatter density. we can ignore anv density structure and use spatially averaged quantities. Le. a conservative fraction of Q,,=0.239 times the critical density. 7."," Since all electrons suffer the same fate and the electron source rate scales linearly with the dark-matter density, we can ignore any density structure and use spatially averaged quantities, i.e. a conservative fraction of $\Omega_m=0.239$ times the critical density, $9.9\cdot 10^{-30}\ {\rm g\,cm^{-3}}$ ."
 For the source function and the energv-loss rate we find and where 2 denotes the redshift., For the source function and the energy-loss rate we find and where $z$ denotes the redshift.
 The average differential number densitv is therefore The intensity of inverse-Conmpton emission is calculated as where is (he Jacobian used to turn the line-ol-sight integral into a recshilt integral., The average differential number density is therefore The intensity of inverse-Compton emission is calculated as where is the Jacobian used to turn the line-of-sight integral into a redshift integral.
 We integrate to redshift 2=5. bevond which the emissivity is neelieibly small.," We integrate to redshift $z=5$, beyond which the emissivity is negligibly small."
 The soft-photon, The soft-photon
Exeept for the northern knot. no radio emission is visible which can be associated with the X-ray halo or the Iimb-brightened feature seen in X-ray.,"Except for the northern knot, no radio emission is visible which can be associated with the X-ray halo or the limb-brightened feature seen in X-ray."
 Conservatively scaling the rms background brightness of our image (260 μὴν aat 1.43 Cllz) to the standard frequency of 1 Cllz using a steep assumed spectral we obtain a 36 upper limit on Xjog; of 1.6te.," Conservatively scaling the rms background brightness of our image (260 $\mu$ at 1.43 GHz) to the standard frequency of 1 GHz using a steep assumed spectral we obtain a $3\sigma$ upper limit on $\Sigma_{\rm \, 1 GHz}$ of 1.6."
 Since the X-ray limb detected at a radius of ~ llikely indicates the location of the forward shock??).. we can place more stringent limits on the radio brightness of the shell by integrating over the shell region.," Since the X-ray limb detected at a radius of $\sim$ likely indicates the location of the forward shock, we can place more stringent limits on the radio brightness of the shell by integrating over the shell region."
 Over an annular region with an outer angular radius of aand a thickness of of the outer radius. the observed total L43-Gllz flux density is 126 mJ. with à 36 upper limit of 30 mJy. corresponding to an average 1.43-Cllz spectral luminosity. of <So107.2U erg s UD4.7kpe) or a surface brightness of «1.2 yJw per square arc-second.," Over an annular region with an outer angular radius of and a thickness of of the outer radius, the observed total 1.43-GHz flux density is $12 \pm 6$ mJy, with a $3\sigma$ upper limit of 30 mJy, corresponding to an average 1.43-GHz spectral luminosity of $< 8\ex{20}$ erg $^{-1}$ $^{-1} (D
/ 4.7 {\rm kpc})$ or a surface brightness of $< 1.2 \; \mu$ Jy per square arc-second."
 Again conservatively scaling to 1 Ισ witha=0.8 results in à 3e limit on the average surface of Xeg;<7L5," Again conservatively scaling to 1 GHz with $\alpha = -0.8$ results in a $3\sigma$ limit on the average surface of $\Sigma_{\rm 1 \, GHz} <
7$."
 Our assumption for the shell gconietry is conservative: for shells thicker than 20%... as might be expected for an age of STO wr2?).. the surfacce-brightness limit would be lower.," Our assumption for the shell geometry is conservative: for shells thicker than , as might be expected for an age of 870 yr, the surface-brightness limit would be lower."
 In αστοί. as noted above. for values of à latter than the assumed 0.8. the limit would also be slightly lower. with a=0.5 resulting in a value of 6 for the limit.," In addition, as noted above, for values of $\alpha$ flatter than the assumed $-0.8$, the limit would also be slightly lower, with $\alpha = -0.5$ resulting in a value of 6 for the limit."
 Finally. the annular region above includes real emission due to0.84... which is probably. not associated with0.," Finally, the annular region above includes real emission due to, which is probably not associated with."
9.. I£ we exclude this contribution. the limit on the average surface brightness decreases by approximately20%.," If we exclude this contribution, the limit on the average surface brightness decreases by approximately."
. The limit) on the radio surface brightness οἱ 0.9'ss shell. whieh corresponds to <6103 times the peak surface brightness of the PWN. is ~17 times lower than those previously obtained for2000.," The limit on the radio surface brightness of s shell, which corresponds to $<6\ex{-4}$ times the peak surface brightness of the PWN, is $\sim$ 17 times lower than those previously obtained for."
. It is expected that the shocks formed. as the shell of supernova ejecta plough through the interstellar medium would. both accelerate. particles and amplify the ambient magnetic field. by compression ancl through instabilities., It is expected that the shocks formed as the shell of supernova ejecta plough through the interstellar medium would both accelerate particles and amplify the ambient magnetic field by compression and through instabilities.
 Raclio emission from this region might therefore be expected. especially for a remnant as voung as0.," Radio emission from this region might therefore be expected, especially for a remnant as young as."
9.. Where then is this radio emission?, Where then is this radio emission?
 We note first that iis not unique in having no detectable radio emission from the supernova shell., We note first that is not unique in having no detectable radio emission from the supernova shell.
 In fact. most other voung PWNe seem to show little radio emission from the putative shell. with the best studied example being the Crab Nebula. which is one of the voungest known ancl also one of the very [ew identified with a supernova (SN 1054). and which doesnot," In fact, most other young PWNe seem to show little radio emission from the putative shell, with the best studied example being the Crab Nebula, which is one of the youngest known and also one of the very few identified with a supernova (SN 1054), and which doesnot"
results can be summarized as Among the considered models. using a variable IME (Model E). provides an acceptable amount of Fe mass. as well as Si/Fe] and O/Fe] ratios. in fair agreement with observations.,"results can be summarized as Among the considered models, using a variable IMF (Model F) provides an acceptable amount of Fe mass, as well as [Si/Fe] and [O/Fe] ratios, in fair agreement with observations."
 Using a Salpeter (1955) LME turns into a lower amount of Fe mass and to supersolar values of O/Fe] in the central cluster region. at variance with observations.," Using a Salpeter (1955) IMF turns into a lower amount of Fe mass and to supersolar values of [O/Fe] in the central cluster region, at variance with observations."
 An ArimotoYoshii (1987) IME provides an even larger Oxvecn abundance. as a consequence of the larger number of ΙΙΙ.," An Arimoto–Yoshii (1987) IMF provides an even larger Oxygen abundance, as a consequence of the larger number of SNII."
 Graclients of the Fe abundance are always steeper than observed in central cluster regions. A25;0.142500. while the Zi profiles on larger scales fall below the observed ones. by an amount which depends on the feedback strength and on the assumed LME.," Gradients of the Fe abundance are always steeper than observed in central cluster regions, $R\mincir 0.1R_{200}$, while the $Z_{\rm Fe}$ profiles on larger scales fall below the observed ones, by an amount which depends on the feedback strength and on the assumed IMF."
 Besides the elleet of the IME. the oversolar value of the OfFe] ratio found in central regions for several models could be due to the presence of a significant recent star formation in central cluster regions.," Besides the effect of the IMF, the oversolar value of the [O/Fe] ratio found in central regions for several models could be due to the presence of a significant recent star formation in central cluster regions."
 Because of such an excess of recent star formation. not shown by observational data. the stars in our simulations lock a laree fraction of metals (see Table 1).," Because of such an excess of recent star formation, not shown by observational data, the stars in our simulations lock a large fraction of metals (see Table 1)."
 Our analysis confirms that. the. observed pattern. of metal enrichment. of the ICM is deeply. connected. το the past history of star formation in clusters and to the feedback scheme that should release energy and heavy elements into the diffuse medium., Our analysis confirms that the observed pattern of metal enrichment of the ICM is deeply connected to the past history of star formation in clusters and to the feedback scheme that should release energy and heavy elements into the diffuse medium.
 The fairly steep gradients of the Fe abundance and the signature of recent. star formation consistently indicate that our simulations are missing a eedback: mechanism. which should quench star formation and spread metals at an early enough epoch. when the moltocluster potential well is still shallow cnough not to retain the produced heavy elements.," The fairly steep gradients of the Fe abundance and the signature of recent star formation consistently indicate that our simulations are missing a feedback mechanism, which should quench star formation and spread metals at an early enough epoch, when the proto–cluster potential well is still shallow enough not to retain the produced heavy elements."
 We verified that this cedhack cannot be easily implemented by resorting to SNLL and la. Neither increasing the strength of the feedback nor changing the IME helps in restoring a better agreement with he observed. profile of the Fe abundance., We verified that this feedback cannot be easily implemented by resorting to SNII and Ia. Neither increasing the strength of the feedback nor changing the IMF helps in restoring a better agreement with the observed profile of the Fe abundance.
 In: our opinion his is à non.trivial result. since it has been obtained in the ramework a rather advanced scheme for star formation and SN feedback. (51103). which is otherwise quite successful at accounting for the pattern of cosmic star formation (Springel Lerquist 2003b).," In our opinion this is a non–trivial result, since it has been obtained in the framework a rather advanced scheme for star formation and SN feedback (SH03), which is otherwise quite successful at accounting for the pattern of cosmic star formation (Springel Herquist 2003b)."
 In turn. this suggests that other energy sources. such as AGN. should be called into play to regulate the cooling structure of the ICM and determine its chemical composition.," In turn, this suggests that other energy sources, such as AGN, should be called into play to regulate the cooling structure of the ICM and determine its chemical composition."
 We are greatly indebted to Volker. Springel for having provided. us with the nonpublic version of GADGET. and for his continuous advices on the code whereabouts.," We are greatly indebted to Volker Springel for having provided us with the non–public version of GADGET, and for his continuous advices on the code whereabouts."
 We acknowledge useful cliscussions with Francesco C'alura. Cristina Chiappini. Sabrina De Crandi. Alexis Finoguenoy and Laura Portinari.," We acknowledge useful discussions with Francesco Calura, Cristina Chiappini, Sabrina De Grandi, Alexis Finoguenov and Laura Portinari."
 We thank the referee Frazer Pearce for his useful and. clever comments., We thank the referee Frazer Pearce for his useful and clever comments.
" The simulations have been realized. using the LBALSP4 machine at the “Centro Interuniversitario cel Nord-IEEst. per il Calcolo Elettronico"" (CINECA. Bologna). with CPU time assigned thanks to an INAFCINECA erant."," The simulations have been realized using the IBM-SP4 machine at the “Centro Interuniversitario del Nord-Est per il Calcolo Elettronico” (CINECA, Bologna), with CPU time assigned thanks to an INAF–CINECA grant."
in the infrared at magnitudes A< 18 follows the approximate distribution do/din=160x10905.10) nae! ? (IXochaneketal.2001).,"in the infrared at magnitudes $K<$ 18 follows the approximate distribution $d\sigma/dm = 160\times10^{0.6\,(K-15)}$ $^{-1}$ $^{-2}$ \citep{kpf+01}."
. Integrating this distribution. we calculate a skv density of about 250 galaxies per square degree of equal or greater brightness to G.," Integrating this distribution, we calculate a sky density of about 250 galaxies per square degree of equal or greater brightness to $G^*$."
 The probability of à given GRD occurring by chance within the observed ollset of ((using the [ar edge of the NRT error circle) from the center of such a galaxy is 22 0.025., The probability of a given GRB occurring by chance within the observed offset of (using the far edge of the XRT error circle) from the center of such a galaxy is $\approx$ 0.025.
 Using the galaxy counts from the Calar Alto Deep Imaging Survey. (hiangetal.2001) we calculate similar probabilities with the A- band magnitude (PLR « 18.5] z 0.03) and D-band magnitude (PB< 20.5] 2 0.05)., Using the galaxy counts from the Calar Alto Deep Imaging Survey \citep{htk+01} we calculate similar probabilities with the $R$ -band magnitude $P$ $R<$ 18.5] $\approx$ 0.03) and $B$ -band magnitude $P$ $B<$ 20.5] $\approx$ 0.05).
 These estimates do not consider host (wpe or classification. the inclusion. of which would hgenerally serve to lower the probabilitv.," These estimates do not consider host type or classification, the inclusion of which would generally serve to lower the probability."
 We address other ealaxies as potential hosts in §3.3.., We address other galaxies as potential hosts in \ref{sec:other}.
 Probabilistic arguments aside. (here are some heuristic arguments for the connection worth noting.," Probabilistic arguments aside, there are some heuristic arguments for the connection worth noting."
 Though not all SIIDs have been associated wilh earlv-tvpe galaxies. there is erowing evidence from (the small sample that SIBs are associated with older stars (Nalkaretal.2006:Guetta&PiranZhengRamirez-Ruiz 2006).. and likely with larger burst offsets from galaxies. than LSBs (Bloom&Prochaska2006).," Though not all SHBs have been associated with early-type galaxies, there is growing evidence from the small sample that SHBs are associated with older stars \citep{ngpf06,pbc+06,gp06,zr06}, and likely with larger burst offsets from galaxies, than LSBs \citep{bp06}."
. Such a configuration is natural in the degenerate merger models: in particular. 15 kpe offsets from Inassive galaxies were predicted [rominilio binary evolution studies Bloometal. 1999)..," Such a configuration is natural in the degenerate merger models; in particular, 75 kpc offsets from massive galaxies were predicted from binary evolution studies \citep{fwh99,bsp99}. ."
 As such. we contend that there is nowpriori precedent to support our Claim (hat G hosted the progenitor birth of 060502D. The C | 0060502D configuration shows some striking similarities with the other SlIBs with putative earlv-tvpe hosts (see Table 3)).," As such, we contend that there is now precedent to support our claim that $G^*$ hosted the progenitor birth of 060502B. The $G^*$ – 060502B configuration shows some striking similarities with the other SHBs with putative early-type hosts (see Table \ref{tab:gang}) )."
 Not only would the redshilt of 2=0.287 be remarkably similar to that of 050509b and 050724 but the inferred. energy would be consistent with that of 050509b., Not only would the redshift of $z=0.287$ be remarkably similar to that of 050509b and 050724 but the inferred energy would be consistent with that of 050509b.
 Indeed in enerev. redshift. putative galaxy. color and (vpe. and offset scale. 0060502b. finds a strong analog in 0050509b.," Indeed in energy, redshift, putative galaxy color and type, and offset scale, 060502b finds a strong analog in 050509b."
 Last. we note that the weak N-ray afterglow and no detected optical afterglow would seem to indicate a low density circumburst environment. as would be expected if the GRB originated far from the progenitor birtlisite.," Last, we note that the weak X-ray afterglow and no detected optical afterglow would seem to indicate a low density circumburst environment, as would be expected if the GRB originated far from the progenitor birthsite."
 With such a large physical offset. the possibility remains that the association with the putative host is coincidentalancl in fact the GRD originates from a different source.," With such a large physical offset, the possibility remains that the association with the putative host is coincidentaland in fact the GRB originates from a different source."
 Llere we, Here we
he timescale of a few minutes. causing depolarisation when ime averaging occurs.,"the timescale of a few minutes, causing depolarisation when time averaging occurs."
 Finally. there may be dillerent values of RAL along dillerent rav paths. especially when the pulsar »comoes scatter broadened.," Finally, there may be different values of RM along different ray paths, especially when the pulsar becomes scatter broadened."
 We believe it is likely hat all hree occur close to the »oint. of eclipse of the pulsar., We believe it is likely that all three occur close to the point of eclipse of the pulsar.
 The RAL values measured are significantly dilferent rom those obtained. by Connors et al. (, The RM values measured are significantly different from those obtained by Connors et al. (
2002) for t1o. 2000 »oriastron.,2002) for the 2000 periastron.
 In 2100 the pulsar was depolarised from 46 onwards. whereas in 20H polarisation was detected up ο T 27.," In 2000 the pulsar was depolarised from $-$ 46 onwards, whereas in 2004 polarisation was detected up to $-$ 27."
 Large and variable polarisation. was «etected ollowing periasron in both 2000 anc 2004. although the arge value of 7300 rad 27 measured in 2000 was not repeated in 2004.," Large and variable polarisation was detected following periastron in both 2000 and 2004, although the large value of $-$ 7700 rad $^{-2}$ measured in 2000 was not repeated in 2004."
 Armed with both the DM and the IM we can compute he magneticDo field parallel to the line of sight.5 D in mG via Values of By are shown in column 5 of Taxe 1..," Armed with both the DM and the RM we can compute the magnetic field parallel to the line of sight, $B_{\Vert}$ in mG via Values of $B_{\Vert}$ are shown in column 5 of Table \ref{dmrm}."
" The error bar in D, is depenent on the RAL error for the pre-periastron data and the DM error for the post-periastron data.", The error bar in $B_{\Vert}$ is dependent on the RM error for the pre-periastron data and the DM error for the post-periastron data.
 ‘Table 2 lists the pulsed. Dux density and the total Dux density detected at the four frequencies observed. with the ATCA., Table \ref{flux} lists the pulsed flux density and the total flux density detected at the four frequencies observed with the ATCA.
 Dashes indicate that the pulsar was not detected at that epoch., Dashes indicate that the pulsar was not detected at that epoch.
 The dates of these observations were carefully selected to provide good sampling of the transient unpulsed emission. based on the observations of the previous three periastron passages., The dates of these observations were carefully selected to provide good sampling of the transient unpulsed emission based on the observations of the previous three periastron passages.
 The non detection of the pulsar at 147 is consistent with the lack of pulsed. emission observed at Parkes one day earlier., The non detection of the pulsar at $-$ 14.7 is consistent with the lack of pulsed emission observed at Parkes one day earlier.
 The re-appearance of the pulsar at |16.1 at the higher frequencies is also consistent ith the Parkes observations., The re-appearance of the pulsar at +16.1 at the higher frequencies is also consistent with the Parkes observations.
 ligue 3 shows the lux density of the transient un»ulsed emission detected rom the sysen hrough the 2004 periastron passage (top panel). logether with the corresponding data [rom the previous three »eriastron passages (Lower xuiel]s).," Figure \ref{fluxfig} shows the flux density of the transient unpulsed emission detected from the system through the 2004 periastron passage (top panel), together with the corresponding data from the previous three periastron passages (lower panels)."
 Although the sampling rate was not as hieh in 2004 as in either 1997 or 2000. it is unlikely that any significant feature of the lieht curve has »en missed.," Although the sampling rate was not as high in 2004 as in either 1997 or 2000, it is unlikely that any significant feature of the light curve has been missed."
 Unpulsed. emission was detected at oa low. level on he first cay that obsersations were mace. at T 22.," Unpulsed emission was detected at a low level on the first day that observations were made, at $-$ 22."
 The lux density at all four frequencics observed then increased steadily. reaching a maximum (~17 mJv at LA 112) tween 10 and 3. and subsequently decreased. to a minimum around |7.," The flux density at all four frequencies observed then increased steadily, reaching a maximum $\sim$ 17 mJy at 1.4 GHz) between $-$ 10 and $-$ 3, and subsequently decreased to a minimum around +7."
 The flux density at all four requencies then inereasecl quite rapidly peaking around Τ|22 (nearly 50 mv at 1.4 Gllz). significantly higher than he level attained: prior to periastron.," The flux density at all four frequencies then increased quite rapidly peaking around +22 (nearly 50 mJy at 1.4 GHz), significantly higher than the level attained prior to periastron."
 Just 5 days. later. ab |27. the flux densiy had cropped to around. half its reas value. and it subsecuenthy decreased more slowly.," Just 5 days later, at +27, the flux density had dropped to around half its peak value, and it subsequently decreased more slowly."
 The unpulsed emission was still detectable at levels of a few mJ. at the time of the final οbservation around |65., The unpulsed emission was still detectable at levels of a few mJy at the time of the final observation around +65.
 There is some suggestion of absortion at [frequencies below 2.4 2 in the emission observe at the earliest times. 22 and T 15.," There is some suggestion of absorption at frequencies below 2.4 GHz in the emission observed at the earliest times, $-$ 22 and $-$ 15."
" M other epochs the spectrum is well fitted. by a simple power law of the orm S,=Cv"" with oa0.6.", At other epochs the spectrum is well fitted by a simple power law of the form $S_{\nu}= C\nu^{\alpha}$ with $\alpha \sim -0.6$.
 The top panel of Figure 3 shows the light curve for each of the four frequencies from the 2004 periastron., The top panel of Figure \ref{fluxfig} shows the light curve for each of the four frequencies from the 2004 periastron.
 Below that, Below that
universe is measuring its deflection of light by gravity.,universe is measuring its deflection of light by gravity.
 The statisties of gravitational lensing can provide us will a very powerful probe of the mass distribution of the Universe., The statistics of gravitational lensing can provide us with a very powerful probe of the mass distribution of the Universe.
" It is well known that the Jodrell-Bank VLA Astrometric Survey (JVAS) and the Cosmic Lens All-Skv Survev (CLASS) (???) have provided us with observations of strong lensing probabilities for small image separations ranging from 0.3"" to 3""."," It is well known that the Jodrell-Bank VLA Astrometric Survey (JVAS) and the Cosmic Lens All-Sky Survey (CLASS) \citep{2000IAUS..201E..47B,2003MNRAS.341....1M,
2003MNRAS.341...13B} have provided us with observations of strong lensing probabilities for small image separations ranging from $0.3''$ to $3''$."
 By comparing predicted lensing probabilities with observations. we can examine the mass distributions of dark matter halos. in particular. (heir inner density slopes (?7)..," By comparing predicted lensing probabilities with observations, we can examine the mass distributions of dark matter halos, in particular, their inner density slopes \citep{2004ApJ...600L...7H,2003MNRAS.344.1237R}."
 Dased on the Cold Dark Matter (CDM) model. whieh has become the standard theory of cosnic structure formation. the lensing probabilities strongly depend on the density profiles of CDM halos.," Based on the Cold Dark Matter (CDM) model, which has become the standard theory of cosmic structure formation, the lensing probabilities strongly depend on the density profiles of CDM halos."
 The lensing model is usually described by a singular isothermal sphere (SIS). the Navarro-Frenk-White (NEW) model (??).. or generalizel NEW (GNEW) density profiles of dark halos (2)..," The lensing model is usually described by a singular isothermal sphere (SIS), the Navarro-Frenk-White (NFW) model \citep{1996ApJ...462..563N,1997ApJ...490..493N}, or generalized NFW (GNFW) density profiles of dark halos \citep{1996MNRAS.278..488Z}."
 ?. emploved a semi-analvtical approach to analvze the gravitational lensing of remote quasars by foreground dark halos and checked the plausibility of various lensine models., \cite{2002ApJ...566..652L} employed a semi-analytical approach to analyze the gravitational lensing of remote quasars by foreground dark halos and checked the plausibility of various lensing models.
 They found that no model can completely explain (he current observations: the Sls models predict too many lenses with large splitting angles. while the NEW models predict too few small splitting angles.," They found that no model can completely explain the current observations: the SIS models predict too many lenses with large splitting angles, while the NFW models predict too few small splitting angles."
 They therefore further developed a (wo-population halo moclel for lensing: small mass halos with a steep inner densitv slope and large mass halos with a shallow inner clensityv slope. concluding (hat a combination of SIS and NEW halo models can reproduce the current observations reasonably well.," They therefore further developed a two-population halo model for lensing: small mass halos with a steep inner density slope and large mass halos with a shallow inner density slope, concluding that a combination of SIS and NFW halo models can reproduce the current observations reasonably well."
" Unlike previous work (hat directly models the clensitw profiles of dark matter halos semi-analviicallv. ? generalized the density profiles of dark matter halos from high-resolution N-bods simulations by means of generalized Navarro-Frenk-White (GNEW) models of three populations with slopes. a. of about -1.5. -1.3 and -1.1 for galaxies. groups anc clusters. respectively,"," Unlike previous work that directly models the density profiles of dark matter halos semi-analytically, \cite{2004ApJ...602L...5Z} generalized the density profiles of dark matter halos from high-resolution N-body simulations by means of generalized Navarro-Frenk-White (GNFW) models of three populations with slopes, $\alpha$, of about -1.5, -1.3 and -1.1 for galaxies, groups and clusters, respectively."
 11ο presented (he cealeulations of lensing probabilities using these GNEW profiles lor three populations in various spatially flat cosmological models with a cosmological constant A., He presented the calculations of lensing probabilities using these GNFW profiles for three populations in various spatially flat cosmological models with a cosmological constant $\Lambda$.
 He showed that the compound model of density profiles does not match well with the lensing probabilities derived [rom the combined data of JVAS/CLASS., He showed that the compound model of density profiles does not match well with the lensing probabilities derived from the combined data of JVAS/CLASS.
 Recently. ?. compared predictions on small scale structure for the ACD model by numerical simulations with observed fIux ratios. and found that the disagreements between monochromatic flux ratios and simple lens models can be explained without anv substructure in (he dark matter halos of primary lenses.," Recently, \cite{2004astro.ph..7298M} compared predictions on small scale structure for the $\Lambda$ CDM model by numerical simulations with observed flux ratios, and found that the disagreements between monochromatic flux ratios and simple lens models can be explained without any substructure in the dark matter halos of primary lenses."
 However. spectroscopic lensing observations of Q2237+0305 require more small mass dark halos than that expected in the ACDAM moclel.," However, spectroscopic lensing observations of Q2237+0305 require more small mass dark halos than that expected in the $\Lambda$ CDM model."
" In particular. a power spectrum of primordial fluctuation. P,(). should be assumed in advance in (he calculation of lensing probabilities."," In particular, a power spectrum of primordial fluctuation, $P_p(k)$, should be assumed in advance in the calculation of lensing probabilities."
" Inflationary models predict a approximately scale-invariant power spectra for primordial density (scalar metric) fuctuation. P,(&)xA with index »=1 (??).."," Inflationary models predict a approximately scale-invariant power spectra for primordial density (scalar metric) fluctuation, $P_p(k)\propto k^n$ with index $n=1$ \citep{1982PhRvL..49.1110G,1983PhRvD..28..679B}."
 The combination of the first-vear Wilkinson Microwave Anisotropy Probe (WAIAP) data with other liner scale cosmic background (CMD) experiments (Cosmic, The combination of the first-year Wilkinson Microwave Anisotropy Probe (WMAP) data with other finer scale cosmic background (CMB) experiments (Cosmic
the LE using a background subtraction and the large field-to-liclel variance. of the background. (he Coma Cluster is sullicienthy distant. that the faint dwar become smaller than the secing ancl we cannot establish membership on the basis of morphology. as we did in the current studs).,"the LF using a background subtraction and the large field-to-field variance of the background (the Coma Cluster is sufficiently distant that the faint dwarfs become smaller than the seeing and we cannot establish membership on the basis of morphology, as we did in the current study)."
 For the Local Group. the error bars are large due to Poisson counting statistics. since there are not many galaxies (there are onlv six. galaxies AI31. the Milky Way. M33. 16 10. LMC and SALC brighter than Mg=/—16 for example).," For the Local Group, the error bars are large due to Poisson counting statistics, since there are not many galaxies (there are only six galaxies – M31, the Milky Way, M33, IC 10, LMC and SMC – brighter than $M_B = -16$ for example)."
 There appear to be two types of galaxy. luminosity function one for evolved. regions (where the elliptical ealaxy [raction is high. the galaxy density is high ane the Crossing time is short) like the Vireo Cluster anc Coma Cluster ancl one for unevolved regions like the Ursa Major Cluster and the Local Group.," There appear to be two types of galaxy luminosity function – one for evolved regions (where the elliptical galaxy fraction is high, the galaxy density is high and the crossing time is short) like the Virgo Cluster and Coma Cluster and one for unevolved regions like the Ursa Major Cluster and the Local Group."
 Phe Virgo ancl Ursa Major LE's represent natural prototypes for the two kinds of LE., The Virgo and Ursa Major LFs represent natural prototypes for the two kinds of LF.
 The two LEs are inconsistent with cach other at a high level of significance: the probability that the two LPs are drawn from a single distribution is <<1 per cent. (reduced v=22.2 [or 5 degrees of freedom)., The two LFs are inconsistent with each other at a high level of significance: the probability that the two LFs are drawn from a single distribution is $<< 1$ per cent (reduced $\chi^2 = 22.2$ for 5 degrees of freedom).
 The reason that such a strong statement can be made follows from the small error xws for these two Les on Figure 11., The reason that such a strong statement can be made follows from the small error bars for these two LFs on Figure 11.
 The evolved region LE appears to be characteristic of many clusters (see ‘Trentham LO9S8e). even though or each cluster individually (like Coma) the LE is xoorlv. determined. due the laree uncertainties following a xuikeground subtraction.," The evolved region LF appears to be characteristic of many clusters (see Trentham 1998c), even though for each cluster individually (like Coma) the LF is poorly determined due the large uncertainties following a background subtraction."
 In the study of Trentham (1998c). he composite cluster LE was determined primarily [rom the LEs of Virgo (Sandage ct al.," In the study of Trentham (1998c), the composite cluster LF was determined primarily from the LFs of Virgo (Sandage et al."
 1985) and Fornax (Ferguson Sandage 1988)., 1985) and Fornax (Ferguson Sandage 1988).
 The current LE. at least in all but the aintest one or two magnitude bins. can to some extent be seen às à verification of the Virgo LE of Sandage et al. (," The current LF, at least in all but the faintest one or two magnitude bins, can to some extent be seen as a verification of the Virgo LF of Sandage et al. ("
1985) and therefore the LE presented in Table 3 may be regarde as being valid. (hen scaled appropriately) for the majority of galaxy clusters.,1985) and therefore the LF presented in Table 3 may be regarded as being valid (when scaled appropriately) for the majority of galaxy clusters.
 Phe main features of this evolved LE are the steep rise at Ag=16 and the fattening faintwari OQ: Mg14., The main features of this evolved LF are the steep rise at $M_B=-16$ and the flattening faintward of $M_B=-14$.
 In the very centres of the richest. clusters. the galaxy density is high enough that many εναν may be destroyed: via cluster-related processes (c.g. Phillipps e al.," In the very centres of the richest clusters, the galaxy density is high enough that many dwarfs may be destroyed via cluster-related processes (e.g. Phillipps et al."
 1998b. Adami ct al.," 1998b, Adami et al."
 2000. Boyce οἱ al.," 2000, Boyce et al."
 2001) and the rise ab Ale=16 is no longer observable there. but the Virgo Cluster is unlikely to be rich enough for this phenomenon to be important.," 2001) and the rise at $M_B=-16$ is no longer observable there, but the Virgo Cluster is unlikely to be rich enough for this phenomenon to be important."
 The unevolved (ie. Ursa Major) LE is dillerent from the evolved one in that it lacks the rise (a= 1.6) at Alp=6 and consequently generates a lower DGR., The unevolved (i.e. Ursa Major) LF is different from the evolved one in that it lacks the rise $\alpha = -1.6$ ) at $M_B = -16$ and consequently generates a lower DGR.
 This LE (a~ l.levervwhere fainter than Mg= 18) is also appropriate for the Local Croup (van den. Bereh 1992. 2000) ancl for the true field. where the LE is determined spectroscopically (see Table 5: the values of a quoted by cilferent authors are derived. in dillerent wavs. for example by Schechter (1976) function fits with dillerent L. but none are as steep as the Virgo LE at around Mg 10).," This LF $\alpha \sim -1.1$ everywhere fainter than $M_B =-18$ ) is also appropriate for the Local Group (van den Bergh 1992, 2000) and for the true field, where the LF is determined spectroscopically (see Table 5; the values of $\alpha$ quoted by different authors are derived in different ways, for example by Schechter (1976) function fits with different $L^{*}$, but none are as steep as the Virgo LF at around $M_B=-16$ )."
 The discussion in the previous section can be summarized by the following results: Ipt, The discussion in the previous section can be summarized by the following results: 1pt
This leads to abiniodel evolution of the final bar sizes with respect to the eas mass fraction (Fig.,This leads to a evolution of the final bar sizes with respect to the gas mass fraction (Fig.
 13)., 13).
 We note ↑↕⋯↑↑∐↕↴∖↴≼∐↖↽↸∖↥⋅≼↴∙⊾↕∐≼↴∙⊾↸∖↖⇁∪↕∏↑↕∪∐↴∖↴∐∪∏∐↴⋝↸∖∪↴⋝↴∖↴↸∖↥⋅↖↽⋜⋔↕↸∖∪∐↕↖⇁ j ↕∐↑∐↸∖↕∪∐∢↴⊨↕↖⇁↸∖≼↧⋝⋜∐⋅↴∖↴↖↖⇁↕∐↸⊳∐∐⋜↧↑↿∐⋅⋜↧∐↖↽↥⋅↸∖↴∖↴↕≼∐∖↕∐↑∐↸∖∪↕≺↸∖↥⋅ disks., We note that this diverging evolution should be observable only in the long-lived bars which naturally reside in the older disks.
 The relevant evolutionary timescale is that of a few CGyrs., The relevant evolutionary timescale is that of a few Gyrs.
" The Milky Way disk is a good candidate, ax it is probably about LO Gyr old aud was not affected by major mergers over this time period (c.g. Ciliuore. Wyse Nonis 2002)"," The Milky Way disk is a good candidate, as it is probably about 10 Gyr old and was not affected by major mergers over this time period (e.g., Gilmore, Wyse Norris 2002)."
 The anti-correlation between the final bar sizes and disk σας fractions. found here. complicates the simplistic picture of bar evolution.," The anti-correlation between the final bar sizes and disk gas fractions, found here, complicates the simplistic picture of bar evolution."
 The reason for this is that our gas-rich models lead. to more massive CMCSs which iucereaseay bulec-to-disleee-to-cdi: massass vatiosratios aud.and. therefore. .should . . . . qo ↴⋝↸∖⋜↧↴∖↴↴∖⋯⊳↕⋜↧↑↸∖≺↧↖↖⇁↕↑∐↸∖⋜," The reason for this is that our gas-rich models lead to more massive CMCs which increase bulge-to-disk mass ratios and, therefore, should be associated with earlier type disks."
∐⋅∐↸∖↥⋅↑⋅↖↴⋉∖≼∐↴∖↴↘↽↴∖↴∙↽∕∏∐↴∖↴⋯↸∖⋜⋯↴∖↴∏↕⋜↧↑ sanaller bars in our models lie in carly-type disks (Fig., This means that smaller bars in our models lie in early-type disks (Fig.
 13). while they are expected to be found iu late-↑⋅↖↴⋉∖≼∐↴∖↴↘↽↴∖↴∙⋜↧↴∖↴∐∪↑↸∖≼⊓⋝⋅↖⇁⋜↧∐⋯⊔↴⋝↸∖↥⋅∪↕⋟↴∖↴↿∐⋅↖⇁↸∖∙↖↽↴∖↴⋖↸∖∙∶↴↜⊾∙∙ Erwin 2005: see also Laine et al.," 13), while they are expected to be found in late-type disks, as noted by a number of surveys (e.g., Erwin 2005; see also Laine et al."
 2002)., 2002).
 The simplest resolution of this discrepancy cau lie in the omission of star formation processes aud especially the feedback from stellar evolution aud frou the central supermassive black oles in this work., The simplest resolution of this discrepancy can lie in the omission of star formation processes and especially the feedback from stellar evolution and from the central supermassive black holes in this work.
 This leads to a gross over-estimate of ∐∖⋜↧⋯∪∏∐↑∪↕≯∶↴∙⊾⋜↧↴∖↴↖↖↽↕∐↸⊳∐↥⋅↸∖⋯⊳∐↸∖↴∖↴↑∐↸∖↸⊳↸∖∐⊓⋅⋜↧↕↨↘↴⋉⊳⋜⋯≼↧ rence contributes to the growth of the CALC by drageing stars and even DAL wards., This leads to a gross over-estimate of the amount of gas which reaches the central kpc and hence contributes to the growth of the CMC by dragging stars and even DM inwards.
 We note. however. that the »irpose ofthis nunerical exercise was to undoerstaud the effect of gas fraction and gas spatial resolution ou the disk-hag-halo iuteractious in the system.," We note, however, that the purpose of this numerical exercise was to understand the effect of gas fraction and gas spatial resolution on the disk-bar-halo interactions in the system."
 Therefore. we rave simplified the long list of processes known to affect ∐∖∶↴∙⊾⋜↧↕⋜↧⊼⋅↖⇁↸∖↖↽∪↕∏↑↕∪∐⋜↧↑↕," Therefore, we have simplified the long list of processes known to affect the galaxy evolution at large."
⋜∐⋅∶↴∙⊾↸∖∙ Tn summary. we find that the spatial resolution iu je eas Colmponent becomes increasingly maportaut for ie bar evolution iu the eas-vich disks.," In summary, we find that the spatial resolution in the gas component becomes increasingly important for the bar evolution in the gas-rich disks."
 This is true for ie dynamical but especially for the secular phase of evolutiou., This is true for the dynamical but especially for the secular phase of evolution.
 In most cases; model sequences with egac— σα μάς OSshowasiiniarbehacior. whiledif feringsubstantiallyf ," In most cases, model sequences with $= 0.016$ and 0.05 show a similar behavior, while differing substantially from the sequence with $=0.1$."
A bimodal behavior has been found for models based on their gas fractions., A bimodal behavior has been found for models based on their gas fractions.
 The border line between the »oor and eas-vich svstenis appears to lie around pe fou higher resolution Is., The border line between the gas-poor and gas-rich systems appears to lie around $5\%-7\%$ for higher resolution models.
 It shifts fo 101 for the lowest resolution maomodels., It shifts to $\sim 10\%-12\%$ for the lowest resolution models.
 The switch from a . ∶↰∎⋜↧↴∖↴⊣∪∪↥∎↑∪⋜↧∶↴∙⋜↧↴∖↴≓↥⋅∐⊳↕↓↴⋝↸∖∐⋜∏⇁↕∪↥⋅⋜∏∏⋉∖⋜∐⋅↴∖↴↑∪↴⋝↸∖↴∖↴, The switch from a gas-poor to a gas-rich behavior appears to be sufficiently abrupt.
∏↕−∏↸⊳↕↸∖∐∏⋅↖↽: ⋅∙ ⋮∏⋝∏↻↾∙↕↾↕↴∖↴↸⋟↕↸∖⋮↕∏⋅↸⊽↸⊽↕↴∖↴∏⋝↕↸∖↕∐⋮↕∐↴⋝⋮↧↴∖↴↕↸↾↸↾↕↕⋮∪⋯⋟↾↸∖⊔↴∖↴⊔↸⋮∖↴∪↕ hayAy OV1 suchach asae tli vybur strength.etree the 20€€AKE nies.eoo the bar evolution.buckling amplitude. the bar size. etc.," It is clearly visible in all basic characteristics of bar evolution, such as the bar strength, the CMC mass, the bar buckling amplitude, the bar size, etc."
 The largest differences in the evolution have been found in the secular phase, The largest differences in the evolution have been found in the secular phase.
 We ∙⋅find that the presence of. the gas conmiponoent severely Tints the bar growth and affects ifs pattern aed , We find that the presence of the gas component severely limits the bar growth and affects its pattern speed evolution.
"Whil pur stella iodIs (Paper 1) exhibit a rapid evolution.slowdown of the bar tumblue. as known for a loug VSe Debattista 1995: Athanassoula .2003). the addition of a substantial οσουςamount of orugas reversesTOVOTSOS thisis trend.Ὃ completely,"," While pure stellar models (Paper I) exhibit a rapid slowdown of the bar tumbling, as known for a long time (e.g., Debattista Sellwood 1998; Athanassoula 2003), the addition of a substantial amount of gas reverses this trend completely."
Bο] Furthermore.⋅∖⋅⋅∖∙ the," Furthermore, the"
Bο] Furthermore.⋅∖⋅⋅∖∙ the∖," Furthermore, the"
dominated by hydrogen or helium. respectively. convective motions drive pulsations 1991:Goldreich&Wu1999:Goldreich. 1999).,"dominated by hydrogen or helium, respectively, convective motions drive pulsations \citep{bri91,gol99,wu99}."
. Driving mechanisms in lor neutron star oscillations are clifferent and lesswell understood., Driving mechanisms in for neutron star oscillations are different and lesswell understood.
 Jessneretal.(2001) show that thermal and field emission [rom the neutron star surface can accelerate electrons along open fiekl lines with the formation of a vacuum gap., \citet{jes01} show that thermal and field emission from the neutron star surface can accelerate electrons along open field lines with the formation of a vacuum gap.
 Therefore. oscillations should be related to thermal variations al the neutron star surlace. as would be produced byg-modes.," Therefore, oscillations should be related to thermal variations at the neutron star surface, as would be produced by."
. The high spherical degree that we observe in (he data. (ancl is predicted. by our model) suggests (hat the pulsation driving energy is concentrated in a small area on the surface of the star., The high spherical degree that we observe in the data (and is predicted by our model) suggests that the pulsation driving energy is concentrated in a small area on the surface of the star.
 Otherwise it would average away over multiple surface zones (Clemens&Rosen2004)., Otherwise it would average away over multiple surface zones \citep{cle04}.
. In one possible scenario. tlie source of the driving energy is al (he magnetic cap and the particle emission exer(s a torque on the open field lines. which is coupled to the rest of the star via magnetic and mechanical dissipation.," In one possible scenario, the source of the driving energy is at the magnetic cap and the particle emission exerts a torque on the open field lines, which is coupled to the rest of the star via magnetic and mechanical dissipation."
 If the magnetic lied is coupled (even weakly) to the surface and it displaces material laterally. the torque on the open field lines results in a displacement of material on (he polar cap.," If the magnetic field is coupled (even weakly) to the surface and it displaces material laterally, the torque on the open field lines results in a displacement of material on the polar cap."
 The heating that results can increase particle enission. which then increases the torque. and drives the oscillations (Clemens&losen2004)..," The heating that results can increase particle emission, which then increases the torque, and drives the oscillations \citep{cle04}."
 Other possibilities for driving mechanisms involving direct shaking of field lines (Boriakoll 1976).. thermal stratification (McDermottetal.1983).. chemical stratification (Finn1987).. and stratification in (he core (Relsenegger&Goldreich1992).," Other possibilities for driving mechanisms involving direct shaking of field lines \citep{bor76}, thermal stratification \citep{mcd83}, chemical stratification \citep{fin87}, and stratification in the core \citep{rei92}."
. The gravitational radiation damping limescale for exceeds (he age of the Universe ancl is therefore a neelieible effect (McDermottοἱal.1950:Reisenegger&Goldreich1992).," The gravitational radiation damping timescale for exceeds the age of the Universe and is therefore a negligible effect \citep{mcd83,rei92}."
. The pulsations we observe in PSRs D0943--10 and D0809—74 appear to persist on hour to month (if not longer) timescales and any driving mechanism must be in agreement with these observations., The pulsations we observe in PSRs B0943+10 and B0809+74 appear to persist on hour to month (if not longer) timescales and any driving mechanism must be in agreement with these observations.
 Other neutron star oscillations have been detected in the form of quasi-periodic oscillations (QPOs) from soft eanmma-ray repeaters., Other neutron star oscillations have been detected in the form of quasi-periodic oscillations (QPOs) from soft gamma-ray repeaters.
 These have been interpreted as torsional shear modes: the Irequencies of QPOs are too high to originate [rom (Watts&Strohmavyer2007)., These have been interpreted as torsional shear modes; the frequencies of QPOs are too high to originate from \citep{wat07}.
. In the standard pulsar model (Goldreich&Julian.1969).. (he magnetosphere is considered to be ‘force-free’ in that the electromagnetic enerey density dominates all other clissipative forces and that radiative emission has a negligible elfect on the spin-down rate (Arons2007).," In the standard pulsar model \citep{gj69}, the magnetosphere is considered to be `force-free' in that the electromagnetic energy density dominates all other dissipative forces and that radiative emission has a negligible effect on the spin-down rate \citep{aro07}."
. Instead. the configuration of the magnetosphere. based on the polar cap cascade zone ancl the current density. within the open field lines. and its change over time cdictates the pulsar spin-down rate (Timokhin2006:Arons2007;Timokhin 2010)..," Instead, the configuration of the magnetosphere, based on the polar cap cascade zone and the current density within the open field lines, and its change over time dictates the pulsar spin-down rate \citep{tim06,aro07,tim10}. ."
 Reeentlh. Timokhin(2010) speculates that the magnetospheres of some pulsars can have several quasi-stable states with," Recently, \citet{tim10} speculates that the magnetospheres of some pulsars can have several quasi-stable states with"
et al. (,et al. (
20092).,2009a).
 The advantages of the lower redshift include the possibility of observing a larger range of the restframe spectra with the same instruments. and increased signal-to-noise in the detections due to the smaller luminosity distance.," The advantages of the lower redshift include the possibility of observing a larger range of the restframe spectra with the same instruments, and increased signal-to-noise in the detections due to the smaller luminosity distance."
 Indications of evolution in the properties of this type of galaxy from redshift.~3 to 2— were reported in Nilsson et al. (, Indications of evolution in the properties of this type of galaxy from redshift $z \sim 3$ to $z \sim 2$ were reported in Nilsson et al. (
2009a); including typically redder colours. smaller equivalent widths and a larger AGN content in the sample.,"2009a); including typically redder colours, smaller equivalent widths and a larger AGN content in the sample."
 In this paper we investigate the stellar properties of the LAEs further by fitting their SEDs with theoretical models., In this paper we investigate the stellar properties of the LAEs further by fitting their SEDs with theoretical models.
 The question we seek to answer is how these properties have evolved from higher to lower redshift., The question we seek to answer is how these properties have evolved from higher to lower redshift.
 This paper is organised as follows: section ?2 describes the sample of Ένα emitters that are being studied. and includes an analysis of the Spitzer detections of the galaxies.," This paper is organised as follows: section \ref{sec:sample} describes the sample of $\alpha$ emitters that are being studied, and includes an analysis of the Spitzer detections of the galaxies."
 In section we outline the method used for the SED fitting. and the results of the fitting are reported in section ??..," In section \ref{sec:method} we outline the method used for the SED fitting, and the results of the fitting are reported in section \ref{sec:results}."
 A discussion of the redshift evolution of LAE stellar properties is found in. section ??.., A discussion of the redshift evolution of LAE stellar properties is found in section \ref{sec:discussion}.
" We end with a general discussion in section ?? and a conclusion in section ??.,", We end with a general discussion in section \ref{sec:conclusions} and a conclusion in section \ref{sec:conclusion}. .
" 5mm Throughout this paper. we assume à cosmology with IH,~7 km | ο = Mand Oa—07,"," 5mm Throughout this paper, we assume a cosmology with $H_0=72$ km $^{-1}$ $^{-1}$, $\Omega _{\rm m}=0.3$ and $\Omega _\Lambda=0.7$."
 Magnitudes are given in Μροthe AB system., Magnitudes are given in the AB system.
 The sample studied in. this paper IS nearly identical to the sample in Nilsson et al (, The sample studied in this paper is nearly identical to the sample in Nilsson et al. (
2009a).,2009a).
 In brief. this sample was found through narrow-band imaging with the ESO2.2n/MPG telescope on La Silla. Chile. using the Wide-Field Imager (WFI: Baade et al.," In brief, this sample was found through narrow-band imaging with the ESO2.2m/MPG telescope on La Silla, Chile, using the Wide-Field Imager (WFI; Baade et al."
 1999)., 1999).
" A central section of the COSMOS field (R.A. 1000727*, Dec 02712/2277, J2000)wosobscrvedwiththef iter N396/12. obsc with :=2.206—2.312."," A central section of the COSMOS field (R.A. $10^h 00^m 27^s$, Dec $02^{\circ} 12' 22$ $7$, J2000) was observed with the filter N396/12, observing $\alpha$ with $z = 2.206 - 2.312$."
 The data reduction and method for selecting emission line objects is explained in detail in Nilsson et al. (, The data reduction and method for selecting emission line objects is explained in detail in Nilsson et al. (
20092).,2009a).
 In the survey. 187 emission-line objects were found.," In the survey, 187 emission-line objects were found."
 Of these. 17 were detected in the public GALEX data available and were flagged as potential [OIL] emitters. although this sub-sample will also contain Lya emitters with high escape fraction in the restframe UV.," Of these, 17 were detected in the public GALEX data available and were flagged as potential [OII] emitters, although this sub-sample will also contain $\alpha$ emitters with high escape fraction in the restframe UV."
 The photometry of these candidates in the optical and near-infrared data available in COSMOS is presented in Nilsson et al. (, The photometry of these candidates in the optical and near-infrared data available in COSMOS is presented in Nilsson et al. (
2009a).,2009a).
 In January/February 2010. multi-object spectroscopy with the VIMOS instrument on VLT UT3 (programme ID 084.A-0318(B)) was carried out on 152 candidates.," In January/February 2010, multi-object spectroscopy with the VIMOS instrument on VLT UT3 (programme ID 084.A-0318(B)) was carried out on 152 candidates."
 The results of this spectroscopic campaign will be presented in a forthcoming publication. but we will in the analysis here exclude those candidates which are clearly confirmed to not be Ένα emitters in the spectroscopy.," The results of this spectroscopic campaign will be presented in a forthcoming publication, but we will in the analysis here exclude those candidates which are clearly confirmed to not be $\alpha$ emitters in the spectroscopy."
 Conversely. a number of less likely (named “unlikely” in Nilsson et al.," Conversely, a number of less likely (named “unlikely” in Nilsson et al."
 2009a) candidates were put on slits., 2009a) candidates were put on slits.
 Those that showed a Lyo detection in the spectroscopy will be added to the analysis here (a total of six)., Those that showed a $\alpha$ detection in the spectroscopy will be added to the analysis here (a total of six).
 The results of the Nilsson et al. (, The results of the Nilsson et al. (
20093) paper do not change significantly from the exclusion/inclusion of the spectroscopic rejections/confirmations.,2009a) paper do not change significantly from the exclusion/inclusion of the spectroscopic rejections/confirmations.
 In Table | we present the different sub-samples of the candidates in the various steps., In Table \ref{tab:sampledef} we present the different sub-samples of the candidates in the various steps.
 In the final sample that will be used throughout the paper here-after. only candidates that are either not rejected in the spectroscopy. or did not get observed spectroscopically. are included.," In the final sample that will be used throughout the paper here-after, only candidates that are either not rejected in the spectroscopy, or did not get observed spectroscopically, are included."
" With “not rejected"" we take to mean those candidates that were spectroscopically observed and that were left after rejecting galaxies with multiple spectral lines inconsistent with the Lya redshift. or which did not have significant line emission on a detected continuum."," With “not rejected” we take to mean those candidates that were spectroscopically observed and that were left after rejecting galaxies with multiple spectral lines inconsistent with the $\alpha$ redshift, or which did not have significant line emission on a detected continuum."
 We further add à few more AGN by studying the data in the COSMOS field (see sec. ??)).," We further add a few more AGN by studying the data in the COSMOS field (see sec. \ref{sec:chandra}) ),"
 reducing the number of AGN-free LAE objects., reducing the number of AGN-free LAE objects.
 The final sample thus consists of 171 LAEs. of which 141 are AGN- and GALEX-undetected.," The final sample thus consists of 171 LAEs, of which 141 are AGN- and GALEX-undetected."
 Note that at least 8 GALEX-detected non-AGN LAEs are confirmed as being true Lyo-emitters., Note that at least 8 GALEX-detected non-AGN LAEs are confirmed as being true $\alpha$ -emitters.
 These represent a unique sub-sample of high-transmission objects at high redshift (in agreement with Moller Jakobsen 1990). and would be worthy a special follow-up.," These represent a unique sub-sample of high-transmission objects at high redshift (in agreement with ller Jakobsen 1990), and would be worthy a special follow-up."
" Since the publication of the original sample. several new images have become available from the COSMOS consortium. including J images from UKIRT. K, images from CFHT and X-ray data from the observatory (see sec. ??))."," Since the publication of the original sample, several new images have become available from the COSMOS consortium, including J images from UKIRT, $_s$ images from CFHT and X-ray data from the observatory (see sec. \ref{sec:chandra}) )."
 The depths of the infrared images are 23.7 magnitudes (57) in both bands (Ilbert et al., The depths of the infrared images are 23.7 magnitudes $5\sigma$ ) in both bands (Ilbert et al.
 2009)., 2009).
 We prepared and extracted fluxes of all the objects in the catalogue in à similar way as described in Nilsson et al. (, We prepared and extracted fluxes of all the objects in the catalogue in a similar way as described in Nilsson et al. (
2009a).,2009a).
" The number of detections was 43 and 86 of the 171 candidates respectively in the J and K,. bands.", The number of detections was 43 and 86 of the 171 candidates respectively in the J and $_s$ bands.
" One of the spectroscopically confirmed. less likely candidates was detected in the K, band."," One of the spectroscopically confirmed, less likely candidates was detected in the $_s$ band."
 These results were incorporated into our main photometric catalogue., These results were incorporated into our main photometric catalogue.
" In the case that an object was already detected in the previously available. but shallower. PINK, band. this magnitude was replaced with the CFHT result for Weconsistency."," In the case that an object was already detected in the previously available, but shallower, KPNO $_s$ band, this magnitude was replaced with the CFHT result for consistency."
" For all optical and near-IR bands used in the fitting (Bj. Vj. ἐν :. J. and Ks). the curves of growth of 25 stars in the field were measured and aperture corrections from 3” diameter apertures to ""infinity"" calculated."," For all optical and near-IR bands used in the fitting (Bj, Vj, $i$, $z$, J, and Ks), the curves of growth of 25 stars in the field were measured and aperture corrections from $3''$ diameter apertures to “infinity” calculated."
 These were applied to all magnitudes before the SED fitting., These were applied to all magnitudes before the SED fitting.
 We also subtracted the observed Lye flux (as calculated from the narrow-band observations. Μασοσυ) from the Bj band. as this line is exceptionally difficult to fit.," We also subtracted the observed $\alpha$ flux (as calculated from the narrow-band observations, $_{3960}$ ) from the Bj band, as this line is exceptionally difficult to fit."
 Elvis et al. (, Elvis et al. (
2009) presented the available X-ray. images. with fluxlimits of 1.9. 7.3. and «10.) ere + 7 in the soft (0.5.—2 keV). hard (2 keV) and total (0.5—10 keV) bands respectively.,"2009) presented the available X-ray images, with fluxlimits of 1.9, 7.3 and $ \times 10^{-16}$ erg $^{-1}$ $^{-2}$ in the soft $0.5-2$ keV), hard $2-10$ keV) and total $0.5-10$ keV) bands respectively."
 To search for detections. aperture photometry with 5” diameter was made onthe positions of the candidates in the 0.5—10 keV band.," To search for detections, aperture photometry with $5''$ diameter was made on the positions of the candidates in the $0.5-10$ keV band."
 For, For
"sstar formation in galaxies, and galaxy evolution in general.","star formation in galaxies, and 	galaxy evolution in general."
This is not surprising. as the photometric redshift selection is primarily based on colors and therefore defines relatively blue colors at low redshift and relatively red colors for higher redshift.,"This is not surprising, as the photometric redshift selection is primarily based on colors and therefore defines relatively blue colors at low redshift and relatively red colors for higher redshift."
 We show in Fig., We show in Fig.
 3 a zoom of the color-magnitude relation for the 142 fLSBs with photo-z«0.2., \ref{fig:cmrsmall} a zoom of the color-magnitude relation for the 142 fLSBs with $-z <0.2$.
 We can define three subsamples: the sequence TLSBs (within zl1co. or £0.29 mag from the red sequence). the b/ue fLSBs (more than Lc below the red sequence). and the red fLSBs (more than Io above the red sequence).," We can define three subsamples: the $sequence$ fLSBs (within $\pm 1\sigma$, or $\pm
0.29$ mag from the red sequence), the $blue$ fLSBs (more than $1\sigma$ below the red sequence), and the $red$ fLSBs (more than $1\sigma$ above the red sequence)."
 This classification is similar to that already proposed for fLSBs in Coma (ASUOG). suggesting that a large fraction (here about 2/3) of £LSBs follows an evolutionary path comparable to that of normal ellipticals in. clusters.," This classification is similar to that already proposed for fLSBs in Coma (ASU06), suggesting that a large fraction (here about 2/3) of fLSBs follows an evolutionary path comparable to that of normal ellipticals in clusters."
 We will discuss this result in more detail in Section 4.., We will discuss this result in more detail in Section \ref{sec:discu}.
 A bi-dimensionnal Kolmogorov Smirnov (KS hereafter) test shows that the a. o spatial distribution of f£LSBs at z«0.2 is different at the 92% level from a uniform distribution; the same KS test shows that the spatial distributions of the z«0.2 and z20.2 fLSBs are different at the 99.9% level., A bi-dimensionnal Kolmogorov Smirnov (KS hereafter) test shows that the $\alpha$ $\delta$ spatial distribution of fLSBs at $<$ 0.2 is different at the $\%$ level from a uniform distribution; the same KS test shows that the spatial distributions of the $<$ 0.2 and $\geq$ 0.2 fLSBs are different at the $\%$ level.
 The fLSBs with a high probability of belonging to Abell 496 are therefore not as uniformly distributed throughout the cluster as the galaxies likely to be non-cluster members., The fLSBs with a high probability of belonging to Abell 496 are therefore not as uniformly distributed throughout the cluster as the galaxies likely to be non-cluster members.
 The «c. 0 spatial distributions of the photo-z«0.2 sequence. red. and blue fLSBs shown in Fig.," The $\alpha$ $\delta$ spatial distributions of the $-z<0.2$ $sequence$, $red$, and $blue$ fLSBs shown in Fig."
 4 are also different., \ref{fig:ad} are also different.
 The distribution of Ρίο fLSBs is different from a uniform spatial distribution only with a probability of less than 1% from a KS test. so we can say that b/ve fLSBs are relatively uniformly distributed.," The distribution of $blue$ fLSBs is different from a uniform spatial distribution only with a probability of less than $\%$ from a KS test, so we can say that $blue$ fLSBs are relatively uniformly distributed."
 On the other hand. sequence and red fLSBs are different from à uniform spatial distribution. with respective probabilities of 90 and 99%. based on a KS test.," On the other hand, $sequence$ and $red$ fLSBs are different from a uniform spatial distribution with respective probabilities of 90 and $\%$, based on a KS test."
 In Fig. 4..," In Fig. \ref{fig:ad},"
 the red fLSBs generally tend to be found preferentially along the large scale filament of galaxies found by Boué et al. (, the $red$ fLSBs generally tend to be found preferentially along the large scale filament of galaxies found by Boué et al. (
2008).,2008).
 This suggests that red fLSBs could be linked with this filament made up of groups infalling toward the Abell 496 center., This suggests that $red$ fLSBs could be linked with this filament made up of groups infalling toward the Abell 496 center.
 Since the cluster Abell 496 is believed to be nearly relaxed (Durret et al., Since the cluster Abell 496 is believed to be nearly relaxed (Durret et al.
 2000). it is important to determine if it is still experiencing an infalling activity.," 2000), it is important to determine if it is still experiencing an infalling activity."
 We searched for substructures in Abell 496 by applying the Serna Gerbal (1996) method to our large spectroscopic redshift sample of 596 galaxies (Durret et al., We searched for substructures in Abell 496 by applying the Serna Gerbal (1996) method to our large spectroscopic redshift sample of 596 galaxies (Durret et al.
 1999)., 1999).
 We show in Fig., We show in Fig.
 5 the spatial distribution of galaxies belonging to various independent dynamical structures inside the Abell 496 cluster., \ref{fig:type} the spatial distribution of galaxies belonging to various independent dynamical structures inside the Abell 496 cluster.
 We only detected three such structures and they are all low mass structures of a few [01 M..., We only detected three such structures and they are all low mass structures of a few $10^{12}$ $_\odot$.
" These masses are very small compared to the overall cluster mass of the order of 3.5 107. M, (e.g. Laganá et al.", These masses are very small compared to the overall cluster mass of the order of 3.5 $10^{14}$ $_\odot$ (e.g. Laganá et al.
 2010) and do not prevent us from classifying the cluster from being relatively well relaxed., 2010) and do not prevent us from classifying the cluster from being relatively well relaxed.
 The description of the Serna Gerbal method and the full analysis of the results thus obtained can be found in Appendix B. We also see from Fig., The description of the Serna Gerbal method and the full analysis of the results thus obtained can be found in Appendix B. We also see from Fig.
 5 that the two main substructures are located towards the northwest and southeast of the cluster. that," \ref{fig:type} that the two main substructures are located towards the northwest and southeast of the cluster, that"
FESLIW nuage to be undergoing a merger event and a radius of «Q7 (ved cutoff of .)).,F814W image to be undergoing a merger event and a radius of $\le0\farcs7$ (red cutoff of ).
" We fud 36 lower Πατς for £,1500/8302223.2 aud a κοπο<0.02 (30 upper Iit) for galaxy mergers (see Figure 7 aud Section 6.3. for further discussion)."," We find $3\sigma$ lower limits for $f_{\nu}{1500}/f_{\nu}{830}=$ 223.2 and a $f_{\mathrm{esc,rel}}<0.02$ $3\sigma$ upper limit) for galaxy mergers (see Figure \ref{fig:stackedmerger} and Section \ref{sec:galaxy-mergers} for further discussion)."
 Flux below the Lyman liuüt was detected in C-UVLC-l? (horoafter T17). however it is uuclear what process is respousible for the ΕΙΝ emission (Figure. 1)).," Flux below the Lyman limit was detected in C-UVLG-17 (hereafter T17), however it is unclear what process is responsible for the FUV emission (Figure \ref{fig:agn17}) )."
 T17 is detected in the N-ray with a Iuninuositv of ~2«10b ere 1 (2-40KeV) C2)... and is a Type 2 AGN based ou the optical pectrui (?)..," T17 is detected in the X-ray with a luminosity of $\sim2\times10^{43}$ erg $^{-1}$ (2-10KeV) \citep{2010ApJ...716..348B}, and is a Type 2 AGN based on the optical spectrum \citep{2006ApJ...644..100P}."
 Although it is highly probable that the LyC flux is coming from the ACN. it is possible that some flux las its origiu im voung massive stars.," Although it is highly probable that the LyC flux is coming from the AGN, it is possible that some flux has its origin in young massive stars."
" The COSMOS photometry. with 30-bands. was fit using a library of ""hybrid templates tuned for sources Lostine an ACN even if hidden (sec?.fordetails)..."," The COSMOS photometry, with 30-bands, was fit using a library of “hybrid” templates tuned for sources hosting an AGN even if hidden \citep[see][for details]{2009ApJ...690.1250S}."
 The best-fit SED is a pure starburst. although the fit is poor.," The best-fit SED is a pure starburst, although the fit is poor."
 The IRAC colors do not place T17 iu the locus of optically bright unobseured ACN and is non-variable (over a five vear period)., The IRAC colors do not place T17 in the locus of optically bright unobscured AGN and is non-variable (over a five year period).
 The spectrmu shows no break at the Lyman huit. with ionizing flux detected down to A~sloA..," The spectrum shows no break at the Lyman limit, with ionizing flux detected down to $\lambda \sim 810$."
 Below this wavelength. the coutimmun is stronely suppressed. indicative of a foreground. cohuun density absorber at z~0.55.," Below this wavelength, the continuum is strongly suppressed, indicative of a foreground, high-column density absorber at $z\sim 0.55$."
 Although this source harbors an ACN. it is worth noting that a large fraction of the LyC radiatiou could be from the starburst. with the ACN clearing lines of sieht.," Although this source harbors an AGN, it is worth noting that a large fraction of the LyC radiation could be from the starburst, with the AGN clearing lines of sight."
 Tt is possible to diseutauele the fractional coutzibution of the LvC radiation from the two sources., It is impossible to disentangle the fractional contribution of the LyC radiation from the two sources.
 Iu the contestof this paper we do not consider the LyC cussion frou this galaxy to be analogous to the LyC detections at liüeh-:. although this type of LyC emissionis interesting and possibly more conumon at higher redshift.," In the contextof this paper we do not consider the LyC emission from this galaxy to be analogous to the LyC detections at $z$, although this type of LyC emissionis interesting and possibly more common at higher redshift."
 Ileher redshift (5~ 3) studies have detected LyC plotous iu approximately LO% of galaxies (??)..," Higher redshift $z\sim3$ ) studies have detected LyC photons in approximately $10\%$ of galaxies \citep{2006ApJ...651..688S,2009ApJ...692.1287I}."
" ? estimate that at 2~3 there is a 50% probability that L/3 of the galaxies with detected LyC emission are the result of foreground coutamination by low-redshift blue ealaxics within —1""of the hiel-redshift ealaxy.", \citet{2010MNRAS.404.1672V} estimate that at $z\sim3$ there is a $50\%$ probability that 1/3 of the galaxies with detected LyC emission are the result of foreground contamination by low-redshift blue galaxies within $\sim$ of the high-redshift galaxy.
 Figure 8 lughlielts an example of foreground contamination found iu C-UVLC-L1 of our sample., Figure \ref{fig:panels} highlights an example of foreground contamination found in C-UVLG-14 of our sample.
 The NUV nunaenitude which is used in our sample selection has a PSF of ~ Iwhich cucompasses both galaxies., The NUV magnitude which is used in our sample selection has a PSF of $\sim4$ which encompasses both galaxies.
 The high-resolution FSIIW image (7) reveals two ealaxics separated bv 1722 (l0kpc) exhibitiue irreenlar morpholosies consistent with a close galaxy pair.," The high-resolution F814W image \citep{2007ApJS..172...38S} reveals two galaxies separated by $\sim$ 2 $<$ 10kpc), exhibiting irregular morphologies consistent with a close galaxy pair."
 The southern galaxy (hereafter CalÀ) has two compact unclei and evidence of long tidal tails., The southern galaxy (hereafter GalA) has two compact nuclei and evidence of long tidal tails.
 The northern galaxy (hereafter CalB) exhibits multiple star formation knots. an asvuuuctric morphologyaud tidal tails.," The northern galaxy (hereafter GalB) exhibits multiple star formation knots, an asymmetric morphologyand tidal tails."
 The two priuary UV bright knots that make up CalB are referred to as GalBl aud CGalD2 as noted in Figure &.., The two primary UV bright knots that make up GalB are referred to as GalB1 and GalB2 as noted in Figure \ref{fig:panels}.
 Although CalÀ was the iuteuded target in our program the high resolution SBC direct PISOLP nuaee (swpeem0.772).revealed that GalB dominated the NUV and FUV flux.," Although GalA was the intended target in our program $z_{\mathrm{spec}}$ =0.772), the high resolution SBC direct F150LP image revealed that GalB dominated the NUV and FUV flux."
 The detection ds ceutere on CalA corresponding to au IR huninosity of Lpquo]2«LOE. aud a SER of ~LOAD. yrτη.," The detection is centered on GalA corresponding to an IR luminosity of $L_{[8-1000\micron\,]}=2.3\times10^{11}L_{\odot}$ and a SFR of $\sim40M_{\odot}$ $yr^{-1}$ \citep{1998ARA&A..36..189K}."
" GalÀ was not detected in the FUW (likely due to its hnieh dust content). however. the UV. spectrum of CalD2 (Figtwe 9)) would nuply arelative escape fraction. fic €M 30+6% and a f,(L500A))/f, (30A)). —1L3. if it was at the sale redshift as CalA. Follow-up spectroscopy with Keck DEIMOS revealed that (να was a low-xedshift interloper at :=0.19."," GalA was not detected in the FUV (likely due to its high dust content), however, the UV spectrum of GalB2 (Figure \ref{fig:interloper}) ) would imply a escape fraction, $f_{\mathrm{esc,rel}}$ of $30\%\pm6\%$ and a $f_{\nu}$ $/f_{\nu}$ ) $=$ 14.3, if it was at the same redshift as GalA. Follow-up spectroscopy with Keck DEIMOS revealed that GalB was a low-redshift interloper at $z=0.19$."
 The close (~1 ) projected separation of these ealaxies is a good exinuple of foreground. contamination and could explain some the Do3 detections of 7. particularly he ones with a | ooffset between the LyC enmüssion and assumed LBC counterpart., The close $\sim1$ ) projected separation of these galaxies is a good example of foreground contamination and could explain some the $z\sim3$ detections of \citet{2009ApJ...692.1287I} particularly the ones with a $\sim1$ offset between the LyC emission and assumed LBG counterpart.
 The deep UV spectra preseuted here achicve the lowest individual limits of the ionizing escape fr:tion at anv redshitt., The deep UV spectra presented here achieve the lowest individual limits of the ionizing escape fraction at any redshift.
 We confirma the results of shallower studies that sugeest low escape fractions i mockvate redslüft starbursts., We confirm the results of shallower studies that suggest low escape fractions in moderate redshift starbursts.
 We now present our findines in the context of recent studies and discuss sole possible»nechamisiis that could be respousible for the appareut lack of 2~1 starbursts with large escape fractions., We now present our findings in the context of recent studies and discuss some possible mechanisms that could be responsible for the apparent lack of $z\sim1$ starbursts with large escape fractions.
 Receutly. ? used HSTACS/SDBC L500 inmaeimugofl15:-1.3starburst galaxies iu the GOODS field. obtaining a stacked 30 limit of f£O00Vf(L500)< 0.02.," Recently, \citet{2010arXiv1001.3412S} used ACS/SBC 1500 imaging of 15 $z\sim1.3$ starburst galaxies in the GOODS field, obtaining a stacked $3\sigma$ limit of $f_{\nu}(700)/f_{\nu}(1500) < 0.02$ ."
 With the inclusion of previous studi(T?) ther state that no more than of star-forming galaxies at Doce have relative escape fractions ercater than 0.50.," With the inclusion of previous studies \citep{2003ApJ...598..878M,2007ApJ...668...62S} they state that no more than of star-forming galaxies at $z\sim$ 1 have relative escape fractions greater than 0.50."
" ? stacked. the GALENfar-UV (1500 ) fluxes of a much larger sample (626 ealaxics) aud obtain a similar 30 upper luit of f,O0000)/f.(1500)<0.012. confirming that starbursts at 2~1 have low ionizing cinissivitics."," \citet{2009ApJ...692.1476C} stacked the far-UV (1500 ) fluxes of a much larger sample (626 galaxies) and obtain a similar $3\sigma$ upper limit of $f_{\nu}(700)/f_{\nu}(1500)< 0.012$, confirming that starbursts at $z\sim1$ have low ionizing emissivities."
 All of these studies have used broadband UV imaecine to probe the Lv€ at ~TO0A whereas the detectious at :~3 have been obtained through spectroscopy (77?) and narrowband inaciue (?) where the LyC is sampled just below the Lxaiuau luit (SNOοἱ AJ).," All of these studies have used broadband UV imaging to probe the LyC at $\sim700$ whereas the detections at $z\sim3$ have been obtained through spectroscopy \citep{2001ApJ...546..665S,2006ApJ...651..688S} and narrowband imaging \citep{2009ApJ...692.1287I} where the LyC is sampled just below the Lyman limit $880-910$ )."
 This is the first 2~1 spectroscopic stulv to provide LyC measurements much closer to the πα linüt iud is therefore more directly comparable to these higher redshift stuclies. ," This is the first $z\sim1$ spectroscopic study to provide LyC measurements much closer to the Lyman limit and is therefore more directly comparable to these higher redshift studies. \citet{2006ApJ...651..688S},"
with a sample of 11 LBCs probe a slightly higher UV luminosity (sec Figure 1) aud detect two objects with large escape fractious(with LyC-to- ratios significantly above our hlnuita)., with a sample of 14 LBGs probe a slightly higher UV luminosity (see Figure 10) and detect two objects with large escape fractions(with LyC-to-UV ratios significantly above our limits).
 One of these objects likely has a lower escape fraction han initially reported as it was not detected in deep nirrowband Huaeine probing the LyC (?).., One of these objects likely has a lower escape fraction than initially reported as it was not detected in deep narrowband imaging probing the LyC \citep{2009ApJ...692.1287I}.
 Therefore. ouly oue of ll objects has a significant detection.," Therefore, only one of 14 objects has a significant detection."
 I ion stack of he 12 undetected sources. 7? find an οἱServed lower nuit ou the UV-to-LvC flux deusitv ratk vat 2. ~3 of fisov/fous> 13.0. compared to our 2~1 ower lint of Fisoo£fsao27 379.," In a stack of the 12 undetected sources, \cite{2006ApJ...651..688S} find an observed lower limit on the UV-to-LyC flux density ratio at $z\sim$ 3 of $f_{1500}/f_{900}>43.0$ , compared to our $z\sim1$ lower limit of $f_{1500}/f_{830}>379$ ."
 Similarly. ?.. which probe comparable rest-frame UV huuinosifies as our 2< lxuuple. detect aree escape fractions dn ~10UX of LBCs and Lyra cluitters at 2= 3.1.," Similarly, \citet{2009ApJ...692.1287I}, which probe comparable rest-frame UV luminosities as our $z<1$ sample, detect large escape fractions in $\sim 10\%$ of LBGs and $\alpha$ emitters at $z=3.1$ ."
 lf the LBG analogs in our sample lave lonizius properties simular to LBs at 2~? 3. we would expect to detect approximately three objects witli arge fractious of escapiug LyC radiation. however. we detect none (exchiding the ACON-starburst composite).," If the LBG analogs in our sample have ionizing properties similar to LBGs at $z\sim3$ , we would expect to detect approximately three objects with large fractions of escaping LyC radiation, however, we detect none (excluding the AGN-starburst composite)."
For a given element and a given atmosphere. our results have always converged towards the same final stratification. regardless of the initial abundances.,"For a given element and a given atmosphere, our results have always converged towards the same final stratification, regardless of the initial abundances."
 Similarly. differences in equilibrium solutions are not significant between computations carried out with different convergence criteria.," Similarly, differences in equilibrium solutions are not significant between computations carried out with different convergence criteria."
 Computations presented in this section were obtained with our new CaratStrat code. which performs the iterative procedure described in Sect. 3..," Computations presented in this section were obtained with our new CaratStrat code, which performs the iterative procedure described in Sect. \ref{sec:numerics}."
 Diffusior velocities are calculated with CARAT. which is now embedded in CaratStrat.," Diffusion velocities are calculated with CARAT, which is now embedded in CaratStrat."
 Generally. about 10 iterations are needed to approach equilibrium solutions of abundance stratifications for each element (each run of the code adjusts the stratification of one element only).," Generally, about 10 iterations are needed to approach equilibrium solutions of abundance stratifications for each element (each run of the code adjusts the stratification of one element only)."
 Sometimes. an equilibrium solution cannot be reached in all parts of the atmosphere (-5.0.<logrXx 2.0).," Sometimes, an equilibrium solution cannot be reached in all parts of the atmosphere $ -5.0 \le \log \tau \le 2.0$ )."
 However. the results shown in this section are significant enough for discussion; places where equilibrium ts not reached are marked in the figures. together with an indication of the trend directions.," However, the results shown in this section are significant enough for discussion; places where equilibrium is not reached are marked in the figures, together with an indication of the trend directions."
 Since computations are quite expensive. we restricted them (except for the Τη=12000 KK model) to elements that have recently published observations and for which abundance stratifications have been estimated from the observed spectra.," Since computations are quite expensive, we restricted them (except for the $T_{\rm eff}=12\,000$ K model) to elements that have recently published observations and for which abundance stratifications have been estimated from the observed spectra."
 We considered models with Zr close to those of the observed stars. but in this study we did not try to match the published effective temperatures and gravities.," We considered models with $T_{\rm eff}$ close to those of the observed stars, but in this study we did not try to match the published effective temperatures and gravities."
 We have considered for each model the zero field case and IOKKkG magnetic fields inclined under several angles., We have considered for each model the zero field case and kG magnetic fields inclined under several angles.
 For the Tay=10000 KK model. we also present computations for kkG. As in our previous papers (Alecian Stift. 2004... 2006)). we relied on Kuruez (1993)) stellar atmospheric models with the tabulated continuous opacities required by CARAT taken directly from the output of ATLAS? and corresponding to solar abundances.," For the $T_{\rm eff}=10\,000$ K model, we also present computations for kG. As in our previous papers (Alecian Stift \cite{als04}, , \cite{als06}) ), we relied on Kurucz \cite{kur93}) ) stellar atmospheric models with the tabulated continuous opacities required by CARAT taken directly from the output of ATLAS9 and corresponding to solar abundances."
 Similar to the slight inconsistency concerning the accelerations from b-f transitions discussed in Alecian Stift (2006)) — eross sections are taken from TopBase (Cunto Mendoza 1992:; Cunto et al. 1993)).," Similar to the slight inconsistency concerning the accelerations from b-f transitions discussed in Alecian Stift \cite{als06}) ) – cross sections are taken from TopBase (Cunto Mendoza \cite{cum92}; Cunto et al. \cite{cum93}) ),"
 continuous opacities for the flux calculations from ATLAS? — for some of the elements in our study we may encounter a discrepancy between the continuous opacities derived with solar abundances and the continuous opacities corresponding to the actual stratifications., continuous opacities for the flux calculations from ATLAS9 – for some of the elements in our study we may encounter a discrepancy between the continuous opacities derived with solar abundances and the continuous opacities corresponding to the actual stratifications.
 The results for species like Ti that do not contribute any conspicuous continua will hardly be affected. but S1 could possibly constitute a different case.," The results for species like Ti that do not contribute any conspicuous continua will hardly be affected, but Si could possibly constitute a different case."
 To clarify this issue. new versions of CARAT and CaratStrat have been established which incorporate the entire ATLASI2 opacity package (for the latter see Bischof 2005). allowing straightforward calculation of stratified opacities.," To clarify this issue, new versions of CARAT and CaratStrat have been established which incorporate the entire ATLAS12 opacity package (for the latter see Bischof 2005), allowing straightforward calculation of stratified opacities."
" In this context one should keep in mind that. even without stratification. there are large differences in the ""cool"" Sitand opacities between ATLAS9 and ATLASI? in the UV."," In this context one should keep in mind that, even without stratification, there are large differences in the “cool"" and opacities between ATLAS9 and ATLAS12 in the UV."
 Therefore a comparison between the respective Si equilibrium stratification obtained with the old and the new versions of CARAT will reflect both the changes from ATLAS9 to ATLASI2 and the influence of fixed vs. stratified continuous opacities., Therefore a comparison between the respective Si equilibrium stratification obtained with the old and the new versions of CARAT will reflect both the changes from ATLAS9 to ATLAS12 and the influence of fixed vs. stratified continuous opacities.
 As it turns out. differences in S1 stratification between the old and the new versions do not exceed 0.2 dex in those places where equilibrium ts achieved.," As it turns out, differences in Si stratification between the old and the new versions do not exceed 0.2 dex in those places where equilibrium is achieved."
 Given the uncertainties in both theory and observations. these differences can be considered marginal.," Given the uncertainties in both theory and observations, these differences can be considered marginal."
 Equilibrium solutions for Si. Ca. and Ti are shown in reftig:Fig.tratSS00lav.," Equilibrium solutions for Si, Ca, and Ti are shown in \\ref{fig:Fig_strat8500lay}."
.Wehaveplottede. which is the abundance (logarithmic particle number. density) with respect to H where «(H)=12.," We have plotted $\varepsilon$ , which is the abundance (logarithmic particle number density) with respect to H where $\varepsilon (\rm H) = 12$."
 The effective temperature of 8500 KK is close to the value of 8400 KK adopted by Kochukhov et al. (2004))," The effective temperature of $8\,500$ K is close to the value of $8\,400$ K adopted by Kochukhov et al. \cite{koc04}) )"
 for CCam. but the gravity of the model we used is higher (4.0 instead of 3.7. see refsubsec:atmos)).," for Cam, but the gravity of the model we used is higher $4.0$ instead of $3.7$, see \\ref{subsec:atmos}) )."
 The heavy-long-dashed and long-dashed lines are stratifications for zero field and for a KKG vertical magnetic field. respectively.," The heavy-long-dashed and long-dashed lines are stratifications for zero field and for a kG vertical magnetic field, respectively."
 Differences between these two curves are thus only due to Zeeman amplifications of the radiative accelerations*., Differences between these two curves are thus only due to Zeeman amplifications of the radiative accelerations.
. The effect of Zeeman amplification is weak for Si. because Zeeman splitting of its strong absorption lines in the UV is comparatively small: this ts in accord with the findings of Alecian Stift (2004)).," The effect of Zeeman amplification is weak for Si, because Zeeman splitting of its strong absorption lines in the UV is comparatively small; this is in accord with the findings of Alecian Stift \cite{als04}) )."
 The role of the magnetic field remains minor for layers deeper than logr=-|.0. because the collision rates increase with particle density (see the discussion on diffusion coefficients in. Alecian Stift 2006... and their 44c).," The role of the magnetic field remains minor for layers deeper than $\log \tau =
-1.0$, because the collision rates increase with particle density (see the discussion on diffusion coefficients in Alecian Stift \cite{als06}, and their 4c)."
 Equilibrium stratifications 1n these layers are — as expected — closely related to radiative accelerations for solar homogeneous abundances. as shown in reffig:erad8500lay.. since these layers are optically thick: Si is not supported by the radiation field for solar abundance. Ca is barely supported around log7=0.0. and Ti is strongly pushed upwards unless it becomes strongly overabundant.," Equilibrium stratifications in these layers are – as expected – closely related to radiative accelerations for solar homogeneous abundances, as shown in \\ref{fig:grad8500lay}, since these layers are optically thick: Si is not supported by the radiation field for solar abundance, Ca is barely supported around $\log \tau = 0.0$, and Ti is strongly pushed upwards unless it becomes strongly overabundant."
 No equilibrium solution is obtained for Ca in layers deeper than logr=Là Ca is ina noble gas configuration 1n. these layers and not enough photons are absorbed to support Ca., No equilibrium solution is obtained for Ca in layers deeper than $\log \tau = 1.5$; Ca is in a noble gas configuration in these layers and not enough photons are absorbed to support Ca.
" Consequently. the Ca abundance must decrease at the bottom of the atmosphere towards a value that is probably lower than the one shown in the figure. indicated by the downward arrows,"," Consequently, the Ca abundance must decrease at the bottom of the atmosphere towards a value that is probably lower than the one shown in the figure, indicated by the downward arrows."
" The final Ca deficiency of the bottom layers of the atmosphere will be determined by the diffusion flux in the envelope and the abundance contrast allowed by the concentration gradient term,", The final Ca deficiency of the bottom layers of the atmosphere will be determined by the diffusion flux in the envelope and the abundance contrast allowed by the concentration gradient term.
 For layers higher than logc=—1.0. the magnetic field is very efficient. especially when it is horizontal.," For layers higher than $\log \tau = -1.0$, the magnetic field is very efficient, especially when it is horizontal."
 This is generally due to the fact that element diffusion in the neutral state 1s favoured by the presence of a horizontal component of the magnetic field., This is generally due to the fact that element diffusion in the neutral state is favoured by the presence of a horizontal component of the magnetic field.
Generally. the neutral state undergoes strong radiative acceleration (absorption lines are notsaturated) and has a large diffusion coefficient.,"Generally, the neutral state undergoes strong radiative acceleration (absorption lines are notsaturated) and has a large diffusion coefficient."
 Silicon is still hardly supported, Silicon is still hardly supported
In any case. we conclude that dense blobs formed by instability will start to flow inward al a speed of ~10—50kms.|.,"In any case, we conclude that dense blobs formed by instability will start to flow inward at a speed of $\sim 10-50 \km \s^{-1}$."
 This speed is larger than the expansion velocity of the shell ~10—20kms. and there will be a backflow at speed μμ73»—30kms!1 made up of blobs.," This speed is larger than the expansion velocity of the shell $\sim 10-20 \km \s^{-1}$, and there will be a backflow at speed $v_{\rm back} \sim 3-30 \km \s^{-1}$ made up of blobs."
 In the 1D calculation of Perinotto et al. (, In the 1D calculation of Perinotto et al. (
2004) the initial expansion velocity of (he shell is 10kms.!.,2004) the initial expansion velocity of the shell is $10 \km \s^{-1}$.
 After ionization starts a zone to the main shell is formed with an expansion velocity of only ~4kms.|., After ionization starts a zone to the main shell is formed with an expansion velocity of only $\sim 4 \km \s^{-1}$.
 Namely. the inner zone of the main shell was substantially slowed down.," Namely, the inner zone of the main shell was substantially slowed down."
 The pressure of the hot bubble prevents further acceleration inwarel. and later accelerates the entire shell outwarel.," The pressure of the hot bubble prevents further acceleration inward, and later accelerates the entire shell outward."
 However. if a blob is disconnected from the main shell. it will have the hot bubble material all around it.," However, if a blob is disconnected from the main shell, it will have the hot bubble material all around it."
 The pressure of the hot bubble is more or less isotropic and it will not slow the blob down., The pressure of the hot bubble is more or less isotropic and it will not slow the blob down.
 This effect cannot be studied with a 1D code., This effect cannot be studied with a 1D code.
 The end product of the initial evolution is a large number of dense (relative to the hot bubble) blobs at a temperature of ~104Ix that are immersed in the hot low density. gas ol the hot bubble., The end product of the initial evolution is a large number of dense (relative to the hot bubble) blobs at a temperature of $\sim 10^4 \K$ that are immersed in the hot low density gas of the hot bubble.
 Many of these will be flowing inward due (to inward acceleration by the pressure of the ionized shell during (he early ionization stage., Many of these will be flowing inward due to inward acceleration by the pressure of the ionized shell during the early ionization stage.
 If à blob does not slow clown much. its backflow time from an initial racius rà is This is about the time required for the mass to be accreted during the PN phase. but before a VLTP occurs.," If a blob does not slow down much, its backflow time from an initial radius $r_0$ is This is about the time required for the mass to be accreted during the PN phase, but before a VLTP occurs."
" For the blob not to slow much it should encounter à massM, not much larger than its initial mass Mj,=Je; pi/3. where a, is the radius of the blob and p, is its density."," For the blob not to slow much it should encounter a mass$M_e$ not much larger than its initial mass $M_b= 4 \pi a_b^3 \rho_b/3$ , where $a_b$ is the radius of the blob and $\rho_b$ is its density."
 For simplicitv we assume the blob is in the shape of a sphere., For simplicity we assume the blob is in the shape of a sphere.
 After flowing a distance ~ry the blob encounters a mass and the condition reads The clensity ratio of 300 comes from pressure equilibrium between (he hot bubble aud the blob. and a temperature ratio of ~3x105IX/10!IK= 300.," After flowing a distance $\sim r_0$ the blob encounters a mass and the condition reads The density ratio of $300$ comes from pressure equilibrium between the hot bubble and the blob, and a temperature ratio of $\sim 3 \times 10^6 \K /10^4 \K
= 300$ ."
 The blobsradius is therefore, The blobs'radius is therefore
solution to the external medium bv selecting the radius at which the pressure of the solution matches that of the medium. then neither the density. nor the temperature will agree.,"solution to the external medium by selecting the radius at which the pressure of the solution matches that of the medium, then neither the density nor the temperature will agree."
 Does this mean that the solution is physically inconsistent?, Does this mean that the solution is physically inconsistent?
 We argue otherwise in this paper., We argue otherwise in this paper.
 We show that there exists a second self-5imilar solution at racii outside the ALNOL ho settling Low. which acts as à bridge between the MNOL solution and the external medium.," We show that there exists a second self-similar solution at radii outside the MN01 hot settling flow, which acts as a bridge between the MN01 solution and the external medium."
 ‘This bridging solution has an extra degree of freedom which allows it to match a general. density. ancl temperature. in the external medium., This bridging solution has an extra degree of freedom which allows it to match a general density and temperature in the external medium.
 Apart from the additional degree of freedom. the solution retains many of the features of the MNOL settling How: 1) 1 is pressure supported. (ii) it resembles a static atmosphere at low mass accretion rates. and (ii) the angular momentum [ux associated with the viscous braking of the central star dominates most of the physies.," Apart from the additional degree of freedom, the solution retains many of the features of the MN01 settling flow: (i) it is pressure supported, (ii) it resembles a static atmosphere at low mass accretion rates, and (iii) the angular momentum flux associated with the viscous braking of the central star dominates most of the physics."
 The paper is organized as follows., The paper is organized as follows.
 In refs:th owe derive analvtical expressions for various selí- solutions., In \\ref{s:th} we derive analytical expressions for various self-similar solutions.
 ln refs:num we present full numerical solutions and. compare them with the analvtical solutions., In \\ref{s:num} we present full numerical solutions and compare them with the analytical solutions.
 Finally. in E44 we conclude with a brief discussion.," Finally, in 4 we conclude with a brief discussion."
 We consider gas accreting viscously onto à compact spinning object., We consider gas accreting viscously onto a compact spinning object.
" The central object has à radius 5. a mass M;= ml. and an angular velocity £2,=SOE). where On(R)=(GAL/R?)Y? is the Keplerian angular velocity at radius 2."," The central object has a radius $R_*$, a mass $M_*=m M_{\sun}$ , and an angular velocity $\Omega_*=s \Omega_K(R_*)$, where $\Omega_K(R)=(GM/R^3)^{1/2}$ is the Keplerian angular velocity at radius $R$."
" We measure the aecretion rate in. Iddington units. =Ανω. and the radius in Sehwarzchild units. r—[BUB. where Mgaa=1.39Lon es"" (corresponding. o a radiative efficiency of 10%)) and 2,=26Mce."," We measure the accretion rate in Eddington units, $\dot m=\dot M/\dot M_{\rm Edd}$, and the radius in Schwarzchild units, $r=R/R_g$, where $\dot M_{\rm
Edd}=1.39\times10^{18}m$ g $^{-1}$ (corresponding to a radiative efficiency of ) and $R_g=2GM/c^2$."
 We assume that the Low is hot and. quasi-spherical. which generally requires a low mass accretion rate (see ανα et al.," We assume that the flow is hot and quasi-spherical, which generally requires a low mass accretion rate (see Narayan et al."
 1997)., 1997).
 The accreting gas has nearly the virial temperature. beso2oCMÍBR~(ORHRY. and he local vertical scale height ££=ὃνιν is comparable o the local radius RR.," The accreting gas has nearly the virial temperature, i.e., $c_s^2\sim GM/R
\sim (\Omega_K R)^2$, and the local vertical scale height $H=c_s/\Omega_K$ is comparable to the local radius $R$."
 We may then use the height integrated hyerodvnamic equations for a steady. rotating. axisvmmetric flow. and for simplicity we may set. Jf=H8 (sco MNOLI). (," We may then use the height integrated hydrodynamic equations for a steady, rotating, axisymmetric flow, and for simplicity we may set $H= R$ (see MN01). ("
Note that. even when ffzA. the stability operties of the [ow may depend on whether we use Lf or Rin the equations: this is briellv. discussed in $44).,"Note that, even when $H\approx R$, the stability properties of the flow may depend on whether we use $H$ or $R$ in the equations; this is briefly discussed in 4)."
 In the ollowing. we closely follow the analysis of MNOI. with a few changes.," In the following, we closely follow the analysis of MN01, with a few changes."
 For simplicity. we set i1=0 and omit the continuity equation.," For simplicity, we set $\dot m=0$ and omit the continuity equation."
 Thus. the eas configuration corresponds. to a ractially static “atmosphere.”," Thus, the gas configuration corresponds to a radially static “atmosphere.”"
 The motivation for this approximation follows from the observation that the density p. temperature Z and the angular velocity Q of the gas in the AINOL self-similar solution are completely. independent of m.," The motivation for this approximation follows from the observation that the density $\rho$, temperature $T$ and the angular velocity $\Omega$ of the gas in the MN01 self-similar solution are completely independent of $\dot m$."
 Only the radial velocity. ο depends on mm. and it is given trivially by the spherical continuity equation," Only the radial velocity $v$ depends on $\dot m$, and it is given trivially by the spherical continuity equation."
 of this. we do not lose any generality by setting m=7=τρ0 in the analysis: we may always introduce a finite 2 and finite e after the fact.," Because of this, we do not lose any generality by setting $\dot
m=v=0$ in the analysis; we may always introduce a finite $\dot m$ and finite $v$ after the fact."
" We assume that the Blow is highly sub-Ixeplerian. OR)OQ,(AR). νο that the centrifugal support is negligible compared to the pressure support."," We assume that the flow is highly sub-Keplerian, $\Omega(R)
\ll\Omega_K(R)$, so that the centrifugal support is negligible compared to the pressure support."
 “Phe racial momentum equation then takes the following simple form..(2)where we have used t1e fact that eO and written thep pressure as p=ρο2 where ὃς is the isothermal sound speed.," The radial momentum equation then takes the following simple form, where we have used the fact that $v\sim0$ and written the pressure as $p=\rho c_s^2$ where $c_s$ is the isothermal sound speed."
 MNOI present a more complete analysis in which they co not assume that {10 rotation is slow., MN01 present a more complete analysis in which they do not assume that the rotation is slow.
 Thev then obtain an extra factor of (157) in their equation. which propagates through to all the results.," They then obtain an extra factor of $(1-s^2)$ in their equation, which propagates through to all the results."
 Since we ignore the factor. our analysis corresponds to the case of a slowlv-spinning star: sv«1.," Since we ignore the factor, our analysis corresponds to the case of a slowly-spinning star: $s^2\ll1$."
 This approximation is made onlv to simplify the analvsis. and all the results may be generalized for arbitrary .," This approximation is made only to simplify the analysis, and all the results may be generalized for arbitrary $s$."
 From the analysis in MNOI. we know that the accreting eas in our problem acts as a brake on the central spinning star and transports angular momentum outward. through the action of viscosity.," From the analysis in MN01, we know that the accreting gas in our problem acts as a brake on the central spinning star and transports angular momentum outward through the action of viscosity."
 We therefore write the angular momentum conservation equation for the gas as follows.constant. (3)where J is the outward angular momentum Lux. and v is the kinematic coellicient. of viscosity.," We therefore write the angular momentum conservation equation for the gas as follows, where $\dot J$ is the outward angular momentum flux, and $\nu$ is the kinematic coefficient of viscosity."
 This equation is exactly valid in steady state if ij)=), This equation is exactly valid in steady state if $\dot m=0$.
 When m is non-zero. there is an additional term. ΑΟ due to the Dux of angular momentum carried in by the accreting gas.," When $\dot m$ is non-zero, there is an additional term, $\dot M\Omega R^2$, due to the flux of angular momentum carried in by the accreting gas."
 The kev feature of the AINOL hot brake solution is that the latter Hux is negligible compared. to. the outward [lux from the star., The key feature of the MN01 hot brake solution is that the latter flux is negligible compared to the outward flux from the star.
" Equation (3)) is. therefore. valid even when m=0. so long as "" his. small enough forB the term ALQL-tD to be negligible."," Equation \ref{jdot}) ) is, therefore, valid even when $\dot m\ne0$, so long as $\dot m$ is small enough for the term $\dot M \Omega R^2$ to be negligible."
". We employ the usual à prescription for the kinematic cocllicient of viscosity. which we write as elphaclH aceR(4A)OLten, in aceretion problems. one makes use of the relation Hi—οὋν and writes v=αμ."," We employ the usual $\alpha$ prescription for the kinematic coefficient of viscosity, which we write as c_s H c_s R. Often, in accretion problems, one makes use of the relation $H=c_s/\Omega_K$ and writes $\nu=\alpha c_s^2/\Omega_K$."
 This prescription is equivalent to equation (4) in the regime of the AINOL hot settling flow., This prescription is equivalent to equation (4) in the regime of the MN01 hot settling flow.
 However. in the outer regions of the flow. where the two new solutions described in 522.2.2.4 apear. df is much less than c;/Ogy.— and vo=000g2 is. not a good approximation.," However, in the outer regions of the flow, where the two new solutions described in 2.2,2.3 apear, $H$ is much less than $c_s/\Omega_K$, and $\nu=\alpha c_s^2/\Omega_K$ is not a good approximation."
. Equation4. (4) is a superior prescription and. is physically better motivated over a wide range of conditions (so long as the How is quasi-spherical)., Equation (4) is a superior prescription and is physically better motivated over a wide range of conditions (so long as the flow is quasi-spherical).
 l'or simplicity. we assume that the gas l8 one-temperature: dit is straightforward to generalize to the two-temperature regime. as done in MNOIL. but the one-temperature analysis sullices for the present paper.," For simplicity, we assume that the gas is one-temperature; it is straightforward to generalize to the two-temperature regime, as done in MN01, but the one-temperature analysis suffices for the present paper."
 Hence do not need to treat electrons ancl protons separately., Hence do not need to treat electrons and protons separately.
 Viscous braking heats the accreting gas. and we assume a steady state in which this heating is balanced by cooling.," Viscous braking heats the accreting gas, and we assume a steady state in which this heating is balanced by cooling."
 The energy. conservation equation thus becomes q=4. where the viscous heating rate per unit volume gq and the radiative cooling per unit volume via bremsstrahlung gq are given BedifoINOD)," The energy conservation equation thus becomes q^+=q^-, where the viscous heating rate per unit volume $q^+$ and the radiative cooling per unit volume via bremsstrahlung $q^-$ are given by (MN01)"
xoperlv.,properly.
 We find that our best-fit slope a is consistent with th. the theoretical expectation aud the slopes derived x other observations and simulations of clusters., We find that our best-fit slope $\alpha$ is consistent with both the theoretical expectation and the slopes derived by other observations and simulations of clusters.
 Our IOS-fit norinalization Ais somewhat lower than. but still consistent with. the normalizatious found by the other observations and simulations.," Our best-fit normalization $A$ is somewhat lower than, but still consistent with, the normalizations found by the other observations and simulations."
 We fiud that relaxed strong chsing clusters follow the same ALT relation as relaxed clusters im ecneral., We find that relaxed strong lensing clusters follow the same $M-T$ relation as relaxed clusters in general.
 We have derived au ALTf power-law relation for relaxed Ieusing clusters. but a amore general AfT relation including both relaxed and uurelaxed clusters may be possible if we account for the differences in cluster concentrations.," We have derived an $M-T$ power-law relation for relaxed lensing clusters, but a more general $M-T$ relation including both relaxed and unrelaxed clusters may be possible if we account for the differences in cluster concentrations."
 First. we define the virial radius of a cluster as the radius rj at which the average cluster deusity equals A41) times the mean density at the cluster redshift z. where Aqu(:)cz(18s?|82039.72)/CL|c) and e=Qut) 1(7).," First, we define the virial radius of a cluster as the radius $r_\mathrm{vir}$ at which the average cluster density equals $\Delta_\mathrm{vir}(z)$ times the mean density at the cluster redshift $z$ , where $\Delta_\mathrm{vir}(z) \simeq (18 \pi^2 + 82x -39x^2)/(1+x)$ and $x \equiv \Omega_{\rm m}(z) -1$ \citep{BR98.2}."
 Using the scale radius kr of the best-fit NEW profile tocach cluster. the," Using the scale radius $r_{\rm s}$ of the best-fit NFW profile toeach cluster, the"
The detection rate is intrinsically Gel (o the distribution of SNe la with respect (o magnitude.,The detection rate is intrinsically tied to the distribution of SNe Ia with respect to magnitude.
 An example of this distribution for 10* SNe Ia generated by the Monte Carlo simulation is given in Figure 5.., An example of this distribution for $10^3$ SNe Ia generated by the Monte Carlo simulation is given in Figure \ref{fig:occurrence}.
 Iu the simulation. all SNe Ia peak at an absolute magnitude of -19.45. so the apparent magnitude of a supernova immediately. vields the distance to the supernova.," In the simulation, all SNe Ia peak at an absolute magnitude of -19.45, so the apparent magnitude of a supernova immediately yields the distance to the supernova."
 The probability of detection of a SN Ia is directly proportional to volume scanned. so SNe la are prelerentially observed αἱ fainter magnitudes.," The probability of detection of a SN Ia is directly proportional to volume scanned, so SNe Ia are preferentially observed at fainter magnitudes."
 Accordingly. the total detection rate is dominated by the lower detection rates lor SNe Ia that peak below 12th magnitude.," Accordingly, the total detection rate is dominated by the lower detection rates for SNe Ia that peak below 12th magnitude."
 We tested the filtering program to determine if it could identify any previously known SNe Ia in the data set., We tested the filtering program to determine if it could identify any previously known SNe Ia in the data set.
 The International Astronomical Union's List of Supernovae was searched for all SNe Ia that meet the following requirements: The SN Ia was observable during the time period and area of skv for which we have data (roughlv from Alay 2000 to April 2001 and north of 0° declination): it was bright enough (magnitude >15.5) to be detected by ROTSE-I: ancl it was located further Chan 30 arcseconds (2 pixels) from the host galaxys center., The International Astronomical Union's List of Supernovae was searched for all SNe Ia that meet the following requirements: The SN Ia was observable during the time period and area of sky for which we have data (roughly from May 2000 to April 2001 and north of $^{\circ}$ declination); it was bright enough (magnitude $> 15.5$ ) to be detected by ROTSE-I; and it was located further than $\sim 30$ arcseconds (2 pixels) from the host galaxy's center.
 IL the SN Ia was too close to the galaxy. the light curve will not resemble the SN Ia template. aud our fillering program is not designed to detect such objects.," If the SN Ia was too close to the galaxy, the light curve will not resemble the SN Ia template, and our filtering program is not designed to detect such objects."
 The only SN Ia found that met all three criteria was SN 2001V. which reached maximum light on March 5. 2001. with D magnitude 14.64 (Mandeletal.2001).," The only SN Ia found that met all three criteria was SN 2001V, which reached maximum light on March 5, 2001, with B magnitude 14.64 \citep{man01}."
. SN 2001V was located 64.6 arcseconds (4.5 pixel widtlis) from its host galaxy. NGC 3987. a Type 5b spiral with B-hand magnitude 14.4 (Vinkóetal.2003).," SN 2001V was located 64.6 arcseconds $\sim 4.5$ pixel widths) from its host galaxy, NGC 3987, a Type Sb spiral with B-band magnitude 14.4 \citep{vin03}."
. The position of SN 2001V was imaged [frequently by ROTSE-I in late February and early March. so the SN In should be observed in the data. though onlv for a short time.," The position of SN 2001V was imaged frequently by ROTSE-I in late February and early March, so the SN Ia should be observed in the data, though only for a short time."
 The filtering program did not identify a possible SN Ia at the position of SN 2001V. This is expected because the filler can only detect supernovae (hat peak at magnitude 14.5 or brighter., The filtering program did not identify a possible SN Ia at the position of SN 2001V. This is expected because the filter can only detect supernovae that peak at magnitude 14.5 or brighter.
 SN 2001V. peaked αἱ 14.64. so it is not possible to detect this supernova with the filtering program.," SN 2001V peaked at 14.64, so it is not possible to detect this supernova with the filtering program."
 We checked (o see if SN 2001V is in the original data set by searching for all objects observed by ROTSE-I near the position of SN 2001V. A lew objects were found within an arcminute of SN 2001V. but they are not likely to be SN 2001V because thev are a few magnitudes brighter (han the supernova ancl show litle variation.," We checked to see if SN 2001V is in the original data set by searching for all objects observed by ROTSE-I near the position of SN 2001V. A few objects were found within an arcminute of SN 2001V, but they are not likely to be SN 2001V because they are a few magnitudes brighter than the supernova and show little variation."
 SN 2001V was brighter (han magnitude 15.5 for only ~20 days (Vinkoetal.2003).. so the supernova may not be in (he original data set.," SN 2001V was brighter than magnitude 15.5 for only $\sim 20$ days \citep{vin03}, so the supernova may not be in the original data set."
 Thus the check for known SNe Ia is not possible. as no good candidates exist.," Thus the check for known SNe Ia is not possible, as no good candidates exist."
iin (he relevant range ~4000—5500A)).,in the relevant range $\sim4000-5500$ ).
 Because our LRIS spectra have a higher spectral resolution (about FFWIIM) than the original Lick/IDS svstem (813 A). we smoothed our spectra to the IDS resolution with a wavelength-dependent Gaussian kernel before measuring the indices.," Because our LRIS spectra have a higher spectral resolution (about FWHM) than the original Lick/IDS system (8–13 ), we smoothed our spectra to the IDS resolution with a wavelength-dependent Gaussian kernel before measuring the indices."
 Another difference between the original Lick/IDS svstem and our LRIS spectra is the fact that we are working on flux-calibrated data. whereas the original Lick/IDS spectra on which the Lick svstem is based were not flux calibrated.," Another difference between the original Lick/IDS system and our LRIS spectra is the fact that we are working on flux-calibrated data, whereas the original Lick/IDS spectra on which the Lick system is based were not flux calibrated."
 However. it is well documented. that differences in flux calibration procedures allect the equivalent widths of most Lick indices only weakly. at the level of <0.1À citep|e.g.|||[nb35.Kis98.]1b02..," However, it is well documented that differences in flux calibration procedures affect the equivalent widths of most Lick indices only weakly, at the level of $\la0.1$ \\citep[e.g.][]{fab85,kis98,lb02}."
 One possible exception is the index. whose continuum passbands are more widely separated. and where offsets between insirumental svstems and the Lick standard svstem have often been found 2000).," One possible exception is the index, whose continuum passbands are more widely separated, and where offsets between instrumental systems and the Lick standard system have often been found \citep[e.g.][]{kun00}."
 For most indices we were able to check the agreement between our instrumental svstem and the Lick standard system using the Lick/1DS standard star observations., For most indices we were able to check the agreement between our instrumental system and the Lick standard system using the Lick/IDS standard star observations.
 Figure 2 shows our standard star measurements versus the standard values 1997).," Figure \ref{fig:stdcmp} shows our standard star measurements versus the standard values \citep{wor94,wo97}."
. The mean olfsets are listed in Table 2.., The mean offsets are listed in Table \ref{tab:stdcmp}.
 Even after smoothing. svstematic olfsets of 0.1—0.2À rremained between our measurements and the standard. values.," Even after smoothing, systematic offsets of $0.1-0.2$ remained between our measurements and the standard values."
 Unfortunately. since the Lick/IDS standard stars were observed in longslit mode. thev did not include the red continuum passbands of aand Fe5335.Qn2t) so we were unable to check these (wo indices.," Unfortunately, since the Lick/IDS standard stars were observed in longslit mode, they did not include the red continuum passbands of and Fe5335, so we were unable to check these two indices."
 Because some of the indices fell outside the spectral range of the standard star observations aud some of the globular cluster spectra have measured indices outside the range spanned by the standard stars. we have not attempted to correct our index measurements on the science spectra for (he offsets between our instrumental svstem and the Lick/IDS stancarel system.," Because some of the indices fell outside the spectral range of the standard star observations and some of the globular cluster spectra have measured indices outside the range spanned by the standard stars, we have not attempted to correct our index measurements on the science spectra for the offsets between our instrumental system and the Lick/IDS standard system."
 However. we note that these sinall offsets are of no consequence to our analvsis or conclusions. and are generally smaller than the random measurement errors and model uncertainties.," However, we note that these small offsets are of no consequence to our analysis or conclusions, and are generally smaller than the random measurement errors and model uncertainties."
 The indices used in this paper are listed in Table 3.., The indices used in this paper are listed in Table \ref{tab:indices_gw}.
 Fie., Fig.
 ὁ shows a(V—AN.. —1)) two-color diagram for GC candidates in NGC! 4365. based on the data in P02.," \ref{fig:pvk_vi} shows a, ) two-color diagram for GC candidates in NGC 4365, based on the data in P02."
 The photometry has been corrected for a foreground reddening of, The photometry has been corrected for a foreground reddening of
"It is clear from 6aa and 6cc that an output power plateau is reached as figuresINR, becomes small for the MKI cancellers.","It is clear from figures \ref{residual power v INR}a a and \ref{residual power v
INR}c c that an output power plateau is reached as $\it{INR}_r$ becomes small for the MK1 cancellers."
" The residual power of the plateau is 0 dB, and indicates that the canceller has turned off."," The residual power of the plateau is 0 dB, and indicates that the canceller has turned off."
" In contrast, the MK2a canceller (6bb) does not turn off and results in more output power than input RFI power for low INR; levels."," In contrast, the MK2a canceller \ref{residual power v INR}b b) does not turn off and results in more output power than input RFI power for low $\it{INR}_r$ levels."
" However, since the residual is entirely noise it averages down in a MK2b canceller, where two independent filters are used (6dd)."," However, since the residual is entirely noise it averages down in a MK2b canceller, where two independent filters are used \ref{residual power v INR}d d)."
 This is highlighted further in the next section., This is highlighted further in the next section.
 We now demonstrate cancellation of real RFI impinging on the Australia adaptiveTelescope Compact Array (ATCA)., We now demonstrate adaptive cancellation of real RFI impinging on the Australia Telescope Compact Array (ATCA).
 The RFI is a point-to-point microwave (MW) television link transmitted from a TV tower on a nearby mountain at 1503 MHz., The RFI is a point-to-point microwave (MW) television link transmitted from a TV tower on a nearby mountain at 1503 MHz.
" The reference antennae were two orthogonal linearly polarised receivers on a small reference horn pointed in the direction of the MW transmitter, as described in Belletal.(2001)."," The reference antennae were two orthogonal linearly polarised receivers on a small reference horn pointed in the direction of the MW transmitter, as described in \citet{Bell2001}."
". A linearly polarised receiver on a regular ATCA antenna, pointing at the sky and receiving the microwave link interference through the antenna side-lobes, was used to collect the main signal."," A linearly polarised receiver on a regular ATCA antenna, pointing at the sky and receiving the microwave link interference through the antenna side-lobes, was used to collect the main signal."
" The RFI is polarised, and as long as all three receivers are at least partially polarised in the same sense as the RFI the cancellers will work correctly (assuming that the polarisation cross-talk between the reference receivers is negligible so the receiver noise is independent)."," The RFI is polarised, and as long as all three receivers are at least partially polarised in the same sense as the RFI the cancellers will work correctly (assuming that the polarisation cross-talk between the reference receivers is negligible so the receiver noise is independent)."
" The received voltages were filtered in a 4MHz band centred at 1503 MHz, downconverted, and sampled with 4-bit precision."," The received voltages were filtered in a 4MHz band centred at 1503 MHz, downconverted, and sampled with 4-bit precision."
 Each of the cancellation techniques discussed has been applied to the MW data using MATLAB (see the MATLABUser'sGuide 1998))., Each of the cancellation techniques discussed has been applied to the MW data using MATLAB (see the \citealt{MATLAB1998}) ).
 All of the spectra shown were generated using 1024-point FFTs., All of the spectra shown were generated using 1024-point FFTs.
 Figure 7 shows the unfiltered and MKla filtered power spectra of the main astronomy voltage series when large reference INRs were available., Figure \ref{high INR mk1a spectrum} shows the unfiltered and MK1a filtered power spectra of the main astronomy voltage series when large reference INRs were available.
 Two synthetic astronomy signals have been added to the astronomy voltage series at 1503.0 MHz and 1503.2 MHz., Two synthetic astronomy signals have been added to the astronomy voltage series at 1503.0 MHz and 1503.2 MHz.
" What we want is to remove the RFI peak (the 1-2 MHz wide peak centred at 1503 MHz) from the main signal spectrum, leaving the broad, main antenna bandpass, and the astronomy."," What we want is to remove the RFI peak (the 1-2 MHz wide peak centred at 1503 MHz) from the main signal spectrum, leaving the broad, main antenna bandpass, and the astronomy."
" This is indeed what is seen, and similar results are achieved for all of the techniques discussed in this paper."," This is indeed what is seen, and similar results are achieved for all of the techniques discussed in this paper."
" Since all of the techniques behave excellently when the reference INR is large, and any contributed reference receiver noise or residual RFI is much smaller than the main signals receiver noise level, it is difficult to compare them."," Since all of the techniques behave excellently when the reference INR is large, and any contributed reference receiver noise or residual RFI is much smaller than the main signals receiver noise level, it is difficult to compare them."
" Figure 8 displays the power spectra of two reference signals that have had Gaussian random noise injected into their sampled voltage series, to set INR,z1 at the centre of the MW band and zero at the edges."," Figure \ref{reference spectra} displays the power spectra of two reference signals that have had Gaussian random noise injected into their sampled voltage series, to set $\it{INR}_r\approx1$ at the centre of the MW band and zero at the edges."
" The reason for adding the fake receiver noise was to lower the INR and accentuate any residual RFI, as detailed in (9)), (10)), and (13))."," The reason for adding the fake receiver noise was to lower the INR and accentuate any residual RFI, as detailed in \ref{mk1 residuals a}) ), \ref{mk1 residuals b}) ), and \ref{mk2 residual power}) )."
 Plots, Plots
subtraction.,subtraction.
 The orientation of this map is roughly along the major axis of the galaxy., The orientation of this map is roughly along the major axis of the galaxy.
 At 170jmn the central area of 29x ssize was also mapped in the AOT-P22 raster staring mode. which almost is free from detector transient effects due to the relatively long integrating time of 10 seconds per raster position.," At $\mu$ m the central area of $\times$ size was also mapped in the AOT-P22 raster staring mode, which almost is free from detector transient effects due to the relatively long integrating time of 10 seconds per raster position."
 The P32 and P22 maps were merged to à common one by using equal weights for both maps in the bright and medium bright areas and zero-weight for the P22 map for areas where the surface brightness falls below MMJy/sr., The P32 and P22 maps were merged to a common one by using equal weights for both maps in the bright and medium bright areas and zero-weight for the P22 map for areas where the surface brightness falls below MJy/sr.
 The data reduction was done using the ISOPHOT Interactive Analysis software package PIA V7 (Gabriel et al., The data reduction was done using the ISOPHOT Interactive Analysis software package PIA V7 (Gabriel et al.
 1998). together with the calibration data set V4.0 (Laureijs et al.," 1998), together with the calibration data set V4.0 (Laureijs et al."
 2000)., 2000).
 A special data handling was required due to signal transient effects of the infrared detectors. which 1s described in sect.," A special data handling was required due to signal transient effects of the infrared detectors, which is described in sect."
 2.2., 2.2.
 The absolute flux calibration was performed with measurements of the internal thermal fine calibration source on board. before and after each map.," The absolute flux calibration was performed with measurements of the internal thermal fine calibration source on board, before and after each map."
 We estimate the error of this flux calibration tobe about 420%., We estimate the error of this flux calibration tobe about $\pm20\%$.
 An additional uncertainty is introduced by the detector transient effects in the P32 observing mode. which generally leads to too low signals for the FIR knots. and which we have only corrected to a certain degree (see below).," An additional uncertainty is introduced by the detector transient effects in the P32 observing mode, which generally leads to too low signals for the FIR knots, and which we have only corrected to a certain degree (see below)."
 At 60 and 100m. where this effect is most critical. we estimate the total error to be 430%.," At 60 and $\mu$ m, where this effect is most critical, we estimate the total error to be $\pm30\%$."
 At um the transient effect Is less severe. and the total error is of the order of 420%.," At $\mu$ m the transient effect is less severe, and the total error is of the order of $\pm20\%$."
 As mentioned above. a difficulty in the reduction of P32 data are signal transient effects of the infrared detectors. leading to small lags of the maxima positions for bright point-like sources along the sean direction. and to a lowering of the maxima and filling up of the minima.," As mentioned above, a difficulty in the reduction of P32 data are signal transient effects of the infrared detectors, leading to small lags of the maxima positions for bright point-like sources along the scan direction, and to a lowering of the maxima and filling up of the minima."
 It also led to ghost images of bright sources at distances of the chopper throw in the scan direction., It also led to ghost images of bright sources at distances of the chopper throw in the scan direction.
 Based on the principles described by Acosta-Pulido et al. (, Based on the principles described by Acosta-Pulido et al. (
2000) we adopted a correction routine to reduce the transient effects: First. separate maps were constructed for each detector pixel. nine for the 60 and 100m maps. which were observed with the C100 detector array.,"2000) we adopted a correction routine to reduce the transient effects: First, separate maps were constructed for each detector pixel, nine for the 60 and $\mu$ m maps, which were observed with the C100 detector array."
 and four in the case of the 170m map. which was observed with the C200 array.," and four in the case of the $\mu$ m map, which was observed with the C200 array."
 Transient effect were reduced by adding to the signal in each pixel of the difference to the signal of the preceeding pixel during the sean., Transient effect were reduced by adding to the signal in each pixel of the difference to the signal of the preceeding pixel during the scan.
 This procedure led to a steepening of the edges of bright sources and improved the coincidence in the forth and back scans., This procedure led to a steepening of the edges of bright sources and improved the coincidence in the forth and back scans.
 It also led to a significant reduction of the ghosts from bright point like sources at the map pixels located in chopper throw separation (here. however. a factor of only was applied to the difference signal).," It also led to a significant reduction of the ghosts from bright point like sources at the map pixels located in chopper throw separation (here, however, a factor of only was applied to the difference signal)."
 Second. the separate pixel maps were scaled to a common level and superimposed.," Second, the separate pixel maps were scaled to a common level and superimposed."
 Due to a displacement of the raster legs by half of the array size and a chopper step of tthe pixel size of the resulting image was 1523” (in the cases of 60 and 100jm)., Due to a displacement of the raster legs by half of the array size and a chopper step of the pixel size of the resulting image was $\times$ (in the cases of 60 and $\mu$ m).
 Each of these pixels was seen by 3 detector pixels in the one raster leg in forth direction and in the adjacent raster leg in opposite direction by 34 other detector pixels., Each of these pixels was seen by 3 detector pixels in the one raster leg in forth direction and in the adjacent raster leg in opposite direction by 3 other detector pixels.
 From the 6 detector signals in each pixel the median signal was derived. and an iterative &« clipping was applied toin the separate pixel maps and to correct them.," From the 6 detector signals in each pixel the median signal was derived, and an iterative $\kappa$ $\sigma$ clipping was applied toin the separate pixel maps and to correct them."
 This also leads to a spatial resolution of aat 601m. of aat 100jm. and of aat 170.m. It was found that each scan had a slight positive slope. recognizable by small offsets at the edges of the forth and back scans.," This also leads to a spatial resolution of at $\mu$ m, of at $\mu$ m, and of at $\mu$ m. It was found that each scan had a slight positive slope, recognizable by small offsets at the edges of the forth and back scans."
 This was corrected by a fine adjustment of the scan slopes until a smooth background was achieved., This was corrected by a fine adjustment of the scan slopes until a smooth background was achieved.
 The background level (from foreground cirrus and zodiacal light) was then determined from the outermost map areas and subtracted., The background level (from foreground cirrus and zodiacal light) was then determined from the outermost map areas and subtracted.
 Por studying the correlation of optical emission with the detailed ISOPHOT maps. 333 was observed in He with the focal reducer at the mm telescope on Calar Alto. Spain.," For studying the correlation of optical emission with the detailed ISOPHOT maps, 33 was observed in $\alpha$ with the focal reducer at the m telescope on Calar Alto, Spain."
 The detector was a 2kx2k SITe chip used in a rebinned mode. to provide a scale of 17006 pixel'. thus covering a field of I5'diameter.," The detector was a $\times$ 2k SITe chip used in a rebinned mode, to provide a scale of 06 $^{-1}$, thus covering a field of diameter."
 The photometric conditions were good., The photometric conditions were good.
 The seeing of 2755 was adequate for this study., The seeing of 5 was adequate for this study.
 For isolating the Πα line emission a 5.2nm wide filter. centered at 657.0nm was used.," For isolating the $\alpha$ line emission a 5.2nm wide filter, centered at 657.0nm was used."
 For continuum subtraction we used a broad band red filter. centered at 650nm.," For continuum subtraction we used a broad band red filter, centered at 650nm."
 To cover the whole galaxy. a mosaic of 13 positions was obtained.," To cover the whole galaxy, a mosaic of 13 positions was obtained."
 The single maps were corrected for the image distortion of the focal reducer (with flux conservation) and then aligned using stellar DSS positions and merged to an Ha map of 55/x35' ssize., The single maps were corrected for the image distortion of the focal reducer (with flux conservation) and then aligned using stellar DSS positions and merged to an $\alpha$ map of $\times$ size.
 The flux calibration for the Ha map was done using the total line flux value given by Devereux et al. (, The flux calibration for the $\alpha$ map was done using the total line flux value given by Devereux et al. (
1997) and using the Ha line fluxes of the prominent regions tabulated in Hippelein (1986). assuming a mean relative intensity of the [NI] lines of 20% (McCall et al.,"1997) and using the $\alpha$ line fluxes of the prominent regions tabulated in Hippelein (1986), assuming a mean relative intensity of the [NII] lines of $\%$ (McCall et al."
 1985)., 1985).
 In this section we will first present the general morphology of M 33. then we present the FIR photometry of discrete sources and their FIR spectral properties.," In this section we will first present the general morphology of M 33, then we present the FIR photometry of discrete sources and their FIR spectral properties."
 Fig., Fig.
" | presents the maps obtained at the three FIR wavelengths. rebinned to a pixel size of5""."," 1 presents the maps obtained at the three FIR wavelengths, rebinned to a pixel size of."
. The spatial resolutions are aat σθµπι and aat 1O0um. as derived from the profile of IC133. the brightregion in the NW edge.," The spatial resolutions are at $\mu$ m and at $\mu$ m, as derived from the profile of IC133, the brightregion in the NW edge."
 In the case of 170um the spatial resolution of +120”... as measured from the profile of NGC604 (IC133 is too faint at 170g). was improved to bby deconvolving the original map with a PSF of 120’.," In the case of $\mu$ m the spatial resolution of $\approx$ , as measured from the profile of NGC604 (IC133 is too faint at $\mu$ m), was improved to by deconvolving the original map with a PSF of ."
p-p interactions to the observed one. and the density varies [rom 25 em. for f— 0.310 19 em. for f=0.5.,"p-p interactions to the observed one, and the density varies from 25 $^{-3}$ for $f=0.3$ to 19 $^{-3}$ for $f=0.5$."
" Moreover. the error of the observed *-ray [lüxes is about50%.. and then the uncertainty of Piu, limited in our mocdel is about 6.0  for f=0.4."," Moreover, the error of the observed $\gamma$ -ray fluxes is about, and then the uncertainty of $n_{\rm ism}$ limited in our model is about 6.0 $^{-3}$ for $f=0.4$."
 W51C is an interesting source for the interaction of the shell with the ALC from the observations of Oll masers and shocked atomic and molecular gases in the direction of the source., W51C is an interesting source for the interaction of the shell with the MC from the observations of OH masers and shocked atomic and molecular gases in the direction of the source.
 It is also the first SNR detected with the LAT in the GeV band., It is also the first SNR detected with the LAT in the GeV band.
 The SNR appears a shell-ty morphology. whereas the GeV signals are clumpy ancl extended:pe within the radio shell.," The SNR appears a shell-type morphology, whereas the GeV signals are clumpy and extended within the radio shell."
 The 5-rays steep above several GeV. and the spectrum cannot be reproduced. via. p-p collisions with an index of 2.0 for the relativistic protons.," The $\gamma$ -rays steep above several GeV, and the spectrum cannot be reproduced via p-p collisions with an index of $\sim2.0$ for the relativistic protons."
 C'osmic ray electrons with a power-law spectrum can be easily steepened by unity duo to losses (Ixardashey.1962)... and it is plausible that this steepening can be explained. in the scenario of a power-law electrons. encountering significant losses.," Cosmic ray electrons with a power-law spectrum can be easily steepened by unity duo to losses \citep[][]{Ka62}, and it is plausible that this steepening can be explained in the scenario of a power-law electrons encountering significant losses."
 Llowever. the multiband nonthermal radiative properties of W51C have also been studied bv Abdoetal.(20096) using a broken power-law spectrum for the energy. distribution of 10. electrons/protons.," However, the multiband nonthermal radiative properties of W51C have also been studied by \citet{Abea09b} using a broken power-law spectrum for the energy distribution of the electrons/protons."
 They. found the observed Bux points in the radio and GeV bands cannot. be well reproduce ov assuming the radio emission and high-energy 5-rays are xoduced by the same population of electrons. and only in he pion-decay scenario in. which the 5-ravs are produce w the protons can the multiband spectrum be well fitted.," They found the observed flux points in the radio and GeV bands cannot be well reproduced by assuming the radio emission and high-energy $\gamma$ -rays are produced by the same population of electrons, and only in the pion-decay scenario in which the $\gamma$ -rays are produced by the protons can the multiband spectrum be well fitted."
 Moreover. it seems unlikely that the GeV signals are [rom he PWN powered by the putative pulsar (Ixooetal.2005) »ecause the nebula is much smaller with a few pe extension in X-rays compared with the GeV source and its racio emission is much weaker (Abeoctal.2009b).," Moreover, it seems unlikely that the GeV signals are from the PWN powered by the putative pulsar \citep{Kea05} because the nebula is much smaller with a few pc extension in X-rays compared with the GeV source and its radio emission is much weaker \citep{Abea09b}."
. We model the source in the case that one part. of 16. shell transports into the MC with dense matter ane 10 other part expands into the interstellar space with a relatively small density., We model the source in the case that one part of the shell transports into the MC with dense matter and the other part expands into the interstellar space with a relatively small density.
 Phe spectra of the particles in )0 (wo. parts of the shell are treated in a semi-analvtica ipproach to the nonlinear shock acceleration., The spectra of the particles in the two parts of the shell are treated in a semi-analytical approach to the nonlinear shock acceleration.
 Note that in us paper the shock structure is assumed to be quasi-paralle rather than quasi-perpendicular., Note that in this paper the shock structure is assumed to be quasi-parallel rather than quasi-perpendicular.
 The maximum enerev of 16 protons accelerated. in the quasi-perpendicular shocks can be significantly higher than that in the quasi-paralle cases with a much smaller perpendicular diffusion elficien compared with the parallel one. and a quasi-parallel shocks cannot possibly be true over all of da Glokipii1987).," The maximum energy of the protons accelerated in the quasi-perpendicular shocks can be significantly higher than that in the quasi-parallel cases with a much smaller perpendicular diffusion efficient compared with the parallel one, and a quasi-parallel shocks cannot possibly be true over all of $4 \pi$ \citep[][]{J87}."
. The contribution of the secondary ¢* pairs produced. from. p-p interactions on the nonthermal emmission is not taken into account in this paper., The contribution of the secondary $e^{\pm}$ pairs produced from p-p interactions on the nonthermal emmission is not taken into account in this paper.
" Including it needs a time-dependent: model to describe the evolution history of the SNK. and the collision between the part of the shock and the MC, and. this complicated: process could. bring more assumptions in the model: moreover. with A,—2.107 the emission of the secondary. pairs is usually insignificant compared with that from the accelerated. electrons."," Including it needs a time-dependent model to describe the evolution history of the SNR and the collision between the part of the shock and the MC, and this complicated process could bring more assumptions in the model; moreover, with $K_{ep}=2\times10^{-2}$, the emission of the secondary pairs is usually insignificant compared with that from the accelerated electrons."
 In fact. the multibancl observed spectrum can be reproduced: with our model. thus we do not take into account the emission from the secondary 67 pairs produced in p-p collisions.," In fact, the multiband observed spectrum can be reproduced with our model, thus we do not take into account the emission from the secondary $e^{\pm}$ pairs produced in p-p collisions."
 Our results indicate that the 5-ravs detected. with theFern LAT and LES.S.S. are mainly from the p-p collisions of the protons in the shell interacting with the MC. whereas the radio emission are produced. via svnchrotron radiation. of the electrons. accelerated. in the shell not interacting with the MC: moreover. the hieh-encerey 5-ravs obtained with Milagro at 35 TeV are possibly from p-p interactions of the protons accelerated in the shell not interacting with the ALC.," Our results indicate that the $\gamma$ -rays detected with the LAT and H.E.S.S. are mainly from the p-p collisions of the protons in the shell interacting with the MC, whereas the radio emission are produced via synchrotron radiation of the electrons accelerated in the shell not interacting with the MC; moreover, the high-energy $\gamma$ -rays obtained with Milagro at 35 TeV are possibly from p-p interactions of the protons accelerated in the shell not interacting with the MC."
 A MC can be illuminated by the particles escaped from a nearby SNR. and high-cnerey 5-ravs can be produced when these particles diffuse into the cloud. (Ciabicial.2009:Fujitaet2009).," A MC can be illuminated by the particles escaped from a nearby SNR, and high-energy $\gamma$ -rays can be produced when these particles diffuse into the cloud \citep[][]{Gea09,Fuea09}."
.. For example. Torresοἱal.(2008) interpreted the source NLAGIC' J0616|225 as TeV emission. from the particles escaped. from the SNR IC 443 and diffusing into a MC located about 20 pc from the SNR.," For example, \citet[][]{Tea08} interpreted the source MAGIC J0616+225 as TeV emission from the particles escaped from the SNR IC 443 and diffusing into a MC located about 20 pc from the SNR."
 Moreover. the nonthermal radiative. propertics of the the open cluster. Westerluncl 2 and. the old-age mixed-morphology SNR W28 can also be modeled as MCs illuminated. by high-energy. particles escaped. from. SNRs (Fujitactal.2009).," Moreover, the nonthermal radiative properties of the the open cluster Westerlund 2 and the old-age mixed-morphology SNR W28 can also be modeled as MCs illuminated by high-energy particles escaped from SNRs \citep[][]{Fuea09}."
. On the other hand. 5-ravys can also be ellectively produced from ἃ shock wave colliding with a MC (e.g.Aharonianctal.1994:Zhang&," On the other hand, $\gamma$ -rays can also be effectively produced from a shock wave colliding with a MC \citep[e.g.,][]{Aea94,ZF08}."
Fang2008).. 5-rav emission. produced. from a MC overtaken by a shock wave with a low Mach number has also been used to discuss the emission properties of the TeV sources. LIESS 1745-303 CX) and LESS J1714-385 (Fang&Zhang2008).," $\gamma$ -ray emission produced from a MC overtaken by a shock wave with a low Mach number has also been used to discuss the emission properties of the TeV sources, HESS J1745-303 (A) and HESS J1714-385 \citep[][]{FZ08}."
. In this paper. we model the SNR W51C€ as the MC around the remnant overtaken by part of the shell. and the other part of the shell expands into the relatively tenuous interstellar medium.," In this paper, we model the SNR W51C as the MC around the remnant overtaken by part of the shell, and the other part of the shell expands into the relatively tenuous interstellar medium."
 The spectrum obtained with the LAP can be reproduced as -ravs from p-p collisions of the protons in the shell with alow Alach number., The spectrum obtained with the LAT can be reproduced as $\gamma$ -rays from p-p collisions of the protons in the shell with a low Mach number.
 We are very. grateful to the anonymous referee for his/her helpful comments., We are very grateful to the anonymous referee for his/her helpful comments.
 “Phis work is partially supported. by the National Natural Science Foundation of China (NSEC 10778702. 10803005). a 973 Program (2009€D8524800). and Yunnan Province under à grant 2000 OC.," This work is partially supported by the National Natural Science Foundation of China (NSFC 10778702, 10803005), a 973 Program (2009CB824800), and Yunnan Province under a grant 2009 OC."
Slalistical statements about (he distribution of 2 can be made by looking at the distribution of apparent axis ratio q lor a large population of spiral galaxies.,Statistical statements about the distribution of $\varepsilon$ can be made by looking at the distribution of apparent axis ratio $q$ for a large population of spiral galaxies.
 investigated a sample of 254 spiral galaxies [rom theGalaxies (deVaucouleurs&de1964)., \citet{sa70} investigated a sample of 254 spiral galaxies from the \citep{de64}.
. They. concluded that the observed. axis ratios of the spiral galaxies were consistent wilh their being a population of circular disks. with (vpical thickness 5s0.25. Dinnev&deVaucouleurs(1981).," They concluded that the observed axis ratios of the spiral galaxies were consistent with their being a population of circular disks, with typical thickness $\gamma \approx 0.25$. \citet{bi81},"
. using data trom theGalaxies (deVaucouleurs.de 19176).. concluded that late-tvpe spirals were better fitted by mildly elliptical disks (2=0.1) than by perfectly. circular disks.," using data from the \citep{de76}, concluded that late-type spirals were better fitted by mildly elliptical disks $\varepsilon = 0.1$ ) than by perfectly circular disks."
 Using a sample of 13.482 spiral galaxies. Loveday(1992) [ound that the ellipticity was reasonably well fitted by a Gaussian peaking als=O: subject to the constraint ο<=<1.," Using a sample of 482 spiral galaxies, \citet{la92} found that the ellipticity was reasonably well fitted by a Gaussian peaking at $\varepsilon = 0$: subject to the constraint $0 \leq \varepsilon \leq 1$."
 The best fit was given by σ.=0.13. vielding an average ellipticity of (7)20.1.," The best fit was given by $\sigma_\varepsilon = 0.13$, yielding an average ellipticity of $\langle \varepsilon \rangle
\approx 0.1$."
 The nonaxisymmetry of disks. which is signaled by a scarcity of apparently circular galaxies. has been confirmed by other photometric studies 1985:Fasanoefal.1993;Alam&Iden 2002).," The nonaxisymmetry of disks, which is signaled by a scarcity of apparently circular galaxies, has been confirmed by other photometric studies \citep{gr85, fa93, al02}."
. Analvses which rely on the measured axis ratios of a large sample of galaxies have certain inürinsie shortcomings., Analyses which rely on the measured axis ratios of a large sample of galaxies have certain intrinsic shortcomings.
 First. (μον provide onlv a statistical statement. about the distribution of disk ellipticities in the sample examined: (hey don't determine (he axis ratio of anv individual galaxy.," First, they provide only a statistical statement about the distribution of disk ellipticities in the sample examined; they don't determine the axis ratio of any individual galaxy."
 Moreover. since (hese studies rely purely on photometry. they provide information about the ellipticitv of the starleht emitted by the galaxy.," Moreover, since these studies rely purely on photometry, they provide information about the ellipticity of the starlight emitted by the galaxy."
 The ellipticity measured in (his wav is alfected by bars. eccentric rings ancl pseudorings. loosely wound spiral aris. and patchy star formation. ancl does not necessarily reflect the overall ellipticity of the potential within which the stars are orbiüng.," The ellipticity measured in this way is affected by bars, eccentric rings and pseudorings, loosely wound spiral arms, and patchy star formation, and does not necessarily reflect the overall ellipticity of the potential within which the stars are orbiting."
 These intrinsic shortcomings are avoided by methods using both photometric ancl kinematic information., These intrinsic shortcomings are avoided by methods using both photometric and kinematic information.
 Consider a disk of test particles orbiting in a potential which is elliptical in the disk plane., Consider a disk of test particles orbiting in a potential which is elliptical in the disk plane.
 The closed particle orbits. when (he potential ellipticity is small. will be elliptical (themselves (Binney1975).," The closed particle orbits, when the potential ellipticity is small, will be elliptical themselves \citep{bi78}."
. If the potential is logarithmic. producing a [lat rotation. curve. (he ellipticity of the orbits will equal the elliplicitw of the potential.," If the potential is logarithmic, producing a flat rotation curve, the ellipticity of the orbits will equal the ellipticity of the potential."
 If the resulting elliptical disk is seen in projection. (he isophotal principal axes will be misaligned with the kinematic principal axes. (," If the resulting elliptical disk is seen in projection, the isophotal principal axes will be misaligned with the kinematic principal axes. ("
The kinematic principal axes can be defined as (he axis along which the line-o[-sight component of the rotation velocity is à maximunm and (he axis along which is is zero.),The kinematic principal axes can be defined as the axis along which the line-of-sight component of the rotation velocity is a maximum and the axis along which is is zero.)
 Because of the misalignment. (here is generally anon-zero velocity gradient along the isophotal minor axis. proporGonal to 2sinδώ. where 5 is the ellipticity of the potential. and ois the azimuthal viewing angle measured relative to the long axis of the potential 1992)..," Because of the misalignment, there is generally anon-zero velocity gradient along the isophotal minor axis, proportional to $\varepsilon \sin 2 \phi$, where $\varepsilon$ is the ellipticity of the potential, and $\phi$ is the azimuthal viewing angle measured relative to the long axis of the potential \citep{fr92}. ."
 Studying the velocity field of gas at large radii. where the dark matter," Studying the velocity field of gas at large radii, where the dark matter"
For a long time one of the most peculiar objects in Che AMlilky Way was believed to be a hypereiant luminous blue variable (LBV) star.,For a long time – one of the most peculiar objects in the Milky Way – was believed to be a hypergiant luminous blue variable (LBV) star.
 Recent observations. however. suggest that it is a binary svslem composed of a massive primary (AL>90.4. ) and a less massive secondary } (seee.g.[Hillierοἱal.2001:Pittard&Corcoran2002:Nielsenet2007).," Recent observations, however, suggest that it is a binary system composed of a massive primary $M \geq 90M_{\odot}$ ) and a less massive secondary $M \leq 30 M_{\odot}$ ) \citep[see e.g.][]{EtaCar:Hillier01,EtaCar:Pittard02,EtaCar:Nielsen07}."
". eexperienced a historical outburst in the 19"" century and ejected ~12.42. of gas which moves outwards at an average speed of ~650 km ! (Smithetal.2003)."," experienced a historical outburst in the $^{\rm th}$ century and ejected $\sim 12\,M_{\odot}$ of gas which moves outwards at an average speed of $\sim650$ km $^{-1}$ \citep{EtaCar:Smith03}."
. This material formed the which is expanding with a kinetic energv. of erg roughly of the οποίον released by a supernova explosion., This material formed the which is expanding with a kinetic energy of $\approx (4-10)\times10^{49}$ erg – roughly of the energy released by a supernova explosion.
 The optical (Damineli1996:Daminelietal.2000) and IB. (Whitelock2004) hlghteurves suggest a binary. period of 5.5 vears. moreover. (he analvsis of (he X-ray lighteurves points to an highly eccentric orbit of e~0.9 al. 2008).," The optical \citep{EtaCar:Damineli96,EtaCar:Damineli00} and IR \citep{EtaCar:Whitelock94,EtaCar:Whitelock04} lightcurves suggest a binary period of 5.5 years, moreover, the analysis of the X-ray lightcurves points to an highly eccentric orbit of $e \sim 0.9$ \citep{EtaCar:Corcoran01,EtaCar:Okazaki08}."
 is a colliding wind binary (CWB) with powerful winds produced by both members of the svstem., is a colliding wind binary (CWB) with powerful winds produced by both members of the system.
" The primary has a very high mass-loss rate of Mp75x10!M,vr (Hillieretal.Parkinetal.2009) and a terminal wind velocity of e,22(500—700)kins4. whereas the secondary has a fast low-density wind with e»23000kms.! and MazL0x10M,vr! (Pillared&Corcoran2002)."," The primary has a very high mass-loss rate of $\dot{M}_1 \geq 5\times 10^{-4}~M_{\odot}~{\rm yr}^{-1}$ \citep{EtaCar:Hillier01, EtaCar:Parkin09} and a terminal wind velocity of $v_1 \approx (500 - 700)~\mathrm{km~s^{-1}}$, whereas the secondary has a fast low-density wind with $v_2 \approx 3000~\mathrm{km~s^{-1}}$ and $\dot{M_2} \approx 1.0\times 10^{-5}~M_{\odot}~{\rm yr}^{-1}$ \citep{EtaCar:Pittard02}."
. When supersonic expanding winds collide. they fori a wind interaction zone where eharged particles can in principle be accelerated to high energies via the diffusive shock acceleration (DSA) process (seee.g.Eichler&Usov1993:Reimeral. 2006).," When supersonic expanding winds collide, they form a wind-wind interaction zone where charged particles can in principle be accelerated to high energies via the diffusive shock acceleration (DSA) process \citep[see e.g.][]{CWB:Eichler,CWB:Reimer06}."
. Observationallv. particle acceleration in the wind-collision region of massive binary systems such as is suggested by (he detection of non-thermal radio emission in several objects a review)..," Observationally, particle acceleration in the wind-collision region of massive binary systems such as is suggested by the detection of non-thermal radio emission in several objects \citep[see][for a review]{CWB:Review}."
 This indicates the existence of high-energy (IE: GeV) electrons in these svstens., This indicates the existence of high-energy (HE; $1~{\rm MeV}\leq {\rm E} \leq100~{\rm GeV}$ ) electrons in these systems.
 There is also evidence for the presence of relativistic particles in wwith non-thermal X-ray emission recently reported by the collaboration., There is also evidence for the presence of relativistic particles in with non-thermal X-ray emission recently reported by the collaboration.
 The authorsobtain an average luminosity of 7x10eress Fin the hard X-ray band (22-100) keV, The authorsobtain an average luminosity of $7\times10^{33}~\mathrm{ergs~s^{-1}}$ in the hard X-ray band $(22-100)$ keV
"analogous two-Inver model (Youdin. unpublished) indicate that instability is not significantly altered by the inclusion of rotation. though the analog of R7, decreases slightly.","analogous two-layer model (Youdin, unpublished) indicate that instability is not significantly altered by the inclusion of rotation, though the analog of $Ri_{\rm c}$ decreases slightly."
 In any event. meaningful quantities (particle scale height ancl critical surface densitv) scale as ψI. so the exact value used for the critical Richardson mumber does not have à strong effect on the numerical results.," In any event, meaningful quantities (particle scale height and critical surface density) scale as $\sqrt{Ri_{\rm c}}$, so the exact value used for the critical Richardson number does not have a strong effect on the numerical results."
 The ansatz of a mareinally stable state. 8;=1/4. defines via (10)) and (13)) an equation for particle density profiles. py(z). at a given radius.," The ansatz of a marginally stable state, $Ri = 1/4$ , defines via \ref{rich}) ) and \ref{grav}) ) an integro-differential equation for particle density profiles, $\rho_{\rm p}(z)$, at a given radius."
 The solution [see eqn. (, The solution [see eqn. (
"18) in Sekiva (1993)]]. requires two boundary conditions: the midplane particulate density. pj(0). and rellection svmmetry across the midplane. Op,/O2=0.","18) in \citet{sek98}] ], requires two boundary conditions: the midplane particulate density, $\rho_{\rm p}(0)$, and reflection symmetry across the midplane, $\partial\rho_{\rm p}/\partial z =
0$."
 The former is equivalent. as a one-to-one mapping. (o an integral constraint on δρ.," The former is equivalent, as a one-to-one mapping, to an integral constraint on $\Sigma_{\rm p}$ ."
 Densitv profiles of this (wpe can be analyzed [ον GI. using (2)).," Density profiles of this type can be analyzed for GI, using \ref{Roche}) )."
 One tvpically finds (hat low mass disks are stable to the Goldreich-Ward mechanism al cosmic abundances for solids/gas., One typically finds that low mass disks are stable to the Goldreich-Ward mechanism at cosmic abundances for solids/gas.
" However increasing the surface density in particles. Xy. while holding X, fixed. leads to the clevelopment of a density cusp (see Fig. 1))."," However increasing the surface density in particles, $\Sigma_{\rm p}$ , while holding $\Sigma_{\rm g}$ fixed, leads to the development of a density cusp (see Fig. \ref{fig:prof1}) ),"
 which quickly leads to GI in the midplane. as we described above.," which quickly leads to GI in the midplane, as we described above."
" Decreasing M, relative to X, has the same effect.", Decreasing $\Sigma_{\rm g}$ relative to $\Sigma_{\rm p}$ has the same effect.
 In (his context. it is well to recall (hat the evidence of the planets of the solar svstem tells us only what the minimun content of thesofds was in (he primitive solar nebula: it saves aluiost nothing about either the content of solids oractual content of gas at the lime of the formation of planets and planetesimals.," In this context, it is well to recall that the evidence of the planets of the solar system tells us only what the minimum content of the was in the primitive solar nebula; it says almost nothing about either the content of solids or content of gas at the time of the formation of planets and planetesimals."
" sekiva(1998) was the first to lind (he appearance of density cusps in (he above type of analysis. but he curiously dismisses the ""seeming infinite density” as ""due to [an] oversimplified analysis.”"," \citet{sek98} was the first to find the appearance of density cusps in the above type of analysis, but he curiously dismisses the “seeming infinite density” as “due to [an] oversimplified analysis.”"
" In contrast. we believe. as already hinted above. that (he appearance of density cusps. ie. the phenomenon of ""gravitational precipitation"" is intimately tied to the process of GI. and is indeed crucial to understanding how the formation of planetesinals might occur in nature."," In contrast, we believe, as already hinted above, that the appearance of density cusps, i.e., the phenomenon of “gravitational precipitation” is intimately tied to the process of GI, and is indeed crucial to understanding how the formation of planetesimals might occur in nature."
 The cusps which appear in constant 777 particle densitv. profiles become singular. reach infinite midplane volume-densities. for finite particulate surface-densities.," The cusps which appear in constant $Ri$ particle density profiles become singular, reach infinite midplane volume-densities, for finite particulate surface-densities."
 Critical profiles cannot be constructed for higher values of X., Critical profiles cannot be constructed for higher values of $\Sigma_{\rm p}$.
 We argue that the particulate laver becomes “saturated” at this eritical surface density. and excess solids will precipitate to the midplane and undergo GI., We argue that the particulate layer becomes “saturated” at this critical surface density and excess solids will precipitate to the midplane and undergo GI.
" The value of this critical surface density is found by taking the p,(0)—x limit of the general result for the surface densitv as afunction ofmidplanedensity. equation (22) in"," The value of this critical surface density is found by taking the $\rho_{\rm p}(0)\rightarrow\infty$ limit of the general result for the surface density as afunction ofmidplanedensity, equation (22) in"
"is (hen simply a special case of (the Tavlor expauded equation x,(u)=x,(0)4vo(0)u—.... ","is then simply a special case of the Taylor expanded equation ${\bf
x}_a(u) = {\bf x}_a(0) + {\bf v}_a(0) u + \dots$ "
stars. estimated frou the radio emission using SERM=DAL)=Lyια&ΠΠ.1) (Cram et al.,"stars, estimated from the radio emission using $M\geq5M_{\odot})=L_{1.4}/(4.0\times10^{21} W Hz^{-1})$ (Cram et al.,"
" 1998) and asstunineg z ~ lL. would be in the range 100-2300. AL, Ll"," 1998) and assuming z $\sim$ 1, would be in the range 100-2300 $M_{\odot}$ $^{-1}$."
" Because of the well established correlation between SFR and far infrared ciuuixssion (SER(M>5M.)=Loy,(54«LOTTE. 1): Cram et al."," Because of the well established correlation between SFR and far infrared emission $(M\geq5M_{\odot})=L_{60_{\mu m}}/(5.1\times10^{23} W Hz^{-1})$ ; Cram et al.,"
 1998). aud assundue the spectral energy distribution of M82. these values of SFR would imply 15 jui fluxes in the range 3-70 mJy aud 90 gam fixes in the range 10-200 indy.," 1998), and assuming the spectral energy distribution of M82, these values of SFR would imply 15 $\mu$ m fluxes in the range 3-70 mJy and 90 $\mu$ m fluxes in the range 10-200 mJy."
 However ISO observations of this field show that noue of the six radio selected EROs selected is detected at 90 jan down to a fiux lamit of ~ 601nJy (Rodighicro ct al..," However ISO observations of this field show that none of the six radio selected EROs selected is detected at 90 $\mu$ m down to a flux limit of $\sim$ 60 mJy (Rodighiero et al.,"
 iu preparation) and ouly two of them (LOCT_66cim_JJ105255|571950 and 431053111573020) are detected at 15 jan with a flux of 1.5 aud 0.7 ταν respectively. with an upper limit of ~ 0.30 mJy for the other four sources (Fadda ct al..," in preparation) and only two of them J105255+571950 and J105314+573020) are detected at 15 $\mu$ m with a flux of 1.5 and 0.7 mJy respectively, with an upper limit of $\sim$ 0.30 mJy for the other four sources (Fadda et al.,"
 2002: Fadda et al., 2002; Fadda et al.
 iu preparation)., in preparation).
 Fren this comparison of optical. radio and ISO data we conclude that most ofour radioselected EROs sources are ikelv not to be associated with dusty starburst galaxies. mt rather with carly-type galaxies. hostiug an Active Galactic Nucleus (ACN) respousible of the radio activity. although some coutributiou from the radio emission also ποια a nuclear starburst activity cau not be excluded.," From this comparison of optical, radio and ISO data we conclude that most of our radio–selected EROs sources are likely not to be associated with dusty starburst galaxies, but rather with early-type galaxies, hosting an Active Galactic Nucleus (AGN) responsible of the radio activity, although some contribution from the radio emission also from a nuclear starburst activity can not be excluded."
 This conclusion is also in agreement with mest of oxevious spectroscopic findings on the nature of extremely red radio sources., This conclusion is also in agreement with most of previous spectroscopic findings on the nature of extremely red radio sources.
 Laing et al. (, Laing et al. (
1983) showed that the light roni the reddest z ~ 1 radio galaxies in the 30RR sample (3C'65) is dominated by an old (~ £C) stellar population.,1983) showed that the light from the reddest z $\sim$ 1 radio galaxies in the 3CRR sample (3C65) is dominated by an old $\sim$ 4Gyr) stellar population.
 Subsequently. two extremely red radio galaxies at z-1.5 rave been discovered in the follow up of the faint Leiden Berkeley Deep Survey (Dunlop ct al..," Subsequently, two extremely red radio galaxies at $\sim$ 1.5 have been discovered in the follow up of the faint Leiden Berkeley Deep Survey (Dunlop et al.,"
 1996: Dunlop. 1999).," 1996; Dunlop, 1999)."
 Iseck spectroscopy of these galaxies shows that also iu his case their red colours are due to aun old stellar opulatiou (23 Gyr) aud not to reddening by dust., Keck spectroscopy of these galaxies shows that also in this case their red colours are due to an old stellar population $\geq$ 3 Gyr) and not to reddening by dust.
 A simular result has been recently obtained by Willott et al. (, A similar result has been recently obtained by Willott et al. (
2001) studving six extremely red sources (RoAK 5.5) roni the 7C radio sample.,2001) studying six extremely red sources $R-K>$ 5.5) from the 7C radio sample.
 The only example so far of au extremely red object with Ll selected. frou a racio survey and identified with a dusty starformune galaxy its been found by Afonso et al. (, The only example so far of an extremely red object with $-$ $>$ 4 selected from a radio survey and identified with a dusty star–forming galaxy has been found by Afonso et al. (
2001) studyiug optical counterparts of the radio sources from the Phoenix Deep Badio Survey (see also Waddiugton et al. (,2001) studying optical counterparts of the radio sources from the Phoenix Deep Radio Survey (see also Waddington et al. (
1999) for a simular dusty galaxy with Ixy 4-I&—2.0 and a likely redshift of z=L.151].,1999) for a similar dusty galaxy with $_{814}$ -K=2.0 and a likely redshift of z=4.424).
 Finally. it is interesting to note that the six racio selected EROs rveprescut only ~ of all the sources with LIN’ 71 present iu the area covered by the I data (~ 300 sources with LK’> l over ~ 220 arcmiu?).," Finally, it is interesting to note that the six radio selected EROs represent only $\sim$ of all the sources with $^{\prime}>$ 4 present in the area covered by the $^{\prime}$ data $\sim$ 300 sources with $^{\prime}>$ 4 over $\sim$ 220 $^2$ )."
 This fraction could approximately double if most of the five radio sources with no I baud counterpart also belong to the EROs class. as suggested. by the observed. treud between colour aud Timaguitude (see Fie. 15)).," This fraction could approximately double if most of the five radio sources with no I band counterpart also belong to the EROs class, as suggested by the observed trend between colour and I magnitude (see Fig. \ref{F15}) )."
 Assumiug that their radio huuinositv is due to ACN activity. the snall fraction of radio detection suggests a relatively simall ACN content iu the optically/uear-iufrared selected EROs population.," Assuming that their radio luminosity is due to AGN activity, the small fraction of radio detection suggests a relatively small AGN content in the optically/near-infrared selected EROs population."
 This result is qualitatively in aerecicut with what sugecsted bv the recent deep ταν survevs., This result is qualitatively in agreement with what suggested by the recent deep X-ray surveys.
 Iu the IIubble Deep Field North Caltech area. only L of the 33 EROs iu the field have a lard N-ray detection in the ~ 220 ksec exposure with the Chandra satellite (Horuschemeier ot al.," In the Hubble Deep Field North Caltech area, only 4 of the 33 EROs in the field have a hard X-ray detection in the $\sim$ 220 ksec exposure with the Chandra satellite (Hornschemeier et al.,"
 2001)., 2001).
 However. it is well known that huuinous radio sources have lifetimes much smaller than the age of the early ealaxics hosting these ACNs (C el Cr)," However, it is well known that luminous radio sources have lifetimes much smaller than the age of the early galaxies hosting these AGNs $\geq$ 3-4 Gyr)."
 Therefore. if individual radio sources lave litetimes of about ~10? vears (Condon. 1992). then the muuber of EROs undergoing radio activity during their life would be much lieher than that observed.," Therefore, if individual radio sources have lifetimes of about $\sim10^8$ years (Condon, 1992), then the number of EROs undergoing radio activity during their life would be much higher than that observed."
 We have used the VLA radio clescope to image at 6 cm a circular region (1O avemun radius) to a 1.5 σ lit of ~ OpeSy iu the Lockman Hole., We have used the VLA radio telescope to image at 6 cm a circular region (10 arcmin radius) to a 4.5 $\sigma$ limit of $\sim50\mu$ Jy in the Lockman Hole.
 The region is centered around the ROSAT ultra-deep WRI field., The region is centered around the ROSAT ultra-deep HRI field.
 A complete sample of 63 radio sources has been obtained., A complete sample of 63 radio sources has been obtained.
" The differeutial source counts are in good aereemoeut with those obtained by other surveys. coufirmine that while the slope of the counts shows a flattening below a flux deusitv of ~1-3 mis. there is no indication for a significaut chanee im the slope in the 6 cmi counts between -0O.1 aux uty,"," The differential source counts are in good agreement with those obtained by other surveys, confirming that while the slope of the counts shows a flattening below a flux density of $\sim$ 1-3 mJy, there is no indication for a significant change in the slope in the 6 cm counts between $\sim$ 0.1 and 1 mJy."
 The availability of a 20 cin survey clown to ~0.12 uJv in the SALLE area (de Ruiter et al.," The availability of a 20 cm survey down to $\sim$ 0.12 mJy in the same area (de Ruiter et al.,"
 1997). eave us the opportunity o study the radio spectral index as Muction of the radio flux.," 1997), gave us the opportunity to study the radio spectral index as function of the radio flux."
 Dividing our 6 cii sample iu wo subsamples with fluxes lower aud ereater than 0.2 uJv. we find a fattening of the radio spectral iudex aud au increase of the population of flat spectra radio sources iu he fainter flux bin.," Dividing our 6 cm sample in two subsamples with fluxes lower and greater than 0.2 mJy, we find a flattening of the radio spectral index and an increase of the population of flat spectra radio sources in the fainter flux bin."
 Several explanations for the observed Hattening compared with sources detected at higher Hux density level are possible. including an increasing iuuber of svuchrotron self-absorbed ACNs amone the wicrojausky population. aud/or a rising component of hermal radiation foun active star formation.," Several explanations for the observed flattening compared with sources detected at higher flux density level are possible, including an increasing number of synchrotron self-absorbed AGNs among the microjansky population, and/or a rising component of thermal radiation from active star formation."
 Using the available optical iniages in. V. and I bauds. we xxtorned the optical identification of the radio sources using the Likelihood Ratio Analysis.," Using the available optical images in V and I bands, we performed the optical identification of the radio sources using the Likelihood Ratio Analysis."
 We found a likely optical ideutification for 58 of the 63 radio sources., We found a likely optical identification for 58 of the 63 radio sources.
" From he reliability associated to the likelihood analysis we estimate that at most four of the proposed identifications nay be spurious and therefore the identification rate with the ""correct optica counterpart is in the rauge NOX -", From the reliability associated to the likelihood analysis we estimate that at most four of the proposed identifications may be spurious and therefore the identification rate with the “correct” optical counterpart is in the range $\sim$ -.
 Aloreovoer. for a subsample of 51 radio sources we have data also in the I’ baud.," Moreover, for a subsample of 51 radio sources we have data also in the $^{\prime}$ band."
 For this subsample we fiud R couuterparts for 19 sources of ideuti&cations)., For this subsample we find $^{\prime}$ counterparts for 49 sources of identifications).
 These high identification rates are consistent with the observed maeuitudoe distribution of the optical counterparts. which appears to reach a maximal at magnitudes (I ~ 20 - 21) well above the hnuitiug magnitude of our optical data.," These high identification rates are consistent with the observed magnitude distribution of the optical counterparts, which appears to reach a maximum at magnitudes (I $\sim$ 20 - 21) well above the limiting magnitude of our optical data."
 A cross correlation between the radio catalogue aud the ROSAT catalogue and the NADLNewton source list, A cross correlation between the radio catalogue and the ROSAT catalogue and the XMM-Newton source list
"On UT 2010 February 7.07, D. Rich of Hampden, Maine discovered a transient in the galaxy NGC11573A at RA(J2000)=04'48™27.75 and ","On UT 2010 February 7.07, D. Rich of Hampden, Maine discovered a transient in the galaxy 1573A at $^{\rm h}$ $^{\rm m}$ $^{\rm s}$ and $^{\circ}$ $\arcmin$ $\arcsec$."
"The discovery was confirmed by P. Burke of Dec(J2000)—--73?28'13"".Pittsfield, Maine, upon which a notification was issued (CBET 2166; Rich&Burke 2010)) and the transient dubbed SN2010X. On UT 2010 February 19.13, the Palomar Transient Factory independently detected this same transient and the pipeline assigned the name, 110bhp."," The discovery was confirmed by P. Burke of Pittsfield, Maine, upon which a notification was issued (CBET 2166; \citealt{rb10}) ) and the transient dubbed SN2010X. On UT 2010 February 19.13, the Palomar Transient Factory independently detected this same transient and the pipeline assigned the name, 10bhp."
" PTF had previously undertaken observations of this field (as a part of the dynamic cadence experiment) on January 11, 17 and 25 but with no detection."," PTF had previously undertaken observations of this field (as a part of the dynamic cadence experiment) on January 11, 17 and 25 but with no detection."
" Energized by the apparent rapid fading, we initiated follow-up observations."," Energized by the apparent rapid fading, we initiated follow-up observations."
" The photometric observations from the 2-m Faulkes North Telescope (FTN) of the Las Cumbres Observatory Global Telescope (LCOGT), PTF, the Palomar Hale 200-inch telescope (P200) as well as white light observations provided by our amateur astronomer colleagues are summarized in Figure 1.."," The photometric observations from the 2-m Faulkes North Telescope (FTN) of the Las Cumbres Observatory Global Telescope (LCOGT), PTF, the Palomar Hale 200-inch telescope (P200) as well as white light observations provided by our amateur astronomer colleagues are summarized in Figure \ref{fig:taumv}."
" 22010X is located close to the nucleus of its host galaxy EE, and as such galaxy light subtraction is critical to produce,NN) reliable photometry."," 2010X is located close to the nucleus of its host galaxy E, N) and as such galaxy light subtraction is critical to produce reliable photometry."
 The images were subtracted from a template image using the software and to measure a convolution kernel and align the images respectively (both codes supplied by A. Becker!8)., The images were subtracted from a template image using the software and to measure a convolution kernel and align the images respectively (both codes supplied by A. ).
 Aperture photometry was performed on each of these in a self-consistent manner using the same set of 22 calibration stars., Aperture photometry was performed on each of these in a self-consistent manner using the same set of 22 calibration stars.
 Conversions from USNO-B1 magnitudes to SDSS gri magnitudes were done adopting Jordietal.(2006)., Conversions from USNO-B1 magnitudes to SDSS gri magnitudes were done adopting \citet{jga06}.
. The resulting light curve is plotted in Figure 1.., The resulting light curve is plotted in Figure \ref{fig:taumv}.
" Overplotting 22002bj, we find that light curves of the two supernovae are remarkably similar."," Overplotting 2002bj, we find that light curves of the two supernovae are remarkably similar."
" Linearly fitting all the r-band detections post maximum light, we measure that 22010X decayed by 0.23+0.01 mag day-!."," Linearly fitting all the r-band detections post maximum light, we measure that 2010X decayed by $0.23\pm0.01$ mag $^{-1}$."
 The corresponding exponential timescale the is 7;=4.7+0.2 ddays., The corresponding exponential timescale (in the $r$ -band) is $\tau_d= 4.7\pm 0.2$ days.
" (in'The foregroundr-band) Galactic extinction along the line of sight is E(B— V)=0.146 or A,=0.4 (Schlegeletal. 1998).", The foreground Galactic extinction along the line of sight is $B-V$ )=0.146 or $_r$ =0.4 \citep{sfd98}.
. The redshift of NGC 1573A is 0.015., The redshift of NGC 1573A is 0.015.
" Assuming standard cosmology we adopt a distance of MMpc and a (anddistance ho=0.72),modulus of 34.0."," Assuming standard cosmology (and $h_{0}$ =0.72), we adopt a distance of Mpc and a distance modulus of 34.0."
" Thus, the peak absolute magnitude of SN22010X is M,—17.0 mmag, mmag less luminous than SN2002bj."," Thus, the peak absolute magnitude of 2010X is $M_{r}\approx\,-$ mag, mag less luminous than SN2002bj."
" On February 8 and 9, the first spectra (Figure 2)) to classify the nature of this transient were taken with CCDS on the 2.4mm Hiltner telescope of the MDM observatory (CBET 2167, Milisavljevic&Fesen 2010))."," On February 8 and 9, the first spectra (Figure \ref{fig:series}) ) to classify the nature of this transient were taken with CCDS on the m Hiltner telescope of the MDM observatory (CBET 2167, \citealt{mf10}) )."
 Comparison with a library of supernova spectra using SNID (Blondin&Tonry showed resemblance to the Type Ic supernovae 2007)119941 and 22004aw a," Comparison with a library of supernova spectra using SNID \citep{bt07}
 showed resemblance to the Type Ic supernovae 1994I and 2004aw a"
"will experience a ""radial flow” depending on (he iniüal enerev density.",will experience a “radial flow” depending on the initial energy density.
" Moreover. if the initial conditions were not spherically sviunetric. as is in [act the cases in peripheral heavy ion collisions. the difference in pressure in different spatial directions will lead to a further ""directed"" or ""elliptic flow."," Moreover, if the initial conditions were not spherically symmetric, as is in fact the cases in peripheral heavy ion collisions, the difference in pressure in different spatial directions will lead to a further “directed” or “elliptic” flow."
 Both forms of flow thus do depend on the initial conditions., Both forms of flow thus do depend on the initial conditions.
 While the abundances of the species are not. affected by such flow aspects. the different momentum distributions are ancl hence studies of hadron spectra can. at least in principle. provide information about (he earlier. pre-hacdronic stages.," While the abundances of the species are not affected by such flow aspects, the different momentum distributions are and hence studies of hadron spectra can, at least in principle, provide information about the earlier, pre-hadronic stages."
 The hot medium also racdiates electromagnetically. ie.. it emits photons and dileptons (e.€ or yepe pairs) [55]..," The hot medium also radiates electromagnetically, i.e., it emits photons and dileptons $e^+e^-$ or $\mu^+\mu^-$ pairs) \cite{e-m}."
 These are formed either by the interaction of quarks and/or gluons. or by quark-antiquark annihilation.," These are formed either by the interaction of quarks and/or gluons, or by quark-antiquark annihilation."
 Since (he photons and leptons interact only electromaegnetically. they will. once they are formed. leave (he medium without anv further mocification.," Since the photons and leptons interact only electromagnetically, they will, once they are formed, leave the medium without any further modification."
 Hence (heir spectra. provide information about (he state of the medium at the place or the time they were formed. and this can be in its deep interior or αἱ very early stages of its evolution.," Hence their spectra provide information about the state of the medium at the place or the time they were formed, and this can be in its deep interior or at very early stages of its evolution."
 Photons and dileptons (hus provide a possible probe of the hot QGP., Photons and dileptons thus provide a possible probe of the hot QGP.
 The only. problem is that Chey can be formed anywhere and at anv (ime. also at later evolution stages and as well as (hrough interaction or decay of the emitted hadrons.," The only problem is that they can be formed anywhere and at any time, also at later evolution stages and as well as through interaction or decay of the emitted hadrons."
" The task in making electromagnetic radiation a viable tool is therefore the identification of the hot ""thermal radiation indeed emitted by the QGP.", The task in making electromagnetic radiation a viable tool is therefore the identification of the hot “thermal” radiation indeed emitted by the QGP.
 For the production of dilepton pair (for illustration. we consider jp.ji ) bv a thermal medium. the lowest order process is quark-antiquark annihilation. as illustrated in relanni..," For the production of dilepton pair (for illustration, we consider $\mu^+\mu^-$ ) by a thermal medium, the lowest order process is quark-antiquark annihilation, as illustrated in \\ref{anni}."
" To caleulate (he mass spectrum of the emitted dileptons. the perturbative annihilation cross-section e(qq—jpfe) has to be convoluted by thermal quark and antiquark momentum distributions [(k,/T) I|/T}.. where fy is the three-momentum of the (massless) quark and T the temperature of the medium."," To calculate the mass spectrum of the emitted dileptons, the perturbative annihilation cross-section $\sigma(q \bar q \to \mu^+\mu^-)$ has to be convoluted by thermal quark and antiquark momentum distributions f(k_q/T) -|k_q|, where $k_q$ is the three-momentum of the (massless) quark and $T$ the temperature of the medium."
 We thus obtain 4 Dh FS)à he) sigima((qq Q8) where AM is (he invariant mass of the dilepton.," We thus obtain d^3 k_q f(k_q) d^3 ) (q q ^-), where $M$ is the invariant mass of the dilepton."
 The convolution leads to the schematic resultA/T}... so (hat a measurement of a thermal dilepton spectrum provicles the temperature of the medium.," The convolution leads to the schematic result, so that a measurement of a thermal dilepton spectrum provides the temperature of the medium."
 As already indicated. if the medium undergoes an evolution (cooling). the observed dileptons originate [rom all stages. so that a temperature measurement is not straight-Dorwaud and will in general depend on (he evolution pattern.," As already indicated, if the medium undergoes an evolution (cooling), the observed dileptons originate from all stages, so that a temperature measurement is not straight-forward and will in general depend on the evolution pattern."
 In actual nuclear collision experiments. (here is in addition competition from non-thermal dileptons Crom hard primary Drell-Yan production at large M. and [rom hadronic decavs al lower AL).," In actual nuclear collision experiments, there is in addition competition from non-thermal dileptons (from hard primary Drell-Yan production at large $M$ and from hadronic decays at lower $M$ )."
decreases so quickly in the second scenario is that (he partial release of CO leads to an increase of CIT that seems to effectively react with CIISOIL,decreases so quickly in the second scenario is that the partial release of CO leads to an increase of CH that seems to effectively react with CH3OH.
 In the model with gas density of 5x10! and FR=0.5. that corresponds to a percentage of CO on grains of αἱ (=5.27x 105 ves. (Fie. 10))," In the model with gas density of $\times$ $^4$ and FR=0.5, that corresponds to a percentage of CO on grains of at $\times$ $^6$ yrs, (Fig. \ref{mod_pro}) )"
 the best agreement with the observation is at (—5.3Xx 10° vis when all the column densities agree with the observed values witliin one order of magnitude apart from that is 2 orders of magnitude lower., the best agreement with the observation is at $\times$ $^6$ yrs when all the column densities agree with the observed values within one order of magnitude apart from that is 2 orders of magnitude lower.
 This model reproduces also the observed. values of ralio even if it predicts a HC3N/NILT; ratio about a factor of 160 100 lower than observed (see Fig. 11))., This model reproduces also the observed values of $_3$ ratio even if it predicts a $_3$ $_3$ ratio about a factor of 10 – 100 lower than observed (see Fig. \ref{mod_ratio}) ).
 In particular the higher observed value of ΗΝ (around. 10) is reached as soon as the collapse is stopped. at ( ~ 5.3x 10° ves. while the lower observed value (around 1) is reached at ( ~ 6x 109 vrs.," In particular the higher observed value of $_3$ (around 10) is reached as soon as the collapse is stopped, at t $\sim$ $\times$ $^6$ yrs, while the lower observed value (around 1) is reached at t $\sim$ $\times$ $^6$ yrs."
Recent observations by Swift and Hete II have confirmed. the long-held suspicion that short GRBs have a different central engine than long bursts: they occur at systematically lower redshifts (Foxetal.2005) afterglows... in galaxies with (Hjorthetal.2005). and without star formation (Bergeretal.2005:Barthelmy2005).. the emitted gamma-ray energy is substantially lower compared to long bursts (Soderbergetal.2006). and no supernova explosion seems 0o accompany the burst (Bloometal.2006:Hjorth2005:Foxetal. 2005).,"Recent observations by Swift and Hete II have confirmed the long-held suspicion that short GRBs have a different central engine than long bursts: they occur at systematically lower redshifts \citep{fox05} , in galaxies with \citep{hjorth05} and without star formation \citep{berger05,barthelmy05}, the emitted gamma-ray energy is substantially lower compared to long bursts \citep{soderberg06} and no supernova explosion seems to accompany the burst \citep{bloom06,hjorth05,fox05}."
. These observations are naturally explained by he most popular central engine for short bursts. the coalescence of a compact binary system (Blinnikovetal.1984:Eichler1989:Paczyiiski 1991). but alternative models do exist (e.g.TacFadyenetal.2005:Levan 2006).," These observations are naturally explained by the most popular central engine for short bursts, the coalescence of a compact binary system \citep{blinnikov84,eichler89,paczynski91}, but alternative models do exist \citep[e.g.][]{macfadyen05,levan06}."
.. The observations. yowever. have also revealed long-lasting X-ray activity after the main gamma-ray emission phase for about half of the bursts (Burrowsetal.2005:Nousek2006:O'Brien2006).," The observations, however, have also revealed long-lasting X-ray activity after the main gamma-ray emission phase for about half of the bursts \citep{burrows05,nousek06,obrien06}."
. Several possible explanations have been suggested (e.g.Kingetal.2005:Zhangetal. 2006).. among them is the fragmentation of the outer parts of an accretion disk due gravitational instabilities (Pernaetal.2006).," Several possible explanations have been suggested \citep[e.g.][]{king05,zhang06}, among them is the fragmentation of the outer parts of an accretion disk due gravitational instabilities \citep{perna06}."
. This late-time X-ray flaring is considered a challenge to most models of short GRBs., This late-time X-ray flaring is considered a challenge to most models of short GRBs.
 In this letter. I discuss the X-ray signature from fallback material in the aftermath of a compact binary merger.," In this letter, I discuss the X-ray signature from fallback material in the aftermath of a compact binary merger."
 A fraction of the debris material is launched into eccentric orbits and. at some later time. falls back towards the central remnant.," A fraction of the debris material is launched into eccentric orbits and, at some later time, falls back towards the central remnant."
 For this material. the time scales are not set by viscous disk time scales. but instead by the distribution of eccentricities within the fallback material which is a result of the torques that acted during the merger process.," For this material, the time scales are not set by viscous disk time scales, but instead by the distribution of eccentricities within the fallback material which is a result of the torques that acted during the merger process."
 This naturally leads to time scales that are orders of magnitudes larger than usual viscous disk time scales., This naturally leads to time scales that are orders of magnitudes larger than usual viscous disk time scales.
 The question of fallback time scales is addressed by means of a simple analytical model whose initial conditions are taken from a set of recent. three-dimensional smooth particle hydrodynamics (SPH) calculations of the merger of both double neutron stars (DNS) and neutron star black hole (NSBH) systems.," The question of fallback time scales is addressed by means of a simple analytical model whose initial conditions are taken from a set of recent, three-dimensional smooth particle hydrodynamics (SPH) calculations of the merger of both double neutron stars (DNS) and neutron star black hole (NSBH) systems."
 The details of the input physics and the numerical techniques are described elsewhere (Rosswog&Davies2002:RosswogLiebendórfer&Price2006:Rosswog 2006)..," The details of the input physics and the numerical techniques are described elsewhere \citep{rosswog02a,rosswog03a,rosswog03c,price06b,rosswog06b,rosswog06c}."
. Here we only summarise the main physical parameters of the calculations. see Tab. |...," Here we only summarise the main physical parameters of the calculations, see Tab. \ref{tab:runs}."
 A few tens of milliseconds after such a binary encounter the remnant consists of the following parts: a central object (either a neutron star-like object or a black hole). a disk. some material flung into eccentric orbits. but gravitationally bound to the remnant (fallback material”) and some dynamically ejected debris material.," A few tens of milliseconds after such a binary encounter the remnant consists of the following parts: a central object (either a neutron star-like object or a black hole), a disk, some material flung into eccentric orbits, but gravitationally bound to the remnant (“fallback material”) and some dynamically ejected debris material."
 The details of the geometry depend on the type of system (DNS or NSBH) and on the mass ratio., The details of the geometry depend on the type of system (DNS or NSBH) and on the mass ratio.
 As an example. Fig.," As an example, Fig."
 |. shows the matter distribution 22.3 ms after the merger of a 1.1 and 1.6 DNS Restricted by the Courant-Friedrichs-Lewy time step criterion (typical time steps are of the order 19' s) the evolution of the, \ref{fig1} shows the matter distribution 22.3 ms after the merger of a 1.1 and 1.6 DNS Restricted by the Courant-Friedrichs-Lewy time step criterion (typical time steps are of the order $10^{-7}$ s) the evolution of the
ealaxies at lower redshifts.,galaxies at lower redshifts.
 What trigecrs the E|A phase remains an open question., What triggers the E+A phase remains an open question.
 Earlier studies sugeest the E|A phase iu the field is associated with ealaxy-ealaxy interactions (???.hereafterZ96).. a scenario cousisteut with galaxy formation models that predict interactions iu the field) are common (7).. aud that interactions trigecr stroug star formation episodes m eas-rich systems (??)..," Earlier studies suggest the E+A phase in the field is associated with galaxy-galaxy interactions \citep[hereafter Z96]{liu:95,yang:04,zabludoff:96}, a scenario consistent with galaxy formation models that predict interactions in the field are common \citep{somerville:99a}, and that interactions trigger strong star formation episodes in gas-rich systems \citep{mihos:94a,mihos:94b}."
 Because morphological signatures due to interactions remain visible for the duration of the E|A phase (??).. we should find E|A’s to be morphologically disturbed if the E|A phase is associated with ealaxy-galaxy interactions.," Because morphological signatures due to interactions remain visible for the duration of the E+A phase \citep{mihos:94a,mihos:94b}, we should find E+A's to be morphologically disturbed if the E+A phase is associated with galaxy-galaxy interactions."
 To imeasure the field ΓΕΙΑ fraction at intermediate redshifts. we draw from an exteusive spectroscopic survey of four different fields.," To measure the field E+A fraction at intermediate redshifts, we draw from an extensive spectroscopic survey of four different fields."
" Our unique dataset contains au ""usually large umber of spectroscopically confined field ealaxies (~ NOO) eathered over a total area of ~90011: our survey ds larger than that of auv other previous Seld E|A study iu this redshift rause.", Our unique dataset contains an unsually large number of spectroscopically confirmed field galaxies $\sim800$ ) gathered over a total area of $\sim200\Box'$; our survey is larger than that of any other previous field E+A study in this redshift range.
 Using the wide-fell UST/WFPC2 imaging that we have obtained as wart of our cluster program. we also characterize the owsieal properties of the field E|A population to better understand the role E|As have in the evolution of ornüueg galaxies into passive svstenuis.," Using the wide-field HST/WFPC2 imaging that we have obtained as part of our cluster program, we also characterize the physical properties of the field E+A population to better understand the role E+A's have in the evolution of star-forming galaxies into passive systems."
 We sunumnuuize our observations in 822. describe our EA selection criteria and determine the field E|A raction in 833. and detail the physical properties of the Ποια E|A population in 811.," We summarize our observations in 2, describe our E+A selection criteria and determine the field E+A fraction in 3, and detail the physical properties of the field E+A population in 4."
 We discuss the importance of the E|A phase in $55 and present our couclusions in 866., We discuss the importance of the E+A phase in 5 and present our conclusions in 6.
" Unless otherwise noted. we use Qa,=03.040.7. and {10=1005 Mpe.+ in this paper."," Unless otherwise noted, we use $\Omega_M=0.3,
\Omega_{\Lambda}=0.7$, and $H_0=100h$ $^{-1}$ in this paper."
 We select E|A ealasics fou a major program to study four fields with IIST/WFEPC?2 tuaeine aud eromud-basecd spectroscopy., We select E+A galaxies from a major program to study four fields with HST/WFPC2 imaging and ground-based spectroscopy.
 The three lower redshift ficlds are centered. ou X-rav luminous clusters at 2=0.33.0.58.& 0.83. and the fourth on a QSO at 2=0.92.," The three lower redshift fields are centered on X-ray luminous clusters at $z=0.33,~0.58,~\&~0.83$ , and the fourth on a QSO at $z=0.92$."
 Our dataset combines TST/WEPC2 mosaics of 612 poiutiugs in cach field with exteusive redshift surveys completed primarily with Neck/LRIS (7).., Our dataset combines HST/WFPC2 mosaics of $6-12$ pointings in each field with extensive redshift surveys completed primarily with Keck/LRIS \citep{oke:95}.
 From ~1500 redshifts obtained iu a total area of ον200L. we isolate 797 field galaxies.," From $\sim$ 1500 redshifts obtained in a total area of $\sim200\Box'$, we isolate 797 field galaxies."
 The observational details of cach field are in Table ??.., The observational details of each field are in Table \ref{fields}.
 Tere we describe briefiv the spectra aud photometry used in this paper., Here we describe briefly the spectra and photometry used in this paper.
 As a significant benefit ofour laree program to study ealaxy evolution iu clusters. we lave obtained redshifts for a large sample of field galaxies to +~2.," As a significant benefit ofour large program to study galaxy evolution in clusters, we have obtained redshifts for a large sample of field galaxies to $z\sim2$."
 During multiple observing ruus frou June 1996 to July 2001. iulti-«lit spectra imm the MS2053.. MS1051. aud 3€356 fields were obtained with Iveck/LRIS.," During multiple observing runs from June 1996 to July 2001, multi-slit spectra in the MS2053, MS1054, and 3C336 fields were obtained with Keck/LRIS."
" Tusets in the MS2055 field were selected using a maguitude cut of asp,x23. and iu both the MS1051 and 303360 fields the maguitude cut was mu,€23.5."," Targets in the MS2053 field were selected using a magnitude cut of $m_{814}\leq23$, and in both the MS1054 and 3C336 fields the magnitude cut was $m_{814}\leq23.5$."
 Spectra in the CL1358 field were collected at the WITT aud AIATT where the primary targets were selected. to have Ro<21., Spectra in the CL1358 field were collected at the WHT and MMT where the primary targets were selected to have $R\leq21$.
 Details of the tarect selection. spectral reduction. wavelength calibration. sky subtraction. and removal of tellure absorption are in ?.. 2.2 2 and ο," Details of the target selection, spectral reduction, wavelength calibration, sky subtraction, and removal of telluric absorption are in \citet{fisher:98}, \citet{tran:99}, \citet{vandokkum:00}, \citet{tran:02}, and \citet{magee:04}."
 Galaxies were assigned redshifts using ΠΑΕ crosscorrelation routines as well as by visual inspection of cach individual spectimu., Galaxies were assigned redshifts using IRAF cross-correlation routines as well as by visual inspection of each individual spectrum.
 Each redshift was given a quality flag where Q=3.2.&1 corresponded to definite. probable. and mavbe (single enuüsson line).," Each redshift was given a quality flag where $Q=3, 2, \&~1$ corresponded to definite, probable, and maybe (single emission line)."
 Ta our analysis. we consider only galaxies with a redshift quality flag of Q=3: this brines the cumulative field sample to 797 ealaxics at 0.05<2«2.06.," In our analysis, we consider only galaxies with a redshift quality flag of $Q=3$ ; this brings the cumulative field sample to 797 galaxies at $0.05<z<2.06$."
 Fieure ?? (bottom: panel) shows the redshift distribution of our field sample for galaxies at O«coxld., Figure \ref{zhistall} (bottom panel) shows the redshift distribution of our field sample for galaxies at $0<z<1$.
 Note we do not include here the ~500 cluster members identified in these fields: all galaxies with redshifts within 5o of a given clusters mean redshift were excised fro the field sample., Note we do not include here the $\sim500$ cluster members identified in these fields; all galaxies with redshifts within $5\sigma$ of a given cluster's mean redshift were excised from the field sample.
 The four fields were nuaged by IIST/WFEPC(C? in the F606W aud ESLIW filters: cach tage mosaic was made of 6—12 overlapping poiutiugs., The four fields were imaged by HST/WFPC2 in the F606W and F814W filters; each image mosaic was made of $6-12$ overlapping pointings.
 The image reduction aud photometry are detailed for CL1358. MS2053. MS1051. and 30336 im 7.. 7.. 7.. aud ?— respectively.," The image reduction and photometry are detailed for CL1358, MS2053, MS1054, and 3C336 in \citet{vandokkum:98a}, , \citet{hoekstra:00}, \citet{vandokkum:00}, and \citet{magee:04} respectively."
" Following the method outlined in ?.. we transform from the WEPC2 filter svstem to redshitted «οίκο macuitudes using: where the coustauts ταςδιο, depend on the galasy’s redshift aud were calculated for an E/SO ealaxy spectral energv distribution (2).."," Following the method outlined in \citet{vandokkum:96}, we transform from the WFPC2 filter system to redshifted Johnson magnitudes using: where the constants $\{a,b,c,d\}$ depend on the galaxy's redshift and were calculated for an E/S0 galaxy spectral energy distribution \citep{pence:76}."
 (BW). colors were measured using a3” diameter aperture., $(B-V)_z$ colors were measured using a $3''$ diameter aperture.
 The E|A fraction depends strongly on how E|A ealaxies ire selected., The E+A fraction depends strongly on how E+A galaxies are selected.
 Although authors generally iuclude [OII|A3727 in their selection criteria. they differ on which Dahuer lines to use and equivalent width limits to adopt (22?) Z96)..," Although authors generally include $\lambda3727$ in their selection criteria, they differ on which Balmer lines to use and equivalent width limits to adopt \citep[Z96]{dressler:83,couch:87,balogh:99,dressler:99}. ."
 For example. the E|A fraction in a given sample can differ by as much as a factor of two if [OT] and only H9. are used as selection criteria compared to a combination of |OIT| and all three Balmer lines. and the E|A fraction from requiringa Baler equivalent width of <SA will be sumaller than that measured using ΙΑ.," For example, the E+A fraction in a given sample can differ by as much as a factor of two if [OII] and only $\delta$ are used as selection criteria compared to a combination of [OII] and all three Balmer lines, and the E+A fraction from requiringa Balmer equivalent width of $\leq-5$ will be smaller than that measured using $\leq-4$."
 Tere we describe our stringeut E|A selection criteria aud estimate the field E|A fraction at intermediate redshifts (οκτς 1)., Here we describe our stringent E+A selection criteria and estimate the field E+A fraction at intermediate redshifts $0.3<z<1$ ).
" To determine the field E|A fraction at intermediate redshifts. we define an average Balmer iudex We consider ouly galaxies at 0.3<2«1 with 20. and for which [OIT[A3727. Πὸ, and IT were included[SYN]pj in the spectral rauge."," To determine the field E+A fraction at intermediate redshifts, we define an average Balmer index We consider only galaxies at $0.3<z<1$ with $[S/N]_{BI}\geq20$ , and for which $\lambda3727$, $\delta$, and $\gamma$ were included in the spectral range."
 These strict criteria reduce the original saluple of 797 galaxies to 220(Fig. ??.. ," These strict criteria reduce the original sample of 797 galaxies to 220(Fig. \ref{zhistall}, ,"
bottom)., bottom).
 We select EA ealaxies as having (Πδ |]II5)/2<LA and no significant [OTT] cmiission (<5AJ)., We select E+A galaxies as having $($$\delta+$ $\gamma)/2\leq-4$ and no significant [OII] emission $<5$).
 The baudpasses used to determine the equivalent widths of these features are the same as those used in? and TO03a., The bandpasses used to determine the equivalent widths of these features are the same as those used in \citet{fisher:98} and T03a.
 Although combining the three Balmer linesto selectΈτA’s is the most robust approach (?).. this is uot," Although combining the three Balmer linesto selectE+A's is the most robust approach \citep{newberry:90}, , this is not"
its carly type.,its early type.
 This galaxy has a spike in the ellipticity and PA profiles around 10”., This galaxy has a spike in the ellipticity and PA profiles around $''$.
 This peak poiuts to the presence of an additional bar iu the inner parts of the galaxy (Aeucrri 19908)., This peak points to the presence of an additional bar in the inner parts of the galaxy (Aguerri 1998).
 The existence of this secondary bar in NGC 1311 has been also proposed by Erwin Sparke (2002) analvsiug images from the Iubble Space telescope (see their fig., The existence of this secondary bar in NGC 4314 has been also proposed by Erwin Sparke (2002) analysing images from the Hubble Space telescope (see their fig.
 2b)., 2b).
 The secoudiry. bar has been fitted. to the residuals after removal of the main componcuts in the averaged brightuess radial profile., The secondary bar has been fitted to the residuals after removal of the main components in the averaged brightness radial profile.
 The resulting inclnatious and PAs are in agreeineut with the data of other authors. iu particular with the RC3.," The resulting inclinations and PAs are in agreement with the data of other authors, in particular with the RC3."
 The major differences are between those galaxies with low PAs. in which the measurements are more απο because of the »oorer definition of this parameter.," The major differences are between those galaxies with low PAs, in which the measurements are more difficult because of the poorer definition of this parameter."
 This] is equally true for the inclination angles., This is equally true for the inclination angles.
 There are minor discrepancies between the nunibers in each filter. with some departures m NGC 3938 because of its shorter exposure time in AY.," There are minor discrepancies between the numbers in each filter, with some departures in NGC 3938 because of its shorter exposure time in $K_{\rm s}$."
 On the oher haud. NGC. L303 and NGC 131I show the ereatest difference in inclination compared with the RCS values in both filters.," On the other hand, NGC 4303 and NGC 4314 show the greatest difference in inclination compared with the RC3 values in both filters."
 NCC 1303 has outer arius that are fainter in the NIB. than in the optical bands. so we might be uuderestimatiug the outer part of the galaxy (ou the other haud. we are comparing visible aud NIR data).," NGC 4303 has outer arms that are fainter in the NIR than in the optical bands, so we might be underestimating the outer part of the galaxy (on the other hand, we are comparing visible and NIR data)."
 The same reason applies to NGC 1311., The same reason applies to NGC 4314.
 Iu general. al the galaxw images are bigeer iu the optical baud. the images being extracted from the DSS. than iu this work.," In general, all the galaxy images are bigger in the optical band, the images being extracted from the DSS, than in this work."
 But the particular orieutatiou of the outer avis aud the central ur causes these larger departures in these two galaxies., But the particular orientation of the outer arms and the central bar causes these larger departures in these two galaxies.
 Some galaxies prescut a ring in RC3 (NGC 3686. NGC3953. NGC 52Ls and NGC 638lL). in NIB. their are very faint in the images and could )o mixed with the arius.," Some galaxies present a ring in RC3 (NGC 3686, NGC3953, NGC 5248 and NGC 6384), in NIR their are very faint in the images and could be mixed with the arms."
 The two iethods that we have used to fit he paramcters of the brightucss distribution for he inorphological components. namely theparameters aud theparameters. give very similar results. as can be seen in Fig. 6..," The two methods that we have used to fit the parameters of the brightness distribution for the morphological components, namely the and the, give very similar results, as can be seen in Fig. \ref{Fig:fitting}."
 This can be attributed o the sinall influence of the bar in the overall brightuess distribution outside the very central regions., This can be attributed to the small influence of the bar in the overall brightness distribution outside the very central regions.
 Iu. addition. xut of the observed differcuces are certainly due to inuaccuracies inherent in the fitting procedures.," In addition, part of the observed differences are certainly due to innaccuracies inherent in the fitting procedures."
 We cau see that galaxies with strong bars (such as NGC 7179 aud NGC. 131) have their isophotal bar parameters overestimated., We can see that galaxies with strong bars (such as NGC 7479 and NGC 4314) have their isophotal bar parameters overestimated.
 This happens because of distortions iu the ellipse fitting duc to the presence of the spiral arms in the interarm region near the bar (NCC 6381. NGC 3953 and NGC 3686: sce Fies. 1..," This happens because of distortions in the ellipse fitting due to the presence of the spiral arms in the interarm region near the bar (NGC 6384, NGC 3953 and NGC 3686; see Figs. \ref{Fig:sf3344-3686},"
 2 aud 5))., \ref{Fig:sf3938-3953} and \ref{Fig:sf6384-7479}) ).
 We have obtained the best results with »=1iu the Sersic Luw for all the bulee fittings., We have obtained the best results with $n=1$ in the Sersic law for all the bulge fittings.
 Prieto et al. (, Prieto et al. (
"20= have argued that » increases with the wavelength of the filters,",2001) have argued that $n$ increases with the wavelength of the filters.
 We cannot discuss this effect since our filters are rather close each other in waveleneth., We cannot discuss this effect since our filters are rather close each other in wavelength.
 Only NCC 1311 (the early-type galaxy) preseuts a possible 5)—23 class bulge. but iu the cllipticity profile there is a peak around rp=107. which indicates a secondary bar (Erwin Sparke 2002: Aeucrri 1998).," Only NGC 4314 (the early-type galaxy) presents a possible $n=2-3$ class bulge, but in the ellipticity profile there is a peak around $r=10''$, which indicates a secondary bar (Erwin Sparke 2002; Aguerri 1998)."
 After the removal of this component. the profile of the bulge is then back of type n0—1.," After the removal of this component, the profile of the bulge is then back of type $n=1$."
 The wniqnencss of this result wav be questioned. since we would have obtained a similarly good agreement with the observed profile using a bigger aud triaxial bulec instead of a secoudary bur.," The uniqueness of this result may be questioned, since we would have obtained a similarly good agreement with the observed profile using a bigger and triaxial bulge instead of a secondary bar."
 However Erwin Sparke (2002). using deep images taken wih the IIubble Space Telescope. have also found these inner structures.," However Erwin Sparke (2002), using deep images taken with the Hubble Space Telescope, have also found these inner structures."
 Some authors (Audredakis e al., Some authors (Andredakis et al.
 L995: Àoriondo e al., 1995; Moriondo et al.
 1998) have reported a correlation between the exponent n iu the Sersic law with the morphological type of the galaxy. which we cannot check here because of the lack of coverage of this parameter.," 1998) have reported a correlation between the exponent n in the Sersic law with the morphological type of the galaxy, which we cannot check here because of the lack of coverage of this parameter."
 It is noteworthy that NGC 131 Land NCC 7179 present the strongest bars in the sample. and that both have a LINER iu their nuclei.," It is noteworthy that NGC 4314 and NGC 7479 present the strongest bars in the sample, and that both have a LINER in their nuclei."
 This fact is discussed by ATartin (1995). Athanasoula ©982) and Friedhi Berg (1993).," This fact is discussed by Martin (1995), Athanasoula (1982) and Friedli Berz (1993)."
 Finally. all the bius fmud in this work are best fitted," Finally, all the bars found in this work are best fitted"
We have verified that the trend we see in the early and late-type hosts of AGN pairs in indeed due to the difference in their concentration rather than a mass selection effect.,We have verified that the trend we see in the early and late-type hosts of AGN pairs in indeed due to the difference in their concentration rather than a mass selection effect.
" First, we compared the stellar masses of the C,>2.8 and the C,«2.8 samples (here we quote the numbers for the pair sample) and found that they defer by only 0.2 dex on average; their stellar mass distributions are consistent with being Gaussian distributions, with the C,>2.8 sample having a median mass of 10.81 (in units of log(M./Mo)) and a standard deviation of 0.34, and the C,«2.8 sample a median stellar mass of 10.62 and a standard deviation of having0.43."," First, we compared the stellar masses of the $C_r > 2.8$ and the $C_r
< 2.8$ samples (here we quote the numbers for the pair sample) and found that they defer by only 0.2 dex on average; their stellar mass distributions are consistent with being Gaussian distributions, with the $C_r > 2.8$ sample having a median mass of 10.81 (in units of $(M_{\ast}/M_{\odot})$ ) and a standard deviation of 0.34, and the $C_r < 2.8$ sample having a median stellar mass of 10.62 and a standard deviation of 0.43."
 This 0.2 dex difference is much smaller than that between the primaries and secondaries (~1 dex) in minor merger pairs ($2?))., This 0.2 dex difference is much smaller than that between the primaries and secondaries $\sim1$ dex) in minor merger pairs \ref{subsubsec:massratio}) ).
" While the C;>2.8 has on average larger stellar masses than the C,«2.8 sample sample(as expected due to the correlation), the stellar mass difference seems to be too small to be the dominant factor of the trend we see."," While the $C_r > 2.8$ sample has on average larger stellar masses than the $C_r < 2.8$ sample (as expected due to the correlation), the stellar mass difference seems to be too small to be the dominant factor of the trend we see."
" Second, to test whether the effect of this small mass difference is indeed minor, we redid our analysis using subsets of the C,>2.8 and the C,«2.8 samples matched in stellar mass distribution."," Second, to test whether the effect of this small mass difference is indeed minor, we redid our analysis using subsets of the $C_r > 2.8$ and the $C_r < 2.8$ samples matched in stellar mass distribution."
" The trend was still present, verifying that it was indeed due to concentration effect rather than a mass selection effect."," The trend was still present, verifying that it was indeed due to concentration effect rather than a mass selection effect."
 In this section we examine the correlations between the two interacting components in each AGN pair., In this section we examine the correlations between the two interacting components in each AGN pair.
 The statistical sample of AGN pairs presented in Paper I allows us to address, The statistical sample of AGN pairs presented in Paper I allows us to address
The ability of interstellar dust eraius to atteuuate light through scattering aud absorption cau lead to large Tuaertainties m the determination of the crucial plivsical parneters of galaxies.,The ability of interstellar dust grains to attenuate light through scattering and absorption can lead to large uncertainties in the determination of the crucial physical parameters of galaxies.
 These parameters not only help detcrinine the evolution of the ealactic system. but are also important for the determination of the star forma1ο rate as functiou of red-shift. a kev parameter iuiuclerstaxdiue the evolution of the universe as a whole.," These parameters not only help determine the evolution of the galactic system, but are also important for the determination of the star formation rate as function of red-shift, a key parameter in understanding the evolution of the universe as a whole."
 The dust correction is complicated by several effects as the continition of scattered light. the geometry. the mixture of the dust with the sources. and the inhomogencous structure of the iuterstellar medimm all affect the elobal atteutation of the Ooealactic starhelt.," The dust correction is complicated by several effects as the contribution of scattered light, the geometry, the mixture of the dust with the sources, and the inhomogeneous structure of the interstellar medium all affect the global attenuation of the galactic starlight."
Oo These effects produce ali attenuation curve which may be quite differeut from a pure exlnction curve derived for an individual star., These effects produce an attenuation curve which may be quite different from a pure extinction curve derived for an individual star.
 It is mavbe not foo surprising that the ealac τοςοι]ic curveL(AV9/EQDV) derived or star-bursealaxies (7) shows two significant deviaticuns from the extiuction curve sown for the diffuse mterstellar iiedima (ISAD) of our own galaxy., It is maybe not too surprising that the galactic reddening curve $E(\lambda-V)/E(B-V)$ derived for star-burstgalaxies \citep{Calzetti2001} shows two significant deviations from the extinction curve known for the diffuse interstellar medium (ISM) of our own galaxy.
 First the reddening at lo1g wavelengths is lower whici points to a larger absolute-to-relative extinction A aud to fiatter extinction curve AxAy and secoud the 21:5 feature which is very pronunent in the extiuctiol οον derived for the Milky Wav or the Large Magcllaic Clowdà (LMC) seems to be rather weak. or absent., First the reddening at long wavelengths is lower which points to a larger absolute-to-relative extinction $R_V$ and to flatter extinction curve $A_\lambda/A_V$ and second the 2175 feature which is very prominent in the extinction curves derived for the Milky Way or the Large Magellanic Cloud (LMC) seems to be rather weak or absent.
 The s100thness makes the Calzetti curve simular to the extiucjon curve derived for the bar of re ΦΠΑ Magellanic Cloud (SAIC) (2)..., The smoothness makes the Calzetti curve similar to the extinction curve derived for the bar of the Small Magellanic Cloud (SMC) \citep{Gordon1998}.
 However. the OVCLall curvature in the optical is steeper in the SAIC with an Ry--walue even slightly lower (2.7 1220.13. 7)) in respect to ιο Milkv. Way (3.1. 24).," However, the overall curvature in the optical is steeper in the SMC with an $R_V$ -value even slightly lower $2.74\pm0.13$ , \citet{Gordon2003}) ) in respect to the Milky Way (3.1, \citet{Fitzpatrick1999}) )."
 A flatter curvature of a pure foregroundC» extinction poiuts in general to a larger grain population as is interred iu 16 case of the Orion region. for example.," A flatter curvature of a pure foreground extinction points in general to a larger grain population as is inferred in the case of the Orion region, for example."
 A flattening of ie effective extinction curve for exteuded sources cal al«| be produced bv the in-homogencity of the dusty iuterstellar που., A flattening of the effective extinction curve for extended sources can also be produced by the in-homogeneity of the dusty interstellar medium.
 The reason for tus lies in the fact that a non-homogencous medium is less opticalv thic- than a homogeneous distribution of matter aud that the reduction iu the effective extinction qnucreases wit1 optical thickuess., The reason for this lies in the fact that a non-homogeneous medium is less optically thick than a homogeneous distribution of matter and that the reduction in the effective extinction increases with optical thickness.
 It has con. found based. on radiative transfer calculations that a chuupy shell can xexoduce he Calzetti curve if dust properties are cousistewt with he smooth SAIC) bulk CXlucjon curve (77)..," It has been found based on radiative transfer calculations that a clumpy shell can reproduce the Calzetti curve if dust properties are consistent with the smooth SMC bulk extinction curve \citep{Gordon1997,Witt2000}."
 We have shown (7?) hat the overall flatter curvature of the Cazotti curve can be naturalv explained by the turnleut nature of he ISM (paver 1)., We have shown \citep{Fischera2003} that the overall flatter curvature of the Calzetti curve can be naturally explained by the turbulent nature of the ISM (paper I).
 Tιο density coutrast needed to produce he flattening is found to be cousisteαι πι he velocity dispersion of t16 cold neutral medium (CNALD) as indicaed xw COoBOLVetious., The density contrast needed to produce the flattening is found to be consistent with the velocity dispersion of the cold neutral medium (CNM) as indicated by CO observations.
 The situajon with regard to the abseuce of he oak at 2175 is rather different., The situation with regard to the absence of the peak at 2175 is rather different.
 It is thought tlat he peak is caused by z-electron resonauce produced iu Su] carbonaceous particles which include erapleues. xilvevelie: aromatic hydrocarbons (PAID) and possidv sla] graphite eraims (72?7??)..," It is thought that the peak is caused by $\pi$ -electron resonance produced in small carbonaceous particles which include graphenes, polycyclic aromatic hydrocarbons (PAH) and possibly small graphite grains \citep{Li2001,Weingartner2001,DraineLi2007,Fischera2008}."
 The UV light is thought to excele the skeleton vibration modes of the molecules which LOCuce in case of PATE molecules the broad. cuiissio- catures seen in the near infrared., The UV light is thought to excite the skeleton vibration modes of the molecules which produce in case of PAH molecules the broad emission features seen in the near infrared.
 The analvsis of the diffise galactic eusson (777) or reflection nebula (7277) sugecstso that he feature is predonmünantlv or even σοιdetelv caused by absorption.," The analysis of the diffuse galactic emission \citep{Witt1973,Lillie1976,Morgan1976} or reflection nebula \citep{Witt1982,Witt1992,Calzetti1995} suggests that the feature is predominantly or even completely caused by absorption."
 If the observed. light coutais a conskerable amount of scattered cussion tlie peak streneth iu he effective extinction curve would eve- increase., If the observed light contains a considerable amount of scattered emission the peak strength in the effective extinction curve would even increase.
 Ceometrical effects for he absence of the feature in the Calzetti ctrye can therefore be excluded as verifiecl by detailed raciaive transfer caculations (DIM," Geometrical effects for the absence of the feature in the Calzetti curve can therefore be excluded as verified by detailed radiative transfer calculations \citep{Gordon1997,Witt2000}."
 The oulv possible explanatioi for the smooth Calzeti curve secus to be the destructiou of the carriers of t1ο peak caused by the strong UV racliation field., The only possible explanation for the smooth Calzetti curve seems to be the destruction of the carriers of the peak caused by the strong UV radiation field.
 This process has been discussed in the conutex of star burst galaxies »* 7.. ancl has con exteusivelv modeled by several authors Cerne) A similar interpretation was eiven for t1C absence of the peak in the SAIC ur extinction curve.," This process has been discussed in the context of star burst galaxies by \citet{Dopita2005}, and has been extensively modeled by several authors \citep{Omont1986,Allamandola1989,Leger1989,Allain1996a,Allain1996b,Page2003} A similar interpretation was given for the absence of the peak in the SMC bar extinction curve."
 T carriers are liought ο be destroved by the pervasive U racdiatiou fied Cause by the lower dust couteut resulti from a ten tinres (7) lower metallicity iu the ISM oft SAIC (2)..., The carriers are thought to be destroyed by the pervasive UV radiation field caused by the lower dust content resulting from a ten times \citep{Russel1992} lower metallicity in the ISM of the SMC \citep{Gordon1998}.
 T1ο destiction iu the ISM cannot be complete as one individual sight line shows a clear extinction bump (222). À," The destruction in the ISM cannot be complete as one individual sight line shows a clear extinction bump \citep{Lequeux1982,Gordon1998,Gordon2003}. ."
 collplete «estructionof the carriers also secuis to be in cout:dictioji with the observed cussion spectra, A complete destructionof the carriers also seems to be in contradiction with the observed emission spectra
maximum of y2 we have χο=2.5.,maximum of $\chi_{12}$ we have $\chi_2=2.5$.
" So in order to have (B3/87)/poV2=10% one needs x12Z;158, which is larger than for any of the models depicted in Figure 1.."," So in order to have $(B_2^2/8\pi)/\rho_0 V_s^2 \gtrsim 10$ one needs $\chi_{12} \gtrsim 158$, which is larger than for any of the models depicted in Figure \ref{fig:epsilon}."
" However, there has been a debate whether B?οςpoV2 (Voelketal. or B?xpoV? (Vink2008;Tatischeff"," However, there has been a debate whether $B^2 \propto \rho_0 V_s^2$ \citep{voelk05}, or $B^2 \propto \rho_0 V_s^3$ \citep{vink08d,tatischeff09}."
" For the 2005),,young SNRs the precise proportionality does 2009)..not change our conclusion very much, but in very young SNRs and/or for radio supernovae this may be relevant."," For the young SNRs the precise proportionality does not change our conclusion very much, but in very young SNRs and/or for radio supernovae this may be relevant."
" In particular for SN 1993J, which was bright radio supernova, magnetic fields as high as 50 G have been inferred, and B?/(8w)~0.1P (e.g.Tatischeff 2009)."," In particular for SN 1993J, which was bright radio supernova, magnetic fields as high as 50 G have been inferred, and $B^2/(8\pi) \sim 0.1 P_{\rm cr}$ \citep[e.g.][]{tatischeff09}."
. At such a level the magnetic fields may start to become dynamically important., At such a level the magnetic fields may start to become dynamically important.
" Apart from amplifying the magnetic field upstream of the shock, cosmic rays in the precursor may also give rise to non-adiabatic gas heating (e.g.Vladimirovetal.2008;Capriolietal."," Apart from amplifying the magnetic field upstream of the shock, cosmic rays in the precursor may also give rise to non-adiabatic gas heating \citep[e.g.][]{vladimirov08,caprioli09}."
" The effects of non-adiabatic heating will be similar to 2009)..having a lower Mach number shock, i.e. non-adiabatic heating in the precursor limits the maximum overall compression ratio and limits the maximum possible fractional cosmic-ray pressure in the downstream region."," The effects of non-adiabatic heating will be similar to having a lower Mach number shock, i.e. non-adiabatic heating in the precursor limits the maximum overall compression ratio and limits the maximum possible fractional cosmic-ray pressure in the downstream region."
 The entropy jump across a shock is given by the relation (e.g.Zel’dovich&Raizer1966):: This neglects the entropy increase associated with the accelerated particles., The entropy jump across a shock is given by the relation \citep[e.g.][]{zeldovich66}: This neglects the entropy increase associated with the accelerated particles.
" Brownetal.(1995) calculated the entropy of non-thermal distributions, which, not surprisingly, always have entropy values below a thermal distribution."," \citet{brown95} calculated the entropy of non-thermal distributions, which, not surprisingly, always have entropy values below a thermal distribution."
" Moreover, they normalize the distribution to the number of particles involved."," Moreover, they normalize the distribution to the number of particles involved."
" However, in reality the cosmic-ray component may contribute a dominant fraction of the pressure, but the number of particles is always much smaller than the number of thermal particles."," However, in reality the cosmic-ray component may contribute a dominant fraction of the pressure, but the number of particles is always much smaller than the number of thermal particles."
 So neglecting the entropy of the cosmic rays is a good approximation., So neglecting the entropy of the cosmic rays is a good approximation.
" Figure 5 shows that, when the fractional cosmic-ray pressure w (left)increases, the jump in entropy decreases."," Figure \ref{fig:entropy} (left) shows that, when the fractional cosmic-ray pressure $w$ increases, the jump in entropy decreases."
 The right hand panel is more interesting as it shows that for certain values of the escaping energy flux εοες there are two possibilities for the jump in entropy., The right hand panel is more interesting as it shows that for certain values of the escaping energy flux $\epsilon_{\rm esc}$ there are two possibilities for the jump in entropy.
 The maximum value of εοκο as a function of entropy change AS again occurs for the value for which x19 has a maximum., The maximum value of $\epsilon_{\rm esc}$ as a function of entropy change $\Delta S$ again occurs for the value for which $\chi_{12}$ has a maximum.
 One can speculate that whenever there are possible solutions to obtain a certain value for ees. the nature chooses the one that offers the highest entropy jump., One can speculate that whenever there are possible solutions to obtain a certain value for $\epsilon_{\rm esc}$ the nature chooses the one that offers the highest entropy jump.
" On the other hand the escape has to be facilitated by the details of the acceleration process and particle spectrum, so one should not discount the low entropy branch too easily."," On the other hand the escape has to be facilitated by the details of the acceleration process and particle spectrum, so one should not discount the low entropy branch too easily."
" The solutions that we presented here for the two- approach to shock with a cosmic-ray component give us a handle on estimating the effects of cosmic-ray acceleration on the post-shock plasma temperature, and"," The solutions that we presented here for the two-fluid approach to shock with a cosmic-ray component give us a handle on estimating the effects of cosmic-ray acceleration on the post-shock plasma temperature, and"
llines (Delaboudiniereetal.1995).. and polarized brightness (pB)) observations by the Mauna Loa Solar Observatory’s (MLSO) MK LV coronameter and the LASCO C2 coronagraph (see Fisheretal.(1981). for a description of the MLSO MKIII coronameter).,"lines \citep{del1995}, and polarized brightness ) observations by the Mauna Loa Solar Observatory's (MLSO) MK IV coronameter and the LASCO C2 coronagraph (see \citet{fisher1981} for a description of the MLSO MKIII coronameter)."
 At heights above the limb. the images have been processed using a Normalizing Radial-Graded Filter (NRGF). described by Morganetal.(2006).," At heights above the limb, the images have been processed using a Normalizing Radial-Graded Filter (NRGF), described by \citet{morgan2006}."
. The NRGF calculates the average and standard deviation of brightness as a function of height within an image. and uses these values to normalize the brightness at each height.," The NRGF calculates the average and standard deviation of brightness as a function of height within an image, and uses these values to normalize the brightness at each height."
 Therefore viewing the coronal structure seen in a NRGF-processed image is equivalent to viewing a large set of normalized latitudinal profiles simultaneously., Therefore viewing the coronal structure seen in a NRGF-processed image is equivalent to viewing a large set of normalized latitudinal profiles simultaneously.
 Images of the corona made near the minimum and maximum of activity shown in Figs., Images of the corona made near the minimum and maximum of activity shown in Figs.
 [BB and ICC show that the general large-scale structure of the corona during 2003 was neither as complex as during solar maximum. nor as simple as during solar minimum when streamers appear primarily at the equator.," \ref{image}B B and \ref{image}C C show that the general large-scale structure of the corona during 2003 was neither as complex as during solar maximum, nor as simple as during solar minimum when streamers appear primarily at the equator."
 Choosing a relatively simple corona with isolated streamers at mid- to high-latitudes greatly facilitates the analysis of the large-scale coronal structure., Choosing a relatively simple corona with isolated streamers at mid- to high-latitudes greatly facilitates the analysis of the large-scale coronal structure.
 Figure IDD shows details of the large helmet streamer seen on the north-west limb in figure |AA. in relation to the position of two prominences (the two northernmost white crosses) and an active region/prominence complex (white cross near the equator) at the west limb. from which the legs of the streamer seem to arise.," Figure \ref{image}D D shows details of the large helmet streamer seen on the north-west limb in figure \ref{image}A A, in relation to the position of two prominences (the two northernmost white crosses) and an active region/prominence complex (white cross near the equator) at the west limb, from which the legs of the streamer seem to arise."
 During the period from 2003/07/25 to 2003/08/10. LASCO C2 made over 800 total brightness observations.," During the period from 2003/07/25 to 2003/08/10, LASCO C2 made over 800 total brightness observations."
 This set of images is calibrated using the standard procedures. of the LASCO Solar Software package. and estimates of the F-coronal brightness (the dust contribution) and stray light brightness are subtracted using procedures described in Morganetal.(2006).," This set of images is calibrated using the standard procedures of the LASCO Solar Software package, and estimates of the F-coronal brightness (the dust contribution) and stray light brightness are subtracted using procedures described in \citet{morgan2006}."
. Latitudinal profiles are extracted from the images at various heights., Latitudinal profiles are extracted from the images at various heights.
 Each profile is normalized to a mean of zero and a standard deviation of one., Each profile is normalized to a mean of zero and a standard deviation of one.
 The profiles are then stacked in time to give the final maps. shown in figure for heights of 2.5 and 4.2R... As shown by the dotted yellow line in Fig.," The profiles are then stacked in time to give the final maps, shown in figure \ref{carr} for heights of 2.5 and As shown by the dotted yellow line in Fig."
 2AA. one streamer traces a quasi-sinusoidal curve with a period of a solar rotation.," \ref{carr}A A, one streamer traces a quasi-sinusoidal curve with a period of a solar rotation."
 The phase and amplitude of this curve associates this streamer with à small active region just north of the equator near longitude 10-307. seen in the disk synoptic map of Fig.," The phase and amplitude of this curve associates this streamer with a small active region just north of the equator near longitude $^{\circ}$, seen in the disk synoptic map of Fig."
 3AA. The most prominent structures in Fig. 2..," \ref{sourcestrmr}A A. The most prominent structures in Fig. \ref{carr},"
 however. are the two streamers highlighted by dashed and dot-dashed lines at the west and east limb respectively.," however, are the two streamers highlighted by dashed and dot-dashed lines at the west and east limb respectively."
 These drift slowly in latitude and do not describe the quasi-sinusoidal path of an isolated bright structure rotating with the Sun., These drift slowly in latitude and do not describe the quasi-sinusoidal path of an isolated bright structure rotating with the Sun.
 During the two weeks. the west-limb streamer migrates slowly in the plane of the sky from -60* tto -20° while the east limb streamer varies between 30° aand 657.," During the two weeks, the west-limb streamer migrates slowly in the plane of the sky from $^{\circ}$ to $^{\circ}$ while the east limb streamer varies between $^{\circ}$ and $^{\circ}$."
 To maintain such a slow variation. the structure of the north corona Is likely to be dominated by an extended longitudinal band of high density.," To maintain such a slow variation, the structure of the north corona is likely to be dominated by an extended longitudinal band of high density."
 The synoptic maps shown for two heights in figure 2 are very similar. a result of the predominantly radial large-scale corona at this phase of the solar cycle.," The synoptic maps shown for two heights in figure \ref{carr} are very similar, a result of the predominantly radial large-scale corona at this phase of the solar cycle."
 However. structures narrow considerably between 2.5 and 4.2R.. where the brightest central regions of the streamers are confined to very narrow latitudinal bands. generally less than 57.," However, structures narrow considerably between 2.5 and $ R_{\odot}$, where the brightest central regions of the streamers are confined to very narrow latitudinal bands, generally less than $^{\circ}$."
 This ts typical of large helmet streamers. and has been shown for solar minimum equatorial streamers by Guhathakurtaetal.(1996).. Wangetal.(1997) and others.," This is typical of large helmet streamers, and has been shown for solar minimum equatorial streamers by \citet{guh1996}, \citet{wang1997} and others."
 We aim to model the large-scale structure of the north corona for dates 2003/08/01 to 2003/08/08., We aim to model the large-scale structure of the north corona for dates 2003/08/01 to 2003/08/08.
 To achieve this. we create a 3D grid within which we can place structures of varying shapes and positions.," To achieve this, we create a 3D grid within which we can place structures of varying shapes and positions."
 The shape and positions can be adjusted as a function of height., The shape and positions can be adjusted as a function of height.
 The grid can be rotated to simulate solar rotation. and synthetic images may be created for comparison with observations by integrating along the various lines of sight (LOS).," The grid can be rotated to simulate solar rotation, and synthetic images may be created for comparison with observations by integrating along the various lines of sight (LOS)."
 As will be described. observations are used to constrain the position and shapes of streamers at the solar surface and at a height of4.," As will be described, observations are used to constrain the position and shapes of streamers at the solar surface and at a height of."
2R... Above this height. streamers maintain a radial structure.," Above this height, streamers maintain a radial structure."
 Between these heights. the streamers evolve smoothly from their initial to their final configuration.," Between these heights, the streamers evolve smoothly from their initial to their final configuration."
 The positions of the footpoints of high-density structures at the solar surface are constrained by the positions of filaments. as given by the synoptic map created by the Paris-Meudon Observatory (PMO) shown in figure 3AA. The filaments are observed in Hw near the central meridian. and are drawn in the synoptic maps as green lines.," The positions of the footpoints of high-density structures at the solar surface are constrained by the positions of filaments, as given by the synoptic map created by the Paris-Meudon Observatory (PMO) shown in figure \ref{sourcestrmr}A A. The filaments are observed in $\alpha$ near the central meridian, and are drawn in the synoptic maps as green lines."
A set of latitude-longitude coordinates along each of these filaments is recorded. and areas,"A set of latitude-longitude coordinates along each of these filaments is recorded, and areas"
"centre to be located at RA(2000) = 1647""04.0. DEC(2000) = —45*51'04.9"".","centre to be located at RA(2000) = $16^{\rm h} 47^{\rm m} 04.0^{\rm s}$, DEC(2000) = $-45^\circ 51' 04.9''$."
 This location is used as a reference for the following discussion., This location is used as a reference for the following discussion.
" Individual Masses for cluster members are derived. by comparison of their location in the CMD with a 3.9MMyr Geneva isochrone for stars more massive than 6.0MM... and a MMyr PS99 isochrone for stars with masses of MM,. and less."," Individual masses for cluster members are derived by comparison of their location in the CMD with a Myr Geneva isochrone for stars more massive than $_\odot$, and a Myr PS99 isochrone for stars with masses of $_\odot$ and less."
 We note that in the evolutionary time scale defined by the tracks by Palla Stahler. a star with a mass of MM. takes about MMyr to cross from the birthline to the zero-age main sequence (ZAMS). while the location of the birthline for a star with MM. coincides with the ZAMS.," We note that in the evolutionary time scale defined by the tracks by Palla Stahler, a star with a mass of $_\odot$ takes about Myr to cross from the birthline to the zero-age main sequence (ZAMS), while the location of the birthline for a star with $_\odot$ coincides with the ZAMS."
 No attempt was made to correct for intrinsic infrared excess and/or extinction towards individual stars., No attempt was made to correct for intrinsic infrared excess and/or extinction towards individual stars.
 This is justified by the fact that a J—- HH-Ks colour-colour diagram of the cluster members indicates that only a small fraction (less than 10%)) have an intrinsic infrared excess., This is justified by the fact that a J--H H–Ks colour-colour diagram of the cluster members indicates that only a small fraction (less than ) have an intrinsic infrared excess.
 Stellar masses were assigned based on the JHKs-brightness and -colours., Stellar masses were assigned based on the JHKs-brightness and -colours.
 For stars above MM... only those with J-Ks colours within —0.3 and 0.4 mmag of the isochrone were considered for the mass function.," For stars above $_\odot$, only those with J–Ks colours within $-0.3$ and $+0.4$ mag of the isochrone were considered for the mass function."
 As the pre-main sequence — main-sequence transition region marks an area with a broader spread in colour. for stars below MM... the J-Ks colour range was extended to allow a variation of —0.3 to 40.6 mmag around the colour indicated by the PS99 isochrone.," As the pre-main sequence – main-sequence transition region marks an area with a broader spread in colour, for stars below $_\odot$ , the J–Ks colour range was extended to allow a variation of $-0.3$ to $+0.6$ mag around the colour indicated by the PS99 isochrone."
 At an age of 3.9MMyr. a star with an initial mass of 30MM. has lost about or of its initial mass for a metallicity of Z = 0.02 or 0.04. respectively. according to the Geneva evolutionary models.," At an age of Myr, a star with an initial mass of $_\odot$ has lost about or of its initial mass for a metallicity of Z = 0.02 or 0.04, respectively, according to the Geneva evolutionary models."
 While this has a minute effect on the mass function. we assign initial rather than present-day masses to each of the stars.," While this has a minute effect on the mass function, we assign initial rather than present-day masses to each of the stars."
 The mass function obtained this way is then corrected for incompleteness. and the slope of the mass function is computed for the range 3.4 to MM...," The mass function obtained this way is then corrected for incompleteness, and the slope of the mass function is computed for the range 3.4 to $_\odot$."
 Mass functions are traditionally visualised as histograms., Mass functions are traditionally visualised as histograms.
 Deriving the mass function slope from a histogram can be problematic. as the value of the fitted slope in general varies with bin size and locations (Maizz-Apellinniz Ubbeda 2005)).," Deriving the mass function slope from a histogram can be problematic, as the value of the fitted slope in general varies with bin size and locations z-Apellánniz Úbbeda \cite{maiz05}) )."
 Slopes derived from cumulative mass functions are much more robust (e.g.. Stolte et citestolte06)).," Slopes derived from cumulative mass functions are much more robust (e.g., Stolte et \\cite{stolte06}) )."
 In the following we discuss both standard histogram mass functions and cumulative mass functions., In the following we discuss both standard histogram mass functions and cumulative mass functions.
 Figure 6 shows the mass function of the cluster assuming solar metallicities for four annuli., Figure \ref{imf_iso} shows the mass function of the cluster assuming solar metallicities for four annuli.
 The mass function slope Γ has been fitted for the mass range 3.4 to MM..., The mass function slope $\Gamma$ has been fitted for the mass range 3.4 to $_\odot$.
 With —0.6. the mass function is shallow in the inner 20.75 ppe with respect to a standard Salpeter mass function with I=—1.35. getting steeper for radial distances from the cluster centre between 0.75 and ppe with I=-1.3. F=-1.6 for radii between l.5ppe and ppe. and Fl=—1.7 for radii larger than ppc.," With $\Gamma = -0.6$ , the mass function is shallow in the inner $\approx$ pc with respect to a standard Salpeter mass function with $\Gamma = -1.35$, getting steeper for radial distances from the cluster centre between 0.75 and pc with $\Gamma = -1.3$, $\Gamma = -1.6$ for radii between pc and pc, and $\Gamma = -1.7$ for radii larger than pc."
 Because of the small number of high mass stars. as well as uncertainties in the statistical subtraction of field stars. the slopes in the two outermost annuli have uncertainties of to10%.. whereas the slopes in the inner annuli have uncertainties smaller thanοσο.," Because of the small number of high mass stars, as well as uncertainties in the statistical subtraction of field stars, the slopes in the two outermost annuli have uncertainties of to, whereas the slopes in the inner annuli have uncertainties smaller than."
 Table 3 summarises the derived mass function slopes for masses between 3.4 and MM..., Table \ref{imf_age} summarises the derived mass function slopes for masses between 3.4 and $_\odot$.
 The lower limit of MM. ensures that also in the innermost annulus only stars with masses above the completeness limit are included., The lower limit of $_\odot$ ensures that also in the innermost annulus only stars with masses above the completeness limit are included.
 The upper limit has been selected such that stars with ΜΜ. are still below our photometric saturation limit even for an age of MMvr., The upper limit has been selected such that stars with $_\odot$ are still below our photometric saturation limit even for an age of Myr.
" The cumulative mass function for the same four annuli is shown in refimf, um.", The cumulative mass function for the same four annuli is shown in \\ref{imf_cum}.
.IHteonfirnisthattheslo peo fthemass functionisgettingstee pers , It confirms that the slope of the mass function is getting steeper with increasing distance from the cluster centre.
sradius(seesections)) provide sagood fito ft," The mass function in the annulus with distances between 0.75 and 1.5 pc, i.e., the annulus centred on the half-mass radius (see section \ref{sec_hmr}) ) provides a good fit of the overall mass function of 1."
heoverallin," The MF slopes in the two outermost annuli (1.5 to pc and 2.1 to pc, respectively) is less well defined."
ass functiono," As discussed already in the case of the histograms, this is in part due to the relatively small number of massive stars in the outermost annulus, and in part due to uncertainties in the subtraction of field stars towards lower masses."
", for the two outermost annuli.", In the following we thus assume an average slope of $\Gamma = - 1.6$ for the two outermost annuli.
" Assuming a single power-law initial mass function for the cluster in the mass range 0.5 to 120MM,, for each of the annuli. we can now estimate the total (initial) number of cluster stars."," Assuming a single power-law initial mass function for the cluster in the mass range 0.5 to $_\odot$ for each of the annuli, we can now estimate the total (initial) number of cluster stars."
 After correction for incompleteness. 1.385 stars with masses between 3.4 and 30 M.. are present in the cluster.," After correction for incompleteness, 1,385 stars with masses between 3.4 and 30 $_\odot$ are present in the cluster."
 Below MM. we assume a Kroupa IMF slope with I2—0.3., Below $_\odot$ we assume a Kroupa IMF slope with $\Gamma = -0.3$.
 Table 6 lists the total number of stars in the cluster., Table \ref{cluster_nstar} lists the total number of stars in the cluster.
 Including the x65 supernovae. which might already have exploded in 11 (see. e.g.. Muno et citemunoO6b... and the estimate below). the extrapolation indicates that we can expect a total of =100.000 stars with initial masses between 0.08 to 120MM. in ΤΙ.," Including the $\approx$ 65 supernovae, which might already have exploded in 1 (see, e.g., Muno et \\cite{muno06b}, and the estimate below), the extrapolation indicates that we can expect a total of $\approx$ 100,000 stars with initial masses between 0.08 to $_\odot$ in 1."
 Table 4 lists bright stars close to the saturation limit of Ks = mmag in our sample. which also have spectral types determined by Clark et ((2005)).," Table \ref{stars_spt_mass} lists bright stars close to the saturation limit of Ks = mag in our sample, which also have spectral types determined by Clark et \cite{clark05}) )."
 Mass estimates derived by comparison with Geneva isochrones show that these stars indeed have masses around 30MM... as also determined by Clark et ffor the faint end of their sample.," Mass estimates derived by comparison with Geneva isochrones show that these stars indeed have masses around $_\odot$, as also determined by Clark et for the faint end of their sample."
 This overlap between the two samples enables us to study the cluster mass over the entire range from our completeness limit upto the highest mass stars identified by Clark et ((2005))., This overlap between the two samples enables us to study the cluster mass over the entire range from our completeness limit upto the highest mass stars identified by Clark et \cite{clark05}) ).
 We determine the total stellar mass of the cluster in two slightly different ways., We determine the total stellar mass of the cluster in two slightly different ways.
 First. we add the mass of each star detected in the Sofl data. correcting this number by the," First, we add the mass of each star detected in the SofI data, correcting this number by the"
and. by Eqs. 12... 13.. 2...,"and, by Eqs. \ref{sprho}, , \ref{sppsi}, \ref{eq:V1},"
 ancl 15.. We are aware of no analytic solution to Eq.," and \ref{lhv}, We are aware of no analytic solution to Eq."
 6 lor No>1. but it can be integrated numerically (o find a unique. steady state solution. [," \ref{eq:full} for $N>1$, but it can be integrated numerically to find a unique, steady state solution. ["
This is not a trivial point because no such solutions can exist lor 3-D Poisson-Doltzmann integrations such as modeling the structive of an isothermal star (Pestana&Eckhardt 2007)..],This is not a trivial point because no such solutions can exist for 3-D Poisson-Boltzmann integrations such as modeling the structure of an isothermal star \citep{PE:07}. .]
 We are accordingly poised to examine the problem by using (he Virial Theorem., We are accordingly poised to examine the problem by using the Virial Theorem.
 The Virial Theorem approach has an advantage over Poisson-Bolizimann integration because it merely requires (hat 274-V—0. so an oscillatory solution is feasible. whereas the Poisson-Doltzmann integration recquires that 274-V—0 and so only a (ime invariant solution is allowed.," The Virial Theorem approach has an advantage over Poisson-Boltzmann integration because it merely requires that $\overline{2T+V}=0$, so an oscillatory solution is feasible, whereas the Poisson-Boltzmann integration requires that $2T+V=0$ and so only a time invariant solution is allowed."
 An infinitesimal laver of matter. p(z)dz. is the source of a specific force in (he direction of the laver.," An infinitesimal layer of matter, $\rho(z)\,dz$, is the source of a specific force in the direction of the layer."
 Thus the gravitational enerev surface density between infinitesimal lavers of matter at 2 and 2+a is and the gravitational energv. surface densitv due to all lavers thal are separated by distance a is where p(z)is the frequency function, Thus the gravitational energy surface density between infinitesimal layers of matter at $z$ and $z+a$ is and the gravitational energy surface density due to all layers that are separated by distance $a$ is where $p(z)$is the frequency function
in energv resolution.,in energy resolution.
 We assumed that the photons are unilormly distributed in flux. and in temperature through the whole source region., We assumed that the photons are uniformly distributed in flux and in temperature through the whole source region.
 This simple assumption may also partly responsible for the above systematic error. because in reality (he source region is apparently cIumpy (see Figure 1)) and max have different temperatures. abundances. and/or ionization lime scales.," This simple assumption may also partly responsible for the above systematic error, because in reality the source region is apparently clumpy (see Figure \ref{images}) ) and may have different temperatures, abundances, and/or ionization time scales."
 Since our principal aim of this paper is to examine the spatial structures. and the spectra of non-thermal component. we do not examine in further detail for the thermal model.," Since our principal aim of this paper is to examine the spatial structures and the spectra of non-thermal component, we do not examine in further detail for the thermal model."
 In (he following analvses and discussion. we use the physical parameters cited in Table L as a good approximation.," In the following analyses and discussion, we use the physical parameters cited in Table \ref{thermal_para}
 as a good approximation."
 The spectrum of the inner region clamp is softer than anv other regions in (he NE shell. which indicates (hat the contribution of the thermal component is the largest.," The spectrum of the inner region clump is softer than any other regions in the NE shell, which indicates that the contribution of the thermal component is the largest."
 Nevertheless the thermal photons are only of the non-thermal ones if we limit the energv band to 2.010.0 keV (the hard band): the non-thermal photons in the hard band are 8.9x102 entss !. while thermal photons are 2.0x10.? ents |.," Nevertheless the thermal photons are only of the non-thermal ones if we limit the energy band to 2.0–10.0 keV (the hard band); the non-thermal photons in the hard band are $\times 10^{-2}$ cnts $^{-1}$, while thermal photons are $\times 10^{-5}$ cnts $^{-1}$."
 Therefore. in the following spatial analyses. we regard (hat all the photons in the hard band are non-thermal origin.," Therefore, in the following spatial analyses, we regard that all the photons in the hard band are non-thermal origin."
 As lor the spatial analvsis of the thermal emission. we use the limited band of keV (herealter: the soft2 band) to optimize the signal-to-noise ratio. in which lx-shell lines [rom Ie-like oxvgen (0.57 keV) contribute a most fraction of the X-ray emission (see Figure 3)).," As for the spatial analysis of the thermal emission, we use the limited band of 0.4--0.8 keV (hereafter; the soft2 band) to optimize the signal-to-noise ratio, in which K-shell lines from He-like oxygen (0.57 keV) contribute a most fraction of the X-ray emission (see Figure \ref{spectrum}) )."
 Even in this thermal-optimuzed band. however. (he count rates of the thermal and non-thermal emissions are comparable: thermal photons are 8S.1x10.1 ents |. while those of non-thermal are 5.4x10.F ents s...," Even in this thermal-optimized band, however, the count rates of the thermal and non-thermal emissions are comparable: thermal photons are $\times 10^{-1}$ cnts $^{-1}$, while those of non-thermal are $\times 10^{-1}$ cnts $^{-1}$."
 The outer edge of the NE shell is outlined by several thin X-ray filaments., The outer edge of the NE shell is outlined by several thin X-ray filaments.
 For the study ol these filaments. we selected 6 rectangle regions in Figure 1.. in which the filaments are straight and free from other structures like another filament and/or clamps.," For the study of these filaments, we selected 6 rectangle regions in Figure \ref{images}, in which the filaments are straight and free from other structures like another filament and/or clumps."
 These regions (solid boxes) are shown in Figure 2. with the designations of No.l6 from north to south.," These regions (solid boxes) are shown in Figure \ref{regions}
 with the designations of No.1–6 from north to south."
 since the SNR. shell is moving (expanding) from the right to the left. we call the right and left side as downstream aud upstream following the terminology of the shock phenomena.," Since the SNR shell is moving (expanding) from the right to the left, we call the right and left side as downstream and upstream following the terminology of the shock phenomena."
 Fieure 4. shows the intensitv profile in (he hard (2.010.0 keV: upper panel) and soft2. (0.4:0.8 keV: lower panel) bands for each filament with (he spatial resolution of 0.5 arcsec. where the horizontal axis Gr-coordinate) runs from (he east to west (upstream to downstream) along the line normal to the filaments.," Figure \ref{profiles} shows the intensity profile in the hard (2.0–10.0 keV: upper panel) and soft2 (0.4–0.8 keV: lower panel) bands for each filament with the spatial resolution of 0.5 arcsec, where the horizontal axis $x$ -coordinate) runs from the east to west (upstream to downstream) along the line normal to the filaments."
 We see very [ast decay in the downstream side and even [aster rise in (le upstream side., We see very fast decay in the downstream side and even faster rise in the upstream side.
 To estimate (he scale width. we deline a simple empirical model as a function of position," To estimate the scale width, we define a simple empirical model as a function of position"
aquark arechosen as ePi yg.ey and,produced from $[ud]_{00}$ and $\{uu\}_{11}$ as follows:
happens to be nearly equal to the Ededineton flux.,happens to be nearly equal to the Eddington flux.
 We would like to suggest that itis perhaps not an accident., We would like to suggest that it is perhaps not an accident.
 lmagine a narrow stream will a mass accretion rate M inpactiing on (the accretion torus ab a radius rp and over a small pateli that subtends a solid angle £4; al the black hole., Imagine a narrow stream with a mass accretion rate $\dot M$ impacting on the accretion torus at a radius $r_T$ and over a small patch that subtends a solid angle $\Delta \Omega_{\rm stream}$ at the black hole.
 Let us suppose that (he kinetic energy in the stream is thermalized aud radiated immediately from the patch., Let us suppose that the kinetic energy in the stream is thermalized and radiated immediately from the patch.
 The radiated [ux is locally given by eMeΠΩ , The radiated flux is locally given by $\epsilon \dot M c^2/\Delta\Omega_{\rm stream}r_T^2$.
would happen if (his flux is greater (han the local Fia?, What would happen if this flux is greater than the local $F_{\rm Edd}$?
 Jeremy Goodman (private communication) suggests that the super-Eddineton flux would cause the local radiating atmosphere to pull up aud that the radiation would be emitted from a Iarger patch than the original impact. region., Jeremy Goodman (private communication) suggests that the super-Eddington flux would cause the local radiating atmosphere to puff up and that the radiation would be emitted from a larger patch than the original impact region.
 Moreover. it would be natural for (he racliating patch to sell-adjust so that the flux is close to the Ecdington limit.," Moreover, it would be natural for the radiating patch to self-adjust so that the flux is close to the Eddington limit."
 According to this picture then. the radius Ay estimated in equation (4)) relers to (he size of the pulled up atmosphere. while the actual transverse size of (he stream is smaller.," According to this picture then, the radius $R_X$ estimated in equation \ref{rx}) ) refers to the size of the puffed up atmosphere, while the actual transverse size of the stream is smaller."
 If the stream is extremely narrow. then the flux would be close to Edclington during a significant [Traction of the light curve.," If the stream is extremely narrow, then the flux would be close to Eddington during a significant fraction of the light curve."
 Ecuivalentlv. the black-bocly temperature of the radiation would remain constant. even while the huminosity decreases.," Equivalently, the black-body temperature of the radiation would remain constant, even while the luminosity decreases."
" This picture (which is predicated on the assumption of a narrow [fallback stream, sugeests (hat most dal disruption events should be visible in soft. N-ravs: the condition Fo-—Frag. coupled with f.3 (see 822). ensures that the blackbody temperature of the radiation will be =50 eV [or a 10*M.. black hole. which is wellanatched to X-ray observations."," This picture (which is predicated on the assumption of a narrow fallback stream) suggests that most tidal disruption events should be visible in soft X-rays; the condition $F=F_{\rm Edd}$, coupled with $f_c\sim3$ (see 2), ensures that the blackbody temperature of the radiation will be $\ga50$ eV for a $10^7M_\odot$ black hole, which is well-matched to X-ray observations."
 Soft. N-rav. surveys should thus be well-suited for an investigation of both the frequency of tidal disruption events and the amount of mass accreted in each event., Soft X-ray surveys should thus be well-suited for an investigation of both the frequency of tidal disruption events and the amount of mass accreted in each event.
 In this connection. it is interesting that. with the exception of the UV flare of Renzini et al. (," In this connection, it is interesting that, with the exception of the UV flare of Renzini et al. ("
1995). all known candidate flares for tidal disruption events have been identified in (he X-ray band (see Ixomossa 2001 for five candidates and Choi et al.,"1995), all known candidate flares for tidal disruption events have been identified in the X-ray band (see Komossa 2001 for five candidates and Choi et al."
 2002 for a possible sixth candidate)., 2002 for a possible sixth candidate).
 Alenou Quataert (2001) have emphasized that. given current estimates of the rate of tidal disruptions. the nuclei of many nearby normal galaxies should be much brighter than observed if a fair fraction of a stellar mass is accreted by the black hole after each tidal disruption event.," Menou Quataert (2001) have emphasized that, given current estimates of the rate of tidal disruptions, the nuclei of many nearby normal galaxies should be much brighter than observed if a fair fraction of a stellar mass is accreted by the black hole after each tidal disruption event."
 This is not relevant for the late accretion phase of the particular NGC 5905 flare cliseussed here because. as we have discussed (see also the Appendix below). very little mass (< 1M.) returned to the DII in this ease.," This is not relevant for the late accretion phase of the particular NGC 5905 flare discussed here because, as we have discussed (see also the Appendix below), very little mass $\ll 1 M_\odot$ ) returned to the BH in this case."
 Ilowever. whether we attribute the small amount of mass in the NGC 5905 flare to partial stripping of a star or to the disruption of a substellar object. it does not help to explain the general problem of why nearby. galactic nuclei are so faint.," However, whether we attribute the small amount of mass in the NGC 5905 flare to partial stripping of a star or to the disruption of a substellar object, it does not help to explain the general problem of why nearby galactic nuclei are so faint."
 In addition to partial disruptions of the sort that mieht have occurred in NGC 5905. we expect total stellar disruptions in significant numbers and these should provide a signilicant mean mass accretion rate in galactic nuclei.," In addition to partial disruptions of the sort that might have occurred in NGC 5905, we expect total stellar disruptions in significant numbers and these should provide a significant mean mass accretion rate in galactic nuclei."
 Disruptions of substellar objects only add to Che purely stellar disruptions considered to date., Disruptions of substellar objects only add to the purely stellar disruptions considered to date.
 Thus. alternative wavs," Thus, alternative ways"
where ¢.(/?) is specified according to Eq. €(18)),where $c_{s}(R)$ is specified according to Eq. \ref{eq:cs}) )
 and we assume a Keplerian rotation profile Q=—CM2., and we assume a Keplerian rotation profile $\Omega = \sqrt{GM/R^{3}}$.
 The corrections to Keplerian rotation due to the pressure gradient are of order (12/Y. which for the thin discs considered in this paper are very small (~10. 3.," The corrections to Keplerian rotation due to the pressure gradient are of order $(H/R)^{2}$, which for the thin discs considered in this paper are very small $\sim 10^{-4}$ )."
" implements the full variable smoothing lengthSPH formulation developed by ? and ?.. whereby the smoothing length. h. and density. p. are mutually dependent via the density sum (for particle «) which is an exact solution to (12). and the relation where n, is the particle mass and Wi,=V(r,ri].fr) is the SPH smoothing kernel (see e.g. 2???) for details)."," implements the full variable smoothing lengthSPH formulation developed by \citet{pm04b} and \citet{pm07}, whereby the smoothing length, $h$, and density, $\rho$, are mutually dependent via the density sum (for particle $a$ ) which is an exact solution to \ref{eq:cty}) ), and the relation where $m_a$ is the particle mass and $W_{ab} \equiv W(\vert {\bf r}_{a} - {\bf r}_{b}\vert, h_{a})$ is the SPH smoothing kernel (see e.g. \citealt{monaghan92,price04,monaghan05} for details)."
 This— results in a resolution that adapts to the local particle number density., This results in a resolution that adapts to the local particle number density.
 Equations (209) and (219) are iterated self-consistently using a Newton-Raphson method as described in ?.. where in this paper we have used Όρο=1.2. giving approximately 58 neighbours per particle in a smooth distribution.," Equations \ref{eq:rhosum}) ) and \ref{eq:hrho}) ) are iterated self-consistently using a Newton-Raphson method as described in \citet{pm07}, where in this paper we have used $h_{\rm fac}=1.2$, giving approximately 58 neighbours per particle in a smooth distribution."
 The equations of motion (13) take the form where © is a dimensionless quantity related to the smoothing length gradients (see ? for details) and the stress tensor is given by The q term in (239) is the artificial viscosity (discussed below) which is introduced in SPH in order to capture shocks and (to a lesser extent) to prevent interpenetration of particles., The equations of motion \ref{eq:mom}) ) take the form where $\Omega$ is a dimensionless quantity related to the smoothing length gradients (see \citealt{pm07} for details) and the stress tensor is given by The $q^{AV}$ term in \ref{eq:sijsph}) ) is the artificial viscosity (discussed below) which is introduced in SPH in order to capture shocks and (to a lesser extent) to prevent interpenetration of particles.
 However. it can be shown (see below) that the artificial viscosity corresponds directly to à Navier-Stokes type term and can thus be used. with minor adjustment of the parameters. to directly represent physical viscous diffusion (in doing so one would obviously discard the remaining terms in Eg. 23..," However, it can be shown (see below) that the artificial viscosity corresponds directly to a Navier-Stokes type term and can thus be used, with minor adjustment of the parameters, to directly represent physical viscous diffusion (in doing so one would obviously discard the remaining terms in Eq. \ref{eq:sijsph},"
 ie. setting ¢=η 0).," i.e., setting $\zeta=\eta=0$ )."
 The disadvantage of doing so is that the resultant viscosity coefficient consists of both shear and bulk components of viscosity. whereas for a dise the viscosity parameterisation (23) should consist of shear viscosity only.," The disadvantage of doing so is that the resultant viscosity coefficient consists of both shear and bulk components of viscosity, whereas for a disc the viscosity parameterisation \ref{eq:shakura}) ) should consist of shear viscosity only."
 The remaining part of the SPH algorithm is the time integration algorithm. for which we use a standard leapfrog scheme equivalent to the velocity Verlet method.," The remaining part of the SPH algorithm is the time integration algorithm, for which we use a standard leapfrog scheme equivalent to the velocity Verlet method."
 For efficiency we assign individual timesteps. set in factors of 2? from a nominal maximum timestep. such that only a subset of the particles is moved on the shortest timestep.," For efficiency we assign individual timesteps, set in factors of 2 from a nominal maximum timestep, such that only a subset of the particles is moved on the shortest timestep."
 With individual timesteps many of the conservation properties of the leapfrog algorithm are only approximately satistied. however the scheme is significantly more efficient.," With individual timesteps many of the conservation properties of the leapfrog algorithm are only approximately satisfied, however the scheme is significantly more efficient."
 The artificial viscosity formulation in follows that of ?.. with the averaging in the density and signal velocity changed slightly in order to more efficiently calculate the terms in (22)).," The artificial viscosity formulation in follows that of \citet{monaghan97}, with the averaging in the density and signal velocity changed slightly in order to more efficiently calculate the terms in \ref{eq:sphmom}) )."
" We use where v,,—v,νι and the viscosity is only applied for approaching particles (van-Yan<0. Le. converging flows)."," We use where ${\bf v}_{ab} \equiv {\bf v}_{a} - {\bf v}_{b}$ and the viscosity is only applied for approaching particles ${\bf v}_{ab}\cdot\hat{\bf r}_{ab} < 0$, i.e., converging flows)."
 The signal velocity for hydrodynamics is given by where in general 4=2., The signal velocity for hydrodynamics is given by where in general $\beta^{\rm AV} = 2$.
 The 3°* term in the signal velocity provides a non-linear term that was originally introduced to prevent particle penetration in high Mach number shocks (see e.g. 2) , The $\beta^{\rm AV}$ term in the signal velocity provides a non-linear term that was originally introduced to prevent particle penetration in high Mach number shocks (see e.g. \citealt{monaghan89}) ).
"For shock capturing — where the aim is to provide as little dissipation as possible whilst resolving shock structures — implements the ? switch to reduce dissipation away from shocks. in which the dissipation parameter e? is evolved according to a source and decay equation where σ=0.1. ὃ=max(0.Vv). o,,;,=0.05 and in general one would enforce ρω=1.0."," For shock capturing — where the aim is to provide as little dissipation as possible whilst resolving shock structures --- implements the \citet{mm97} switch to reduce dissipation away from shocks, in which the dissipation parameter $\alpha^{\rm AV}$ is evolved according to a source and decay equation where $\sigma=0.1$, $\mathcal{S} = \max (0,-\nabla\cdot{\bf v})$, $\alpha_{min} = 0.05$ and in general one would enforce $\alpha_{max}=1.0$."
 It has been known for quite some time (e.g.2?) that the artificial viscosity terms in SPH can be understood. straightforwardly as numerical representations of second derivatives of the velocity.," It has been known for quite some time \citep[e.g.][]{lubow94,murray96} that the artificial viscosity terms in SPH can be understood straightforwardly as numerical representations of second derivatives of the velocity."
 This is because the standard procedure for evaluating second derivatives in SPH is to use an integral formulation based on only the first derivative of the SPH kernel., This is because the standard procedure for evaluating second derivatives in SPH is to use an integral formulation based on only the first derivative of the SPH kernel.
 For example the Laplacian for a scalar quantity <4 is represented by (222) which is more clearly expressed by writing the kernel gradient as VMuu= Paptue. giving For a vector quantity the corresponding expressions are (2? where δὲ—n i.e.. the number of spatial dimensions.," For example the Laplacian for a scalar quantity $A$ is represented by \citep{brookshaw85,price04,monaghan05}
 which is more clearly expressed by writing the kernel gradient as $\nabla_{a} W_{ab} \equiv \hat{\bf r}_{ab} F_{ab}$ , giving For a vector quantity the corresponding expressions are \citep{er03,monaghan05}
 where $\delta^{k}_{k} \equiv n$ i.e., the number of spatial dimensions."
 The above expressions mean that it is possible to give clear interpretation to the artificial viscosity terms. since for example in three dimensions we have. from (299) and (C30). For non-constant coefficients the expressions are similar (22).. but with an average of the coefficients on the particles. for example," The above expressions mean that it is possible to give clear interpretation to the artificial viscosity terms, since for example in three dimensions we have, from \ref{eq:del2A}) ) and \ref{eq:graddivA}) ), For non-constant coefficients the expressions are similar\citep{cm99,monaghan05}, , but with an average of the coefficients on the particles, for example"
Since the above compressive instabilities appear to saturate at a level too small (08/8~ 1) to allow Fermi acceleration over a broad range of energies. the possible existence of non-compressive instability becomes crucial.,"Since the above compressive instabilities appear to saturate at a level too small $\delta B/B\sim 1$ ) to allow Fermi acceleration over a broad range of energies, the possible existence of non-compressive instability becomes crucial."
 One can search for such modes by selecting the wave vectors accordingly. in which case the reduced system becomes: It is easy to verify that this system possesses no unstable solution but only damped solutions.," One can search for such modes by selecting the wave vectors accordingly, in which case the reduced system becomes: It is easy to verify that this system possesses no unstable solution but only damped solutions."
 Hence incompressible unstable modes do not exist in this MHD description., Hence incompressible unstable modes do not exist in this MHD description.
 In this study. we have examined the amplitication of a pre-existing magnetic field upstream of an ultra-relativistic shock wave.," In this study, we have examined the amplification of a pre-existing magnetic field upstream of an ultra-relativistic shock wave."
" We have assumed that the magnetic field is fully perpendicular to the shock normal in the shock front frame. as generally expected in the ultra-relativistic limit Ty,z|."," We have assumed that the magnetic field is fully perpendicular to the shock normal in the shock front frame, as generally expected in the ultra-relativistic limit $\Gamma_{\rm sh}\,\gg\,1$."
 In the shock frame. the cosmic rays do not induce any current at zeroth order. only a net charge density. which is partly sereened by the inflowing plasma.," In the shock frame, the cosmic rays do not induce any current at zeroth order, only a net charge density, which is partly screened by the inflowing plasma."
 This charge distribution then triggers an instability on very short spatial scales. with a growth rate increasing with the wavenumber.," This charge distribution then triggers an instability on very short spatial scales, with a growth rate increasing with the wavenumber."
 Cosmic rays do not respond to this amplitication as it takes on scales much shorter than the typical Larmor radius., Cosmic rays do not respond to this amplification as it takes on scales much shorter than the typical Larmor radius.
 It is important to stress that these instabilities are of a ditferent nature than the resonant or non-resonant instability studied by Bell (2004) in the ease of a non-relativistic parallel shock wave. most notably because they are essentiallycompressive.," It is important to stress that these instabilities are of a different nature than the resonant or non-resonant instability studied by Bell (2004) in the case of a non-relativistic parallel shock wave, most notably because they are essentially."
 Since density depletions are naturally limited. our linear analysis indicates that these instabilities saturate at a moderate level of amplitication. OB/By~|.," Since density depletions are naturally limited, our linear analysis indicates that these instabilities saturate at a moderate level of amplification, $\delta B/B_0 \, \sim\, 1$."
 Furthermore. there is no unstable incompressible mode within the present MHD approximation which could provide a higher level of amplification.," Furthermore, there is no unstable incompressible mode within the present MHD approximation which could provide a higher level of amplification."
 Therefore. we conclude that. within the framework of ideal MAD. instabilities at. ultra-relativistie magnetized shock waves appear limited in their ethciency.," Therefore, we conclude that, within the framework of ideal MHD, instabilities at ultra-relativistic magnetized shock waves appear limited in their efficiency."
 Such instabilities cannot therefore account for the degree of amplification that has been inferred from the modeling of the afterglow radiation of gamma-ray bursts., Such instabilities cannot therefore account for the degree of amplification that has been inferred from the modeling of the afterglow radiation of gamma-ray bursts.
 We have also argued in Section ??. that the ratio 0B/By sets the dynamic range of energies over which powerlaw spectra can be produced through Fermi acceleration., We have also argued in Section \ref{sec:fermi} that the ratio $\delta B/B_0$ sets the dynamic range of energies over which powerlaw spectra can be produced through Fermi acceleration.
 The present instabilities thus cannot allow successful Fermi acceleration., The present instabilities thus cannot allow successful Fermi acceleration.
 Nevertheless. it would certainly be useful to pursue the present investigation with dedicated numerical simlations. which would allow one to go beyond the present linear approximation and study whether non-linear effects can push the small scale magnetic field to higher values.," Nevertheless, it would certainly be useful to pursue the present investigation with dedicated numerical simlations, which would allow one to go beyond the present linear approximation and study whether non-linear effects can push the small scale magnetic field to higher values."
 If the standard interpretation of gamma-ray burst afterglows as the synchrotron light of electrons accelerated at the forward shock (but see Uhm Beloborodov 2006. Genet. Daigne Mochkoviteh 2007 for recent alternatives involving the reverse shock) holds. one is led to conclude that some other instability is able to amplify the upstream magnetic field on short spatial scales. or that some other form of acceleration mechanism is operating (see for instance Hoshino 2008 for an alternative involving radiative pressure ettects).," If the standard interpretation of gamma-ray burst afterglows as the synchrotron light of electrons accelerated at the forward shock (but see Uhm Beloborodov 2006, Genet, Daigne Mochkovitch 2007 for recent alternatives involving the reverse shock) holds, one is led to conclude that some other instability is able to amplify the upstream magnetic field on short spatial scales, or that some other form of acceleration mechanism is operating (see for instance Hoshino 2008 for an alternative involving radiative pressure effects)."
 The present work indicates that such cosmic ray induced instabilities would involve non-MHD ettects., The present work indicates that such cosmic ray induced instabilities would involve non-MHD effects.
 The short spatial scales ul.«Γον required are in conflict with the usual synchrotron resonance between cosmic rays and MHD waves: this remark is actually one of the motivation of the present work in a full MHD framework.," The short spatial scales $\lambda_{\rm
 c}\,\ll\,r_{\rm L}/\Gamma_{\rm sh}$ required are in conflict with the usual synchrotron resonance between cosmic rays and MHD waves; this remark is actually one of the motivation of the present work in a full MHD framework."
 However. one cannot rule out that other types of resonance could become relevant and yet involve incompressible modes. such as Alfvénn waves.," However, one cannot rule out that other types of resonance could become relevant and yet involve incompressible modes, such as Alfvénn waves."
" One promising instability. currently under study. involves a Cerenkov resonance (o0.=K,c) between plasma waves and the cosmic ray beam. generating a modified two stream instability."," One promising instability, currently under study, involves a Cerenkov resonance $\omega = k_xc$ ) between plasma waves and the cosmic ray beam, generating a modified two stream instability."
 The growth rates appear quite promising and the details will be given in a forthcoming article., The growth rates appear quite promising and the details will be given in a forthcoming article.
 In the shock front frame. the electric field. current and charge density read: The four velocity of the inflowing plasma is written yc.uc) (hence u=yf is dimensionless).," In the shock front frame, the electric field, current and charge density read: The four velocity of the inflowing plasma is written $(\gamma
c,\mathbf{u}c)$ (hence $\mathbf{u}=\gamma\mathbf{\beta}$ is dimensionless)."
" In this equation. y represents the total Lorentz factor of the upstream plasma: it will be shown to coincide nearly with Py, in the following."," In this equation, $\gamma$ represents the total Lorentz factor of the upstream plasma; it will be shown to coincide nearly with $\Gamma_{\rm sh}$ in the following."
" Note that in the shock front. there is no current at zeroth order associated with the cosmic rays. only a net charge density p, which may be partially screened by an induced non-zero plasma charge density py."," Note that in the shock front, there is no current at zeroth order associated with the cosmic rays, only a net charge density $\rho_{\rm
 cr}$ which may be partially screened by an induced non-zero plasma charge density $\rho_{\rm pl}$."
" Faraday's law implies in this stationary regime: Hence the Gauss equation can be rewritten as: Energy momentum conservation for the upstream fluid implies: where p, is the proper mass density of the upstream plasma.", Faraday's law implies in this stationary regime: Hence the Gauss equation can be rewritten as: Energy momentum conservation for the upstream fluid implies: where $\rho_{\rm u}$ is the proper mass density of the upstream plasma.
" Denoting Fy,=-pycin, the mass flux (times ο) through the shock front: Since: y=(Eri Επ."," Denoting $F_{\rm m}\equiv -\rho_{\rm u}c^2 u_x$ the mass flux (times $c$ ) through the shock front: Since: $\gamma=(1 + u_x^2 + u_z^2)^{1/2}$ ,"
v.s. IRASI2. and LIS8W v.s. IRAS25. respectively (see also Ishihara et al.. 2010)).,"v.s. IRAS12, and L18W v.s. IRAS25, respectively (see also Ishihara et al., \cite{ishihara2010}) )."
 The comparison also reveals that there are about 25.000 good IRAS sources that are without AKARI counterparts.," The comparison also reveals that there are about 25,000 good IRAS sources that are without AKARI counterparts."
 Their galactic spatial distribution is shown in the upper panel of the Figure 2.., Their galactic spatial distribution is shown in the upper panel of the Figure \ref{galdist}.
 There are several possibilities to explain why some of the IRAS sources (especially bright ones) are not listed in the IRC-PSC., There are several possibilities to explain why some of the IRAS sources (especially bright ones) are not listed in the IRC-PSC.
" The possible explanations are. (1) saturated in the AKARI survey (2) the IRAS point-like source can be recognized as an extended source to the AKARIUs eye. and excluded from the “point source"" catalog. (3) the IRAS source can be resolved into several fainter sources to the AKARI's eye. (4) difference in the sky coverage (~ for AKARI and ~ for IRAS) or located in the unexplored sky region (Ishihara et al. 2010))."," The possible explanations are, (1) saturated in the AKARI survey (2) the IRAS point-like source can be recognized as an extended source to the AKARI's eye, and excluded from the ""point source"" catalog, (3) the IRAS source can be resolved into several fainter sources to the AKARI's eye, (4) difference in the sky coverage $\sim$ for AKARI and $\sim$ for IRAS) or located in the unexplored sky region (Ishihara et al. \cite{ishihara2010}) )."
 The 2MASS point source catalog (2MASS-PSC: Skrutskie et al. 2006)), The 2MASS point source catalog (2MASS-PSC; Skrutskie et al. \cite{skrutskie2006}) )
" is complete down to K,«14.3 mag in the absence ofconfusion*.", is complete down to $K_s < 14.3$ mag in the absence of.
. Then. all normal stars seen by AKARI should be prominent in the 2MASS-PSC.," Then, all normal stars seen by AKARI should be prominent in the 2MASS-PSC."
 Therefore. we use the 2MASS-PSC to assess the positional accuracy of the IRC-PSC.," Therefore, we use the 2MASS-PSC to assess the positional accuracy of the IRC-PSC."
 There are 761.565 sources with S/N > 5 at the SOW band in the IRC-PSC.," There are 761,565 sources with S/N $>$ 5 at the $S9W$ band in the IRC-PSC."
 We refer these 761.565 sources as good IRC sources.," We refer these 761,565 sources as good IRC sources."
 We search the 2MASS counterparts brighter than 14.3 mag and S/N > 5 in Κι band for the good IRC sources., We search the 2MASS counterparts brighter than 14.3 mag and S/N $>$ 5 in $K_s$ band for the good IRC sources.
 If more than one 2MASS sources are found within the tolerance radius from an AKARI source. we only adopt the closest one and regard the other(s) as unmatched.," If more than one 2MASS sources are found within the tolerance radius from an AKARI source, we only adopt the closest one and regard the other(s) as unmatched."
 We find counterpart for ia=aAοA0 (6656). 673.730 (960). 713.705 (94%). 724.739 (0560). and 728.178 (96%)) good IRC sources using the positional tolerance radit of 1. 2. 3.4. and 5 aresec. respectively.," We find counterpart for 505,350 ), 673,730 ), 713,705 ), 724,739 ), and 728,178 ) good IRC sources using the positional tolerance radii of 1, 2, 3, 4, and 5 arcsec, respectively."
 If we use a subsample of 562.598 high quality (S/N >10 at the SOW band) IRC-PSC sources. the results would beοδός.886t..93%... 94%... and for the positional tolerance radi of 1. 2. 3. 4. and 5 aresec. respectively.," If we use a subsample of 562,598 high quality (S/N $> 10$ at the $S9W$ band) IRC-PSC sources, the results would be, and for the positional tolerance radii of 1, 2, 3, 4, and 5 arcsec, respectively."
 These results suggest that the positional accuracy of the IRC-PSC doesnot depend on the source brightness. and the accuracy 1s uniform at least for sources with S/N > 5.," These results suggest that the positional accuracy of the IRC-PSC doesnot depend on the source brightness, and the accuracy is uniform at least for sources with S/N $>$ 5."
 Also. it seems that the chance of false matches may get large if we use the tolerance radius larger than 4 aresec.," Also, it seems that the chance of false matches may get large if we use the tolerance radius larger than 4 arcsec."
" To see the dependence of positional accuracy on the source density. we make the same 2MASS counterpart search with a subsample of 78.171 high galactic latitude (0> 30°) good IRC-PSC sources. where we do not suffer from severe confusion,"," To see the dependence of positional accuracy on the source density, we make the same 2MASS counterpart search with a subsample of 78,171 high galactic latitude $|b| > 30^\circ$ ) good IRC-PSC sources, where we do not suffer from severe confusion."
" We search the 2MASS counterpart brighter than 14.3 mag and S/N > 5 in K, band for these high latitude good IRC-PSC sources. and find counterpart for 61.619 (79%)). 70.446 )). 71.877 (92%)). 72.334 (03950). and 72.528 (93%)) sources using the positional tolerance radi of ]. 2. 3. 4. and 5 aresec. respectively."," We search the 2MASS counterpart brighter than 14.3 mag and S/N $>$ 5 in $K_s$ band for these high latitude good IRC-PSC sources, and find counterpart for 61,619 ), 70,446 ), 71,877 ), 72,334 ), and 72,528 ) sources using the positional tolerance radii of 1, 2, 3, 4, and 5 arcsec, respectively."
 This result indicates that the positional accuracy of the IRC-PSC may depend on the source density. but it does not matter if we use the match radius larger than 2 arcsec.," This result indicates that the positional accuracy of the IRC-PSC may depend on the source density, but it does not matter if we use the match radius larger than 2 arcsec."
 Considering the above test results. we conclude that the positional accuracy of the IRC-PSC sources is better than 3 aresec for most of the sources.," Considering the above test results, we conclude that the positional accuracy of the IRC-PSC sources is better than 3 arcsec for most of the sources."
 This result is compatible with the pointing accuracy estimated in Ishihara et al. (2010))., This result is compatible with the pointing accuracy estimated in Ishihara et al. \cite{ishihara2010}) ).
 Then we decide to use a tolerance radius of 3 aresee for catalog comparisons made in the next section., Then we decide to use a tolerance radius of 3 arcsec for catalog comparisons made in the next section.
 Finally. the AKARI sources without 2MASS counterpart should be of particular interest because such sources can be deeply dust enshrouded objects (e.g.. OH/IR stars. dusty carbon stars. etc.)," Finally, the AKARI sources without 2MASS counterpart should be of particular interest because such sources can be deeply dust enshrouded objects (e.g., OH/IR stars, dusty carbon stars, etc.)"
 or distant galaxies., or distant galaxies.
 There are 47.860 good IRC sources without 2MASS counterpart (brighter than 14.3 mag and S/N > 5 in Κι band) within a radius of 3 arcsec.," There are 47,860 good IRC sources without 2MASS counterpart (brighter than 14.3 mag and S/N $>$ 5 in $K_s$ band) within a radius of 3 arcsec."
 We show the galactic spatial distribution of these 2MASS-drop AKARI sources in the lower panel of the Figure 2.., We show the galactic spatial distribution of these 2MASS-drop AKARI sources in the lower panel of the Figure \ref{galdist}.
 Follow-up observations are definitely needed to identify these sources., Follow-up observations are definitely needed to identify these sources.
 The IRC-PSC is cross-identified with existing all-sky survey catalogs. namely the new Hipparcos astrometric catalog (van Leeuwen 2007)) and the 2MASS PSC (Skrutskie et al. 2006)).," The IRC-PSC is cross-identified with existing all-sky survey catalogs, namely the new Hipparcos astrometric catalog (van Leeuwen \cite{vanLeeuwen2007}) ) and the 2MASS PSC (Skrutskie et al. \cite{skrutskie2006}) ),"
 using a simple positional correlation method., using a simple positional correlation method.
 The epoch of the source positions listed in the new Hippareos catalog ts 1991.25. while that of the IRC-PSC is 2000.0.," The epoch of the source positions listed in the new Hipparcos catalog is 1991.25, while that of the IRC-PSC is 2000.0."
 There are 15.052 Hippareos sources whose total proper motions are larger than 100 milliaresee/year.," There are 15,052 Hipparcos sources whose total proper motions are larger than 100 milliarcsec/year."
 Their positions should be corrected for the proper motion over the 8.75 year interval., Their positions should be corrected for the proper motion over the 8.75 year interval.
" We calculate the positions 1n epoch 2000.0 for the Hipparcos sources with good proper motion measurements (σαµα«0.2 and 0.2. where ji, and jj; are proper motions in right ascension and declination. respectively)."," We calculate the positions in epoch 2000.0 for the Hipparcos sources with good proper motion measurements $\sigma \mu_\alpha/\mu_\alpha < 0.2$ and $\sigma \mu_\delta/\mu_\delta < 0.2$ , where $\mu_\alpha$ and $\mu_\delta$ are proper motions in right ascension and declination, respectively)."
 Then we use the new positions for the cross-identification., Then we use the new positions for the cross-identification.
As indicated above. the local solutions in this work refer to local solutions in the vicinity of a critical point.,"As indicated above, the local solutions in this work refer to local solutions in the vicinity of a critical point."
" The requirement of a critical point for the existence of a steady solution was discussed in re[sec,oz zle..", The requirement of a critical point for the existence of a steady solution was discussed in \\ref{sec_nozzle}.
" Thus. the requirements for the existence of local steady solutions are: and The existence of a global solution (a solution that spans throughout the spatial range of the model) requires tlie existence of a critical point relsec,oz fe). ichiehinturnimpliesthatthecriticalpointeondilionsmustholdalthegivenpoint(S secirilicalpoint)).andrequires.ofcourse.tlheevistenceofalocalsolulion(s seciocalsteady))whicheanbeevtended [ romltheeriticalpointtowardsinfinitgintheoutiwarddirectionandi "," Thus, the requirements for the existence of local steady solutions are: and The existence of a global solution (a solution that spans throughout the spatial range of the model) requires the existence of a critical point \\ref{sec_nozzle}) ), which in turn implies that the critical point conditions must hold at the given point \\ref{sec_criticalpoint}) ), and requires, of course, the existence of a local solution \\ref{sec_localsteady}) ) which can be extended from the critical point towards infinity in the outward direction and towards the sonic point in the inward direction."
Additionally. it is required that the global solution be such that upon integration in the inward direction the wind reaches souid speed at (he sonic point.," Additionally, it is required that the global solution be such that upon integration in the inward direction the wind reaches sound speed at the sonic point."
 The exact position of the sonic point is a boundary condition of the model (e.e.. in the CARNT5 stellar wind moclel the position of the sonic point is assumed to be approximately equal to the stellar photospheric radius).," The exact position of the sonic point is a boundary condition of the model (e.g., in the CAK75 stellar wind model the position of the sonic point is assumed to be approximately equal to the stellar photospheric radius)."
 The set of points for which the critical point. conditions hold. and that allow a local solution. define (he range in which the critical point must be if à global solution exists.," The set of points for which the critical point conditions hold, and that allow a local solution, define the range in which the critical point must be if a global solution exists."
 The exact position of the critical point is determined by initially guessing with a value within (his range. ancl iterativelv adjusting the critical point position until the correct sonic point is achieved when integrating inward.," The exact position of the critical point is determined by initially guessing with a value within this range, and iteratively adjusting the critical point position until the correct sonic point is achieved when integrating inward."
 This iterative process to determine (the exact critical point position in a LD line-driven wind was originally applied by CAIT5 in the study of stellar winds., This iterative process to determine the exact critical point position in a 1D line-driven wind was originally applied by CAK75 in the study of stellar winds.
 Although CAIX75 did not present an independent. proof of the existence of, Although CAK75 did not present an independent proof of the existence of
Cohen et 11985: Escalante et 11989).,Cohen et 1985; Escalante et 1989).
 The kinematics of the ionized gas associated with MWC 349A presents several problems that require additional research., The kinematics of the ionized gas associated with MWC 349A presents several problems that require additional research.
" For instance, the direction of rotation determined from the em thermal lines (eastern side blueshifted and western side redshifted: guez Bastian 1994) is opposite to that found in the mm maser lines (Planesas et 11992; Weintroub et 22008)."," For instance, the direction of rotation determined from the cm thermal lines (eastern side blueshifted and western side redshifted; guez Bastian 1994) is opposite to that found in the mm maser lines (Planesas et 1992; Weintroub et 2008)."
" Also, while the thermal radio recombination lines at em wavelengths peak at negative velocities (typically Vj. ~-20 km ': guez Bastian 1994), the centroid of maser mm radio recombination lines is at positive velocities (Vi, » -lOkms !: WWeintroub et 22008)."," Also, while the thermal radio recombination lines at cm wavelengths peak at negative velocities (typically $V_{lsr}$ $\sim$ –20 km $^{-1}$; guez Bastian 1994), the centroid of maser mm radio recombination lines is at positive velocities $V_{lsr}$ $\sim$ $+$ 10 km $^{-1}$; Weintroub et 2008)."
" In our unconstrained fit, the LSR velocity of the He66q@ line appears to be —15.2 + 4.3 km | whereas the LSR velocity of the He41a line reported by Thum et (1992) is 231 4 8 km |."," In our unconstrained fit, the LSR velocity of the $\alpha$ line appears to be –15.2 $\pm$ 4.3 km $^{-1}$ whereas the LSR velocity of the $\alpha$ line reported by Thum et (1992) is –31 $\pm$ 8 km $^{-1}$ ."
 Thus. on average. the Helium lines appear to peak at Vj; -- —20 km |. similar to the velocity of the thermal em lines of hydrogen.," Thus, on average, the Helium lines appear to peak at $V_{lsr}$ $\sim$ –20 km $^{-1}$, similar to the velocity of the thermal cm lines of hydrogen."
 This strongly suggests that the helium lines originate in the same gas às the thermal em hydrogen lines., This strongly suggests that the helium lines originate in the same gas as the thermal cm hydrogen lines.
" The H66a line detected here peaks at a velocity (—7.0 3: 0.7 km ! — Section 2). intermediate between the +10 km ! masing mm lines, and the 220 km ' thermal em lines."," The $\alpha$ line detected here peaks at a velocity (–7.0 $\pm$ 0.7 km $^{-1}$ – Section 2), intermediate between the $+$ 10 km $^{-1}$ masing mm lines, and the –20 km $^{-1}$ thermal cm lines."
 A plausible (albeit somewhat fioc) explanation is that the H66q line is largely dominated by a thermal component at 20 km ! but also contains a moderate masing component around +10 kms |., A plausible (albeit somewhat ) explanation is that the $\alpha$ line is largely dominated by a thermal component at –20 km $^{-1}$ but also contains a moderate masing component around $+$ 10 km $^{-1}$.
 The reversed situation might occur with the H41« line at 92 GHz reported by Thum et ((1992) which peaks at 21.02: 0.9 km |., The reversed situation might occur with the $\alpha$ line at 92 GHz reported by Thum et (1992) which peaks at $+$ 1.0 $\pm$ 0.9 km $^{-1}$.
 In that second case. the emission might be dominated by the masing line at +10kms ! but with a moderate thermal contribution.," In that second case, the emission might be dominated by the masing line at $+$ 10 km $^{-1}$ but with a moderate thermal contribution."
" It would be interesting to analyze further the relative kinematics of the hydrogen and helium lines, for instance by obtaining high resolution EVLA observations of the 53@ and όσα lines at 0.7 and 1.3 em, respectively."," It would be interesting to analyze further the relative kinematics of the hydrogen and helium lines, for instance by obtaining high resolution EVLA observations of the $\alpha$ and $\alpha$ lines at 0.7 and 1.3 cm, respectively."
 We have presented new EVLA observations of the 22.3 GHz continuum and the H66a line emissions toward the well-studied Galactic emission-line star MWC 349A. The continuum flux density (411 + 41 mJy) is in good agreement with previous determinations., We have presented new EVLA observations of the 22.3 GHz continuum and the $\alpha$ line emissions toward the well-studied Galactic emission-line star MWC 349A. The continuum flux density (411 $\pm$ 41 mJy) is in good agreement with previous determinations.
" The intensity of the H66a line (25 mJy) and the line-to-continuum flux density ratio (5%)), on the other hand, are those expected for local thermodynamic equilibrium."," The intensity of the $\alpha$ line (25 mJy) and the line-to-continuum flux density ratio ), on the other hand, are those expected for local thermodynamic equilibrium."
" Thisshows that the H66q@ line excitation is largely thermal, and that the line is not strongly masing as had been proposed by"," Thisshows that the $\alpha$ line excitation is largely thermal, and that the line is not strongly masing as had been proposed by"
"If has dual AGN separated by 1.9 kpc that are the result of a galaxy merger, we might hzexpect the two AGN to be coincident with two stellar components that are the remnants of the progenitor galaxies in the merger.","If has dual AGN separated by 1.9 $h^{-1}_{70}$ kpc that are the result of a galaxy merger, we might expect the two AGN to be coincident with two stellar components that are the remnants of the progenitor galaxies in the merger."
" In fact, was one of 50 SDSS galaxies with double-peaked lines that was targeted for Keck II laser guide-star adaptive-optics (LGSAO) observations in Fuetal.(2010),, which found that 16 of these galaxies exhibited double stellar components with separations 0.6 — 12 kpc (or 0.2 — 3""), suggestive of merging systems."," In fact, was one of 50 SDSS galaxies with double-peaked lines that was targeted for Keck II laser guide-star adaptive-optics (LGSAO) observations in \cite{FU10.1}, which found that 16 of these galaxies exhibited double stellar components with separations 0.6 – 12 $h^{-1}_{70}$ kpc (or 0.2 – $^{\prime\prime}$ ), suggestive of merging systems."
" hzWhile Fuetal.(2010) do not show the image ofJ171544.054-600835.7,, they report that the Keck/LGSAO K'-band image reveals only a single component with K'—14.8 and classify the galaxy as “isolated”."," While \cite{FU10.1} do not show the image of, they report that the Keck/LGSAO $K'$ -band image reveals only a single component with $K'=14.8$ and classify the galaxy as “isolated""."
" The PSF FWHMs for their observations were 0""065 to 0/130, suggesting that may have no substructure at 2071 visible in these K'-band observations."," The PSF FWHMs for their observations were $0\farcs065$ to $0\farcs130$, suggesting that may have no substructure at $\simgt0\farcs1$ visible in these $K'$ -band observations."
" Based on its SDSS has a rest-frame photometry,u—r color of 2.62 and an absolute r-band magnitude of -22.0, placing it on the red sequence of SDSS galaxies (Baldry 2004).."," Based on its SDSS photometry, has a rest-frame $u-r$ color of 2.62 and an absolute $r$ -band magnitude of -22.0, placing it on the red sequence of SDSS galaxies \citep{BA04.3}."
 The SDSS image of the galaxy shows no signatures of galaxy interaction (Figure 3))., The SDSS image of the galaxy shows no signatures of galaxy interaction (Figure \ref{fig:sdss}) ).
 Here we explore the physical mechanisms that could explain the observations of double AGN emission components and X-ray sources in J171544., Here we explore the physical mechanisms that could explain the observations of double AGN emission components and X-ray sources in .
"05+600835.7.. The sources’ high X-ray luminosities lead us to consider the possibility that they are ultra-luminous sources (ULXs), which are variable off-nuclear X-ray sources."," The sources' high X-ray luminosities lead us to consider the possibility that they are ultra-luminous X-ray sources (ULXs), which are variable off-nuclear X-ray sources."
 Some ULXs are also candidate intermediate mass black holes Kaaretetal.2003;Farrell 2009)).," Some ULXs are also candidate intermediate mass black holes (e.g., \citealt{KA03.4, FA09.1}) )."
" However, estimates(e.g., of the black hole mass from the optical spectra place in the supermassive black hole regime (Fu et al."," However, estimates of the black hole mass from the optical spectra place in the supermassive black hole regime (Fu et al."
 2010)., 2010).
" Further, the measured fluxes and luminosities are well above those typically measured in ULXs (e.g., Porter2010;Csehetal.2011))."," Further, the measured fluxes and luminosities are well above those typically measured in ULXs (e.g., \citealt{PO10.1, CS11.1}) )."
" Another possibility is that the galaxy hosts dual AGN that are the result of a triple SMBH interaction, where a gravitational slingshot effect etal.1974) ejected the least massive SMBH(Saslaw (corresponding to the southern AGN) while the remaining two SMBHs merged (producing the northern AGN)."," Another possibility is that the galaxy hosts dual AGN that are the result of a triple SMBH interaction, where a gravitational slingshot effect \citep{SA74.1} ejected the least massive SMBH (corresponding to the southern AGN) while the remaining two SMBHs merged (producing the northern AGN)."
 The remaining stellar component associated with the southern AGN could be too faint to appear in the Keck/LGSAO observations., The remaining stellar component associated with the southern AGN could be too faint to appear in the Keck/LGSAO observations.
" However, the optical observations suggest that both AGN have associated narrow-line regions and it is unclear how the ejected SMBH would maintain its narrow-line region."," However, the optical observations suggest that both AGN have associated narrow-line regions and it is unclear how the ejected SMBH would maintain its narrow-line region."
" We note also that if there is only a single source visible in the image, a second stellar component could beKeck/LGSAO either obscured or too faint to be within the detection threshold of the Keck/LGSAO observation."," We note also that if there is only a single source visible in the Keck/LGSAO image, a second stellar component could be either obscured or too faint to be within the detection threshold of the Keck/LGSAO observation."
" If there are two AGN with associated stellar components, the stellar component accompanying the southern AGN is more likely to be obscured since it is harder and consequently more absorbed than the northern AGN."," If there are two AGN with associated stellar components, the stellar component accompanying the southern AGN is more likely to be obscured since it is harder and consequently more absorbed than the northern AGN."
" If the southern AGN is obscured and the northern AGN is not, the overall extinction for the system could be skewed towards the low value measured in 2.3.."," If the southern AGN is obscured and the northern AGN is not, the overall extinction for the system could be skewed towards the low value measured in \ref{chandra}."
" Another explanation for our observations is that the galaxy hosts AGN jets that produce both and X-rays from a combination of photoionization[OΠΠ from the AGN and collisional ionization from the jets (e.g., Kraemeretal.2009;Bianchi 2010))."," Another explanation for our observations is that the galaxy hosts AGN jets that produce both and X-rays from a combination of photoionization from the AGN and collisional ionization from the jets (e.g., \citealt{ KR09.1, BI10.1}) )."
" For this scenario to explain our observations, either the AGN is completely obscured and only the jets are visible or one of the sources in our observations is the AGN while the other is the foreground jet and the background jet is obscured."," For this scenario to explain our observations, either the AGN is completely obscured and only the jets are visible or one of the sources in our observations is the AGN while the other is the foreground jet and the background jet is obscured."
" Both scenarios rely on significant obscuration in part of the galaxy, but this could be consistent with the low column density we measured if the rest of the galaxy is relatively unobscured."," Both scenarios rely on significant obscuration in part of the galaxy, but this could be consistent with the low column density we measured if the rest of the galaxy is relatively unobscured."
" However, the jet scenario typically produces a bright core and a much fainter jet, whereas our observations show two sources that differ by only a factor of 2 in 2-10 keV luminosities."," However, the jet scenario typically produces a bright core and a much fainter jet, whereas our observations show two sources that differ by only a factor of 2 in 2–10 keV luminosities."
 The observations may also be explained by dual AGN that are Compton thick., The observations may also be explained by dual AGN that are Compton thick.
" The X-ray spectra alone -- if confirmed — exclude Compton-intermediate AGN, where the absorption would correspond to a column of ~1033—104 cm?, as there the observed X-ray flux would be dominated by partially (photoelectrically) absorbed continuum that is detectable as a hard X-ray spectrum."," The X-ray spectra alone -- if confirmed – exclude Compton-intermediate AGN, where the absorption would correspond to a column of $\sim 10^{22} - 10^{24}$ $^{-2}$, as there the observed X-ray flux would be dominated by partially (photoelectrically) absorbed continuum that is detectable as a hard X-ray spectrum."
" Instead the data suggest that both sources are either unabsorbed or the absorption is severe, essentially resulting in a Compton-thick spectrum."," Instead the data suggest that both sources are either unabsorbed or the absorption is severe, essentially resulting in a Compton-thick spectrum."
" The optical spectra seem to exclude classical, unabsorbed Type 1 AGN, so we are left with a Compton-thick scenario, with Trhomson Of at least a few (column >1035 cm~?)."," The optical spectra seem to exclude classical, unabsorbed Type 1 AGN, so we are left with a Compton-thick scenario, with $\tau_{\rm Thomson}$ of at least a few (column $> 10^{25}$ $^{-2}$ )."
" There, not only the primary nuclear soft X-ray flux is photoelectrically absorbed, but even the hard X-rays are suppressed by Compton opacity, and we detect only primary soft X-rays scattered back to our line of sight, as is the case in, e.g., NGC 1068 and other Compton- AGN."," There, not only the primary nuclear soft X-ray flux is photoelectrically absorbed, but even the hard X-rays are suppressed by Compton opacity, and we detect only primary soft X-rays scattered back to our line of sight, as is the case in, e.g., NGC 1068 and other Compton-thick AGN."
" The measured 2-10 keV luminosities for thenorthern and southern components are within the range of values measured for Compton-thick AGN (e.g.,"," The measured 2–10 keV luminosities for thenorthern and southern components are within the range of values measured for Compton-thick AGN (e.g.,"
lack dark matter halos. we will use the FAL to coustrain thestellar mass-to-light ratio. TY... as a function of cluster parameters such as man sequence turn-off age aud color.,"lack dark matter halos, we will use the FM to constrain the mass-to-light ratio, $\Upsilon_*$, as a function of cluster parameters such as main sequence turn-off age and color."
 We will then compare these measures to values calculated using stellar population models as a test of those models., We will then compare these measures to values calculated using stellar population models as a test of those models.
 Iu ΜΑΝ. by considering star clusters and UCDs. we test whether the FAL formalisin extends to the mass. stellaa-douunated extrem of eravitatioually-bound stellar systems in 833.," In summary, by considering star clusters and UCDs, we test whether the FM formalism extends to the low-mass, stellar-dominated extremum of gravitationally-bound stellar systems in 3."
 We find that star clusters do lie ou the FAL but with apparcutly ereater scatter than observed among the ealaxics., We find that star clusters do lie on the FM but with apparently greater scatter than observed among the galaxies.
 We then explore both observational aud plivsical sources of that scatter., We then explore both observational and physical sources of that scatter.
" We find that there is a correlation between cluster age and deviation from the FM. in the seuse expected for variations in Y, due to the evolution of the stellar »pulatiou. but in quantitative disagreement with the xedictious frou stellar population models."," We find that there is a correlation between cluster age and deviation from the FM, in the sense expected for variations in $\Upsilon_e$ due to the evolution of the stellar population, but in quantitative disagreement with the predictions from stellar population models."
" We explore lis behavior aud preseut enmipirical derivations of the relationships between Y,. age. and BoV in sll."," We explore this behavior and present empirical derivations of the relationships between $\Upsilon_e$, age, and $B-V$ in 4."
 We find that the cominaut source of scatter iu the current data set is observational. arising from the uncertainties iu he cluster velocity dispersions.," We find that the dominant source of scatter in the current data set is observational, arising from the uncertainties in the cluster velocity dispersions."
 We use the FAL to make xedictious for the velocity dispersions of those clusters without measured dispersions., We use the FM to make predictions for the velocity dispersions of those clusters without measured dispersions.
 In 855 we stmunarize our &udines aud discuss he implications., In 5 we summarize our findings and discuss the implications.
 In an Appendix we revisit previous clainis that are in apparent conflict with our results (Forbesοal.2008:Tollerudet2010) aud xovide a resolution.," In an Appendix we revisit previous claims that are in apparent conflict with our results \citep{forbes, tollerud} and provide a resolution."
" We draw the measurements of structural parameters. velocity dispersious.modeled stellar population mass-o-light ratios (ον ρα). ages. colors (B V» aud uetallicities (Ρο ΙΓ frou, the compilation by MeLanellin&vauderMarel(2005) of Local Group star clusters."," We draw the measurements of structural parameters, velocity dispersions, stellar population mass-to-light ratios $\Upsilon_{*,mod}$ ), ages, colors $B-V$ ), and metallicities $\langle Fe/H \rangle$ ) from the compilation by \cite{clusters} of Local Group star clusters."
 That sample consists of 153) spatially resolved clusters from a range of nearby galaxies., That sample consists of 153 spatially resolved clusters from a range of nearby galaxies.
 Within hat szuuple there is a subset of 57 clusters for which they ave also compiled velocity dispersion nieasurenieuts., Within that sample there is a subset of 57 clusters for which they have also compiled velocity dispersion measurements.
 As such. it inchides clusters of all ages. a wide range of uctallicities. aud the full rauge of euvironimneuts found in the Local Group.," As such, it includes clusters of all ages, a wide range of metallicities, and the full range of environments found in the Local Group."
" The data for stellar svstenis ranging from dwarf spheroidals to galaxy cluster spheroids (CSphlstodistiu-etal.2008) are draw from Zaritskyetal.(2008) aud for ultra-compact cliwarts from Mieskeetal.(2008)... selecting ouly objects with estimated masses >5&ΠΛΗ, to distinguish the UCDs from the stellar clusters in their saluple."," The data for stellar systems ranging from dwarf spheroidals to galaxy cluster spheroids \cite[CSphs to distinguish them from stellar clusters throughout, see][]{zzg} are drawn from \cite{zzg} and for ultra-compact dwarfs from \cite{mieske}, selecting only objects with estimated masses $> 5 \times10^6 M_\odot$ to distinguish the UCDs from the stellar clusters in their sample."
 To define the manifold. we use only the spheroidal ealaxies and CSpls from Zaritskyctal.(2008) as our conparison sample to minimize poteutial problems arising frou composite stellar populations and to Init ourselves to svstenis supported by velocity. dispersion rather than rotation.," To define the manifold, we use only the spheroidal galaxies and CSphs from \cite{zzg} as our comparison sample to minimize potential problems arising from composite stellar populations and to limit ourselves to systems supported by velocity dispersion rather than rotation."
" In the vast majority of local ealaxies. either e, or 6 dominates. aud therefore we have not vet truly tested whether V?=0.502|a? is preferable to other parameterizations. such as V?=mas|0.502.07]. or whether 0.5 is the optimal coefficieut for the e, term and such paraueterizatious have been used elsewhere (Bursteinetal.1997:IKassinal2007:Cov-inetonetal."," In the vast majority of local galaxies, either $v_r$ or $\sigma$ dominates, and therefore we have not yet truly tested whether $V^2 \equiv 0.5v_r^2 + \sigma^2$ is preferable to other parameterizations, such as $V ^2\equiv {\rm max}[0.5v_r^2,\sigma^2]$, or whether 0.5 is the optimal coefficient for the $v_r$ term and such parameterizations have been used elsewhere \citep{burstein, kassin, covington}."
2010).. Here. we avoid questions regarding the incorporation of rotation supported svstenus in the FAL formalisin bv only analyzing svstenis m which σ doniünates.," Here, we avoid questions regarding the incorporation of rotation supported systems in the FM formalism by only analyzing systems in which $\sigma$ dominates."
 The low relative rotation of Milkv Way clusters is inferred from their low cllipticitics (Freeman&NorrisH981)., The low relative rotation of Milky Way clusters is inferred from their low ellipticities \citep{freeman}.
. This aremmeut is weaker for other cluster opulatious. such as those iu the Magellanic Clouds. where larger cllipticitics are sometimes found.," This argument is weaker for other cluster populations, such as those in the Magellanic Clouds, where larger ellipticities are sometimes found."
 However. even in the Clouds. the cluster ellipticities are generally ess than 0.5 (IDll&Zaritsky2006).. similar to the ellipticity of one of the most extreme MW. clusters. uw Cen. which has e/o~0.5 (Reijusetal.20063.," However, even in the Clouds, the cluster ellipticities are generally less than 0.5 \citep{hill}, similar to the ellipticity of one of the most extreme MW clusters, $\omega$ Cen, which has $v/\sigma \sim 0.5$ \citep{omegacen}."
. Therefore. or the remainder of this study. we adopt V—o.," Therefore, for the remainder of this study, we adopt $V\equiv \sigma$."
 Using oulv spheroidal galaxies further simplifics our work bv removing svstenis with ougonmeg or recent star formation. or Which Y. iav have a dramatic dependence on mea stellar age.," Using only spheroidal galaxies further simplifies our work by removing systems with ongoing or recent star formation, for which $\Upsilon_e$ may have a dramatic dependence on mean stellar age."
 The final relevant technical issue with the galaxy suuple is the heterogeneous nature of the source saluples and Low one should compare it to the cluster saluple., The final relevant technical issue with the galaxy sample is the heterogeneous nature of the source samples and how one should compare it to the cluster sample.
 In particular. the cluster sample coutains V- baud photometry. while the galaxy sample coutais a range of photometry frou V. to [-bauds.," In particular, the cluster sample contains $V$ -band photometry, while the galaxy sample contains a range of photometry from $V$ to $I$ -bands."
" Equation (1) is band-independent iu that Z. aud Y, for a particular objectneed to be in the same baud. but that baud cau be different for differeut objects."," Equation (1) is band-independent in that $I_e$ and $\Upsilon_e$ for a particular objectneed to be in the same band, but that band can be different for different objects."
 IHTowever. the manifold that we fit to describe Y. Yη. is baud-specifBe and has been derived using the heterogeneous galaxy sample. corrected to the 7-baud.," However, the manifold that we fit to describe $\Upsilon_e$ , $\Upsilon_{e,fit}$, is band-specific and has been derived using the heterogeneous galaxy sample, corrected to the $I$ -band."
" The values of Jf, used to determine Y.gu ave in solar units. so the filter dependence arises from the difference ia colors between the ealaxy aud the Sun when converting £, to ων"," The values of $I_e$ used to determine $\Upsilon_{e,fit}$ are in solar units, so the filter dependence arises from the difference in colors between the galaxy and the Sun when converting $L_e$ to $I_e$."
 In effect we are assundue solar colors for the galaxies. although any uniform color difference among all galaxies is absorbed iuto the calibration of € in Equation (1).," In effect we are assuming solar colors for the galaxies, although any uniform color difference among all galaxies is absorbed into the calibration of $C$ in Equation (1)."
 The remaining concerns are color differences that vary across the sample and band-arelated differeuces iu rj., The remaining concerns are color differences that vary across the sample and band-related differences in $r_e$.
 If these exist. then they are inappropriately incorporated iuto our fit for Y...," If these exist, then they are inappropriately incorporated into our fit for $\Upsilon_e$."
 Oue clear path to progress is obtaining a single. uniforii data set for the further study of the FAL," One clear path to progress is obtaining a single, uniform data set for the further study of the FM."
" Hosvever. in the interim. we proceed with the motley sample available aud caution that for svsteius with colors uch ciffercut than solar colors there will be a vet unknown color-correction to Y, ri."," However, in the interim, we proceed with the motley sample available and caution that for systems with colors much different than solar colors there will be a yet unknown color-correction to $\Upsilon_{e,fit}$ ."
 The eipiricallv-coufiriied s1nall scatter amoug ealaxies. even when including star forming galaxies (Zaritskyctal.2008). sugeests that this effect will be neeligible for a sample consisting only of spheroidal ealaxies. but could be a factor among the star clusters. which span a wider age rauge.," The empirically-confirmed small scatter among galaxies, even when including star forming galaxies \citep{zzg}, suggests that this effect will be negligible for a sample consisting only of spheroidal galaxies, but could be a factor among the star clusters, which span a wider age range."
 We revaluate Ἐνεπ using only those galaxies. the spheroids. from Ζανctal.(2008) that are σ dominated. iucliding galaxy cluster spheroids (CSph).," We revaluate $\Upsilon_{e,fit}$ using only those galaxies, the spheroids, from \cite{zzg}
 that are $\sigma$ dominated, including galaxy cluster spheroids (CSph)."
 Iu doing so. we lave also reevaluated the constant C in Equation (1) using the Cappellarietal.(2007) salple. for which they have full dvwnamical modeling fit to 2-dinieusional spectral data for spheroidal galaxies. and find €= 0.75.," In doing so, we have also reevaluated the constant $C$ in Equation (1) using the \cite{cappellari} sample, for which they have full dynamical modeling fit to 2-dimensional spectral data for spheroidal galaxies, and find $C = 0.75$ ."
 In Figured. we show where the 57 globularclusters with measured velocity dispersions and the UCDs with Af>5&LOCAL. frou Mieskeet fall when using this fitting function.," In Figure\ref{fig:fit} we show where the 57 globularclusters with measured velocity dispersions and the UCDs with $M > 5\times 10^6 M_\odot$ from \cite{mieske}
 fall when using this fitting function, ."
" CCDs. Iu απο, we show with small poiuts the range of"," In addition, we show with small points the range of"
procedures.,procedures.
 The nuclear offsets deteruüned w fitting ellipses to the liebt distribution were perfectly jornial (top panels of Fie.2))., The nuclear offsets determined by fitting ellipses to the light distribution were perfectly normal (top panels of \ref{fig2}) ).
 The first sjeus of unusual behaviour came from the ellipticitv aud position angle variations of the ellipse fits., The first signs of unusual behaviour came from the ellipticity and position angle variations of the ellipse fits.
 The coherent wigeles at smaller radii (roc 30%) suesested interesting. but low level structure. which could be seen as a spiral pattern iu he contour maps.," The coherent wiggles at smaller radii $r<30\arcsec$ ) suggested interesting, but low level structure, which could be seen as a spiral pattern in the contour maps."
 Contour maps. aud iu particular the smoothed contour laps reconstructed from the ellipse fits are powerful tools for revealing faint structure. but are uot inunediatolv suitable for quantitative analvsis ofthe light distribution.," Contour maps, and in particular the smoothed contour maps reconstructed from the ellipse fits are powerful tools for revealing faint structure, but are not immediately suitable for quantitative analysis of the light distribution."
" The presence of a smooth spiral indicates that we are dealing with a disk or a disk ορούσα, in a spheroidal niass distribution.", The presence of a smooth spiral indicates that we are dealing with a disk or a disk embedded in a spheroidal mass distribution.
 The iuost straight-forward analysis consists of guessing the orientation of the disk andl expanding the deprojected elt distribution iu à Fourier series in the azimuthal anele 0: The amplitude of the two-armed spiral. Γον is quite sensitive to chauges iu inclination. and less so to the position angle: a wrong inclination will produce modulations in the amplitude.," The most straight-forward analysis consists of guessing the orientation of the disk and expanding the deprojected light distribution in a Fourier series in the azimuthal angle $\theta$: The amplitude of the two-armed spiral, $I_2 (r)$, is quite sensitive to changes in inclination, and less so to the position angle; a wrong inclination will produce modulations in the amplitude."
 An inclination of 2572 (which corresponds to the ellipticity e= 1.095). aud the position angle of 8275 produced the zn00thest tivo-anned conrponeut.," An inclination of $25\fdg 2$ (which corresponds to the ellipticity $e=0.095$ ), and the position angle of $82\fdg 5$ produced the smoothest two-armed component."
 The amplitude aud phaseof this spiral is shown in Fig. 3.., The amplitude and phaseof this spiral is shown in Fig. \ref{fig3}.
 The fractional amplitude of 3 Is extremely low., The fractional amplitude of $3-4\%$ is extremely low.
" The one-arined. or cos0 terms become important close to the center (« 5"")."," The one-armed, or $\cos \theta$ terms become important close to the center $ < 5\arcsec$ )."
" In the interval 5""<r<30” the pliase Oeste) is well approximated by a straight line.", In the interval $ 5\arcsec < r < 30\arcsec$ the phase $\theta_2 (r)$ is well approximated by a straight line.
 Such a phase variation corresponds to a two-armed logarithiuic spiral inclined at 1271 to a circle., Such a phase variation corresponds to a two-armed logarithmic spiral inclined at $12 \fdg 1$ to a circle.
 The aneular winding of the arms is 130°, The angular winding of the arms is $430^\circ$ .
 The cold dark matter (CDM) paradigm of structure formation is successful at recovering the basic skeletal structure of the universe — the large-scale distribution of galaxies (Springel et al., The cold dark matter (CDM) paradigm of structure formation is successful at recovering the basic skeletal structure of the universe – the large-scale distribution of galaxies (Springel et al.
 2006)., 2006).
 However. the agreement between theory and observation ts less secure when this model is applied to galactic (and sub-galactic) scales.," However, the agreement between theory and observation is less secure when this model is applied to galactic (and sub-galactic) scales."
 While the existence of dark matter halos in galaxies was observationally inferred in the 197078 (Rubin et al., While the existence of dark matter halos in galaxies was observationally inferred in the 1970's (Rubin et al.
 1977; Bosma 1978). there are few observational probes that can be used to infer the details of the distribution of dark matter.," 1977; Bosma 1978), there are few observational probes that can be used to infer the details of the distribution of dark matter."
 Simulations have not yet been able to resolve the mitigating effects of gas cooling (Gnedin et al., Simulations have not yet been able to resolve the mitigating effects of gas cooling (Gnedin et al.
 2004) versus outflows (Governato et al., 2004) versus outflows (Governato et al.
 2010). which can act to increase (decrease) the distribution of dark matter in galaxies.," 2010), which can act to increase (decrease) the distribution of dark matter in galaxies."
 In the coming decades. the CDM paradigm will be increasingly vetted against detailed observations of the innards of galaxies that will delve even more deeply into galaxy evolution.," In the coming decades, the CDM paradigm will be increasingly vetted against detailed observations of the innards of galaxies that will delve even more deeply into galaxy evolution."
 Navarro. Frenk White (1996; 1997; NEW) found that dark matter halos formed through dissipationless hierarchical clustering have an universal density profile.," Navarro, Frenk White (1996; 1997; NFW) found that dark matter halos formed through dissipationless hierarchical clustering have an universal density profile."
 Due to the absence of scale in this heirarchical structure formation scenario. dark matter haloes are scaled versions of each other. with the total mass being the scaling parameter.," Due to the absence of scale in this heirarchical structure formation scenario, dark matter haloes are scaled versions of each other, with the total mass being the scaling parameter."
" The NFW density profile is given by: where p, is the critical density for closure of the universe. and à, is a characteristic overdensity for the halo."," The NFW density profile is given by: where $\rho_{c}$ is the critical density for closure of the universe, and $\delta_{c}$ is a characteristic overdensity for the halo."
" The scale radius. R,Λοο is a characteristic radius. and ο is the concentration parameter that relates this characteristic radius and Roo. which is the radius at which the mean enclosed dark matter density is 200 times the critical density."," The scale radius, $R_{s}=R_{200}/c$ is a characteristic radius, and $c$ is the concentration parameter that relates this characteristic radius and $R_{200}$, which is the radius at which the mean enclosed dark matter density is 200 times the critical density."
 The characteristic overdensity of the halo. 4.. is simply a function of the concentration parameter c (NEW).," The characteristic overdensity of the halo, $\delta_{c}$, is simply a function of the concentration parameter $c$ (NFW)."
 The NFW profile differs from the Hernquist (1990) profile in its asympotie behavior. scaling as 77 rather than 77 for |.," The NFW profile differs from the Hernquist (1990) profile in its asympotic behavior, scaling as $r^{-3}$ rather than $r^{-4}$ for $r/r_{s} \gg 1$ ."
 The scale radius of the dark matter halo along with the concentration parameter specify the density distribution for a given halo mass in the NEW formalism., The scale radius of the dark matter halo along with the concentration parameter specify the density distribution for a given halo mass in the NFW formalism.
 Currently. these parameters are prescribed from large cosmological N-body simulations (Bullock et al.," Currently, these parameters are prescribed from large cosmological N-body simulations (Bullock et al."
 2001: Maceio et al., 2001; Maccio et al.
 2008)., 2008).
 It ts not presently clear how we can determine these values for individual galaxies., It is not presently clear how we can determine these values for individual galaxies.
 What we seek to do here tis to develop an independent. observationally motivated probe of the scale radius of dark matter halos. and apply it to the well-known Whirlpool Galaxy (M51) to infer its scale radius.," What we seek to do here is to develop an independent, observationally motivated probe of the scale radius of dark matter halos, and apply it to the well-known Whirlpool Galaxy (M51) to infer its scale radius."
 The density switches its behavior at the scale radius. from 7! for r< to 77 for r>>Ry. and passes through the transitional ο region for r~Αι.," The density switches its behavior at the scale radius, from $r^{-1}$ for $r \ll R_{s}$ to $r^{-3}$ for $r \gg R_{s}$, and passes through the transitional $r^{-2}$ region for $r \sim R_{s}$."
 Thus. the scale radius of dark matter halos is a critical parameter for specifying the density distribution of dark matter in galaxies. and therefore a fundamental parameter for modeling galaxies.," Thus, the scale radius of dark matter halos is a critical parameter for specifying the density distribution of dark matter in galaxies, and therefore a fundamental parameter for modeling galaxies."
 The extended atomic hydrogen (HI) disks of galaxies provide an unique probe of galaxy evolution., The extended atomic hydrogen (HI) disks of galaxies provide an unique probe of galaxy evolution.
 They are ideal tracers of tidal interactions with satellites and. the galactic gravitational potential well., They are ideal tracers of tidal interactions with satellites and the galactic gravitational potential well.
 We recently developed a novel method whereby one can infer the mass. and relative position (in radius and azimuth) of satellites from analysis of observed disturbances in outer gas disks. without requiring knowledge of their optical light (Chakrabarti Blitz 2009. henceforth CBO9; Chakrabarti Blitz 2011. henceforth CBI1: Chakrabarti. Bigiel. Chang Blitz 2011. henceforth CBCB: Chang Chakrabarti 2011. henceforth CCI1).," We recently developed a novel method whereby one can infer the mass, and relative position (in radius and azimuth) of satellites from analysis of observed disturbances in outer gas disks, without requiring knowledge of their optical light (Chakrabarti Blitz 2009, henceforth CB09; Chakrabarti Blitz 2011, henceforth CB11; Chakrabarti, Bigiel, Chang Blitz 2011, henceforth CBCB; Chang Chakrabarti 2011, henceforth CC11)."
 We applied this method to M51 and inferred that its satellite has amass one-third that of the primary galaxy. with a pericentric approach distance of kpe.," We applied this method to M51 and inferred that its satellite has a mass one-third that of the primary galaxy, with a pericentric approach distance of $~\rm kpc$."
 We found these estimates to be corroborated by observations (Smith et al., We found these estimates to be corroborated by observations (Smith et al.
 1990) and recent simulation studies (Salo Laurikainen 2000: Dobbs et al., 1990) and recent simulation studies (Salo Laurikainen 2000; Dobbs et al.
 2010)., 2010).
 Moreover. at the time when our simulations achieve the best-fit to the HI data. the azimuth of the satellite in the simulations agrees closely with its observed location.," Moreover, at the time when our simulations achieve the best-fit to the HI data, the azimuth of the satellite in the simulations agrees closely with its observed location."
 CBCB note that the derivation of these numbers Is uncertain at the factor of two level due to variations in the initial conditions of the simulated M51 galaxy. orbital inclination and orbital velocity of the satellite.," CBCB note that the derivation of these numbers is uncertain at the factor of two level due to variations in the initial conditions of the simulated M51 galaxy, orbital inclination and orbital velocity of the satellite."
" We call this method ""Tidal Analysis”."," We call this method ""Tidal Analysis""."
 We frame the problem here in the following way — for galaxies like M51. for which we have demonstrated that our Tidal Analysis method works. can we determine the scale radius of the dark matter halo of M51?," We frame the problem here in the following way – for galaxies like M51, for which we have demonstrated that our Tidal Analysis method works, can we determine the scale radius of the dark matter halo of M51?"
 We take the satellite mass and pericentric distance from our earlier studies as an input., We take the satellite mass and pericentric distance from our earlier studies as an input.
 It is worth noting that such a procedure has viable and immediate applicability., It is worth noting that such a procedure has viable and immediate applicability.
 The THINGS survey produced, The THINGS survey produced
eiven period.,given period.
 The LAV points for field SRWs are in agreement with the SRMVs of similar period with low mass-loss., The LW points for field SRVs are in agreement with the SRVs of similar period with low mass-loss.
 The Miras form a well-defined sequence which. however. starts below the average (lfAvsjy of the SRVs at the same period (~1s0d).," The Miras form a well-defined sequence which, however, starts below the average $(H-K_S)_0$ of the SRVs at the same period $\sim$ 180d)."
 “Phe HE relation appears to stradcdle the LW field Aliras satisfactorily. though the scatter of the latter is rathor large.," The I relation appears to straddle the LW field Miras satisfactorily, though the scatter of the latter is rather large."
 The (JAvsjo index. like the others. increases steacilv with period. for the SRWs. especially those with strong mass-Ioss [rom 7] 15] photometry.," The $(J-K_S)_0$ index, like the others, increases steadily with period for the SRVs, especially those with strong mass-loss from [7] –[15] photometry."
 The redder colours of the losing objects are even more obvious., The redder colours of the mass-losing objects are even more obvious.
 A version of this diagram. based on transformed sem mags. was presented by lard ct al. (," A version of this diagram, based on transformed $\mu$ m mags, was presented by Alard et al. ("
2001).,2001).
 Ht is given here with As mags directly from 2NLASS., It is given here with $K_S$ mags directly from 2MASS.
 The conclusions of Alarel et al., The conclusions of Alard et al.
 remain unchanged., remain unchanged.
 Absolute A magnitudes. of SRVs with periods are available for only a few other samples., Absolute $K$ magnitudes of SRVs with periods are available for only a few other samples.
 Fhey include nearby objects with parallaxes from. the Hipparcos. Catalogue (Bedding Zijlstra. 1998) and those in the Large Magellanie Cloud (Wood. 2000). with periods. also. clerivec from. ALACIIO.," They include nearby objects with parallaxes from the Hipparcos Catalogue (Bedding Zijlstra, 1998) and those in the Large Magellanic Cloud (Wood, 2000) with periods also derived from MACHO."
 Whitelock (1986) showed that SRVs in low-metallicity galactic elobular clusters exhibit a P-L sequence that falls about 0.5 mag below that of Bedding Zijlstra., Whitelock (1986) showed that SRVs in low-metallicity galactic globular clusters exhibit a P-L sequence that falls about 0.8 mag below that of Bedding Zijlstra.
 1n the Large. Magellanic Cloud the Miras. the SR\s and the small-amplitude SIVs seem to form distinct parallel sequences C. D. X ete (see 99) which have been identified by Wood (2000) as pulsators in the fundamental. first. and," In the Large Magellanic Cloud the Miras, the SRVs and the small-amplitude SRVs seem to form distinct parallel sequences C, B, A etc (see 9) which have been identified by Wood (2000) as pulsators in the fundamental, first and"
(see Tables 1 and 2)) which does not agree with the rise of a flux tube in a stratified atmosphere.,(see Tables \ref{tab:1} and \ref{tab:2}) ) which does not agree with the rise of a flux tube in a stratified atmosphere.
" For instance, ? obtain a final rise velocity ~5 times larger than the rms-velocity."," For instance, \cite{fan+etal_03} obtain a final rise velocity $\approx5$ times larger than the rms-velocity."
" We should point out that in the simulations here, the strong shear increases U;ms by a factor of two or even more."," We should point out that in the simulations here, the strong shear increases $\urms$ by a factor of two or even more."
" If we compare the rise velocity of the magnetic field with the rms-velocity of a non-shearing case (Run S00), we find that wy is slightly larger."," If we compare the rise velocity of the magnetic field with the rms-velocity of a non-shearing case (Run S00), we find that $u_b$ is slightly larger."
" Magnetic pumping effects, which are evaluated below, may also play a role in braking the magnetic flux and in defining its final velocity."," Magnetic pumping effects, which are evaluated below, may also play a role in braking the magnetic flux and in defining its final velocity."
" The results mentioned above do not fully agree with those found by ?,, where a toroidal magnetic layer is generated from a purely vertical field through an imposed radial shear layer."," The results mentioned above do not fully agree with those found by \cite{vasil+etal_08}, where a toroidal magnetic layer is generated from a purely vertical field through an imposed radial shear layer."
" Although their stratification is smaller than in our case, the buoyancy instability is hard to excite in their simulations and the buoyancy events are slowed down rather quickly."," Although their stratification is smaller than in our case, the buoyancy instability is hard to excite in their simulations and the buoyancy events are slowed down rather quickly."
" The lack of a dynamo mechanism, able to sustain the magnetic field, is maybe the reason of its rapid diffusion."," The lack of a dynamo mechanism, able to sustain the magnetic field, is maybe the reason of its rapid diffusion."
 Temporal analysis of helioseismic data has revealed that the solar angular velocity varies by around 5 per cent with respect to its mean value., Temporal analysis of helioseismic data has revealed that the solar angular velocity varies by around $5$ per cent with respect to its mean value.
" This fluctuation pattern, like the sunspots, follows an 11-year cycle, which suggests that it corresponds to the back reaction of the magnetic field on the plasma motion (e.g.??).."," This fluctuation pattern, like the sunspots, follows an 11-year cycle, which suggests that it corresponds to the back reaction of the magnetic field on the plasma motion \citep[e.g.][]{basu+antia_03,howe+etal_09}."
" It is also known that the amplitude of the meridional circulation varies with the amplitude of the magnetic field, being smaller when the cycle reaches its maximum (see ?).."," It is also known that the amplitude of the meridional circulation varies with the amplitude of the magnetic field, being smaller when the cycle reaches its maximum \citep[see e.g][]{basu+antia_03}."
" Apart from large scale effects, the magnetic field may also affect the local properties of the plasma."," Apart from large scale effects, the magnetic field may also affect the local properties of the plasma."
 This is possible the case in the downflows found by ? nearby the bipolar active regions., This is possible the case in the downflows found by \cite{hindman+etal_09} nearby the bipolar active regions.
" In the simulations presented here, due to the different nature of the dynamo and to the numerical setup, there are neither periodic oscillations of the magnetic field nor large-scale circulation."," In the simulations presented here, due to the different nature of the dynamo and to the numerical setup, there are neither periodic oscillations of the magnetic field nor large-scale circulation."
" We are able, however, to distinguish the differences between the plasma properties in the kinematic and the saturated stages."," We are able, however, to distinguish the differences between the plasma properties in the kinematic and the saturated stages."
 We also follow the deviations of the averaged flow occurring during peaks of the magnetic field amplitude., We also follow the deviations of the averaged flow occurring during peaks of the magnetic field amplitude.
" We find that also the turbulent rms-velocity, as well as the imposed large-scale shear flow, are affected by the magnetic field."," We find that also the turbulent rms-velocity, as well as the imposed large-scale shear flow, are affected by the magnetic field."
 In the top panel of Fig., In the top panel of Fig.
 9 we show the vertical profile of the horizontal and time averaged u;ms at the kinematic (dotted line) and saturated (continuous line) regimes of the dynamo., \ref{fig:br} we show the vertical profile of the horizontal and time averaged $\urms$ at the kinematic (dotted line) and saturated (continuous line) regimes of the dynamo.
 A, A
cosmological constant.,cosmological constant.
 Asstining that the mean redshift of the blue ares is about +=1. Wu aud Mao 7 noted that their umuber is indeed. cuhauced if the cosimological constaut is large.," Assuming that the mean redshift of the blue arcs is about $z =1$, Wu and Mao \cite{WuandMao1996} noted that their number is indeed enhanced if the cosmological constant is large."
 But they coufirm the earlier results of ο that rceeular distribution of masses increase also the probability to find an are so that no claims can be done on O4=0 without a detailed modeling of clusters frou strong aud weak leusiug., But they confirm the earlier results of Bartelmann \cite{bart95} that irregular distribution of masses increase also the probability to find an arc so that no claims can be done on $\Omega_{\Lambda}=0$ without a detailed modeling of clusters from strong and weak lensing.
 Besides. Wilson et al.," Besides, Wilson et al."
 7! xopose to constrain cosmological coustauts from the cosiic evolution of condensations of masses probed by leus modeling., \cite{Wilsonetal1996} propose to constrain cosmological constants from the cosmic evolution of condensations of masses probed by lens modeling.
" Simmlatious shows that the method could be efficient to discriminate an Eiusteiu-«de Sitter Qy universe frou any low mass density universe but they are almost iuscusitive to discriminate a flat universe with a cosmological constant O4<0.7 from the corresponding O4=0 universe,", Simulations shows that the method could be efficient to discriminate an Einstein-de Sitter $\Omega_0$ universe from any low mass density universe but they are almost insensitive to discriminate a flat universe with a cosmological constant $\Omega_{\Lambda}< 0.7$ from the corresponding $\Omega_{\Lambda}=0$ universe.
 The same result is obtained analytically for iuterpretations of the “cosmic shear” both in the linear aud non linear regime (see Mollier et al. this conference}.," The same result is obtained analytically for interpretations of the ""cosmic shear"" both in the linear and non linear regime (see Mellier et al, this conference)."
 This comes from the fact that even for very distant sources the leusine probability by anv foreground condcusation of nass is maxi at redshift iu the range 0.3-0.6., This comes from the fact that even for very distant sources the lensing probability by any foreground condensation of mass is maximum at redshift in the range 0.3-0.6.
 ence the lensing effect mainly probe an intermediate-redshift Universe which mostly depends on Qy aud the power spectrum of initial density fluctuation ΠΛ)., Hence the lensing effect mainly probe an intermediate-redshift Universe which mostly depends on $\Omega_0$ and the power spectrum of initial density fluctuation $P(k)$.
 Good modeling of several nultiple arcs within a same cluster having different redshifts range like 0.5-1 and 3-5 could give constraints on the the value of the cosinologieal coustant 5., Good modeling of several multiple arcs within a same cluster having different redshifts range like 0.5-1 and 3-5 could give constraints on the the value of the cosmological constant \cite{FortandMellier1994}.
 As an example. for an isothermal lens poteutial. as soon as the velocity dispersion is kuown. the radial position of the critical hues where arcs at a eiven redshift are formed depends only upon the effective aneular distance D(:.99.O4) defined above.," As an example, for an isothermal lens potential, as soon as the velocity dispersion is known, the radial position of the critical lines where arcs at a given redshift are formed depends only upon the effective angular distance $D(z,\Omega_0,\Omega_{\Lambda})$ defined above."
 The position ofthe most distaut arcs depends on O4 after the modeling has fitted the low redshift arcs., The position of the most distant arcs depends on $\Omega_{\Lambda}$ after the modeling has fitted the low redshift arcs.
" The effect of the cosmological constant is then detectable for O4>0.5 on a few areseconds scale,", The effect of the cosmological constant is then detectable for $\Omega_{\Lambda} > 0.5$ on a few arcseconds scale.
 Actual cluster potentials are by far more couples that these models which miss small scale structures. but the outstanding images obtained with UST mages peruüt to considerably improve detailed investigations because the critical line where inultiple arcs aud unresolved pairs merece can be located with high accuracy.," Actual cluster potentials are by far more complex that these models which miss small scale structures, but the outstanding images obtained with HST images permit to considerably improve detailed investigations because the critical line where multiple arcs and unresolved pairs merge can be located with high accuracy."
 Thus. sood models that coutrol the various poteutial eradieuts on an arcnünute scale cau be done froin strong and weals leusing.," Thus, good models that control the various potential gradients on an arcminute scale can be done from strong and weak lensing."
 AMasimuim likelihood methods should iu principle be applied as soon as such nr using events will be observed., Maximum likelihood methods should in principle be applied as soon as such fair lensing events will be observed.
 Since the work of Mellier et al. °°..," Since the work of Mellier et al. \cite{mellieretal93},"
" the »ossdibilitv of doing almost perfect modoeliug of arcs svsteuis is demonstrated and has been used im nuuerous leusing-clusters observed with IIST (see the uost recent splendid examples eiven by Seitz et al. οτι,"," the possibility of doing almost perfect modeling of arcs systems is demonstrated and has been used in numerous lensing-clusters observed with HST (see the most recent splendid examples given by Seitz et al. \cite{Seitzetal1997},"
 and also by. Kncib et ab? du A2218)., and also by Kneib et al \cite{kneibetal96} in A2218).
 In sunuuary. for a eiven lens model the method compares he location of a low-redshift critical line to that of a high-redshift oue.," In summary, for a given lens model, the method compares the location of a low-redshift critical line to that of a high-redshift one."
 So far. 10 cases Where found where the modeling of two arc svstem at very different," So far, no cases where found where the modeling of two arc system at very different"
"hypothesised motion of zero, would be almost entirely in position angle, 0.27 deg, while 0.001” in separation.","hypothesised motion of zero, would be almost entirely in position angle, 0.27 deg, while 0.001"" in separation."
" Therefore, with an uncertainty in position angle of 0.24 degrees, a ~3c detection of the relative proper motion of it and WASP-33 could be made with a 3-year baseline, if the tentative companion were instead a low proper motion background star."," Therefore, with an uncertainty in position angle of 0.24 degrees, a $\sim3\sigma$ detection of the relative proper motion of it and WASP-33 could be made with a 3-year baseline, if the tentative companion were instead a low proper motion background star."
" If the tentative companion were a faint foreground star, with a consequently large proper motion, a non-zero relative proper motion would be even more obvious."," If the tentative companion were a faint foreground star, with a consequently large proper motion, a non-zero relative proper motion would be even more obvious."
" Conversely, a zero relative position in 3 years would indicate common proper motion and confirm that the two objects are physical associated with one another."," Conversely, a zero relative position in 3 years would indicate common proper motion and confirm that the two objects are physical associated with one another."
" Finally, if the new discovered object is a companion of WASP-33, its mass is in the range [<0.1,0.2]Mo and its Το,=3050+ 2509."," Finally, if the new discovered object is a companion of WASP-33, its mass is in the range $[<0.1,0.2]M_\odot$ and its $T_{eff}=3050\pm250
\,^{\b{o}}K$ ."
 These ranges have been obtained comparing the observed J-Ks vs. J photometry with the isochrones used for Fig., These ranges have been obtained comparing the observed J-Ks vs. J photometry with the isochrones used for Fig.
" 3 (Siess et al. 2000)),"," \ref{edad}
 (Siess et al. \cite{isoc}) ),"
" with ages in the range [10, 1500] Myr."," with ages in the range [10, 1500] Myr."
 The absence of additional objects in the image obtained offers clear constraints to the presence of very low mass stars or brown dwarfs orbiting WASP-33., The absence of additional objects in the image obtained offers clear constraints to the presence of very low mass stars or brown dwarfs orbiting WASP-33.
 In Fig., In Fig.
" 4 we show the sensitivity of the present observations for different filters, as a function of the angular separation."," \ref{sensi2} we show the sensitivity of the present observations for different filters, as a function of the angular separation."
" The solid line is the observational limit obtained with the Kc-filter, respectively the dash line - Hc-filter, dot line - Jc-filter and, dash-dot line"," The solid line is the observational limit obtained with the Kc-filter, respectively the dash line - Hc-filter, dot line - Jc-filter and, dash-dot line"
chemical rate equations one traces only ravs and their child ravs which carry an opacity time step less or equal to the current chemical times step.,chemical rate equations one traces only rays and their child rays which carry an opacity time step less or equal to the current chemical times step.
 Such a scheme that is also adaptive in time is necessarily more complex ancl needs to be tailored to the specific problem at hand. as well as the method emploved. for solving the hydrodynamies., Such a scheme that is also adaptive in time is necessarily more complex and needs to be tailored to the specific problem at hand as well as the method employed for solving the hydrodynamics.
 We are currently exploring such time adaptive schemes to be implemented. for smoothed. particle as well as structured adaptive mesh refinement techniques., We are currently exploring such time adaptive schemes to be implemented for smoothed particle as well as structured adaptive mesh refinement techniques.
 TA. acknowledges stimulating and insightful. ciseussions with Gree Bryan on adaptive numerical. schemes ancl Jenedetta Cardi lor comments on the manuscript., T.A. acknowledges stimulating and insightful discussions with Greg Bryan on adaptive numerical schemes and Benedetta Ciardi for comments on the manuscript.
 This work has partially been supported through NSE grants ACI96-19019. anc AST-9803137., This work has partially been supported through NSF grants ACI96-19019 and AST-9803137.
. PLA. also acknowledge support from the Grand Challenge Cosmology Consortium., T.A. also acknowledge support from the Grand Challenge Cosmology Consortium.
 BDAY. is supported by the NASA ALAP/AILDIEN program., B.D.W. is supported by the NASA MAP/MIDEX program.
as well as in the larger aud larger πο of galaxies that appear thin iu projection.,as well as in the larger and larger number of galaxies that appear thin in projection.
 This geometric picture also fif» verv well with the kincmatic evidence that shows that most such carly types are ‘rapid rotator’. at least in the present-day universe.," This geometric picture also fits very well with the kinematic evidence that shows that most such early types are 'rapid rotators', at least in the present-day universe."
 Once again. the anxis-ratio distribution appears to evolve little out to Dol.," Once again, the axis-ratio distribution appears to evolve little out to $z\sim1$."
 The nou-evolvius shape of the mass function of flat versus round ealaxics we find inFigure & coupled with the overall erowth of the normalization iuplics that AL* early-type galaxies form ina similar wav over the last 7 Cvrs., The non-evolving shape of the mass function of flat versus round galaxies we find inFigure \ref{mf} coupled with the overall growth of the normalization implies that $M^{\star}$ early-type galaxies form in a similar way over the last 7 Gyrs.
 The erowth mechanism must roughly double to triple the umuber of earh-tvpe galaxies. producing a mix bulge-to-disk ratios that varies with ealaxy lass. but the process must not vary with time in the mass range we study," The growth mechanism must roughly double to triple the number of early-type galaxies, producing a mix bulge-to-disk ratios that varies with galaxy mass, but the process must not vary with time in the mass range we study."
 The leading puzzle for carly-type formation is a unifviug model for how to explain this erowth in mass density with so little chanec in the shapes of galaxies over the same look-back time., The leading puzzle for early-type formation is a unifying model for how to explain this growth in mass density with so little change in the shapes of galaxies over the same look-back time.
 The authors would like to thauk Exik Dell Dan Melnutosh. που Rudnick. Sandra Faber aud David. Noo for useful discussions. comments and feedback.," The authors would like to thank Erik Bell, Dan McIntosh, Greg Rudnick, Sandra Faber and David Koo for useful discussions, comments and feedback."
 BPI would also like to thauk the scicutists aud staff of the Mas Planck Institute for Astronomy in Hoeidelbere for hosting him while working ou this project., BPH would also like to thank the scientists and staff of the Max Planck Institute for Astronomy in Heidelberg for hosting him while working on this project.
"purely acoustic mechanism because the oscillation period is much longer than the acoustic time, while ? have shown that the oscillation period could be explained if one considers a non radial acoustic path.","purely acoustic mechanism because the oscillation period is much longer than the acoustic time, while \citet{blondin06} have shown that the oscillation period could be explained if one considers a non radial acoustic path."
" On the otherhand, ? excluded the advective-acoustic cycle without considering the possibility that the acoustic feedback be created at a larger radius than the PNS surface."," On the otherhand, \citet{blondin06} excluded the advective-acoustic cycle without considering the possibility that the acoustic feedback be created at a larger radius than the PNS surface."
" The determination of the frequency of each cycle thus suffers some uncertainty due to our lack of knowledge of the coupling radius (for the advective-acoustic cycle), and of the non-radial path to be considered (for a purely acoustic cycle)."," The determination of the frequency of each cycle thus suffers some uncertainty due to our lack of knowledge of the coupling radius (for the advective-acoustic cycle), and of the non-radial path to be considered (for a purely acoustic cycle)."
" Later, ? have shown that the oscillation period observed in their simulations was compatible with both mechanisms if the advective-acoustic coupling radius lies where the deceleration is maximum, or if an non radial acoustic path is chosen (their Figure 16)."," Later, \citet{scheck08} have shown that the oscillation period observed in their simulations was compatible with both mechanisms if the advective-acoustic coupling radius lies where the deceleration is maximum, or if an non radial acoustic path is chosen (their Figure 16)."
 ? have proposed an argument that can be applied to the regime in which the WKB method is inapplicable., \citet{fernandez09a} have proposed an argument that can be applied to the regime in which the WKB method is inapplicable.
" They followed the variation of a SASI mode growth rate as the shock radius is varied, which changes the ratio of the azimuthal acoustic time to the advection time from the shock to the PNS."," They followed the variation of a SASI mode growth rate as the shock radius is varied, which changes the ratio of the azimuthal acoustic time to the advection time from the shock to the PNS."
" They observed that the mode has a maximum growth rate when the two times coincide, and interpreted this as an indication that the advective-acoustic cycle is at work (because both advection and acoustic times play a role in the instability)."," They observed that the mode has a maximum growth rate when the two times coincide, and interpreted this as an indication that the advective-acoustic cycle is at work (because both advection and acoustic times play a role in the instability)."
" While this observation is indeed suggestive that the advection plays a role in determining the growth rate, it does not rule out the possibility of the acoustic cycle playing a dominant role with only a minor help from the advection."," While this observation is indeed suggestive that the advection plays a role in determining the growth rate, it does not rule out the possibility of the acoustic cycle playing a dominant role with only a minor help from the advection."
 Some more indirect information about the instability mechanism can be found by considering the effect of a magnetic field on SASI., Some more indirect information about the instability mechanism can be found by considering the effect of a magnetic field on SASI.
 ? have performed numerical simulations of SASI in the presence of a radial magnetic field (a split monopole)., \citet{endeve10} have performed numerical simulations of SASI in the presence of a radial magnetic field (a split monopole).
" They obtained the surprising result that a magnetic field, which magnetic pressure is negligible compared the thermal one (Pmag/P:n« 1073), is capable of entirely stabilising SASI (in their model 2DB14Am)."," They obtained the surprising result that a magnetic field, which magnetic pressure is negligible compared the thermal one $P_{\rm mag}/P_{\rm th} < 10^{-3}$ ), is capable of entirely stabilising SASI (in their model 2DB14Am)."
 This seems to contradict a purely acoustic mechanism because the acoustic waves should be almost unaffected by such a weak magnetic field., This seems to contradict a purely acoustic mechanism because the acoustic waves should be almost unaffected by such a weak magnetic field.
" By contrast, this result can be naturally interpreted in the framework of the advective-acoustic cycle."," By contrast, this result can be naturally interpreted in the framework of the advective-acoustic cycle."
" Indeed ? have shown that the advective-acoustic cycle is significantly affected by a magnetic field if the Alfvénn speed is comparable to the advection velocity, which can happen even if the magnetic pressure is negligibly small."," Indeed \citet{guilet10a} have shown that the advective-acoustic cycle is significantly affected by a magnetic field if the Alfvénn speed is comparable to the advection velocity, which can happen even if the magnetic pressure is negligibly small."
" In their model 2DB14Am, the Alfvénn speed is indeed comparable to the advection velocity in the vicinity of the PNS."," In their model 2DB14Am, the Alfvénn speed is indeed comparable to the advection velocity in the vicinity of the PNS."
" To summarise this subsection, the advective-acoustic mechanism is favoured by most arguments."," To summarise this subsection, the advective-acoustic mechanism is favoured by most arguments."
 However none of these arguments can rule out the purely acoustic mechanism for realistic flow parameters., However none of these arguments can rule out the purely acoustic mechanism for realistic flow parameters.
 The goal of this paper is to find a method to definitely distinguish the two mechanisms for realistic flow parameters., The goal of this paper is to find a method to definitely distinguish the two mechanisms for realistic flow parameters.
" As discussed in the last subsection, previous studies were not successful in determining the instability mechanism from SASI oscillation frequency, because the fundamental mode frequency can be explained by both mechanisms."," As discussed in the last subsection, previous studies were not successful in determining the instability mechanism from SASI oscillation frequency, because the fundamental mode frequency can be explained by both mechanisms."
" This is due to the fact, that the (radial) advective-acoustic time and the acoustic time are both comparable to the oscillation period, as is illustrated by Figure 2.."," This is due to the fact, that the (radial) advective-acoustic time and the acoustic time are both comparable to the oscillation period, as is illustrated by Figure \ref{fig:period_SASI}."
 In Section 3 we present a method to avoid this difficulty by extracting a time from the frequencies of several unstable radial harmonics., In Section \ref{sec:radial_time} we present a method to avoid this difficulty by extracting a time from the frequencies of several unstable radial harmonics.
" The large difference between acoustic and advective-acoustic radial times allows us to distinguish clearly the two mechanisms (the radial acoustic time is shorter by a factor 3 to 10, as shown in Figure 2))."," The large difference between acoustic and advective-acoustic radial times allows us to distinguish clearly the two mechanisms (the radial acoustic time is shorter by a factor 3 to 10, as shown in Figure \ref{fig:period_SASI}) )."
" Another reason for the remaining ambiguity on the instability mechanism is that, for realistic flow parameters, the unstable modes cannot be described by the WKB method."," Another reason for the remaining ambiguity on the instability mechanism is that, for realistic flow parameters, the unstable modes cannot be described by the WKB method."
" In Section 4 we present a new method to compute purely acoustic modes, which partially avoids this difficulty."," In Section \ref{sec:acoustic_modes} we present a new method to compute purely acoustic modes, which partially avoids this difficulty."
 This method makes use of the fact that the wavelength of advected perturbations is shorter than the acoustic wavelength., This method makes use of the fact that the wavelength of advected perturbations is shorter than the acoustic wavelength.
" As a consequence, the identification of advected perturbations through a WKB approximation is valid at lower frequency."," As a consequence, the identification of advected perturbations through a WKB approximation is valid at lower frequency."
" Finally, in Section 5 we develop an analytical description of the frequency spectrum of the two cycles, in order to confirm the validity of the argument presented in Section 3.."," Finally, in Section \ref{sec:details} we develop an analytical description of the frequency spectrum of the two cycles, in order to confirm the validity of the argument presented in Section \ref{sec:radial_time}."
 This analytical treatment is checked against the acoustic modes computed in Section 4.., This analytical treatment is checked against the acoustic modes computed in Section \ref{sec:acoustic_modes}.
 In the following we apply our two arguments to the classical model of SASI briefly described in Section 2.1.., In the following we apply our two arguments to the classical model of SASI briefly described in Section \ref{sec:SASI_models}.
 The reader is referred to ? and ? for a more detailed description., The reader is referred to \citet{blondin06} and \citet{foglizzo07} for a more detailed description.
" We focus on a shock radius rep= 2.5r., which is typical of supernovae and for which the unstable"," We focus on a shock radius $r_\sh = 2.5 r_* $ , which is typical of supernovae and for which the unstable"
The jet we investigated was observed over a radial range from the solar surface out to five solar radii.,The jet we investigated was observed over a radial range from the solar surface out to five solar radii.
 We used observations from the EUVI and two white light coronagraphs (CORI and COR2)., We used observations from the EUVI and two white light coronagraphs (COR1 and COR2).
" They belong to the SECCHI instrument suit etal., 2008).", They belong to the SECCHI instrument suit \citep{Howard:etal:2008}.
. EUVI is a full disk imager with a FOV of 1.7 ro., EUVI is a full disk imager with a FOV of 1.7 $r_{\odot}$.
" CORI and COR2 are two traditional Lyot coronagraphs, with the FOV in the range of 1.5 ro to 4 ro, and 2.5 ro to 15 ro, respectively."," COR1 and COR2 are two traditional Lyot coronagraphs, with the FOV in the range of 1.5 $r_{\odot}$ to 4 $r_{\odot}$ , and 2.5 $r_{\odot}$ to 15 $r_{\odot}$, respectively."
" The angular resolution of one pixel in EUVI, CORI, and COR2 is 1.6 arcsec, 7.5 arcsec, and 14 arcsec, respectively."," The angular resolution of one pixel in EUVI, COR1, and COR2 is 1.6 arcsec, 7.5 arcsec, and 14 arcsec, respectively."
" In EUV, the jet could be observed at all four wavelengths from the EUVI telescope."," In EUV, the jet could be observed at all four wavelengths from the EUVI telescope."
" The time cadence was 10 minutes for 304À and 195À, and 20 minutes for 284À."," The time cadence was 10 minutes for 304 and 195, and 20 minutes for 284."
" For 171À, the temporal resolution was as high as 2.5 minutes."," For 171, the temporal resolution was as high as 2.5 minutes."
 In Figs., In Figs.
 and 2 we show the difference images of the event at four wavelengths of EUVI observed by STEREO A. They were created by subtracting the pre-event images shown in color in the leftmost column of Figs., \ref{fig:eu_304195284} and \ref{fig:eu_171} we show the difference images of the event at four wavelengths of EUVI observed by STEREO A. They were created by subtracting the pre-event images shown in color in the leftmost column of Figs.
 1 and 2.., \ref{fig:eu_304195284} and \ref{fig:eu_171}.
 The following frames displaying the jet at later times is running from left to right with time., The following frames displaying the jet at later times is running from left to right with time.
 Nearly simultaneous images at different wavelengths are stacked vertically., Nearly simultaneous images at different wavelengths are stacked vertically.
 The EUVI observations indicate that this jet contains both hot and cool material., The EUVI observations indicate that this jet contains both hot and cool material.
" The jet eruption first clearly appeared in hotter lines 195À and 284 at around 05:06 UT, later in 171 at around 05:11, and finally in 304À at around 05:16 UT."," The jet eruption first clearly appeared in hotter lines 195 and 284 at around 05:06 UT, later in 171 at around 05:11, and finally in 304 at around 05:16 UT."
" The jet life time appeared to be shorter in the hotter lines (171, 195 and 284 À), and was clearly longer in the cooler line (304 À)."," The jet life time appeared to be shorter in the hotter lines (171, 195 and 284 ), and was clearly longer in the cooler line (304 )."
 More detailed descriptions of the EUV observations of this jet are provided in Patsourakosetal.(2008)., More detailed descriptions of the EUV observations of this jet are provided in \citet{Patsourakos:etal:2008}.
. The jet we are studying here was also traced in the CORI and even in the COR2 field of view., The jet we are studying here was also traced in the COR1 and even in the COR2 field of view.
 These observations are the main object of our analysis., These observations are the main object of our analysis.
 COR has a polarizer measuring polarized brightness in three directions separated by 120°., COR has a polarizer measuring polarized brightness in three directions separated by $120 ^\circ$.
 From this the total brightness is obtained by the standard procedure secchi.prep., From this the total brightness is obtained by the standard procedure $secchi\_prep$.
 In Fig., In Fig.
 3 we show the total brightness of the jet observations as difference images with respect to the closest pre-event image., \ref{fig:co12} we show the total brightness of the jet observations as difference images with respect to the closest pre-event image.
 Again the images are arranged with observation time from left to right and stacked roughly synchronously for different telescopes., Again the images are arranged with observation time from left to right and stacked roughly synchronously for different telescopes.
" In Fig 4 the jet geometry traced in the FOV of EUVI, CORI, and COR2 is shown by the three thick curve segments."," In Fig \ref{fig:euco12} the jet geometry traced in the FOV of EUVI, COR1, and COR2 is shown by the three thick curve segments."
 A smoothing spline is employed to connect the jet orbit over the entire height range., A smoothing spline is employed to connect the jet orbit over the entire height range.
 In the next section the trajectory of jet particles is calculated along this thin solid curve in Fig 4.., In the next section the trajectory of jet particles is calculated along this thin solid curve in Fig \ref{fig:euco12}.
 The good alignment of the jet segments from the three instruments indicates that they are part of the same jet., The good alignment of the jet segments from the three instruments indicates that they are part of the same jet.
 Notice that there was a slight change of about 6 degrees between the jet direction close to the surface as seen in EUVI and at altitudes beyond 1.5ro seen in CORI., Notice that there was a slight change of about 6 degrees between the jet direction close to the surface as seen in EUVI and at altitudes beyond $1.5~r_\odot$ seen in COR1.
" As a summary, the jet extended out to 5 ro."," As a summary, the jet extended out to 5 $r_{\odot}$."
" The lifetime in EUVI was around several tens of minutes, in CORI the event could be observed for about 1.5 hours and in COR2 for about 3 hours."," The lifetime in EUVI was around several tens of minutes, in COR1 the event could be observed for about 1.5 hours and in COR2 for about 3 hours."
" At 171 which is the preferred EUV wavelength for plume Observations, we noticed a preexisting plume to the right-hand side of the jet."," At 171 which is the preferred EUV wavelength for plume observations, we noticed a preexisting plume to the right-hand side of the jet."
" In CORI, the plume was found cospatial with the jet."," In COR1, the plume was found cospatial with the jet."
" It is not exceptional that a plume is aligned with a jet in a projected 2D image (Wilhelmetal.,2011).", It is not exceptional that a plume is aligned with a jet in a projected 2D image \citep{Wilhelm:etal:2011}.
". However, this more or less close alignment along the same line of sight (LOS) may be a coincidence."," However, this more or less close alignment along the same line of sight (LOS) may be a coincidence."
" In STEREOB images at 171 we also found a preexisting plume slightly to right-hand side of the jet, in CORI B the plume signal was too faint to conclude that the plume was really close to the jet."," In STEREO B images at 171 we also found a preexisting plume slightly to right-hand side of the jet, in COR1 B the plume signal was too faint to conclude that the plume was really close to the jet."
" In view of the small separation of the two spacecraft of only 10 degrees during this event, we still hesitate to assume that the jet has a physical relation to the preexisting plume."," In view of the small separation of the two spacecraft of only 10 degrees during this event, we still hesitate to assume that the jet has a physical relation to the preexisting plume."
" By using difference images, the emission of the plume is eliminated for the subsequent analysis."," By using difference images, the emission of the plume is eliminated for the subsequent analysis."
" Based on the difference images above, we determined the jet intensity in the EUVI images at 304 and the white-light total brightness in COR1 and COR2 images for successive times and different distances along the jet axis."," Based on the difference images above, we determined the jet intensity in the EUVI images at 304 and the white-light total brightness in COR1 and COR2 images for successive times and different distances along the jet axis."
 The total brightness was integrated across the jet cross section for each exposure and for each position along the jet axis after the pre-event background was subtracted., The total brightness was integrated across the jet cross section for each exposure and for each position along the jet axis after the pre-event background was subtracted.
" By integrating the brightness across the jet width, at each distance s the density decrease caused by the magnetic field line divergence was removed."," By integrating the brightness across the jet width, at each distance $s$ the density decrease caused by the magnetic field line divergence was removed."
 Note that the integration along the line-of-sight direction is implicit in the observation of the optically thin jet plasma., Note that the integration along the line-of-sight direction is implicit in the observation of the optically thin jet plasma.
 The distance s along the jet axis remains the only relevant spatial coordinate., The distance $s$ along the jet axis remains the only relevant spatial coordinate.
 The resulting distance-time (DT) total brightness plot is shown in Fig. 5.., The resulting distance-time (DT) total brightness plot is shown in Fig. \ref{fig:DT_euco}.
" For a clearer view, the brightnesses of CORI and COR2 in Fig."," For a clearer view, the brightnesses of COR1 and COR2 in Fig."
" 5 are multiplied by 10? and 10!°, respectively, to match the intensity at 304À."," \ref{fig:DT_euco} are multiplied by $10^9$ and $10^{10}$, respectively, to match the intensity at 304."
 Therefore the absolute values in Fig., Therefore the absolute values in Fig.
 5 are not comparable among different instruments., \ref{fig:DT_euco} are not comparable among different instruments.
 The distance on the ordinate is the length along the jet axis from its footpoint at 1 ro., The distance on the ordinate is the length along the jet axis from its footpoint at 1 $r_{\odot}$.
 The sampling ds in the direction alongthe jet axis corresponds to the size of one pixel in the respective original images., The sampling $ds$ in the direction alongthe jet axis corresponds to the size of one pixel in the respective original images.
 The time is in units of minutes and starts at, The time is in units of minutes and starts at
"of the compressible part in the model with Vi,~0.7 and even up to in models with 1,>I.",of the compressible part in the model with ${\cal M}_s \sim 0.7$ and even up to in models with ${\cal M}_s>1$.
 The consequence of the presence of à strong magnetic field results 1n à reduction of the compressible part of the velocity field by à factor 2., The consequence of the presence of a strong magnetic field results in a reduction of the compressible part of the velocity field by a factor 2.
 This indicates à substantial role of the magnetic field in the damping of the generation of the compressible flows., This indicates a substantial role of the magnetic field in the damping of the generation of the compressible flows.
 Due to a substantial dominance of the incompressible part of the velocity field. we expect that its spectra should follow the spectra for the total velocity field.," Due to a substantial dominance of the incompressible part of the velocity field, we expect that its spectra should follow the spectra for the total velocity field."
 In the middle row of Figure 2. we present the spectra for the incompressible part of the velocity field., In the middle row of Figure \ref{fig:velo_spectra} we present the spectra for the incompressible part of the velocity field.
 We see that the spectra. at least within the inertial range. are very similar to those observed for the velocity field.," We see that the spectra, at least within the inertial range, are very similar to those observed for the velocity field."
 Also the spectral indices have very close values for models with strong and weak magnetic field., Also the spectral indices have very close values for models with strong and weak magnetic field.
 In the case of compressible turbulence. more interesting are spectra of the potential component (the bottom row in Figure 2)).," In the case of compressible turbulence, more interesting are spectra of the potential component (the bottom row in Figure \ref{fig:velo_spectra}) )."
 We see that these spectra are different from those for the incompressible part., We see that these spectra are different from those for the incompressible part.
 The strength of the compressible part confirms the change of contribution of the compressible part., The strength of the compressible part confirms the change of contribution of the compressible part.
 It is smaller for subsonic models than for supersonic models. which can be seen in the bottom row of Figure 2..," It is smaller for subsonic models than for supersonic models, which can be seen in the bottom row of Figure \ref{fig:velo_spectra}."
 However. both supersonic models have almost the same spectra with the spectral indices about —2 for subAlfvénnic turbulence and for superalfvénnic turbulence.," However, both supersonic models have almost the same spectra with the spectral indices about $-2$ for subAlfvénnic turbulence and for superalfvénnic turbulence."
 Both supersonic spectra show almost exactly the same profiles and amplitudes at all scales. even within the dissipation range.," Both supersonic spectra show almost exactly the same profiles and amplitudes at all scales, even within the dissipation range."
 This means that the amount of compressible part of the velocity field do not change with τν when its value is larger than one.," This means that the amount of compressible part of the velocity field do not change with ${\cal
M}_s$ when its value is larger than one."
 The second decomposition. more important for MHD turbulence. separates the velocity field into three different MHD waves: an incompressible Alfvénn and slow and fast magneto acoustic waves. which both are compressible.," The second decomposition, more important for MHD turbulence, separates the velocity field into three different MHD waves: an incompressible Alfvénn and slow and fast magneto acoustic waves, which both are compressible."
 In Table 2. we included the percentage amount of these components in the total velocity field., In Table \ref{tab:energies} we included the percentage amount of these components in the total velocity field.
 As we see. the most of energy is contained in the Alfvénn wave.," As we see, the most of energy is contained in the Alfvénn wave."
 It ts almost in the case of subAlfvénn turbulence. and about for superAlfvénnic turbulence.," It is almost in the case of subAlfvénn turbulence, and about for superAlfvénnic turbulence."
 The slow wave contains approximately 1/3 of the total energy., The slow wave contains approximately 1/3 of the total energy.
 However. for superAlIfvénnie case. this amount is slightly higher.," However, for superAlfvénnic case, this amount is slightly higher."
 Table 2 suggests. that the slow wave is weaker when the turbulence become supersonic.," Table \ref{tab:energies} suggests, that the slow wave is weaker when the turbulence become supersonic."
 We do not see similar behavior for the Alfvénn wave in the case of models with à strong magnetic field., We do not see similar behavior for the Alfvénn wave in the case of models with a strong magnetic field.
 This effect could take place also in the superAlfvénnic models. but it is weakened by relatively large errors.," This effect could take place also in the superAlfvénnic models, but it is weakened by relatively large errors."
 An interesting dependence is observed in the case of the fast wave., An interesting dependence is observed in the case of the fast wave.
 Although. the fast wave is the weakest among all MHD waves. it strongly depends on the regime of turbulence.," Although, the fast wave is the weakest among all MHD waves, it strongly depends on the regime of turbulence."
 Similarly to the compressible part of velocity field. it is stronger for models with weak magnetic field.," Similarly to the compressible part of velocity field, it is stronger for models with weak magnetic field."
" In addition. it is much stronger when turbulence are supersonic. but this ""strength seems to be weakly dependent on the sonic. Mach number."," In addition, it is much stronger when turbulence are supersonic, but this strength seems to be weakly dependent on the sonic Mach number."
 In Figure 3. we present spectra for the MHD waves for all models from Table 1.., In Figure \ref{fig:spectra_waves} we present spectra for the MHD waves for all models from Table \ref{tab:models}.
 In the left column we show spectra for models with a strong magnetic field. while in the right column spectra for models with a weak magnetic field.," In the left column we show spectra for models with a strong magnetic field, while in the right column spectra for models with a weak magnetic field."
 Top. middle and bottom rows show the Alfvénn. slow and fast mode spectra. respectively.," Top, middle and bottom rows show the Alfvénn, slow and fast mode spectra, respectively."
 In the case of Alfvénn wave we see that the spectral indices depend on the sonic Mach number weakly., In the case of Alfvénn wave we see that the spectral indices depend on the sonic Mach number weakly.
 All indices lay between —2 and —5/3 with a slight dependence on «Ντι," All indices lay between $-2$ and $-5/3$ with a slight dependence on ${\cal
M}_s$."
 This is similar situation like for spectra of velocity field., This is similar situation like for spectra of velocity field.
 For superAlfvénnic models we observe similar situation. however. since the mean field is weaker. the power spectra are shifted down to smaller amplitudes.," For superAlfvénnic models we observe similar situation, however, since the mean field is weaker, the power spectra are shifted down to smaller amplitudes."
 The similarities in spectra between the Alfvénn mode and velocity field are due to the fact. that the Alfvénn mode constitutes the major part of the velocity field.," The similarities in spectra between the Alfvénn mode and velocity field are due to the fact, that the Alfvénn mode constitutes the major part of the velocity field."
 The slow wave. however. constitutes also a substantial part of the velocity field.," The slow wave, however, constitutes also a substantial part of the velocity field."
" Looking closer in the spectral indices for the slow mode plotted in Figure 3 we see that their values do not change significantly with ,V4, when mean magnetic field is strong. although it is difficult to determine one spectral index do to changing profile of the spectrum with the wave number."," Looking closer in the spectral indices for the slow mode plotted in Figure \ref{fig:spectra_waves} we see that their values do not change significantly with ${\cal M}_s$ when mean magnetic field is strong, although it is difficult to determine one spectral index do to changing profile of the spectrum with the wave number."
 There seems to be stronger dependence of the spectral indices on the sonic Mach number when the mean field is weak. where the inertial region is easter to determine.," There seems to be stronger dependence of the spectral indices on the sonic Mach number when the mean field is weak, where the inertial region is easier to determine."
 The fast wave. the weakest mode of the velocity field. shows two types of spectra depending on the sonic and Alfvénnie regime of turbulence.," The fast wave, the weakest mode of the velocity field, shows two types of spectra depending on the sonic and Alfvénnic regime of turbulence."
 In the case of subsonie models we see that the fast mode spectrum has index close to —2., In the case of subsonic models we see that the fast mode spectrum has index close to $-2$.
 When the field is weak. the value of index is a bit flatter then —2.," When the field is weak, the value of index is a bit flatter then $-2$."
 This indicates a clear dissimilarity of spectra for subsonic turbulence. for different strength of the magnetic field.," This indicates a clear dissimilarity of spectra for subsonic turbulence, for different strength of the magnetic field."
 In supersonic models. however. the spectral indices are going closer to the value —2. independently of the sonic Mach number.," In supersonic models, however, the spectral indices are going closer to the value $-2$, independently of the sonic Mach number."
 This signifies a growing role of the shock compression in supersonic turbulence., This signifies a growing role of the shock compression in supersonic turbulence.
 If we want to study the anisotropy of turbulent structures we need to introduce a reference frame., If we want to study the anisotropy of turbulent structures we need to introduce a reference frame.
 In the case of magnetized turbulence the reference frame is defined in the natural way by the local mean magnetic field., In the case of magnetized turbulence the reference frame is defined in the natural way by the local mean magnetic field.
 The local magnetic field is computed using the procedure of smoothing by a three- Gaussian profile with the width equal to the separation length., The local magnetic field is computed using the procedure of smoothing by a three-dimensional Gaussian profile with the width equal to the separation length.
 Since the volume of smoothing grows with the separation length /. the direction of local mean magnetic field might change with / at arbitrary point.," Since the volume of smoothing grows with the separation length $l$ , the direction of local mean magnetic field might change with $l$ at arbitrary point."
 This is an extension of procedures employed in and(20021., This is an extension of procedures employed in and.
 To analyze the anisotropy of different components of the velocity field we use the total structure function where àv is a total increment and denotes an ensemble averaging., To analyze the anisotropy of different components of the velocity field we use the total structure function where $\delta v$ is a total increment and $\langle ... \rangle$ denotes an ensemble averaging.
 For each component we evaluate the parallel and perpendicular structure functions taking respectively the directions of the separation length | parallel and perpendicular to the local mean magnetic field., For each component we evaluate the parallel and perpendicular structure functions taking respectively the directions of the separation length ${\bf l}$ parallel and perpendicular to the local mean magnetic field.
 To show the degree of anisotropy we plot the structure function in direction perpendicular to the local, To show the degree of anisotropy we plot the structure function in direction perpendicular to the local
dwarf galaxies will be more numerous and may have an effect on the orbit of these dwarfs.,dwarf galaxies will be more numerous and may have an effect on the orbit of these dwarfs.
 This lack of interaction may arise from the LMC stabilizing the orbits of dwarfs against minor perturbations., This lack of interaction may arise from the LMC stabilizing the orbits of dwarfs against minor perturbations.
" Interactions with larger galaxies, such as dwarfs interacting with LMC sized galaxies, or the LMC/SMC interactions can produce noticeable differences in the orbits and morphology of dwarf galaxies 2010).."," Interactions with larger galaxies, such as dwarfs interacting with LMC sized galaxies, or the LMC/SMC interactions can produce noticeable differences in the orbits and morphology of dwarf galaxies ."
" Of the dwarfs listed by as possibly part of the Magellanic system when falling in, only Sagittarius, Ursa Minor, Sculptor, Carina and Draco are located within the area that our model dwarfs end up."," Of the dwarfs listed by as possibly part of the Magellanic system when falling in, only Sagittarius, Ursa Minor, Sculptor, Carina and Draco are located within the area that our model dwarfs end up."
" Sextans and Fornax, located slightly outside the range of dwarfs, may also have fallen in with the Magellanic system having become unbound before the previous two apogalacticons."," Sextans and Fornax, located slightly outside the range of dwarfs, may also have fallen in with the Magellanic system having become unbound before the previous two apogalacticons."
 Using the velocities from we examine the direction of travel of the dwarfs in, Using the velocities from we examine the direction of travel of the dwarfs in
to be orders of magnitude larger than that of other stars. including M dwarts earlier than spectral type MT.,"to be orders of magnitude larger than that of other stars, including M dwarfs earlier than spectral type M7."
 Second. the level of radio activity appears to increase with later spectral type.," Second, the level of radio activity appears to increase with later spectral type."
 Finally. there may be a correlation between the streneth of the radio activity aud rotation velocity. such that rapid rotators exlibit stronger radio activity.," Finally, there may be a correlation between the strength of the radio activity and rotation velocity, such that rapid rotators exhibit stronger radio activity."
 We first investigate any trends in the strength of the radio activity as a fiction of spectral type., We first investigate any trends in the strength of the radio activity as a function of spectral type.
 A proper coluparison requires uormalization by the bolometric DhDuumositv of cach source., A proper comparison requires normalization by the bolometric luminosity of each source.
 These are available iu the literature for about half of the survey sources. includiug all of the T dwarf.," These are available in the literature for about half of the survey sources, including all of the T dwarf."
 For the rest we use published bolometric correction factors., For the rest we use published bolometric correction factors.
" For the L dwwufs BC,=3.12|QOTS(SPE) for LO Lland BC;=5.12.Ομτο1D for L5L9. with SP=0 for LO (Dahuetal.2002:Nakajimaetal. 2001)."," For the L dwarfs $BC_K=3.42+0.075
({\rm SP}-4)$ for L0–L4 and $BC_K=3.42-0.075({\rm SP}-4)$ for L5–L9, with ${\rm SP}=0$ for L0 \citep{dhv+02,nty04}."
". For the Mdwarts we use the mean of BC;=0.0895SP and Πο—1.53|O.LISSP001ISP, with SP=0 for MO (Wilkiueetal.1999)."," For the Mdwarfs we use the mean of $BC_J=2.43+ 0.0895{\rm SP}$ and $BC_K=1.53+0.148{\rm
SP}-0.0105{\rm SP}^2$, with ${\rm SP}=0$ for M0 \citep{wgm99}."
. With these values. we plot the ratio of radio to bolometric Iuninositv. Lyag/Lye). as a function of spectra type in Figure 3..," With these values, we plot the ratio of radio to bolometric luminosity, $L_{\rm rad}/L_{\rm bol}$, as a function of spectral type in Figure \ref{fig:activity}."
 Two trends are clear frou this figure., Two trends are clear from this figure.
 First. the fraction of detected objects drops considerably as a function of spectral type. from about 30% for the N dwarfs. to about LX for the L cowarts.," First, the fraction of detected objects drops considerably as a function of spectral type, from about $30\%$ for the M dwarfs, to about $4\%$ for the L dwarfs."
" If we consider oulv jon-detectious that are lower than the level of activity in he detected objects. these fractious are roughly £556 anc TA. respectively,"," If we consider only non-detections that are lower than the level of activity in the detected objects, these fractions are roughly $45\%$ and $7\%$, respectively."
 Second. aud. perhaps more mauportaut. he level of radio activity teuds to ducrease with later spectral types. with the active L dwarts exhibiting a leve of activity at least an order of maeuitucde larger than the wicL-AL cawarts.," Second, and perhaps more important, the level of radio activity tends to increase with later spectral types, with the active L dwarfs exhibiting a level of activity at least an order of magnitude larger than the mid-M dwarfs."
 Whether this trend continues to late-L aux T spectral types remains unclear due to the relatively ual iuuber of observed objects aud the observed. decrease iu he fraction of active sources., Whether this trend continues to late-L and T spectral types remains unclear due to the relatively small number of observed objects and the observed decrease in the fraction of active sources.
 Still. the increased level of activity supports our inference that the magnetic Πο] streugths are note siguificautlv lower in late-M and L dwarts.," Still, the increased level of activity supports our inference that the magnetic field strengths are note significantly lower in late-M and L dwarfs."
 Ou the other hand. with the larecr sample we do no find clear evidence for a correlation between the level of activity and rotation velocity.," On the other hand, with the larger sample we do not find clear evidence for a correlation between the level of activity and rotation velocity."
" Specifically. for the seven detected sources with a spectral type later than MT aud a measured rotation velocity. the average value of να, is roughly the same for esiné<20 kn | and >20 lan s+."," Specifically, for the seven detected sources with a spectral type later than M7 and a measured rotation velocity, the average value of $L_{\rm R}/L_{\rm bol}$ is roughly the same for $v{\rm sin}i<20$ km $^{-1}$ and $>20$ km $^{-1}$."
 A more careful analysis of this possible treud requires rotation velocity nieasureieuts for a significantly larecr sample., A more careful analysis of this possible trend requires rotation velocity measurements for a significantly larger sample.
 Ax can be seeu from Table 1.. less than a quarter of the observed objects have measured velocities.," As can be seen from Table \ref{tab:obs}, less than a quarter of the observed objects have measured velocities."
 Finally. we find continued evidence that the correlation οσοι radio and X-ray hununositvs which is roughly constant at a value of log(Ly/Ly)~15.5 for a wide range of stars (Caredel&Benz1993:BeuzgCuedel1991).. wreaks down at spectral type of about AIT (Figure 5)).," Finally, we find continued evidence that the correlation between radio and X-ray luminosity, which is roughly constant at a value of ${\rm
log}\,(L_R/L_X)\sim -15.5$ for a wide range of stars \citep{gb93,bg94}, breaks down at spectral type of about M7 (Figure \ref{fig:gb}) )."
 Possible explanatious for the breakdown iu this correlation wave heen discussed previously (Berger2002:Bergeretal.2005:Osten 2006).. aud focus on efficieut rapping of the relativistic electrons. thereby reducing he efficiency of coronal and chromiospherie heating. or inefficient. production of N-ravs due to a reduction in the iuuber of free ions in the cool atmospheres of these dwarf stars.," Possible explanations for the breakdown in this correlation have been discussed previously \citep{ber02,brr+05,ohb+06}, and focus on efficient trapping of the relativistic electrons, thereby reducing the efficiency of coronal and chromospheric heating, or inefficient production of X-rays due to a reduction in the number of free ions in the cool atmospheres of these dwarf stars."
 From a purely observational standpoiut. the data indicate that the decrease i N-rayv luminosity bv three orders of magnitude occurs over a narrow range in spectral type at about M? (or Tigz20002700 KJ). roughly the sale spectral type where a transition to predonminautlv neutral atumospheres occurs (Alohantyetal.2002).," From a purely observational standpoint, the data indicate that the decrease in X-ray luminosity by three orders of magnitude occurs over a narrow range in spectral type at about M7 (or $T_{\rm eff}\approx 2500-2700$ K), roughly the same spectral type where a transition to predominantly neutral atmospheres occurs \citep{mbs+02}."
". This is also the same location at which a significant drop in Ia activity occurs. frou an average value of log(Ly,3.6 carlicr than M5 to =L3 later than MT (Westetal.2001)."," This is also the same location at which a significant drop in $\alpha$ activity occurs, from an average value of ${\rm
log}\,(L_{\rm H\alpha}/L_{\rm bol})\approx -3.6$ earlier than M5 to $\approx -4.3$ later than M7 \citep{whw+04}."
. The fact that the magnetic field streneths aud radio activity do not decrease significantly indicates that the drop in X-rav and Πα activity is related instead to the structure of the atinosphiere. chromosphere and corona.," The fact that the magnetic field strengths and radio activity do not decrease significantly indicates that the drop in X-ray and $\alpha$ activity is related instead to the structure of the atmosphere, chromosphere and corona."
 We presented radio observations of SS dwarf stars aud brown clwarts in the rauee M?Ts. along with a sinele MD and a single M5.5 deaf.," We presented radio observations of 88 dwarf stars and brown dwarfs in the range M7–T8, along with a single M5 and a single M5.5 dwarf."
 This sample is ucarly comparable to the number of objects with Ta measurements. but is siguificantly larger than the uuuber of objects observed in the N-ravs.," This sample is nearly comparable to the number of objects with $\alpha$ measurements, but is significantly larger than the number of objects observed in the X-rays."
 The drop iu the fraction of active sources at the M/L transition. which is observed iu Πα. is also apparent in the radio observations.," The drop in the fraction of active sources at the M/L transition, which is observed in $\alpha$, is also apparent in the radio observations."
 Towever. the strength of the activity in the detected objects is iu fact higher for the L dwarts. both in quiescence aud chiving flares.," However, the strength of the activity in the detected objects is in fact higher for the L dwarfs, both in quiescence and during flares."
 As we have shown in retsec:plivs.. this is probably because the magnetic field streneths remain roughly uuchauged despite the drop iu effective temperature and huninosity with later spectral type.," As we have shown in \\ref{sec:phys}, this is probably because the magnetic field strengths remain roughly unchanged despite the drop in effective temperature and luminosity with later spectral type."
 The iuplication is that the magnetic dynamo process may be simular in early-M and E dwarts. aud is not stronely dependent on Imuninositv or temperature.," The implication is that the magnetic dynamo process may be similar in early-M and L dwarfs, and is not strongly dependent on luminosity or temperature."
 We also stress that while Wa observations are relatively siuple to carry out. it is uot trivial to trauslate th5 observed emission fo an estimate of the magnetic field streugth.," We also stress that while $\alpha$ observations are relatively simple to carry out, it is not trivial to translate the observed emission to an estimate of the magnetic field strength."
 The advantage ofradio observations is that they directly trace the streneth of the field. aud provide iu addition information on the physical properties of the enission region. such as its size aud deusitv.," The advantage of radio observations is that they directly trace the strength of the field, and provide in addition information on the physical properties of the emission region, such as its size and density."
 We therefore sugeest that a three-pronged approach is required for continued progress in our understauding of magnetic fields in dwarf stars and brown cwarfs., We therefore suggest that a three-pronged approach is required for continued progress in our understanding of magnetic fields in dwarf stars and brown dwarfs.
 First. the survey for radio cussion from these objects should be expanded to all of the ~500 currently known L and T dwarfs as well as a laree suuple of objects iu he spectral range M5.M9. which covers the breakdown iu he radio/N-rav correlation.," First, the survey for radio emission from these objects should be expanded to all of the $\sim 500$ currently known L and T dwarfs, as well as a large sample of objects in the spectral range M5–M9, which covers the breakdown in the radio/X-ray correlation."
 Such a survey cau be carried out cficieutly with the EVLA. which is scheduled to come ou-line iu the next few wears aud which will deliver a rearly order of magnitude increase in seusitivitv.," Such a survey can be carried out efficiently with the EVLA, which is scheduled to come on-line in the next few years and which will deliver a nearly order of magnitude increase in sensitivity."
 This is essential since the majority of the current detections are rear the threshold of the VLA., This is essential since the majority of the current detections are near the threshold of the VLA.
 We estimate that about 500.1.000 lir of observing time would be required for such an undertaking. delivering a seusitivitv of ew«10? at LO and ~107 at TO.," We estimate that about $500-1,000$ hr of observing time would be required for such an undertaking, delivering a sensitivity of $L_{\rm
rad}/L_{\rm bol}\sim {\rm few}\times 10^{-9}$ at L0 and $\sim 10^{-8}$ at T0."
 Second. the objects that have been detected κο far. and will be detected with the expanded survey. should j Observed over a wide frequency range to better characterize the shape of their spectra and the frequency dependence of their polarization.," Second, the objects that have been detected so far, and will be detected with the expanded survey, should be observed over a wide frequency range to better characterize the shape of their spectrum and the frequency dependence of their polarization."
 This is csseutial for deriving magnetic feld strengths to better accuracy than is possible with the current single-frequency observations., This is essential for deriving magnetic field strengths to better accuracy than is possible with the current single-frequency observations.
 We expect that at the current signal-to-noise level. the magnetic field streneths can be interred to an accuracy of 20 30%. which is comparable to. or better than. nüeasurenients made from Zeeman broadening for," We expect that at the current signal-to-noise level, the magnetic field strengths can be inferred to an accuracy of $\sim 20-30\%$ , which is comparable to, or better than, measurements made from Zeeman broadening for"
"In this section the results of the molecular line and radio observations will be used to evaluate the pressure balance between the hot ionised gas of the IBLs, and the cooler neutral gas within the BRCs.","In this section the results of the molecular line and radio observations will be used to evaluate the pressure balance between the hot ionised gas of the IBLs, and the cooler neutral gas within the BRCs."
" Following the method described in Paper I we calculated the internal (Pint) and external (P.xt) pressures (N cm?) using, where σ is the square of the velocity dispersion (i.e. c?= (Av)?/(81n2), where Av is the core-averaged C150 line width s~'))), pint is the core-averaged density calculated in Section Pext and c are the ionised gas density and sound ih,speed (assumed to be ~ 11.4 1) respectively."," Following the method described in Paper I we calculated the internal $P_{\rm{int}}$ ) and external $P_{\rm{ext}}$ ) pressures (N $^{-2}$ ) using, where $\sigma^2$ is the square of the velocity dispersion (i.e. $\sigma^2=\langle\Delta
v\rangle^2/(8\rm{ln}2$ ), where $\Delta v$ is the core-averaged $^{18}$ O line width )), $\rho_{\rm{int}}$ is the core-averaged density calculated in Section \ref{sect:co_analysis}, $\rho_{\rm{ext}}$ and $c$ are the ionised gas density and sound speed (assumed to be $\sim$ 11.4 ) respectively."
 The external pressure term includes contributions from both thermal and ram pressure., The external pressure term includes contributions from both thermal and ram pressure.
 The electron densities calculated in Section were used to estimate the ionised gas pressures for each cloud’s IBL.," The electron densities calculated in Section \ref{sect:IBL}
 were used to estimate the ionised gas pressures for each cloud's IBL."
 The calculated internal and external pressures are presented in Table [I0]., The calculated internal and external pressures are presented in Table \ref{tbl:pressure_balance}.
" The largest two uncertainties in the calculation of the molecular pressure are: the uncertainty in the observed line temperature, and the possibility that the C!%O derived density may be affected by depletion, either onto dust grain ice mantles, or through selective photo-dissociation."," The largest two uncertainties in the calculation of the molecular pressure are: the uncertainty in the observed line temperature, and the possibility that the $^{18}$ O derived density may be affected by depletion, either onto dust grain ice mantles, or through selective photo-dissociation."
" The uncertainties in the densities are thought to be no more than a factor of two, the effects of depletion and photo-dissociation are harder to quantify."," The uncertainties in the densities are thought to be no more than a factor of two, the effects of depletion and photo-dissociation are harder to quantify."
" However, all of the core temperatures are considerably larger than 10 K, where depletion is expected to be greatest, and given that they are embedded within the clouds, away from the ionisation front, where they are shielded from much of the ionising radiation, these effects are not thought to be significant."," However, all of the core temperatures are considerably larger than 10 K, where depletion is expected to be greatest, and given that they are embedded within the clouds, away from the ionisation front, where they are shielded from much of the ionising radiation, these effects are not thought to be significant."
 We estimate the molecular pressures presented to be accurate to within a factor of two., We estimate the molecular pressures presented to be accurate to within a factor of two.
 The IBL pressures are lower limits (due to the electron densities being lower limits) and taking account of the uncertainties are considered to be accurate to ~ 30%., The IBL pressures are lower limits (due to the electron densities being lower limits) and taking account of the uncertainties are considered to be accurate to $\sim$ 30.
. As discussed in Section 3.1 theoretical models (??)) have revealed the pressure balance to be a sensitive diagnostic that can be used to determine the evolutionary state of BRCs.," As discussed in Section 3.1 theoretical models \citealt{bertoldi1989,lefloch1994}) ) have revealed the pressure balance to be a sensitive diagnostic that can be used to determine the evolutionary state of BRCs."
" Comparing the internal and external pressures calculated from the molecular line and radio observations (presented in Table ᾖ0)), reveals that all of the clouds are under pressured with respect to their IBLs, and are thus in the process of having shocks driven into them."," Comparing the internal and external pressures calculated from the molecular line and radio observations (presented in Table \ref{tbl:pressure_balance}) ), reveals that all of the clouds are under pressured with respect to their IBLs, and are thus in the process of having shocks driven into them."
" However, taking account of the possible factor of two uncertainty in our calculations of these parameters, it is possible that two of these clouds are in approximate pressure balance (i.e. SFO 58 and SFO 68); these clouds are likely to be in a post-pressure balance state, and it is therefore possible that any current, or imminent, star formation within these clouds could have been triggered."," However, taking account of the possible factor of two uncertainty in our calculations of these parameters, it is possible that two of these clouds are in approximate pressure balance (i.e. SFO 58 and SFO 68); these clouds are likely to be in a post-pressure balance state, and it is therefore possible that any current, or imminent, star formation within these clouds could have been triggered."
" The remaining two clouds, SFO 75 and SFO 76, are under-pressured by factors of three and twelve respectively, with respect to their IBLs, strongly suggesting that these clouds have only recently been exposed to the HII region and that shocks are currently being driven into the surface layers of these clouds, closely followed by a D-critical ionisation front."," The remaining two clouds, SFO 75 and SFO 76, are under-pressured by factors of three and twelve respectively, with respect to their IBLs, strongly suggesting that these clouds have only recently been exposed to the HII region and that shocks are currently being driven into the surface layers of these clouds, closely followed by a D-critical ionisation front."
" These clouds are likely to be in a pre-pressure balance state where the shocks have not propagated very far into the surface layers; it is therefore unlikely that the molecular cores within these two clouds have been formed by RDI, but are more likely to pre-date the arrival of the ionisation front and have only recently been exposed to the HII region."," These clouds are likely to be in a pre-pressure balance state where the shocks have not propagated very far into the surface layers; it is therefore unlikely that the molecular cores within these two clouds have been formed by RDI, but are more likely to pre-date the arrival of the ionisation front and have only recently been exposed to the HII region."
 Any current star formation taking place within these clouds is unlikely to have been triggered., Any current star formation taking place within these clouds is unlikely to have been triggered.
" The 6 cm radio continuum image (see Figure 3) of SFO 58 clearly shows the presence of a radio source positionally coincident with the CO core embedded within this BRC, both of which lie at the focus of the BRC where the photoionisation induced shock is expected to concentrate the majority of the mass within the cloud."," The 6 cm radio continuum image (see Figure 3) of SFO 58 clearly shows the presence of a radio source positionally coincident with the $^{13}$ CO core embedded within this BRC, both of which lie at the focus of the BRC where the photoionisation induced shock is expected to concentrate the majority of the mass within the cloud."
" The radio source and embedded !?CO core are offset from the IRAS point source, but their positional correlation hints at a possible association between the two."," The radio source and embedded $^{13}$ CO core are offset from the IRAS point source, but their positional correlation hints at a possible association between the two."
" At a distance of 700 pc the angular size of the compact radio source (~ 18"")) corresponds to a physical diameter of « 0.06 pc, which suggested it might be a compact HII region similar to those found within other BRCs reported in (i.e. SFO 59, SFO 62, SFO 74, SFO 79 and SFO 85; see ? for a detailed investigation of SFO 79)."," At a distance of 700 pc the angular size of the compact radio source $\sim$ ) corresponds to a physical diameter of $<$ 0.06 pc, which suggested it might be a compact HII region similar to those found within other BRCs reported in (i.e. SFO 59, SFO 62, SFO 74, SFO 79 and SFO 85; see \citealt{urquhart2004} for a detailed investigation of SFO 79)."
 The radio flux of the compact radio source is consistent with the presence of a single embedded B2-B3 ZAMS star., The radio flux of the compact radio source is consistent with the presence of a single embedded B2–B3 ZAMS star.
" Furthermore, the correlation of the position of the radio source with that of the molecular core detected in the CO observations, both of which are located at the focus of the bright rim (see Figure ??)), offer some circumstantial support for this hypothesis."," Furthermore, the correlation of the position of the radio source with that of the molecular core detected in the CO observations, both of which are located at the focus of the bright rim (see Figure \ref{fig:co_sfo58}) ), offer some circumstantial support for this hypothesis."
" However, it is possible that the presence of the radio source is an unfortunate alignment of the cloud with an extragalactic background source."," However, it is possible that the presence of the radio source is an unfortunate alignment of the cloud with an extragalactic background source."
" To try to determine the nature of this radio emission we attempted to calculate the spectral index (o) of the emission using the integrated flux at both frequencies (Le. S,ος νά), however, this proved inconclusive due"," To try to determine the nature of this radio emission we attempted to calculate the spectral index $\alpha$ ) of the emission using the integrated flux at both frequencies (i.e. $S_\nu \propto \nu^{\alpha}$ ), however, this proved inconclusive due"
dwarfs. the two theories differ on several points.,"dwarfs, the two theories differ on several points."
 A fundamental difference. in particular. concerns the role of nonthermal support ou the determination of the IME.," A fundamental difference, in particular, concerns the role of nonthermal support on the determination of the IMF."
 Ou oue haud. PN do not inchide turbulent support in their theory. and must mvoke maeguetie field aud. MIID. shock conditions to obtain the proper Salpeter slope for the IME.," On one hand, PN do not include turbulent support in their theory, and must invoke magnetic field and MHD shock conditions to obtain the proper Salpeter slope for the IMF."
" Iu contrast. in the IIC theory. random turbulent motions inside bound massive overdeuse regious. identified at the very carly stages of star formation. counteract the action of eravity aud thus stabilize these iuitia lass Yosorvolrs - precursors of the eravitationally bound prestellar ""cores? - which would otherwise have collapsed before collecting such an amount of mass."," In contrast, in the HC theory, random turbulent motions inside bound massive overdense regions, identified at the very early stages of star formation, counteract the action of gravity and thus stabilize these initial mass reservoirs - precursors of the gravitationally bound prestellar ""cores"" - which would otherwise have collapsed before collecting such an amount of mass."
" As such. these turbulent motions are acting like a source of nouthermal support Gdeutified in the IIC theory by the quantity ντι, the Mach amber at the Jeaus scale. see Eqxsttl) aud (13) of IICOS ) against eravitv."," As such, these turbulent motions are acting like a source of nonthermal support (identified in the HC theory by the quantity ${\cal M}_\star$, the Mach number at the Jeans scale, see Eqs.(41) and (43) of HC08 ) against gravity."
 As demonstrated in IIECOS. this turbuleu support is mandatory to obtain the ΧΟΡΟΙ Salpeter slope.," As demonstrated in HC08, this turbulent support is mandatory to obtain the proper Salpeter slope."
 However. bv the time the (massive) cores/stars form. ou of the Gnassive) reservoirs. turbulence will have had ample time to clissipate.," However, by the time the (massive) cores/stars form out of the (massive) reservoirs, turbulence will have had ample time to dissipate."
 We come back to this important concep of turbulent “support” at the cud of the paper.," We come back to this important concept of turbulent ""support"" at the end of the paper."
 Conversely. a fundamental xedietion of the WC theory is that. in the absence of nou-thermal support. the slope of the IALF is significautly steeper than the Salpeter ouc.," Conversely, a fundamental prediction of the HC theory is that, in the absence of non-thermal support, the slope of the IMF is significantly steeper than the Salpeter one."
 This result. hence the importance of the aforementioned source of nouthermal support in order to get the proper Salpeter slope or the IME. has received some support from recent sinulations aimed at exploring this issue (Sclunidt et al.," This result, hence the importance of the aforementioned source of nonthermal support in order to get the proper Salpeter slope for the IMF, has received some support from recent simulations aimed at exploring this issue (Schmidt et al."
 2010). even though more work is definitely needed to nail down this issuc.," 2010), even though more work is definitely needed to nail down this issue."
 Tn this short paper. we present a siuple dimensional aremment. based on the well-known scaling properties of turbulence. to demonstrate that indeed. turbulent support ix needed to recover the proper Salpeter higliuass tail of the CMP/IME.," In this short paper, we present a simple dimensional argument, based on the well-known scaling properties of turbulence, to demonstrate that indeed, turbulent support is needed to recover the proper Salpeter high-mass tail of the CMF/IMF."
" The average statistical properties of a turbulent deusitv aud velocity field can be described by the scale depeudeuce of the corresponding 3D power spectra iu Fourier space. as described by power-law relatiouships. ο)=Pf)x hoe, where s denotes either the velocitv (6— 7). deusity (6— p£p)) or ofdensity Ge= loe(p/p)) Huctuatious."," The average statistical properties of a turbulent density and velocity field can be described by the scale dependence of the corresponding 3D power spectra in Fourier space, as described by power-law relationships, $P_{3D}(x)\equiv P_x(k)\propto k^{-n_x}$ , where $x$ denotes either the velocity $x \equiv\sigma$ ), density $x \equiv \rho/{\bar \rho})$ ) or of density $x \equiv \log(\rho/{\bar \rho}) $ ) fluctuations."
" The euergw προςσπα. DO. which is the snetic energev per unit nass por unit svavenunaboer. ds equal to the angular average of he power spectruu: E(k)-ThPan(hy)x512) i 3D. It correspouds to he spectrum of velocity fluctuations over scales sinaller hana size⋅ > R.o$-—,[Lgοx[XMn1dk IUOC. where σῃ2 describes: the variance. of. the 3D. velocity. field. or.4g.τὸ. within a volune R?."," The energy spectrum, E(k), which is the kinetic energy per unit mass per unit wavenumber, is equal to the angular average of the power spectrum: $E(k) =4\pi k^2 \langle P_{3D}(k)\rangle \propto k^{(-n+2)}$ in 3D. It corresponds to the spectrum of velocity fluctuations over scales smaller than a size $ R $, $\sigma_R^2 =\int_{2\pi/R}^\infty E(k)dk \propto \int_{2\pi/R}^\infty k^{(-n+2)}dk \propto R ^{n-3}$ , where $\sigma_ R ^2$ describes the variance of the 3D velocity field, $\sigma(x, y, z)$, within a volume $R ^3$."
 Iu real space. the enerev spectrum thus corresponds to the seconcd-order riis velocity. fluctuationsH measured on scale Fe. PLUS(05).," In real space, the energy spectrum thus corresponds to the second-order rms velocity fluctuations measured on scale $R$, $\langle \sigma_R ^2 \rangle$."
 The two well known lanits of incompressible and pressureless turbulence correspoud to the Ixoluosorov and Burecrs lanits. with respective 3D velocity power spectimun dudexes vo=11/3 and os=lL.," The two well known limits of incompressible and pressureless turbulence correspond to the Kolmogorov and Burgers limits, with respective 3D velocity power spectrum indexes $n=11/3$ and $n =4$."
" Numerical siuulatious of compressible. shock-dominated turbulence uuder Mach values typical of molecular cloud coucditious tend to show that the powerspectrum of turbulent velocity and of density fluctuations exhibit a power-law behaviour. with a simular mdex. namely 1,Mowipy~38 (INritsuk et al."," Numerical simulations of compressible, shock-dominated turbulence under Mach values typical of molecular cloud conditions tend to show that the powerspectrum of turbulent velocity and of density fluctuations exhibit a power-law behaviour, with a similar index, namely $n_\sigma \sim n_{\log(\rho)} \sim 3.8$ (Kritsuk et al."
 2007)., 2007).
" According to the IHeunebelle-Chnabrier theory. in the random field of density fluctuations characteristic of the clouds structure. initial pieces of fluid out of which mestellar cores and individual stars (or multiple star systems such as binarics) will eventually fori. are identified as overdeuse regions that isolate themsclyes roni the surrounding medium aud start to contract under he action of gravity,"," According to the Hennebelle-Chabrier theory, in the random field of density fluctuations characteristic of the cloud's structure, initial pieces of fluid out of which prestellar cores and individual stars (or multiple star systems such as binaries) will eventually form, are identified as overdense regions that isolate themselves from the surrounding medium and start to contract under the action of gravity."
" The condition to select such a given uaremallv unstable niece of fluid of mass AL and size R. with internal velocity dispersion ση—96. simply stcus roni the virial coudition: 2E,;,|E,=0. whore Lyin~(1/2)poqo2 denotes the kinetic: cucrey and E, he eravitational energy."," The condition to select such a given marginally unstable piece of fluid of mass $M$ and size $R$, with internal velocity dispersion $\sigma_R\equiv\sig$, simply stems from the virial condition: $2E_{kin}+E_{pot}=0$, where $E_{kin}\sim (1/2)\rho \sig^2 $ denotes the kinetic energy and $E_{pot}\sim \rho G\frac{M}{R}$ the gravitational energy."
 Usiug dimensional analysis. this vields the relation Iu the πμ where the velocity dispersion is dominated by thermal notions.and assunüng ucarly isotlermal conditions. σ docs uot depend ou A aud condition (2)) vields Conversely. in the nuit where the velocity dispersion is dominated by turbulent motions. 9XR= (oo rofscale)). vieldiug for the marginal instability condition with 4—(» 3)/2.," Using dimensional analysis, this yields the relation In the limit where the velocity dispersion is dominated by thermal motions,and assuming nearly isothermal conditions, $\sig$ does not depend on $R$ and condition \ref{vir}) ) yields Conversely, in the limit where the velocity dispersion is dominated by turbulent motions, $\sig \propto R^{{(n-3)\over 2}}$ (see \\ref{scale}) ), yielding for the marginal instability condition with $\eta=(n-3)/2$."
 The thermal case is recovered for po— D.de.aqp=0.," The thermal case is recovered for $n=3$, i.e. $\eta=0$."
 For s>3. Ley>0. we note the strouser dependeuce of the mass AL upon the size R iu he presence of turbulent support. compared with the pure hermal case (Eq.(3))).," For $n>3$, i.e. $\eta>0$, we note the stronger dependence of the mass $M$ upon the size $R$ in the presence of turbulent support, compared with the pure thermal case \ref{therm}) ))."
 The complete relation is obtained in Cos (heir equ.(26)) iux illustrates that a )ound stable region can achieve larecr masses for a given size hanks to the non-thermal support at the characteristic Jeans leugth. uaturally leading to a larger number of ugh mass reservoirs (then of massive prestellar cores). which would otherwise have collapsed loug before.," The complete relation is obtained in HC08 (their eqn.(26)) and illustrates that a bound stable region can achieve larger masses for a given size thanks to the non-thermal support at the characteristic Jeans length, naturally leading to a larger number of high mass reservoirs (then of massive prestellar cores), which would otherwise have collapsed long before."
 This iupact of uouthermal support ou the mass-size relation of massive bound cores has been coufirined bv recent munerical πατοις (Schinidt et al., This impact of nonthermal support on the mass-size relation of massive bound cores has been confirmed by recent numerical simulations (Schmidt et al.
 2010. Fie.," 2010, Fig."
 7)., 7).
 AssumingC» a largeOo enoughC» multi-scale structured space size ∙L aud dimension D.:> thus volune LZ. of the," Assuming a large enough multi-scale structured space of size $L$ and dimension $D$ , thus volume $L^D$ the"
to expect the strong and wide photospheric D lines typical of a cool giant to be visible in the compositespectrum?.,to expect the strong and wide photospheric D lines typical of a cool giant to be visible in the composite.
". Therefore, a possible explanation for the changes in the D absorption features during the quiescent phase (see Fig.2,,"," Therefore, a possible explanation for the changes in the D absorption features during the quiescent phase (see Fig.\ref{fig:ca},"
 lower panel) is the variation of the lines in the M giant spectrum., lower panel) is the variation of the lines in the M giant spectrum.
" These might be explained in terms of wavelength shifts due to the orbital motion, but also as intrinsic line variability."," These might be explained in terms of wavelength shifts due to the orbital motion, but also as intrinsic line variability."
" In fact, the hot components of symbiotic systems are known to heat the facing hemispheres of the red companion, hence producing temperature changes in their atmospheres large enough to change the lines shapes (see Kenyon etal."," In fact, the hot components of symbiotic systems are known to heat the facing hemispheres of the red companion, hence producing temperature changes in their atmospheres large enough to change the lines shapes (see Kenyon etal."
 and references therein)., \cite{kenyon93} and references therein).
" Indeed, in the case of RS Oph both mechanisms might be at work."," Indeed, in the case of RS Oph both mechanisms might be at work."
" This is shown in the upper panel of Fig. 2,,"," This is shown in the upper panel of Fig. \ref{fig:ca},"
 where we plotted the region of the 46718 line for the first (7672 days) and the last (—530 days) pre-outburst epochs in our data set., where we plotted the region of the $\lambda$ 6718 line for the first $-$ 672 days) and the last $-$ 530 days) pre-outburst epochs in our data set.
" Besides the velocity shift observed between the two epochs (~25 km s!), the Ca I line shows a significant depth increase, a behavior that is common also to other stellar lines (like 46707, very neatly detected in our spectra)."," Besides the velocity shift observed between the two epochs $\sim$ 25 km $^{-1}$ ), the Ca I line shows a significant depth increase, a behavior that is common also to other stellar lines (like $\lambda$ 6707, very neatly detected in our spectra)."
" This might explain, at least partially, the evolution of the D absorption profiles observed during the quiescence phase (Fig. 2,,"," This might explain, at least partially, the evolution of the D absorption profiles observed during the quiescence phase (Fig. \ref{fig:ca},"
 lower panel)., lower panel).
" An important fact to be noticed is that D andCau H&KK regions are most probably affected by the presence of components arising in the circumbinary environment, which are characterized by the complex profiles seen in other prominentlines like H and He (see for instance Zamanov et al. 2005;;"," An important fact to be noticed is that D and K regions are most probably affected by the presence of components arising in the circumbinary environment, which are characterized by the complex profiles seen in other prominentlines like H and He (see for instance Zamanov et al. \cite{zamanov};"
 Brandi et al. 2009))., Brandi et al. \cite{brandi}) ).
" Because of the presence of interstellar and possible circumstellar components, it is very difficult to distinguish these components inNai D,Cau H&KK, and lines."," Because of the presence of interstellar and possible circumstellar components, it is very difficult to distinguish these components in D, K, and lines."
" Nevertheless, this becomes feasible for other strong lines, where the circum/interstellar components are absent, like the near-IR triplet."," Nevertheless, this becomes feasible for other strong lines, where the circum/interstellar components are absent, like the near-IR triplet."
" An example is presented in Fig. 3,,"," An example is presented in Fig. \ref{fig:ircana}, ,"
" where the evolution of 48662.14 is compared to the one of D,.", where the evolution of $\lambda$ 8662.14 is compared to the one of $_1$.
" The changes seen in the lines are followed by those in the profile and can be explained, at least partially, by the radial velocity shift of the M giant, traced by the 46718 line."," The changes seen in the lines are followed by those in the profile and can be explained, at least partially, by the radial velocity shift of the M giant, traced by the $\lambda$ 6718 line."
" Therefore, during quiescence there certainly is a stellar component, possibly characterized by a complex structure, which affects the observed profile of the narrow absorption lines arising in the inter/circumstellar environment."," Therefore, during quiescence there certainly is a stellar component, possibly characterized by a complex structure, which affects the observed profile of the narrow absorption lines arising in the inter/circumstellar environment."
" The time evolution during one pre-outburst (—672 days), two outburst (4-1.5, +12.5 days), and one post-outburst (+742 days) epochs is presentedin Figs. 4,, 5,,"," The time evolution during one pre-outburst $-$672 days), two outburst (+1.5, +12.5 days), and one post-outburst (+742 days) epochs is presentedin Figs. \ref{fig:caevol}, , \ref{fig:naevol}, ,"
"6 for H, Dj, and","\ref{fig:kievol} for H, $_1$ , and"
"tetrahedron, and where the surface element is given by Thus for each particle we have a measure of both V-v and ó.Figure 2. shows V-VW as a function of 6 and In(1+6) at z=0, calculated using the Delaunay tessellation (bottom plot) and the other methods.","tetrahedron, and where the surface element is given by Thus for each particle we have a measure of both $\grad\cdot\bPsi$ and $\delta$ .Figure \ref{fig:divz0} shows $\grad\cdot\bPsi$ as a function of $\delta$ and $\ln(1+\delta)$ at $z=0$, calculated using the Delaunay tessellation (bottom plot) and the other methods."
" Both the divergence of Ψ and the density calculated with the Delaunay tessellation lead to a large scatter at high densities beyond the range of the plot, with the maximum values of V- reaching around +1000."," Both the divergence of $\bPsi$ and the density calculated with the Delaunay tessellation lead to a large scatter at high densities beyond the range of the plot, with the maximum values of $\grad\cdot\bPsi$ reaching around $\pm 1000$."
" This large scatter is not surprising because neighbors in high-density regions are unlikely to be true Lagrangian neighbors, so their displacements should be fairly random; additionally, the length-scales associated with the highest densities are smaller than the scale over which we would expect the logarithmic approximation to hold."," This large scatter is not surprising because neighbors in high-density regions are unlikely to be true Lagrangian neighbors, so their displacements should be fairly random; additionally, the length-scales associated with the highest densities are smaller than the scale over which we would expect the logarithmic approximation to hold."
" While the low-density success of the logarithmic approximation is encouraging, it seems that a Lagrangian kernel method is not the most appropriate choice for relating the density and displacement fields."," While the low-density success of the logarithmic approximation is encouraging, it seems that a Lagrangian kernel method is not the most appropriate choice for relating the density and displacement fields."
" Motivated by the success of the logarithmic density field in improving the statistics of large scale structure into the nonlinear regime, we have compared the linear relation between the density and displacement fields to a logarithmic approach."," Motivated by the success of the logarithmic density field in improving the statistics of large scale structure into the nonlinear regime, we have compared the linear relation between the density and displacement fields to a logarithmic approach."
" We have used different methods of measuring the divergence of the displacement field, V-V, and the density field in cosmological N-body simulations, and have investigated their relation for different redshifts and smoothing scales."," We have used different methods of measuring the divergence of the displacement field, $\grad\cdot\,\bPsi$, and the density field in cosmological $N$ -body simulations, and have investigated their relation for different redshifts and smoothing scales."
 The logarithmic approach fares better even on scales as small as ~2 h! where the linear approximation is no longer valid.," The logarithmic approach fares better even on scales as small as $\sim$ 2 $^{-1}$ Mpc, where the linear approximation is no longer valid."
" SmoothingMpc, over a uniform grid in Eulerian coordinates seems to outperform a tessellation-based Lagrangian method, though both work well at low to average densities."," Smoothing over a uniform grid in Eulerian coordinates seems to outperform a tessellation-based Lagrangian method, though both work well at low to average densities."
" Because a key advantage of the logarithmic transformation is the ability to use the density field on weakly nonlinear scales, this method would be most effective for a low-redshift galaxy survey (such that the effect of nonlinear evolution is strongest) with a high galaxy density (such that the mean separation of galaxies is small and in the nonlinear regime)."," Because a key advantage of the logarithmic transformation is the ability to use the density field on weakly nonlinear scales, this method would be most effective for a low-redshift galaxy survey (such that the effect of nonlinear evolution is strongest) with a high galaxy density (such that the mean separation of galaxies is small and in the nonlinear regime)."
" Using a logarithmic transform of the density to reconstruct the displacement field is simpler than advanced algorithms such as MAK reconstruction (Brenieretal.2003) and thus may require only small changes to existing analysis codes, providing an improvement over the linear method while maintaining a high degree of computational efficiency."," Using a logarithmic transform of the density to reconstruct the displacement field is simpler than advanced algorithms such as MAK reconstruction \citep{bre03} and thus may require only small changes to existing analysis codes, providing an improvement over the linear method while maintaining a high degree of computational efficiency."
 Our full investigation of a reconstruction algorithm that uses a logarithmic transform of the density field is left to future work and will be applied to a large suite of cosmological simulations., Our full investigation of a reconstruction algorithm that uses a logarithmic transform of the density field is left to future work and will be applied to a large suite of cosmological simulations.
" When applying this method to an observed galaxy distribution, additional considerations must be accounted for, such as discreteness noise, galaxy bias, and redshift-space distortions."," When applying this method to an observed galaxy distribution, additional considerations must be accounted for, such as discreteness noise, galaxy bias, and redshift-space distortions."
" A log-transform can enhance the effective shot noise caused by particle (or galaxy) discreteness, but the log-density can still be usefully estimated in the presence of shot noise."," A log-transform can enhance the effective shot noise caused by particle (or galaxy) discreteness, but the log-density can still be usefully estimated in the presence of (low-enough) shot noise."
" Neyrincketal.(2011) found that(low-enough) even with a rather sparse galaxy sample, added power-spectrum Fisher information in the non-linear regime can be tapped with a log (or similar) transform, suggesting that shot noise can be overcome in the present case, as well."," \citet{ney10} found that even with a rather sparse galaxy sample, added power-spectrum Fisher information in the non-linear regime can be tapped with a log (or similar) transform, suggesting that shot noise can be overcome in the present case, as well."
" However, it is likely that higher sampling for the log-density field than for the overdensity field will be necessary to resolve the fields at a given resolution."," However, it is likely that higher sampling for the log-density field than for the overdensity field will be necessary to resolve the fields at a given resolution."
" Though a full reconstruction algorithm using a log-density field remains to be tested, we doubt that a logarithmic transform of the density would exacerbate problems caused by galaxy bias or redshift-space distortions, and these problems seem to be manageable in the case of BAO reconstruction."," Though a full reconstruction algorithm using a log-density field remains to be tested, we doubt that a logarithmic transform of the density would exacerbate problems caused by galaxy bias or redshift-space distortions, and these problems seem to be manageable in the case of BAO reconstruction."
" For example, it has been shown that linear reconstruction of the BAO peak reduces the effect of bias, including the induced shift in the location of the BAO peak (Mehtaetal. 2011)."," For example, it has been shown that linear reconstruction of the BAO peak reduces the effect of bias, including the induced shift in the location of the BAO peak \citep{meh11}."
". Additionally, Eisensteinetal.(2007) showed that reconstruction of the BAO peak is effective in both real- and redshift-space."," Additionally, \citet{eisrec} showed that reconstruction of the BAO peak is effective in both real- and redshift-space."
" However, we anticipate that Fingers of God will at some point prevent the push to smaller scales in redshift-space using a logarithmic transform."," However, we anticipate that Fingers of God will at some point prevent the push to smaller scales in redshift-space using a logarithmic transform."
 We have shown that a simple logarithmic transformation of the density field provides a substantial improvement of the linear theory relation between the density and displacement fields on sub-linear scales., We have shown that a simple logarithmic transformation of the density field provides a substantial improvement of the linear theory relation between the density and displacement fields on sub-linear scales.
 This improvement is greatest at low redshift and for Eulerian smoothing on small (~2 h! Mpc) scales., This improvement is greatest at low redshift and for Eulerian smoothing on small $\sim$ 2 $^{-1}$ Mpc) scales.
" This result is in line with the finding that the logarithmic density field restores some lost information to the power spectrum of density fluctuations (Neyrincketal. 2009),, and provides more evidence that a logarithmic transform of the density field isà powerful density variable on weakly nonlinear scales."," This result is in line with the finding that the logarithmic density field restores some lost information to the power spectrum of density fluctuations \citep{ney09}, , and provides more evidence that a logarithmic transform of the density field isa powerful density variable on weakly nonlinear scales."
Receutly. the BCS catalog has been published (Ebelingetal. 1998)).,"Recently, the BCS catalog has been published \cite{ebe98}) )."
 Uulike the NBAC's catalog which is based on the Abell cluster catalog. the BC'S clusters are selected purely by their A-ray properties.," Unlike the XBACs catalog which is based on the Abell cluster catalog, the BCS clusters are selected purely by their X-ray properties."
 The BCS contains 201 N-rav brightest clusters of galaxies with measured redshifts in the northern hemisphere (ὁ= 07) and at z207. aud is 90 complete at the N-rax flux limit of [P|LL«101Dergemn28um tin the 0.1~2.1 keV baud.," The BCS contains 201 X-ray brightest clusters of galaxies with measured redshifts in the northern hemisphere $\delta \ge 0\arcdeg$ ) and at $|b| \ge 20\arcdeg$, and is 90 complete at the X-ray flux limit of $4.4 \fxcgs$ in the $0.1 \sim 2.4$ keV band."
 Six sources. identified as three double clusters in the Abell catalog. are considered as six independent N-rav clusters since the sample should be based only on the N-ray information.," Six sources, identified as three double clusters in the Abell catalog, are considered as six independent X-ray clusters since the sample should be based only on the X-ray information."
 Adding these clusters and excluding three clusters with fluxes lower than the fiux lint. we have 201 X-ray clusters.," Adding these clusters and excluding three clusters with fluxes lower than the flux limit, we have 201 X-ray clusters."
 We have used the BCS to make four volumce-Iuited subsamples with £4>0.21. 0.18. 0.70. and 0.90. <Lol! hteres+ and with the redshift limits of 0.070. 0.099. 0.118. and 0.124 (see Fig.," We have used the BCS to make four volume-limited subsamples with $\lx \ge 0.24$, 0.48, 0.70, and 0.90 ${\rm \, \times 10^{44}\;}$ $h^{-2} {\rm erg\;s^{-1}}$ and with the redshift limits of 0.070, 0.099, 0.118, and 0.134 (see Fig."
 2)., 2).
 These sabsauiples contain 33. 19. LO. and 31 clusters. respectively.," These subsamples contain 33, 49, 40, and 34 clusters, respectively."
 Our high L.-limited subsaiuples of the NBAC's and the BCS clusters contain very rare objects (see Table 2))., Our high $\lx$ -limited subsamples of the XBACs and the BCS clusters contain very rare objects (see Table \ref{table_x}) ).
 The correlation function is an estimate of excess clustering over the random Poisson distribution., The correlation function is an estimate of excess clustering over the random Poisson distribution.
 We estimate. the CFs usine the conventional estimator DD/DR., We estimate the CFs using the conventional estimator DD/DR.
 We have also used. the Παποι. (1993)'s estimator which is less affected by uncertainties iu the selection function for £4.<1 compared to the DD/DR-uethocl., We have also used the Hamilton (1993)'s estimator which is less affected by uncertainties in the selection function for $\xi_{cc} < 1$ compared to the DD/DR-method.
 We fud that the differcuces between two estimators are insignificant in our analysis., We find that the differences between two estimators are insignificant in our analysis.
" Tere DD is the nuuber of pairs at separation r iu the sample with Αν clusters. RR is the number of pairs in a random sample with AV, vaudom poiuts. occupying the same survey volume and with the same selection function as the real cluster saluple. aud DR is the cluster-raudom pair count."," Here DD is the number of pairs at separation $r$ in the sample with $N_c$ clusters, RR is the number of pairs in a random sample with $N_r$ random points, occupying the same survey volume and with the same selection function as the real cluster sample, and DR is the cluster-random pair count."
" We conrpute the uncertainties of £,. using the formula δε=(11£,)/VDD.", We compute the uncertainties of $\xi_{cc}$ using the formula $\delta \xi_{cc} = (1 + \xi_{cc}) / \sqrt{{\rm DD}}$.
 Table 3. lists the CF data we have calculated., Table \ref{table_cf} lists the CF data we have calculated.
 Least-square fits of a power law equation (1) to the vest estimates of CE are presented in Table d. for the richness subsamples of the Abell and the APM clusters.," Least-square fits of a power law equation (1) to the best estimates of CF are presented in Table \ref{table_op}
 for the richness subsamples of the Abell and the APM clusters."
 We determine the confidence hHinits of cach xuranmeter individually assmuine that the distribution or the unucertaiuties of ©... is Caassian and different ©. ius are independent of cach other. which is a popular. mt strictly speaking. imiprecise asstuiption.," We determine the confidence limits of each parameter individually assuming that the distribution for the uncertainties of $\xi_{cc}$ is Gaussian and different $\xi_{cc}$ bins are independent of each other, which is a popular, but strictly speaking, imprecise assumption."
 Figure laa shows the CFs of the Abell clusters witee RC>0 (circle) and RCO>d (square)., Figure \ref{fig_xi}a a shows the CFs of the Abell clusters with $RC \ge 0$ (circle) and $RC \ge 1$ (square).
 The dashie« ine is Postman oet al. (, The dashed line is Postman et al. (
1992)s power law fit wit ry=20.6fhàMpe and 5=1.86 estimated for the AbeCRSP RC>0 sample.,1992)'s power law fit with $r_0 = 20.6 \hmpc$ and $\gamma = 1.86$ estimated for the Abell $RC \ge 0$ sample.
 The CFs in Figure Hob are those ο he APM clusters with R750 (filled circle). R>6 (triangle). R=70 (square). aud R>80 (open circle).," The CFs in Figure \ref{fig_xi}b b are those of the APM clusters with ${\cal R} \ge 50$ (filled circle), ${\cal R} \ge 60$ (triangle), ${\cal R} \ge 70$ (square), and ${\cal R} \ge 80$ (open circle)."
 The dotted line is a power law with ry=1L35.t\Ipe and 5=2.05 (CR.= 50) aud the dashed line is with ry=166hb!Mpe and 5=240 (R 10) both determined by Croft et al. (, The dotted line is a power law with $r_0 = 14.3 \hmpc$ and $\gamma = 2.05$ ${\cal R} \ge 50$ ) and the dashed line is with $r_0 = 16.6 \hmpc$ and $\gamma = 2.10$ ${\cal R} \ge 70$ ) both determined by Croft et al. (
1997).,1997).
" It can be noted that the amplitude of CF steadily increases as the richness lnhcreases,", It can be noted that the amplitude of CF steadily increases as the richness increases.
critical line structure in all previously published moclels for (Ηραία et al.,critical line structure in all previously published models for (Ibata et al.
 1999: σαι et al., 1999; Egami et al.
 2000: Munoz et al 2001). the resulting structure for the Einstein ring of a source centred upon the quasar nucleus should be quite circular. with a radius of ~0.2 aresecs. passing through the two brighter quasar images: such images for extended source can be seen in the models of σαι! et al. (," 2000; Munoz et al 2001), the resulting structure for the Einstein ring of a source centred upon the quasar nucleus should be quite circular, with a radius of $\sim0.2$ arcsecs, passing through the two brighter quasar images; such images for extended source can be seen in the models of Egami et al. ("
2000).,2000).
 Εις is quite cilferent to the CO structure displaved. in Figure L.. with the CO emission clearly showing a roughly cast-west extension. with the hole in the ring occurring 0.5 arcsecs [rom image A. Using the model derived. from the HIST data (bata et al.," This is quite different to the CO structure displayed in Figure \ref{fig1}, with the CO emission clearly showing a roughly east-west extension, with the hole in the ring occurring $\sim0.5$ arcsecs from image A. Using the model derived from the HST data (Ibata et al."
 1999). we explored the image configurations à range of sizes and shapes. centred. upon the quasar source. for the CO emitting region.," 1999), we explored the image configurations a range of sizes and shapes, centred upon the quasar source, for the CO emitting region."
 None reproduced the observed. image structure and we reject this previous model., None reproduced the observed image structure and we reject this previous model.
 Naked cusps occur in highly elliptical svstenis. such as lattened disks. when the inner diamond. caustic extends outside the elliptical caustic.," Naked cusps occur in highly elliptical systems, such as flattened disks, when the inner diamond caustic extends outside the elliptical caustic."
 A source inside this extension ooduces three roughly colinear images of similar brightness (Maller.. Flores Primack 1997: Bartelmann Loch 1998: Weeton Ixochanek. 1998: Moller Blain 1998: Blain. Moller Maller 1999: Bartelmann 2000).," A source inside this extension produces three roughly colinear images of similar brightness (Maller, Flores Primack 1997; Bartelmann Loeb 1998; Keeton Kochanek 1998; Moller Blain 1998; Blain, Moller Maller 1999; Bartelmann 2000)."
 While eravitational lensing by spiral galaxies has been observed (c.g. B 1600|434: Koopmans. Bruyn Jackson 1998) no observed. lensecl quasar svstem has so far been. associated with a naked cusp.," While gravitational lensing by spiral galaxies has been observed (e.g. B 1600+434; Koopmans, Bruyn Jackson 1998) no observed lensed quasar system has so far been associated with a naked cusp."
 To examine the possibility that the observed image configuration is due to gravitational lensing by a naked cusp. we constructed a simple mass model.," To examine the possibility that the observed image configuration is due to gravitational lensing by a naked cusp, we constructed a simple mass model."
 Following Datelmann and Loeb (1998). this consists of a truncated Ilattened clisk in a spherical halo.," Following Batelmann and Loeb (1998), this consists of a truncated flattened disk in a spherical halo."
 has brightened considerably since its discovery (Lewis. Robb Lhata 1999: IE. Ofek priv.," has brightened considerably since its discovery (Lewis, Robb Ibata 1999; E. Ofek priv."
 comnr.," comm.,"
 see http://wise-obs.tau.ac.il/--eran/LM). potentially due to the elfects of gravitational microlensing.," see ), potentially due to the effects of gravitational microlensing."
 Comparing the images obtained in 1998 (Ηραία et al., Comparing the images obtained in 1998 (Ibata et al.
 1999: σαι et al., 1999; Egami et al.
 2000) and those obtained in 1999 (Munoz et al., 2000) and those obtained in 1999 (Munoz et al.
 2001). the relative image brightness have changed. appreciably. with image D changing from being of image A to only in the latter epoch: such behaviour is extremely suggestive of the action of gravitational microlensing. although longer term monitoring is required to confirm this.," 2001), the relative image brightness have changed appreciably, with image B changing from being of image A to only in the latter epoch; such behaviour is extremely suggestive of the action of gravitational microlensing, although longer term monitoring is required to confirm this."
 Hence. the relative image brightnesses cannot be used to constrain any mass model.," Hence, the relative image brightnesses cannot be used to constrain any mass model."
 Given the sparsity of constraints. we choose to find à model that can recover the image positions. while providing a reasonable description. of the observed. CO emission.," Given the sparsity of constraints, we choose to find a model that can recover the image positions, while providing a reasonable description of the observed CO emission."
 As can be imagined. the parameter space is large. so a range of models that reproduced the quasar positions were chosen and then modeling of the CO emission. was undertaken by-eve.," As can be imagined, the parameter space is large, so a range of models that reproduced the quasar positions were chosen and then modeling of the CO emission was undertaken by-eye."
 With this. therefore. we do not. claim that the model presented here is unique. only consistent with the general form of data.," With this, therefore, we do not claim that the model presented here is unique, only consistent with the general form of data."
 In our chosen model. the disk is highlv inclined. presenting a projected. axis ratio of 0.25. and the disk truncated. at Sh tkpe and possess a core radius of," In our chosen model, the disk is highly inclined, presenting a projected axis ratio of 0.25, and the disk truncated at $h^{-1}$ kpc, and possess a core radius of"
vield. minimal zeropoints that solve the set.,yield minimal zeropoints that solve the set.
 Llowever. we rave used faint CCD photometry to externally fix as many zeropoints as possible over the survey region.," However, we have used faint CCD photometry to externally fix as many zeropoints as possible over the survey region."
 This makes he equation set nonsingular and vields a unique vector of zeropoints that are tied. to an external system., This makes the equation set non–singular and yields a unique vector of zeropoints that are tied to an external system.
 This »ocedure is similar to that adopted by Maddox. Efstathiou Sutherland (1990) for the APAL Galaxy Survey except wt we have solved for the fieldtofield. dillerences in 1e eradients of the photometric scales.," This procedure is similar to that adopted by Maddox, Efstathiou Sutherland (1990) for the APM Galaxy Survey except that we have solved for the field–to–field differences in the gradients of the photometric scales."
 Also. our sources ( external CCD photometry included data from the Guide Star Photometric Catalogue LE (Postman et al.," Also, our sources of external CCD photometry included data from the Guide Star Photometric Catalogue II (Postman et al."
 1997). Bovle et al. (," 1997), Boyle et al. ("
1995). Croom et al. (,"1995), Croom et al. ("
1999). Cunow et al. (,"1999), Cunow et al. ("
1997) and references therein. unpublished data used in the calibration of the Edinburgh.Durham Southern Galaxy Catalogue (e.g. Nichol 1993 and references therein) and Stobie. Sagar Gilmore (1985) in addition to that published in Maddox et al. (,"1997) and references therein, unpublished data used in the calibration of the Edinburgh–Durham Southern Galaxy Catalogue (e.g. Nichol 1993 and references therein) and Stobie, Sagar Gilmore (1985) in addition to that published in Maddox et al. ("
1990).,1990).
 At the time of writing. approximately of all southern hemisphere fields have external CCD data defining their photometrie zeropoint.," At the time of writing, approximately of all southern hemisphere fields have external CCD data defining their photometric zeropoint."
 The photometric calibration of photographic plates based on calibrating stars necessarily assumes that there exists a unique calibration curve that is applicable over the cntire plate., The photometric calibration of photographic plates based on calibrating stars necessarily assumes that there exists a unique calibration curve that is applicable over the entire plate.
 In general. this is the case.," In general, this is the case."
 For example. graphs of external photoclectric magnitude versus internal linearised profile magnitude. as a function. of plate position. show significant changes in gradient.," For example, graphs of external photoelectric magnitude versus internal linearised profile magnitude, as a function of plate position, show significant changes in gradient."
 One possible cause of this is that the response of the photographic emulsion is not uniform over the plate ic. the characteristic curve of the emulsion is not constant., One possible cause of this is that the response of the photographic emulsion is not uniform over the plate – i.e. the characteristic curve of the emulsion is not constant.
 Whatever the cause. the results are the same: systematic errors in photometry as a function of magnitude ancl position occur. and those errors manifest themselves most. visibly when magnitudes are combined to generate colour indices.," Whatever the cause, the results are the same: systematic errors in photometry as a function of magnitude and position occur, and those errors manifest themselves most visibly when magnitudes are combined to generate colour indices."
 Moreover. we have assumed a constant value of the gradient of the profile magnitude scale in any given passband. and as Table 3. shows there is a significant dispersion about the mean values adopted which adds to any. systematic effects within a given plate.," Moreover, we have assumed a constant value of the gradient of the profile magnitude scale in any given passband, and as Table \ref{gradients} shows there is a significant dispersion about the mean values adopted which adds to any systematic effects within a given plate."
 For example. Figure 7 shows an L versus (1t1). colourmagnitude diagram Lor survey field 758.," For example, Figure \ref{cmdbefore} shows an I versus (R–I) colour--magnitude diagram for survey field 758."
 There is apparently a trend for brighter stars to get. become bluer in this diagram. along with a significant increase in scatter about the modal colour for brighter magnitude. ranges.," There is apparently a trend for brighter stars to get become bluer in this diagram, along with a significant increase in scatter about the modal colour for brighter magnitude ranges."
 ποσο elfects are both due to systematic errors in photonietry as a function of magnitude ancl position., These effects are both due to systematic errors in photometry as a function of magnitude and position.
 Furthermore. Figure S shows a stellar GJ1t) versus (1t1) twocolour diagram for a mosaic of 9 [fields at the South Galactic Pole for the magnitude range 17«DjIs.," Furthermore, Figure \ref{twocolbefore} shows a stellar (J–R) versus (R–I) two–colour diagram for a mosaic of 9 fields at the South Galactic Pole for the magnitude range $17<{\rm B}_{\rm J}<18$."
 While the general trend of red. objects being red in both colours is apparent. it is also true that stars having intermediate colours do not show a good correlation between (J.RJ and (I.D.," While the general trend of red objects being red in both colours is apparent, it is also true that stars having intermediate colours do not show a good correlation between (J–R) and (R–I)."
 Phe scatter in Figure Sis rather large. and masks astrophysically useful information.," The scatter in Figure \ref{twocolbefore}
 is rather large, and masks astrophysically useful information."
 These problems have been documented in the past (e.g. Εαν et al., These problems have been documented in the past (e.g. Hambly et al.
 1995: Goldschmidt Miller: 1998. and references therein)., 1995; Goldschmidt Miller 1998 and references therein).
 In the abscence of largescale external calibration sequences. there is no option other than to," In the abscence of large–scale external calibration sequences, there is no option other than to"
main sequence stars. may be measured from the variations in the H K and photometric fluxes.,"main sequence stars, may be measured from the variations in the H K and photometric fluxes."
 The presence of magnetic features on a stellar surface can also cause radial velocity and photometrie variations that ean mask or mimic a planet's orbital or transit signature (222)..," The presence of magnetic features on a stellar surface can also cause radial velocity and photometric variations that can mask or mimic a planet's orbital or transit signature \citep{SD97,DDB97,Paulson04}."
 HD 166435 is a prime example: its radial velocity variations were shown to be stellar in nature. explaining the apparent orbital period equalling the stellar rotation period (2)..," HD 166435 is a prime example; its radial velocity variations were shown to be stellar in nature, explaining the apparent orbital period equalling the stellar rotation period \citep{Queloz01}."
 The detection of planets around T Tauri stars presents even. more of a challenge. where stellar activity is stronger than in main sequence stars and the absence of a correlation between visible-light radial velocity variations and line bisector span is not sufficient to rule out the presence of starspots as the cause of the variations (2)..," The detection of planets around T Tauri stars presents even more of a challenge, where stellar activity is stronger than in main sequence stars and the absence of a correlation between visible-light radial velocity variations and line bisector span is not sufficient to rule out the presence of starspots as the cause of the variations \citep{Prato08}."
 It is therefore very important to monitor the magnetic activity of exoplanet host stars in order to: a) confirm or refute intrinsic stellar variability as the cause of observations attributed to the presence of exoplanets and b) to find an effective method to remove stellar jitter. allowing us to detect smaller planets and to probe the planet populations around magnetically active stars.," It is therefore very important to monitor the magnetic activity of exoplanet host stars in order to: a) confirm or refute intrinsic stellar variability as the cause of observations attributed to the presence of exoplanets and b) to find an effective method to remove stellar jitter, allowing us to detect smaller planets and to probe the planet populations around magnetically active stars."
 Surveys at Mount Wilson and Fairborn Observatories have been making such observations for several decades., Surveys at Mount Wilson and Fairborn Observatories have been making such observations for several decades.
" With additional data. such as from astrometric observations. /, can be found for non-transiting systems (e.g..22) and compared to 7, to determine the line-of-sight alignment."," With additional data, such as from astrometric observations, $i_{p}$ can be found for non-transiting systems \citep[e.g.,][]{Benedict06,McArthur10} and compared to $i_{*}$ to determine the line-of-sight alignment."
 In the case of planets that have migrated inwards towards their host stars. the migration mechanism can be probed.," In the case of planets that have migrated inwards towards their host stars, the migration mechanism can be probed."
 Migration theories such as disc-planet interactions (2). are thought not to perturb the orbital inclination and may even drive the system further toward alignment., Migration theories such as disc-planet interactions \citep{Lin96} are thought not to perturb the orbital inclination and may even drive the system further toward alignment.
 In contrast. theories involving planet-planet interactions (22). or the Kozai mechanism ¢??) could cause axial misalignment.," In contrast, theories involving planet-planet interactions \citep{RF96, WM96} or the Kozai mechanism \citep{Kozai62, WM03} could cause axial misalignment."
 Measuring he alignment therefore offers a means of discriminating between migration mechanisms., Measuring the alignment therefore offers a means of discriminating between migration mechanisms.
" In the case of non-migrating planets. the comparison between ἐν and /, tells us about the planet formation oroeesses and whether the assumption of coplanarity is correct. because the timescale for coplanarisation is thought to be longer han the main sequence lifetime (e.g..22).."," In the case of non-migrating planets, the comparison between $i_{p}$ and $i_{*}$ tells us about the planet formation processes and whether the assumption of coplanarity is correct, because the timescale for coplanarisation is thought to be longer than the main sequence lifetime \citep[e.g.,][]{Winn05,Hale94}."
 In this paper we infer the rotation periods of ten exoplanet 108t stars from periodic variations in H K and photometric observations., In this paper we infer the rotation periods of ten exoplanet host stars from periodic variations in H K and photometric observations.
 We then test that the exoplanet inference is not due to magnetic activity., We then test that the exoplanet inference is not due to magnetic activity.
 Finally. we calculate the inclination of the stellar rotation axes and. under the assumption of alignment. estimate the planetary mass.," Finally, we calculate the inclination of the stellar rotation axes and, under the assumption of alignment, estimate the planetary mass."
 Out of the approximately 350 stars hosting exoplanet companions. HH K measurements of 57 have been made during the decades of the Mount Wilson HK project. see ? Του details.," Out of the approximately 350 stars hosting exoplanet companions, H K measurements of 57 have been made during the decades of the Mount Wilson HK project, see \citet{Bal05} for details."
 Denser. intra-seasonal sampling sufficient. to. reveal rotational modulation. begun in 1980. yields a sample of 36 exoplanet host stars observed on more than 30 occasions.," Denser, intra-seasonal sampling sufficient to reveal rotational modulation, begun in 1980, yields a sample of 36 exoplanet host stars observed on more than 50 occasions."
 Rotational periodicities in several of these stars have previously been reported (222).," Rotational periodicities in several of these stars have previously been reported \citep{Bal96,Don96,Henry00}."
 The records were re-calibrated in 2003 to compensate for long term variations in the instruments. standard stars and are calibration lamp.," The records were re-calibrated in 2003 to compensate for long term variations in the instruments, standard stars and arc calibration lamp."
 This. combined with an increased dataset. allowed a search for previously unknown rotation periods.," This, combined with an increased dataset, allowed a search for previously unknown rotation periods."
 In addition. photometric records taken using Tennessee State's TIL O.80-m high-precision automatic photometric telescope (APT) of HD 130322. the most magnetically active (highest log exoplanet host star without an already determined rotation Rperiod.g4 were analysed.," In addition, photometric records taken using Tennessee State's T11 0.80-m high-precision automatic photometric telescope (APT) of HD 130322, the most magnetically active (highest $_{HK}$ )) exoplanet host star without an already determined rotation period, were analysed."
 The Strómmgren b and jj filter data were combined into a single measurement. (b.|y)/2. to improve precision to | mmag for a nightly observation and [-2 mmag over a season. see 22??? for further details of instrumental and. data reduction procedures.," The Strömmgren $b$ and $y$ filter data were combined into a single measurement, $(b+y)/2$ , to improve precision to 1 mmag for a nightly observation and 1-2 mmag over a season, see \citet{Henry95b,Henry95a, Henry96, Henry99} for further details of instrumental and data reduction procedures."
 Nightly observations of the target star and two comparison stars were made between 2002 and 2007 and differential magnitudes calculated., Nightly observations of the target star and two comparison stars were made between 2002 and 2007 and differential magnitudes calculated.
 A moditied Lomb-Seargle periodogram analysis (2)... with a technique outlined by ? and tailored for the HK database was used to determine periodicities in both datasets.," A modified Lomb-Scargle periodogram analysis \citep{Scargle82}, with a technique outlined by \citet{HB86} and tailored for the HK database was used to determine periodicities in both datasets."
 Any seasonal trend was fitted with a low order polynomial and removed from the data and the periodogram analysis applied., Any seasonal trend was fitted with a low order polynomial and removed from the data and the periodogram analysis applied.
 The significance of the periodogram peaks was estimated by the false alarm probability. FAP (??)..," The significance of the periodogram peaks was estimated by the false alarm probability, FAP \citep{Scargle82,HB86}."
 A FAP of is equivalent to a confidence level of that the peak does not arise by chance and is the cut-off used to define the detection of a periodicity., A FAP of is equivalent to a confidence level of that the peak does not arise by chance and is the cut-off used to define the detection of a periodicity.
 Biases can be introduced) by. time-dependent stellar phenomena such as the growth and decay of active regions., Biases can be introduced by time-dependent stellar phenomena such as the growth and decay of active regions.
— Occasionally. this can affect part of a season so subdivided sections of the seasonal light curve were analysed separately (typically half).," Occasionally, this can affect part of a season so subdivided sections of the seasonal light curve were analysed separately (typically half)."
 The growth and decay of active regions occurs on timescales of 2 560-300 d. which can mimic or influence the appearance of a rotational period ( 1—100 d) (22)..," The growth and decay of active regions occurs on timescales of $\simeq$ 50–300 d, which can mimic or influence the appearance of a rotational period $\simeq$ 1–100 d) \citep{Don93,DDB97}."
 The number of cycles contained in a season is generally small and a transient variation could dramatically alter the power at a particular frequeney., The number of cycles contained in a season is generally small and a transient variation could dramatically alter the power at a particular frequency.
 This exemplifies the need to determine the persistence of a period in more than one season., This exemplifies the need to determine the persistence of a period in more than one season.
 ? found an empirical relationship between a lower main-sequence stars average magnetic activity. £52. and its rotation period. arising from increased magnetic activity induced by rapid rotation.," \citet{Noyes84} found an empirical relationship between a lower main-sequence star's average magnetic activity, $\langle S \rangle$, and its rotation period, arising from increased magnetic activity induced by rapid rotation."
 Therefore. from an estimate of surface magnetic activity. the rotation period. {λαο of a star can be estimated and compared with the observationally inferred period.," Therefore, from an estimate of surface magnetic activity, the rotation period, $P_{calc}$ of a star can be estimated and compared with the observationally inferred period."
 The HK project has been monitoring stars for up to four decades and. in many cases. over at least one activity cycle.," The HK project has been monitoring stars for up to four decades and, in many cases, over at least one activity cycle."
 Therefore the average magnetic activity of the stars in this sample are well known., Therefore the average magnetic activity of the stars in this sample are well known.
 We have redetermined ae for these stars using all the available data from the HK records. and we tind that they have not changed significantly from the values previously determined from the dataset (e.g... 29).," We have redetermined $P_{calc}$ for these stars using all the available data from the HK records, and we find that they have not changed significantly from the values previously determined from the dataset (e.g., \citealt{Henry00}) )."
 The signiticance of a determined rotation period is based on three criteria: The determination of the rotation period is qualified by a grade: (periodicities show a very low FAP < 0.0001 and all three criteria are met). (moderate to low FAP ~ 0.001 and meets most or all of the criteria). (a weaker FAP ~ 0.01 but meets criteria (1) and (Gl).," The significance of a determined rotation period is based on three criteria: The determination of the rotation period is qualified by a grade; (periodicities show a very low FAP $<$ 0.0001 and all three criteria are met), (moderate to low FAP $\sim$ 0.001 and meets most or all of the criteria), (a weaker FAP $\sim$ 0.01 but meets criteria (i) and (iii))."
 We searched for periodicities associated with stellar rotation in exoplanet host stars in the ΤΠ K records of 36 stars and photometric measurements of HD 130322., We searched for periodicities associated with stellar rotation in exoplanet host stars in the H K records of 36 stars and photometric measurements of HD 130322.
 Eighteen of these stars showed no vriability consistent with rotation (see Table 1)., Eighteen of these stars showed no variability consistent with rotation (see Table 1).
 The rotation periods ofeight stars in our sample have previously been, The rotation periods ofeight stars in our sample have previously been
required and have not been considered so far.,required and have not been considered so far.
 In this section we are going to show how the radial scale height is related to the mass continuity equation., 	In this section we are going to show how the radial scale height is related to the mass continuity equation.
 We also show (hat. in order to have a disk scale heieht varving with racial distance. one needs to look for processes that add an extra term to the continuity equation.," We also show that, in order to have a disk scale height varying with radial distance, one needs to look for processes that add an extra term to the continuity equation."
 Since the disk is assumed to have azvimuthal sviumetry. being under hyvedrostatic equilibrium in z-«lirection. the continuity equation reads. with r.p. V4 bemg. respectively. radial distance. mass densitv and radial velocity.," Since the disk is assumed to have azymuthal symmetry, being under hydrostatic equilibrium in z-direction, the continuity equation reads, with $r$ ,$\rho$, $V_{r}$ being, respectively, radial distance, mass density and radial velocity."
 I1 should be said that the above equation neglects mass (iransport due to turbulence. which is equivalent (o assuming sub sonic turbulence regime.," It should be said that the above equation neglects mass transport due to turbulence, which is equivalent to assuming sub sonic turbulence regime."
" Now. we sel f/(r.z)=rpWM, and expand f in powers of z to obtain where account was taken of reflexion svinmnetry over z."," Now, we set $f{\left(r\, , z\, \right)}= r\, \rho\, V_{r}\, $ and expand $f$ in powers of $z$ to obtain where account was taken of reflexion symmetry over $z$."
 Inserting f(r.z) given by eq.(2) into eq.(1) gives selling z= 0. we must have or where Cy is constant.," Inserting $f{\left(r\, , z\, \right)}$ given by eq.(2) into eq.(1) gives Setting $z=0$ , we must have or where $C_{0}$ is constant."
 For z40. we recall that which. bv eq.(1). should give," For $z \neq 0$ we recall that which, by eq.(1), should give"
 columu density from the Rao&Turushek(2000) coliunu deusity distribution. aud (2) no evolution in the column density distribution [rom (2)20.8.," column density from the \citet{rt2000}
 column density distribution, and (2) no evolution in the column density distribution from $\left< z\right> \simeq 0.8$."
 Note that the distribution at (23X220.8 was observed to significantly evolve [rom (2)222.3 in that the lower redshift distribution has a greater [raction of large N(HI) systems (Rao&Turushek2000)., Note that the distribution at $\left< z\right> \simeq 0.8$ was observed to significantly evolve from $\left< z \right> \simeq 2.3$ in that the lower redshift distribution has a greater fraction of large $N({\HI})$ systems \citep{rt2000}.
". IL this evolutionary treu continued. the deduced £2,4 would be greater. a result that would increase the diserepaucy between the absorption line aud data."," If this evolutionary trend continued, the deduced $\Omega _{ DLA}$ would be greater, a result that would increase the discrepancy between the absorption line and data."
 Sincem «αςrif is. proportional. to the product (o=πιή.> redshift⋅⋅ evolution⋅ in⋅ dVTd/d2 would üunply redshift evolution in this product.," Since $dN/dz$ is proportional to the product $ n\sigma = \pi \Phi
_{\ast} R_{\ast}^{2}$, redshift evolution in $dN/dz$ would imply redshift evolution in this product."
 There is also a depeudeuce ou the faiut-eud slope of the luminosity function. whieli has beeu seeu to weakly evolve from intermediate redshlifts 1998).," There is also a dependence on the faint–end slope of the luminosity function, which has been seen to weakly evolve from intermediate redshifts \citep[e.g.,][]{marzke98}."
. However. this will not be cousidered here.," However, this will not be considered here."
 For 0.2€z1. the normalization of the galaxy. luminosity fiction. 9. for absorption selected. galaxies (Steideletal.1991). is cousistent with that of photometric galaxies surveys (e.o..Lillyetal.1995:Ellis1996:Lin1999).," For $0.2 \leq z \leq 1$, the normalization of the galaxy luminosity function, $\Phi _{\ast}$ for absorption selected galaxies \citep{sdp94} is consistent with that of photometric galaxies surveys \citep[e.g.,][]{lilly95,ellis96,lin99}."
". However. there is someambiguity ancl disagreement as to whether d, is smaller by a factor of ~2 over the redshift range 0€z<0.2 fe.e..Maddoxetal.1990:Loveday1992:Bertin&Denuneleld1997:Marzke1995)."," However, there is someambiguity and disagreement as to whether $\Phi_{\ast}$ is smaller by a factor of $\sim 2$ over the redshift range $0\leq z \leq
0.2$ \citep[e.g.,][]{maddox90,loveday92,bertin97,marzke98}."
". Asstuning uo evolution in &,. the upper limit on absorber sizes would be kpe."," Assuming no evolution in $\Phi_{\ast}$, the upper limit on absorber sizes would be $R_{\ast} \leq \sqrt{0.32/0.56} \cdot 40 =
30$ kpc."
 Smaller absorbing cross sections could result from a general relaxation of “halo” gas with time., Smaller absorbing cross sections could result from a general relaxation of “halo” gas with time.
 As such. this mieht result in the average absorber at 2~0 having a relatively largee equivalent width aud arisingOm at relatively lower impact parameters.," As such, this might result in the average absorber at $z \simeq 0$ having a relatively large equivalent width and arising at relatively lower impact parameters."
" This mighte explain why uo W,.(2796)<0.6 systems were fouud in this survey.", This might explain why no $W_{r}(2796) < 0.6$ systems were found in this survey.
" Thisis also consistent with the results of Bowen.Blades.&Pettini(1995).. who found 1,(2796)>0.6 within 10 kpe for four out of [ive galaxies aud. uo absorption down to 0.01<WW).0.09 (2 σ) beyond 30 kpc for nine of ten galaxies."," Thisis also consistent with the results of \citet{bbp95}, who found $W_{r}(2796) > 0.6$ within $10$ kpc for four out of five galaxies and no absorption down to $0.04 \leq W_{r}
\leq 0.09$ $2~\sigma$ ) beyond $30$ kpc for nine of ten galaxies."
 Unfortuuately. they did uot sample the impact parameters between ~10 aud ~30 kpe.," Unfortunately, they did not sample the impact parameters between $\sim10$ and $\sim 30$ kpc."
 These statements depeud upon a relatively small survey in which the lack of detected small W.€2796) systems could be dominating the number statistics., These statements depend upon a relatively small survey in which the lack of detected small $W_{r}(2796)$ systems could be dominating the number statistics.
" Smaller galaxy. gas cross-sections would require some level of turnover at simall H,(2796) in the equivalent width distribution at zcQ.", Smaller galaxy gas cross–sections would require some level of turnover at small $W_{r}(2796)$ in the equivalent width distribution at $z\simeq 0$.
 Au unbiased survey for absorption systems at 2<0.15 was couducted in 147 FOS spectra., An unbiased survey for absorption systems at $z < 0.15$ was conducted in 147 FOS spectra.
 The total redshift path was Az= 18.8. with a rapid decline below (τος—0.5 A (5 6).," The total redshift path was $\Delta z =
18.8$ , with a rapid decline below $W_{r}(2796) = 0.5$ $5~\sigma$ )."
 Main results of this work are: (1) Four “unbiased” systems were fouud.two of which were previously published," Main results of this work are: (1) Four “unbiased” systems were found,two of which were previously published"
and lock the vertical alignment.,and lock the vertical alignment.
 Another possible interpretation of 2D analyses is that they capture the dynamics of vortices that are confined to the midplane of (he disk., Another possible interpretation of 2D analyses is that they capture the dynamics of vortices that are confined to the midplane of the disk.
 We initialized linite-height. evlindrical vortices straddling the midplane of the disk and allowed them to evolve into quasi-equilibria.," We initialized finite-height, cylindrical vortices straddling the midplane of the disk and allowed them to evolve into quasi-equilibria."
 These vor(üces were high-pressure anticvelones in which the inward Coriolis Loree balanced the outward. pressure force., These vortices were high-pressure anticyclones in which the inward Coriolis force balanced the outward pressure force.
 In the vertical direction. the vortex needed cool. dense lids to exert a buovant force toward the midplane to balance the pressure force away from the midplane (see Figure 2)).," In the vertical direction, the vortex needed cool, dense lids to exert a buoyant force toward the midplane to balance the pressure force away from the midplane (see Figure \ref{F:force_balance}) )."
" Long-term simulations of such vortices revealed that they too are unstable equilibria,", Long-term simulations of such vortices revealed that they too are unstable equilibria.
 We isolated an antisvinmetrie (wilh respect to the midplane) eigenmode that grew with an e-Iolding time of only a few orbital periods around the protostar., We isolated an antisymmetric (with respect to the midplane) eigenmode that grew with an $e$ -folding time of only a few orbital periods around the protostar.
 These vortices only seemed (o last a long time because our initial conditions were svnuuetric wilh respect to the midplane. and the antisvimnetric eigenmoce was seeded only with numerical round-olff error.," These vortices only seemed to last a long time because our initial conditions were symmetric with respect to the midplane, and the antisymmetric eigenmode was seeded only with numerical round-off error."
" We confess that when we started this work. we too believed vortices in protoplanetary disks would be either quasi-2D infinie"" columns. or short truncated cxvlindrical vortices confined to the midplane of the disk."," We confess that when we started this work, we too believed vortices in protoplanetary disks would be either quasi-2D “infinite” columns, or short truncated cylindrical vortices confined to the midplane of the disk."
 Surprisingly. our simulations revealed ai unexpected (hirel possibility: off-iidplane vortices a few scale heiehts above and below the midplane.," Surprisingly, our simulations revealed an unexpected third possibility: off-midplane vortices a few scale heights above and below the midplane."
 These vortices are also high pressure anticvclones., These vortices are also high pressure anticyclones.
 For a vortex in the upper half of the disk. the high-pressure core is balanced by a cool. dense top lid which pushes clownward. and a warm. low-density bottom lid which pushes upward.," For a vortex in the upper half of the disk, the high-pressure core is balanced by a cool, dense top lid which pushes downward, and a warm, low-density bottom lid which pushes upward."
 The density ancl temperature of these lids are maintained by the vertical motions within the vortex: rising (falling) motion acdiabaticallv cools (heats) a stably-stratified. fluid. (see Figure 2bb)., The density and temperature of these lids are maintained by the vertical motions within the vortex: rising (falling) motion adiabatically cools (heats) a stably-stratified fluid (see Figure \ref{F:force_balance}b b).
 Simulations with no vertical gravitv and/or those with barotropic equations of state will fail to [ind such vortices., Simulations with no vertical gravity and/or those with barotropic equations of state will fail to find such vortices.
 Also. numerical caleulations must have sufficient resolution to capture the thermal lids. which tvpically have thicknesses much smaller (han the local pressure scale height.," Also, numerical calculations must have sufficient resolution to capture the thermal lids, which typically have thicknesses much smaller than the local pressure scale height."
 Unlike the tall. columnar vortices and the finite-heieht cvlindrical midplane vortices which we put in the disk bx hand. the off-imidplane vortices formed naturally from perturbations in the disk.," Unlike the tall, columnar vortices and the finite-height cylindrical midplane vortices which we put in the disk by hand, the off-midplane vortices formed naturally from perturbations in the disk."
 For example. as a midplane vortex oscillatecl ancl relaxed toward ils equiasi- (he cataclysmic motions as it succumbed to (he antlisvuumetric instability). il excited internal gravity. waves which propagated away from (he midplane. steepened. ancl broke. creating vorlicily (a baroclinic effect).," For example, as a midplane vortex oscillated and relaxed toward its quasi-equilibrium the cataclysmic motions as it succumbed to the antisymmetric instability), it excited internal gravity waves which propagated away from the midplane, steepened, and broke, creating vorticity (a baroclinic effect)."
 Regions of antievclonic vorticity rolled-up and coalesced into new antievelones. whereas regions of evelonic vorticity were stretched into thin azimuthal bands and sheets by the ambient shear.," Regions of anticyclonic vorticity rolled-up and coalesced into new anticyclones, whereas regions of cyclonic vorticity were stretched into thin azimuthal bands and sheets by the ambient shear."
 In simulations where we had only one Olfinidplane vortex as an initial condition. new vortices reformed. filling every available racial band.," In simulations where we had only one off-midplane vortex as an initial condition, new vortices reformed, filling every available radial band."
 These off-midplane vortices are robust. surviving indelinitelv in our simulations (over 400 orbits) despite countless close encounters and interactions with other vortices.," These off-midplane vortices are robust, surviving indefinitely in our simulations (over 400 orbits) despite countless close encounters and interactions with other vortices."
 The svinetries of an isolated vortex preclude significant angular momentum (ransport., The symmetries of an isolated vortex preclude significant angular momentum transport.
turning on the shaping mechanism can be narrowed to the late AGB/fearly post-AGB phase.,turning on the shaping mechanism can be narrowed to the late AGB/early post-AGB phase.
 Further. the slowly-growing subclass of water fountain! sources (first discovered. anc aptlv named: by Likkel Morris 1988). with about LO members(Imai2007).. can potentially clucidate the mystery of the shaping mechanism.," Further, the slowly-growing subclass of `water fountain' sources (first discovered and aptly named by Likkel Morris 1988), with about 10 members\citep{imai07}, can potentially elucidate the mystery of the shaping mechanism."
 Water fountains are bipolar post-ACGB stars that display. highly collimated and high. velocity. expanding regions (typically. Poxp X LOO kin YY ο maser emission.," Water fountains are bipolar post-AGB stars that display highly collimated and high velocity expanding regions (typically $v_{\rm
exp}$ $<$ 100 km $^{-1}$ ) of maser emission."
 The spectral profile of the maser emission displavs a larger velocity range of emission compared to that of Oll. where present: maps of the sources reveal that the OLI emission. traces the remnant molecular shell while the emission. is shock-excited in collimated bipolar jets (imaictal.2002).," The spectral profile of the maser emission displays a larger velocity range of emission compared to that of OH, where present; maps of the sources reveal that the OH emission traces the remnant molecular shell while the emission is shock-excited in collimated bipolar jets \citep{imai02}."
. Observations seem to confirm the theory that these hieh velocity jets are likely driven by magneto-hyclrocnamical orocesses (Vlemnmüngsetal.2006)., Observations seem to confirm the theory that these high velocity jets are likely driven by magneto-hydrodynamical processes \citep{vlemmings06}.
.. llowever. whether 16 observed. strong magnetic fields originate from. single gaars or through binary interactions is still unclear.," However, whether the observed strong magnetic fields originate from single stars or through binary interactions is still unclear."
 Water untains may therefore represent an extremely short-IHved hase of post-AGB evolution that all such objects. pass ough. where much of the sjiping takes place via the sculpting caused by the high velocity jets.," Water fountains may therefore represent an extremely short-lived phase of post-AGB evolution that all such objects pass through, where much of the shaping takes place via the sculpting caused by the high velocity jets."
 Alternatively. rev may be a special subset of stars. perhaps the more massive ones that evolve quicker and have sulliciently thick envelopes to shield. clouds of vapour and. preserve wm to later be shocked into masing by the fast wind (Suarez ct al.," Alternatively, they may be a special subset of stars, perhaps the more massive ones that evolve quicker and have sufficiently thick envelopes to shield clouds of vapour and preserve them to later be shocked into masing by the fast wind (Suarez et al."
 2007)., 2007).
 Either way. their discovery. represents ui exciting new adcdition to the study of the [ate stages of gaellar In this Letter. we report on the detection of a maser towards the voung post-AGB star known as OLI 009.1.0.4 and b292 (Sevensterοἱal.1997).. which shows maser emission over the widest velocity range known in our Galaxy. confirming it as a new addition to the short [ist of known water fountains.," Either way, their discovery represents an exciting new addition to the study of the late stages of stellar In this Letter, we report on the detection of a maser towards the young post-AGB star known as OH 009.1–0.4 and b292 \citep{sevenster97}, which shows maser emission over the widest velocity range known in our Galaxy, confirming it as a new addition to the short list of known water fountains."
 The post-AGB star is associated with the LRAS source. 18045.2116., The post-AGB star is associated with the IRAS source 18043–2116.
 It is unusual in that it exhibits MMlIz and. MMIIz OLI maser emission. but not at MMIIz (Deaconetal.2004).," It is unusual in that it exhibits MHz and MHz OH maser emission, but not at MHz \citep{deacon04}."
. Furthermore. itis the only known post-AGB star to show MMIZ OLLI maser emission. which is thought to arise in the region where the AGB and starting planetary nebula winds collide (Sevenster&Chapman 2001)...," Furthermore, it is the only known post-AGB star to show MHz OH maser emission, which is thought to arise in the region where the AGB and starting planetary nebula winds collide \citep{sevenster01}. ."
 Previous observations of maser emission towards OLL 009.10.4 2007) showed emission coveringkms.. although the authors noted that there could be other maser features that were outside the observed velocity The Australia Telescope National Facility Mopra telescope is à 22mm antenna located. 26kkm outside the town of Coonabarrabran in New South Wales. Australia.," Previous observations of maser emission towards OH 009.1–0.4 \citep{deacon07} showed emission covering, although the authors noted that there could be other maser features that were outside the observed velocity The Australia Telescope National Facility Mopra telescope is a m antenna located km outside the town of Coonabarrabran in New South Wales, Australia."
 It is at an elevation of 850 metres above sea level and at a latitucle of 31° Observations of ΟΕ 009.10.4. were. performed. as part of the Large survey LOPS on 2008 March. 9 and 10. using the on-the-Is. mapping method.," It is at an elevation of 850 metres above sea level and at a latitude of $^\circ$ Observations of OH 009.1–0.4 were performed as part of the large survey HOPS on 2008 March 9 and 10, using the on-the-fly mapping method."
 Total. on-source integration time is approximately two minutes., Total on-source integration time is approximately two minutes.
" The Mopra spectrometer. (ALORS) was used in. ""zoom"" mode. which allows us to simultaneously observe 16 different frequencies. each with 4096 channels across a bandwidth of MMIIz. corresponding to per channel."," The Mopra spectrometer (MOPS) was used in “zoom” mode, which allows us to simultaneously observe 16 different frequencies, each with 4096 channels across a bandwidth of MHz, corresponding to per channel."
 To observe masers. we emploved two contiguous zoom bands. allowing us to search for maser emission over a velocity range between 2395 and. Data were reduced using livedata and ericizilla. which are both IPS]|. packages written |for the Parkes raciotelescope and adapted for Mopra.," To observe masers, we employed two contiguous zoom bands, allowing us to search for maser emission over a velocity range between –2395 and Data were reduced using livedata and gridzilla, which are both AIPS++ packages written for the Parkes radiotelescope and adapted for Mopra."
 Followup observations of OLL 000.1.0.4 were made with the Australia Telescope Compact Array (ATCA) on 2008 July 12 and 19. using the W214 hybricd array.," Followup observations of OH 009.1–0.4 were made with the Australia Telescope Compact Array (ATCA) on 2008 July 12 and 13, using the H214 hybrid array."
 Observations were mace using three dillerent pequencies spaced. MMIIz apart. cach MMIIz wide :uxl containing 512 channels. equivalent to per channel.," Observations were made using three different frequencies spaced MHz apart, each MHz wide and containing 512 channels, equivalent to per channel."
 Together. the three frequencies covered a velocity range of 395 to. with respect to the local standard of rest. (LSR).," Together, the three frequencies covered a velocity range of –395 to with respect to the local standard of rest (LSR)."
 Observations were made with one linear. polarisation. were phase referenced to either 1730.130 or 1817.254 and lux calibrated using 1934.638.," Observations were made with one linear polarisation, were phase referenced to either 1730–130 or 1817–254 and flux calibrated using 1934–638."
 We estimate the Dux scale will be accurate to around.104... which is typical for observations at this For each frequency. seven snapshot observations of two minutes each were taken.," We estimate the flux scale will be accurate to around, which is typical for observations at this For each frequency, seven snapshot observations of two minutes each were taken."
 The snapshots were evenly spaced throughout eight. hours. to ensure a wide coverage of the UV plane.," The snapshots were evenly spaced throughout eight hours, to ensure a wide coverage of the UV plane."
 The data were reduced using the package using similar techniques described in (Walshetal.2007)., The data were reduced using the package using similar techniques described in \citep{walsh07}.
". Strong maser emission was used to self-calibrate the data. ancl allowed data from antenna 6 to be included. greatly reducing the svnthesised beam to 2.15"","," Strong maser emission was used to self-calibrate the data, and allowed data from antenna 6 to be included, greatly reducing the synthesised beam to $\times$."
 The initial \lopra observations showed: maser emission detected at velocities from 48 to.kms. as shown in the bottom spectrum of Figure 1..," The initial Mopra observations showed maser emission detected at velocities from –48 to, as shown in the bottom spectrum of Figure \ref{fig1}."
 This emission. comprises of eleven individual maser spots., This emission comprises of eleven individual maser spots.
 Followup observations with the APCA (top spectrum in Figure 1)) showed emission s»nning a larger velocity range [rom |109 to and comprising of 32 individual maser spots., Followup observations with the ATCA (top spectrum in Figure \ref{fig1}) ) showed emission spanning a larger velocity range from –109 to and comprising of 32 individual maser spots.
 The ereater number of maser spots identified. in the ATCA observations appears to be a result. of the lower noise level in the APCA spectrum. allowing weaker spots to be identified.," The greater number of maser spots identified in the ATCA observations appears to be a result of the lower noise level in the ATCA spectrum, allowing weaker spots to be identified."
 Llowever. intrinsic variablilitv of the masers has resulted in some brighter spots in the APCA observations.," However, intrinsic variablility of the masers has resulted in some brighter spots in the ATCA observations."
 This variability has taken place over 125 days ancl is most noticeable in the velocity range of |40 to kms. where the brightest emission. occurs in theATCA," This variability has taken place over 125 days and is most noticeable in the velocity range of +40 to , where the brightest emission occurs in theATCA"
0=-24:0053 (/=5.27%. b=0.78),"$\delta=-24:00:53$ $l=5.27^\circ$, $b=0.78^\circ$ )."
 Applying the procedure by (??).. the statistical significance of the over-density at the coordinates given above is Sz 9.31.," Applying the procedure by \cite[][]{koposov08,belokurov09}, the statistical significance of the over-density at the coordinates given above is S= 9.31."
 There is no source identified at this location based on radio. infrared. and visible data on the SIMBAD. 2MASS and NED databases. or any other star cluster catalog.," There is no source identified at this location based on radio, infrared, and visible data on the SIMBAD, 2MASS and NED databases, or any other star cluster catalog."
 The second obvious density peak ata=17:54: 38.02—24:0049 is due to a saturated star.," The second obvious density peak at $\alpha=17:54:38$, $\delta=-24:00:49$ is due to a saturated star."
 The proximity of VVV CLOOI and UKS | on the sky (Figure 1)) made it appropriate to use the latter cluster as comparison in order to measure the reddening and distance of the new globular cluster candidate., The proximity of VVV CL001 and UKS 1 on the sky (Figure \ref{fig1}) ) made it appropriate to use the latter cluster as comparison in order to measure the reddening and distance of the new globular cluster candidate.
 Therefore. we concentrate first on measuring the parameters of UKS ] using VVV Survey data.," Therefore, we concentrate first on measuring the parameters of UKS 1 using VVV Survey data."
 Previous infrared photometry and spectroscopy of UKS | giants revealed that it is a very distant and reddened cluster. with distance modulus = 15. and E(B-V) = 3 (2). and moderately metal-rich. with [Fe/H]=-0.78 (?)..," Previous infrared photometry and spectroscopy of UKS 1 giants revealed that it is a very distant and reddened cluster, with distance modulus $\approx 15$ , and E(B-V) $\approx$ 3 \citep{Minniti95}, and moderately metal-rich, with [Fe/H]=-0.78 \citep{Origlia05}."
 In order to determine the distance to UKS | we will use the horizontal branch red clump. which ts very conspicuous in this cluster.," In order to determine the distance to UKS 1 we will use the horizontal branch red clump, which is very conspicuous in this cluster."
 The red clump stars with known parallaxes measured by the Hipparcos satellite are well calibrated standard candles (??)..," The red clump stars with known parallaxes measured by the Hipparcos satellite are well calibrated standard candles \citep[][]{Paczynski1998,Alves2000}."
 ? obtained a K-band calibration of the horizontal branch red clump luminosity. and applied the calibration to the rec clump of the Galactic bulge.," \cite{Alves2000}
 obtained a K-band calibration of the horizontal branch red clump luminosity, and applied the calibration to the red clump of the Galactic bulge."
 For example. this calibratio also been applied to the red clump of the Large Magellanic Cloud (e.g..222)..," For example, this calibration has also been applied to the red clump of the Large Magellanic Cloud \citep[e.g.,][]{Alves2002,Pietrzynski,Borissova}."
 The uncertainties in the reddening should i all cases be larger than the uncertainties due to the unkOwl metallicity., The uncertainties in the reddening should in all cases be larger than the uncertainties due to the unknown metallicity.
 Our As magnitudes are in the 2MASS magnitude system., Our $K_{\rm S}$ magnitudes are in the 2MASS magnitude system.
 Therefore we transform the A-band magnitudes of rec clump stars of ? to Ks magnitudes using K=Ks+0.044 (from?).., Therefore we transform the $K$ -band magnitudes of red clump stars of \cite{Alves2000} to $K_{\rm S}$ magnitudes using $K=K_{\rm S} +0.044$ \citep[from][]{Grocholski}.
 The zero point differences should be less than 0.02 magnitudes (?).., The zero point differences should be less than $0.02$ magnitudes \citep{Alves2002}.
 From the previously cited works. we adopt the following mean values for the red clump stars: —1.65x 0.03. and (J—Ko=0.71x0.03 (2).," From the previously cited works, we adopt the following mean values for the red clump stars: $M_{K_s} = -1.65\pm0.03$ , and $(J-K_s)_{0} = 0.71\pm0.03$ \citep[][]{lopez02}."
. The distance modulus to the horizontal branch red clump in the globular cluster would be: Adopting the mean red clump magnitudes and colors discussed above. and the reddening coefficients from ?.. this simplifies to Using this equation we compute the mean distance modulus (and distance in kpe) for the horizontal branch red clump in UKS 1. which has mean Ks=15.3 and /—Ks=2.0 (Figure4)).," The distance modulus to the horizontal branch red clump in the globular cluster would be: Adopting the mean red clump magnitudes and colors discussed above, and the reddening coefficients from \cite{Cardelli}, , this simplifies to Using this equation we compute the mean distance modulus (and distance in kpc) for the horizontal branch red clump in UKS 1, which has mean $K_{\rm S}=15.3$ and $J-K_{\rm S}=2.0$ (Figure \ref{fig4}) )."
 This yields a mean E(J—K)=1.30. equivalent to E(B—V)= 2.5. and a distance modulus Gu—M);=16.01. equivalent to 15.9 kpe.," This yields a mean $E(J-K)=1.30$, equivalent to $E(B-V)= 2.5$ , and a distance modulus $(m-M)_{0}= 16.01$, equivalent to 15.9 kpc."
" The uncertainty in thered clump position. was estimated to be Am4,20.012 mag and ACJ—Ks )=0.08 mag. based on analysis of the relevant region of the CMD."," The uncertainty in thered clump position was estimated to be $\Delta$ $_{K_{\rm S}}$ =0.012 $\mathrm {mag}$ and $\Delta(J-K_{\rm S})$ =0.08 $\mathrm{mag}$, based on analysis of the relevant region of the CMD."
 This results in an error m the distance modulus and corresponding distance of Ajpz0.078 and AD=0.6 kpe., This results in an error in the distance modulus and corresponding distance of $\Delta\mu$ =0.078 and $\Delta$ D=0.6 kpc.
 The distance to UKS | was also measured by ? using deep CST photometry., The distance to UKS 1 was also measured by \cite{Ortolani07} using deep CST photometry.
 They find the mean magnitude of the horizontal branch at J=17.69. and the mean colour /—H=1.39mag or 1.71mag depending on the calibration. and estimated D=9.3 to 14.3 kpe. placing it beyond the Galactic center.," They find the mean magnitude of the horizontal branch at $J=17.69$, and the mean colour $J-H=1.39 \mathrm {mag}$ or $1.71 \mathrm {mag}$ depending on the calibration, and estimated $D=9.3$ to $14.3$ kpc, placing it beyond the Galactic center."
 They find a total reddening of E(B—V)=2.94mag to 3.59mag also depending on the calibration., They find a total reddening of $E(B-V)=2.94 \mathrm {mag}$ to $3.59 \mathrm {mag}$ also depending on the calibration.
 Our values support the lower reddening values of ?.., Our values support the lower reddening values of \cite{Ortolani07}.
 However. our distance measurement favors the largest distance measurement of ?.. and it is consistent with the fact that UKS | is located well beyond the Galactic center. but not as far as the Ser dwarf galaxy discovered by ?..," However, our distance measurement favors the largest distance measurement of \cite{Ortolani07}, and it is consistent with the fact that UKS 1 is located well beyond the Galactic center, but not as far as the Sgr dwarf galaxy discovered by \cite{Ibata94}."
 Figure 3. shows that the red giant branch of VVV CLOOL is well defined. but the precise location of the horizontal branch red clump is not. and we cannot use the same method to estimate the distance.," Figure \ref{cmd} shows that the red giant branch of VVV CL001 is well defined, but the precise location of the horizontal branch red clump is not, and we cannot use the same method to estimate the distance."
 However. Figure + shows that the RGB of VVV CLO0OI is bluer than that of UKS 1.," However, Figure \ref{fig4} shows that the RGB of VVV CL001 is bluer than that of UKS 1."
 This may be due to a lower extinction or to a lower metallicity. or to a combinatior of both etfects.," This may be due to a lower extinction or to a lower metallicity, or to a combination of both effects."
 Within the selected sample. the saturation of the brightest RGB stars prevents us from using the tip of the RGB for an independent distance determination.," Within the selected sample, the saturation of the brightest RGB stars prevents us from using the tip of the RGB for an independent distance determination."
 The comparisor between red clump and tip of the RGB distance estimates could otherwise be used to assess the accuracy of the distance., The comparison between red clump and tip of the RGB distance estimates could otherwise be used to assess the accuracy of the distance.
 Although the absence of a populated horizontal branch rec clump in VVV 06001 may be due to low metallicity. we test the possibility that this is a statiestical effect. due to the small sample.," Although the absence of a populated horizontal branch red clump in VVV CL001 may be due to low metallicity, we test the possibility that this is a staticstical effect, due to the small sample."
 The CMDs of a randomly selected UKS 1 stars. corresponding to the VVV CLOOI sample size don't feature a distinet HB either.," The CMDs of a randomly selected UKS 1 stars, corresponding to the VVV CL001 sample size don't feature a distinct HB either."
 This leads us to the conclusion that the missing HB is mostly a statistical effect., This leads us to the conclusion that the missing HB is mostly a statistical effect.
 Refing the selection criteria and an increased spatial resolution may help to detect some HB stars., Refing the selection criteria and an increased spatial resolution may help to detect some HB stars.
 Based on the CMD. and assuming similar reddenings for both clusters. we can conclude that VVV 61001 has similar metallicity or is slightly more metal-poor than UKS 1.," Based on the CMD, and assuming similar reddenings for both clusters, we can conclude that VVV CL001 has similar metallicity or is slightly more metal-poor than UKS 1."
 Otherwise it would be hard to reconcile the clearly differing colours of the RGBs of these two clusters (see Figure 3)). but they do not allow for a large difference in metallicity.," Otherwise it would be hard to reconcile the clearly differing colours of the RGBs of these two clusters (see Figure \ref{cmd}) ), but they do not allow for a large difference in metallicity."
 The integrated near-infrared luminosity for Milky Way globular clusters are not very well known (?.andreferencestherein). nevertheless by comparing the RGB population in VVV CLO0OI and UKS 1 we also estimate that the new cluster candidate is z3.7 mag fainter in Ks then UKS 1.," The integrated near-infrared luminosity for Milky Way globular clusters are not very well known \citep[][and references therein]{cohen07}, nevertheless by comparing the RGB population in VVV CL001 and UKS 1 we also estimate that the new cluster candidate is $\approx$ 3.7 mag fainter in $K_{\rm S}$ then UKS 1."
 Thus. even though we do not have an accurate distance. the comparison with UKS | allows us to conclude that VVV CLO0OI is located beyond the Galactic center. on the opposite side of the Milky Way.," Thus, even though we do not have an accurate distance, the comparison with UKS 1 allows us to conclude that VVV CL001 is located beyond the Galactic center, on the opposite side of the Milky Way."
 Therefore. this does not appear to be a bulge globular cluster. as defined by ??..," Therefore, this does not appear to be a bulge globular cluster, as defined by \cite{Minniti95,Barbuy}."
 For consistency. we can also determine the reddening from the mean location of the VVV CLOOI red giants in the J-H vs H—Ks colour-colour diagram.," For consistency, we can also determine the reddening from the mean location of the VVV CL001 red giants in the J-H vs $H-K_{\rm S}$ colour-colour diagram."
 The mean /—H=1.4and H— K4z0.4 yields Ay2 6mag and E(B—V)= 2.0. slightly less reddened than UKS 1.," The mean $J-H=1.4$and $H-K_{\rm S}$ =0.4 yields $A_{\rm V}$ = $\mathrm{mag}$ and $E(B-V)=~2.0$ , slightly less reddened than UKS 1."
 On the other hand. the naps of ? give mean reddening of E(B—V)=3.3 for this region of VVVfield b351. which is larger than our measurements. but the reddening towards the bulge is known to be nonuniform and patchy.," On the other hand, the maps of \cite{Schlegel} give mean reddening of $E(B-V)\approx3.3$ for this region of VVVfield b351, which is larger than our measurements, but the reddening towards the bulge is known to be nonuniform and patchy."
Low-auass stars (LMS). ie. ALtype stars in the preseut context. represent an overwheluine fraction of the Galactic stellar population (Chabrier 2003)).,"Low-mass stars (LMS), i.e., M-type stars in the present context, represent an overwhelming fraction of the Galactic stellar population \cite{Chabrier03}) )."
 Observational determination of their mass-raclius relationship provides a stringent testing of the theoretical description of their structure and evolution., Observational determination of their mass-radius relationship provides a stringent testing of the theoretical description of their structure and evolution.
 Although observations of this relationship agree well with the theoretical xedietions in ai huge number of cases (Séerausanetal.20001: Chabrieretal. 20051). the radius deteriunations of eclipsing binaries (EBs) depart sienificautly (~10-15%)) from these precdictious (Torres&Ribas2002:: Chabrieretal. 20053).," Although observations of this relationship agree well with the theoretical predictions in a large number of cases \cite{Segransan03}; \cite{CBAH05}) ), the radius determinations of eclipsing binaries (EBs) depart significantly $\sim$ ) from these predictions \cite{Torres}; \cite{CBAH05}) )."
 These discrepancies are unlikely to be due to inaccurate equation of state or opacities. whose treatment is relatively well mastered for nimO.M. aud τω000 IX (Chabrier Baraffe 2000. CDBOQ0).," These discrepancies are unlikely to be due to inaccurate equation of state or opacities, whose treatment is relatively well mastered for $m\ga 0.4\msol$ and $\te\ga 4000$ K (Chabrier Baraffe 2000, CB00)."
 Furthermore. active LAIS are observed to be redder. ic. cooler. than the other LAIS (Tawlevetal. 1996)).," Furthermore, active LMS are observed to be redder, i.e. cooler, than the other LMS \cite{Hawley96}) )."
 These particular behaviours pose a challenge to theorists., These particular behaviours pose a challenge to theorists.
" Ou the other haud. the majority of LMS. notably EBs. are fast rotators and exhibit strong persistent coronal (X-ray) aud chromospheric (IL, ) activity or large flares (Cüzisetal. 2002)). indicating the oesenuce of a strong inagnetic field (Donatictal. 2006))."," On the other hand, the majority of LMS, notably EBs, are fast rotators and exhibit strong persistent coronal (X-ray) and chromospheric $_\alpha$ ) activity or large flares \cite{Gizis02}) ), indicating the presence of a strong magnetic field \cite{Donati06}) )."
" Iu this Letter. we sugeest that the discrepancy between he observed mass-radius relationship of EBs iux of other LMS does not stem from inaccurate cquation-ofstate or opacity problems. but is due to a rotation or naenetic Ποια, induced reduction of the efficiency of large-scale hermal convection iu their interior. leading to less cficicut heat transport."," In this Letter, we suggest that the discrepancy between the observed mass-radius relationship of EBs and of other LMS does not stem from inaccurate equation-of-state or opacity problems, but is due to a rotation or magnetic field induced reduction of the efficiency of large-scale thermal convection in their interior, leading to less efficient heat transport."
 We show that the reduction of he stars radiating surface due to nuaenetie spot coverage also vields a πιαο Tig and a larger radius., We show that the reduction of the star's radiating surface due to magnetic spot coverage also yields a smaller $\te$ and a larger radius.
 The EBs aud. more generally. active LMS ave fast rotators with rotation periods of P<3 days and rotation velocities of viu;zLOkus! (Delfosseetal.1998: Reidetal.2002.Mohlauty&Dazi 2003)).," The EBs and, more generally, active LMS are fast rotators with rotation periods of $P\la 3$ days and rotation velocities of $\vrot \ga 10\kms$ \cite{Delfosse98}; \cite{Reid02,MB03}) )."
 Typical convective time scales in their interior arc toneDotipπριHoIo LILO s where Ip~R. is the pressure scale height (CD00)).," Typical convective time scales in their interior are $\tconv$$\sim$${H_P \over \vconv}$$\sim$${10^9\over (10^2-10^3)}$$\sim$$10^6$ $10^7$ s, where $H_P$$\sim$$ R_\star$ is the pressure scale height \cite{CB00}) )."
 This vields Rossby uuuibers Ποσο Eu2) , This yields Rossby numbers $Ro$ ${P\over \tconv}\la 10^{-2} $.
At a very ΕΕ Rossby nmuuber. the Proudian-Taylox theorem euforces fluid motions to columnar or shect-like structures with a characteristic cheth scale perpendicular to the rotation axis that is uuch smaller than the one along the rotation axis (of the order of Πιν].," At a very small Rossby number, the Proudman-Taylor theorem enforces fluid motions to columnar or sheet-like structures with a characteristic length scale perpendicular to the rotation axis that is much smaller than the one along the rotation axis (of the order of $R_\star$ )."
 Althoueh the conditions of this theorem do not exactly apply for spherical objects with finite viscosity. rotation-dominated convective motions are severely affected by rotation. cading to lighly anisotropic patterus with larec-scale Huid iotious being confined to cobunus aloug the rotation axis aud motions iu the other directions being strongly inhibitec (Zhang&Jones 1997)).," Although the conditions of this theorem do not exactly apply for spherical objects with finite viscosity, rotation-dominated convective motions are severely affected by rotation, leading to highly anisotropic patterns with large-scale fluid motions being confined to columns along the rotation axis and motions in the other directions being strongly inhibited \cite{ZhangJones97}) )."
 As a whole. tlis reduces he characteristic leneth scale along these directious and the mean convective velocity amplitudes. thus the cticiency of thermal convection to transport the internal reat flux.," As a whole, this reduces the characteristic length scale along these directions and the mean convective velocity amplitudes, thus the efficiency of thermal convection to transport the internal heat flux."
 On the other haud. fully 3onised interiors of LMS are exccllent electrical conductors.," On the other hand, fully ionised interiors of LMS are excellent electrical conductors."
 The interaction between he aaenetic field aud the fiui motious induces an electrical current aud a Lorentz force. which iu turn affects. the motions.," The interaction between the magnetic field and the fluid motions induces an electrical current and a Lorentz force, which in turn affects the motions."
 In the presence of a magnetic field. the anisotropy of rotatiou-domunated convection j* reduced and the large-scale flows reach the ποτcalled MAC (Alaguetic. Archimedean. Coriolis) balance Tüswee the lnovancy. Coriolis. and Lorentz forces (Starchenko&Jones 2002)).," In the presence of a magnetic field, the anisotropy of rotation-dominated convection is reduced and the large-scale flows reach the so-called MAC (Magnetic, Archimedean, Coriolis) balance between the buoyancy, Coriolis, and Lorentz forces \cite{StarchenkoJones}) )."
. Equipartition between the movaucy force. ~pyd(AT/T) (where 6= (zs)p and AT is the temperature excess over a pressure scale height). and the Coriolis force. ~2pOv Gvhere 0=a is the star angular velocity). viclds for the typical larec-scale velocity.," Equipartition between the buoyancy force, $\sim \rho g\delta (\Delta T/T)$ (where $\delta$ $-({\partial \ln \rho \over \partial \ln T})_P$ and $\Delta T$ is the temperature excess over a pressure scale height), and the Coriolis force, $\sim 2\rho\Omega \vconv$ (where $\Omega={\vrot\over R_\star}$ is the star angular velocity), yields for the typical large-scale velocity."
 For Ὁ~10! +. typical values of the various quantities over tle LMS domain give Vigne 710-100cnis about a factor of 10 lower than the predictions of the usual mixing length theory.," For $\Omega \sim 10^{-4}$ $^{-1}$, typical values of the various quantities over the LMS domain give $\vconv \sim$ $\cms$, about a factor of 10 lower than the predictions of the usual mixing length theory."
 There is presentle uo clear understanding of the interaction between convection aud maguctic feld under, There is presently no clear understanding of the interaction between convection and magnetic field under
 and varPetk))—covPetk).Pe(R)).,", and ${\rm var}[\widehat{P}_{\rm F}(\bfk)] \equiv {\rm cov}[\widehat{P}_{\rm F}(\bfk), \widehat{P}_{\rm F}(\bfk)]$."
" Here. ος,/ has been defined⋅ so that 0,4−FN, ↗⊥⊐⊀is the precision.. at. which. Dy, can be measured in a Á-space shell witbY, independent mocles."," Here, $\delta {P}_{\rm F, \mu}$ has been defined so that $\delta {P}_{\rm F, \mu}/{\cal N}_k^{1/2}$ is the precision at which $P_{\rm F, \mu}$ can be measured in a $k$ -space shell with ${\cal N}_k$ independent modes."
 The value of Var/(4)AL] is near unity when à survey is sample variance-limitec.," The value of $V_{\rm eff, \mu}(k)/[{\cal A} \, L]$ is near unity when a survey is sample variance-limited."
 For a BOSS-like quasar survey in which mar=107Alpe ab 2«<3. this quantity reaches a maximum of 0.5 at the smallest wavevectors and falls oll rapidly at &0.1 .," For a BOSS-like quasar survey in which $\bar{n}_{\rm eff} = 10^{-3}~$ $^{-2}$ at $2 <z <3$, this quantity reaches a maximum of $0.5$ at the smallest wavevectors and falls off rapidly at $k\gtrsim 0.1~$ $^{-1}$."
 Even mar=10? | roughly the maximum censity that can be achieve in a quasar survey ἰ not sample variance-Iimited atkOO ο. , Even $\bar{n}_{\rm eff} = 10^{-2}~$ $^{-2}$ – roughly the maximum density that can be achieve in a quasar survey – is not sample variance-limited at $k\gtrsim 0.1~$ $^{-1}$ .
Figure 3o also emphasizes that mapem 7 marks the critical number density at which a survey becomes sample variance-limited at &0.1 +. such that the gains [rom a 3D analysis become large.," Figure \ref{fig:Veff} also emphasizes that $\bar{n}_{\rm eff} \approx 10^{-3}~$ $^{-2}$ marks the critical number density at which a survey becomes sample variance-limited at $k\lesssim 0.1~$ $^{-1}$, such that the gains from a $3$ D analysis become large."
" The plotted. quantity in Figure 3. can also be related to the S/N of quasar survey to Lj, in a A-space shell of width Af."," The plotted quantity in Figure \ref{fig:Veff} can also be related to the $S/N$ of quasar survey to ${P}_{\rm F, \mu}$ in a $k$ -space shell of width $\Delta k$."
" Vhis shell contains Aj=f°AbAL/(2x7)E independent samples. so that the SAN ratio at which Li.) can be measured in this shell equals where op,—04-ChANHp) and. the recishiftIp dependence is approximate."," This shell contains ${\cal N}_{k} \equiv k^2 \Delta k \, {\cal A} \, L/(2 \pi^2)$ independent samples, so that the $S/N$ ratio at which $P_{\rm F, \mu}$ can be measured in this shell equals where $\sigma_{\rm F, \mu} \equiv \delta {P}_{\rm F, \mu} (k) / {\cal N}_k^{1/2}$ and the redshift dependence is approximate."
 1n practice. it will be easier to measure 3D Lye correlations in configuration space via the 3D. correlation function.," In practice, it will be easier to measure $3$ D $\alpha$ correlations in configuration space via the $3$ D correlation function."
" In configuration space. the Fourier-space weights proposed in Section 2.2. become the line-of-xght. convolution of w,tr) the Fourier Transform of «(41) with the Hux field of sightline 5."," In configuration space, the Fourier-space weights proposed in Section \ref{ss:weights} become the line-of-sight convolution of $w_n(r)$ – the Fourier Transform of $\tilde{w}_n(k_{\parallel})$ – with the flux field of sightline $n$."
 Conveniently. πρ(ή) will be relatively localized in real-space because d;(ki)zmds(0) for ky)&0.5 1," Conveniently, $w_n(r)$ will be relatively localized in real-space because $\tilde{w}_n(k_{\parallel}) \approx \tilde{w}_n(0)$ for $k_{\parallel} \lesssim 0.5~$ $^{-1}$."
 Llowever. for estimates of the correlation function. a simpler weighting for each sightline of (0) is likely sullicient.," However, for estimates of the correlation function, a simpler weighting for each sightline of $\tilde{w}_n(0)$ is likely sufficient."
" In fact. this weighting is identical to the full weighting to the extent that 1. and the P, are white."," In fact, this weighting is identical to the full weighting to the extent that $P_{\rm los}$ and the $P_{\rm N, n}$ are white."
 We find that var£3] is not significantly increased with these simpler weights., We find that ${\rm var}[\widehat{P}_{\rm F}]$ is not significantly increased with these simpler weights.
 lteal data will be more complicated than the idealized case of uniform noise that we have considered thus far., Real data will be more complicated than the idealized case of uniform noise that we have considered thus far.
 For example. there will be high-noise regionsin the spectra owing to sky lines. and there may also beholes in the data where damipec svstems have been excised.," For example, there will be high-noise regionsin the spectra owing to sky lines, and there may also beholes in the data where damped systems have been excised."
 We have expressed our weights in terms of the noise and the Lye forest power spectra., We have expressed our weights in terms of the noise and the $\alpha$ forest power spectra.
" Llowever. the suggested. weights are equivalent to simply weighting each sightline by (1|σσ). ὃν where eg and e, are respectively the variance of the noise and the Lya forest. smoothed on a large enough scale that P, is white."," However, the suggested weights are equivalent to simply weighting each sightline by $(1 +\sigma_{{\rm N}}^2/\sigma_{\rm los}^2)^{-1}$ , where $\sigma_{\rm N}^2$ and $\sigma_{\rm los}^2$ are respectively the variance of the noise and the $\alpha$ forest, smoothed on a large enough scale that $P_{\rm los}$ is white."
 Fhis scale corresponds to 10 Alpe. and we find that the exact choice of the smoothing scale weakly allects var£i].," This scale corresponds to $\gtrsim 10~$ Mpc, and we find that the exact choice of the smoothing scale weakly affects ${\rm var}[\widehat{P}_{\rm F}]$."
 Such weights can more readily be applied to real data., Such weights can more readily be applied to real data.
 This section derives the minimum variance estimator that is quadratic in op and compares it to the estimator derived in the Section 2.., This section derives the minimum variance estimator that is quadratic in $\delta_{\rm F}$ and compares it to the estimator derived in the Section \ref{sec:sensitivity}.
 To proceed. we decompose the covariance of the flux overdensityat Aj into a component that depends on the parameter we aim to measure. Pp(R). and one that does not.," To proceed, we decompose the covariance of the flux overdensityat $k_{\parallel}$ into a component that depends on the parameter we aim to measure, $P_{\rm F}({\bfk})$, and one that does not."
" Namely. where Op, is the Fourier transform of the flux. along sightline a and we consider a single 4. Here. tion—[ti| is the transverse separation between sightlines 7 and m. AA is the width of the Fourier space pixel. in which we estimate. Pp(&). and. equation. (22)) assumes that PEGNu«mmauu)."," Namely, where $\tilde{\delta}_{{\rm F}, n}$ is the Fourier transform of the flux along sightline $n$ and we consider a single $k_{\parallel}$, Here, $r_{nm} \equiv |\bfr_{nm}|$ is the transverse separation between sightlines $n$ and $m$, $\Delta k_\perp$ is the width of the Fourier space pixel in which we estimate $P_{\rm F}({\bfk})$, and equation \ref{eqn:Pkr}) ) assumes that $P_{\rm F}({\bfk}) \, X_{nm} \ll P(k_{\parallel}, \bfr_{nm})$."
 The variancePOS estimator for Pek) that is quacratic Minin dp. and unbiased is given by where Equation (24)) is derived by minimizing the variance of IcΟΕ. assuming. dp −⋠is Gaussian. so that and subject to the condition that it is unbiased so that irQX]= 1.," The minimum variance estimator for $P_{\rm F}({\bfk})$ that is quadratic in $\tilde{\delta}_{{\rm F}, n}$ and unbiased is given by where Equation \ref{eqn:Q}) ) is derived by minimizing the variance of $\widehat{P}_{\rm F}^{\rm QE}$ assuming $\delta_{\rm F}$ is Gaussian so that and subject to the condition that it is unbiased so that ${\rm tr} [ \bfQ \, \bfX] = 1$ ."
 Note that equation (25)) does not. include sample variance. which would contribute the term 2£p.," Note that equation \ref{eqn:varQE}) ) does not include sample variance, which would contribute the term $2 \,P_{\rm F}^2$ ."
 Our aim is to understand how the weights suggested in the previous section relate to the above minimum variance quadratic estimator., Our aim is to understand how the weights suggested in the previous section relate to the above minimum variance quadratic estimator.
" Lo proceed. we set the olf diagonal terms in C, to zero (Le... PUA|.Pi)-:0 for ray,4 0)."," To proceed, we set the off diagonal terms in $C_{nm}$ to zero (i.e., $P(k_{\parallel}, \bfr_{n m}) \rightarrow 0$ for $\bfr_{n m} \neq 0$ )."
 The estimator is still unbiased. with thisapproximation., The estimator is still unbiased with thisapproximation.
 The motivation for this approximation is that the typical separation of quasars in such surveys is rj10 Alpe., The motivation for this approximation is that the typical separation of quasars in such surveys is $r_\perp \gtrsim 10~$ Mpc.
 At these ry and at relevant Ay. {μιr1) is down by a [actor of &4 from its τι=0 value.," At these $r_\perp$ and at relevant $k_\parallel$ , $P(k_{\parallel}, \bfr_\perp)$ is down by a factor of $\gtrsim 4$ from its $\bfr_\perp=0$ value."
" In this ""zeroth-order"" approximation. Qyi, becomes where £1,=P(h4.0) and The last line assumes thatthe noise is uncorrelated betweensightlines anc neelects the terms with m= n. whose [fractional contribution vanish as NV ewe"," In this “zeroth-order” approximation, $Q_{nm}$ becomes where $P_{\rm los} = P(k_{\parallel}, 0)$ and The last line assumes thatthe noise is uncorrelated betweensightlines and neglects the terms with $m=n$ , whose fractional contribution vanish as $N\rightarrow \infty$ ."
 The, The
"To understand why we can marginalize over //, in fitting SN Ia data and (reat. 77, as a parameter in fitting WAIAPS data. we should think that we actually treat Q,. not Jj as a parameter when fitting the WAIAP3 data.","To understand why we can marginalize over $H_0$ in fitting SN Ia data and treat $H_0$ as a parameter in fitting WMAP3 data, we should think that we actually treat $\Omega_r$, not $H_0$ as a parameter when fitting the WMAP3 data."
 The parameter fy is not the observed Hubble constant when fitting the SN data because the normalization of the distance modulus was chosen arbitrarily., The parameter $H_0$ is not the observed Hubble constant when fitting the SN data because the normalization of the distance modulus was chosen arbitrarily.
 In summary. we have six fitting parameters for the DE models (5)) and (1)).," In summary, we have six fitting parameters for the DE models \ref{lind}) ) and \ref{wzeq}) )."
 In (his section. we present our results.," In this section, we present our results."
 We first use the 182 gold SN Ia data 2006).. Chen we use (he ESSENCE data (Riessetal. 2007)..," We first use the 182 gold SN Ia data \citep{riess06}, then we use the ESSENCE data \citep{riess06, essence,essence1}."
 For the SN Ia data. we consider both the SN Ia flux averaging with marginalization over [fy (Wane2000:Wane&Mukherjee2004:WangTeemark2004) and the analvtical mareinalization without the flix averaging.," For the SN Ia data, we consider both the SN Ia flux averaging with marginalization over $H_0$ \citep{flux,flux1,flux2} and the analytical marginalization without the flux averaging."
 The results with the analvtical marginalization are shown in solid lines and (he results with [Iux averaging are shown in dashed lines., The results with the analytical marginalization are shown in solid lines and the results with flux averaging are shown in dashed lines.
 We also put the ACDAI model with the svanbol + in the contourplot., We also put the $\Lambda$ CDM model with the symbol + in the contourplot.
 Fie., Fig.
" 3 shows the marginalized probabilities for QO,,. 5. wp and ie; for the DE model /(L+2)."," \ref{fig3} shows the marginalized probabilities for $\Omega_m$, $\Omega_k$, $w_0$ and $w_a$ for the DE model $w_0+w_a z/(1+z)$ ."
 Fig., Fig.
" d shows the mareinalized Q,,,-Q) and (09-04; contours.", \ref{fig4} shows the marginalized $\Omega_m$ $\Omega_k$ and $w_0$ $w_a$ contours.
 The ορ contour with the flux averaging is consistent with the result in Wang&Mukherjee(2007)., The $w_0$ $w_a$ contour with the flux averaging is consistent with the result in \citet{wang07}.
. From Figs., From Figs.
 3 and 4.. we see that the difference in (he results between the analvtical marginalization and the [ιν averaging is small.," \ref{fig3} and \ref{fig4}, we see that the difference in the results between the analytical marginalization and the flux averaging is small."
 The ACDM model is consistent with the observation at the lo level., The $\Lambda$ CDM model is consistent with the observation at the $1\sigma$ level.
" The value of ve, is better constrained with the analvtieal margimalization.", The value of $w_a$ is better constrained with the analytical marginalization.
 Fie., Fig.
" 5 shows the mareinalizecl probabilities for Q,,. O5. i04 ane i; for the DE model wyd-uwuz/(1-2zy."," \ref{fig5} shows the marginalized probabilities for $\Omega_m$, $\Omega_k$, $w_0$ and $w_a$ for the DE model $w_0+w_a z/(1+z)^2$."
 Fie., Fig.
" 6 shows the marginalized ,,-O; and wy-i, contours.", \ref{fig6} shows the marginalized $\Omega_m$ $\Omega_k$ and $w_0$ $w_a$ contours.
 From Figs., From Figs.
 and 6.. we see that the parameters are a little better constrained with the {lis averaging.," \ref{fig5} and \ref{fig6}, we see that the parameters are a little better constrained with the flux averaging."
 Forthe analvtical marginalization. the ACDM model is consistent with the observation al the 2o level.," Forthe analytical marginalization, the $\Lambda$ CDM model is consistent with the observation at the $2\sigma$ level."
 For the flux averaging. the ACDM model is consistent with the observation at ihe lo level.," For the flux averaging, the $\Lambda$ CDM model is consistent with the observation at the $1\sigma$ level."
 Fie., Fig.
" 7 shows the mareinalizecl probabilities for Q,,. £5. i04 and i; for the DE model"," \ref{fig7} shows the marginalized probabilities for $\Omega_m$ , $\Omega_k$ , $w_0$ and $w_a$ for the DE model"
et al 1991)):,et al. \cite{Huang}) ):
 Sswou hu των |) = Llν," $\Sigma_{8.4\mathrm{GHz}}$ $^{-1}$ $^{-2}$ $^{-1}$ ) = $4.4\times10^{-16}\,D_{\mathrm{pc}}^{-3.5\pm0.1}$."
" Then for the augular size 15.1’ aud above fitting of S,. the distance de13 kpe aud the diameter D-—61 pe."," Then for the angular size $18.4\arcmin$ and above fitting of $_\nu$, the distance $\sim$ 13 kpc and the diameter $\sim$ 64 pc."
" A new refined XD relation was obtained by Case Bhattachatva (1998)) for a sample of 36 Galactic shell SNRs: “ye Iuνι 1!) = oxqrMp.d0DDUt7,"," A new refined $\Sigma-D$ relation was obtained by Case Bhattachatya \cite{S-D}) ) for a sample of 36 Galactic shell SNRs: $\Sigma_{1\mathrm{GHz}}$ $^{-1}$ $^{-2}$ $^{-1}$ ) = $2.07^{+3.10}_{-1.24}\times10^{-17}\,D_{\mathrm{pc}}^{-2.38\pm0.26}$."
" Fa NüGHz-edc0.110.2AV HHIIz.tua 2sr 3 i gives D=35/545!1"" pe and d=6.5En Then the distance from the Galactic plane L== 3001j Apepe.", For $\Sigma$ $ = (1\pm0.1)10^{-21}$ $^{-1}$ $^{-2}$ $^{-1}$ it gives $=35^{+10}_{-5}$ pc and $6.5^{+2.0}_{-1.0}$ kpc Then the distance from the Galactic plane z = $^{+75}_{-40}$ pc.
 The new previously unidentified shell supernova roimnaut 2.7 has been discovered iu the First Galactic quadrant., The new previously unidentified shell supernova remnant $-$ 2.7 has been discovered in the First Galactic quadrant.
 The radio map at 1.1 GIIz frou NVSS maps has beeu plotted aud the SNR has been clearly shown to be a barrel- or bilateral SNR with the axis of svuuucetry aligned closely with the Galactic plane., The radio map at 1.4 GHz from NVSS maps has been plotted and the SNR has been clearly shown to be a barrel-shaped or bilateral SNR with the axis of symmetry aligned closely with the Galactic plane.
 Aueular diameter of oof a circular shell has been fited to peaks of brightucss ou its limb., Angular diameter of of a circular shell has been fitted to peaks of brightness on its limb.
 Using a simple model of a spherical hollow shell. a outer diameter Diyas = Le!l and width AR=V’ are well fitted to the NVSS aud the Effelsbere survey data.," Using a simple model of a spherical hollow shell, a outer diameter $_{\mathrm{max}}$ = $18\farcm4$ and width $\Delta$ $1\arcmin$ are well fitted to the NVSS and the Effelsberg survey data."
 The sSpectruni based RATAN-GOO) and Effelshere survevs at eni waveleueths is fitted by a power law with a PAoectral iudex à=0.51+ 0.10., The spectrum based RATAN-600 and Effelsberg surveys at cm wavelengths is fitted by a power law with a spectral index $\alpha=-0.51\pm0.10$ .
 The polarization data frou: the NVSS show that the xieht arcs of the SNR are nearly polarized to indicating a svuchrotron radiation and an ordered iaenetic field in the shell., The polarization data from the NVSS show that the bright arcs of the SNR are linearly polarized to indicating a synchrotron radiation and an ordered magnetic field in the shell.
In this second order approximation. J(iw) is derived [rom two relations.,"In this second order approximation, $J(\omega)$ is derived from two relations."
 dz --, J = J_- dz_-; dz_- =
 (??)..," \citep{art-Spergeletal2007,art-Komatsuetal2009}."
 oue of the best studied candidates for plivsics bevoud he Standard Model (2).., one of the best studied candidates for physics beyond the Standard Model \citep{rev-BertoneHS2005}.
 Dark matter particles must ο Inassive particles. clectrically neutral aud. very ikely. nou-coloured.," Dark matter particles must be massive particles, electrically neutral and, very likely, non-coloured."
 A lightest supersviuuetrie particle (LSP). such as the neutralino. is the favourite SUSY xuwticdle amoug the particle plysics couunuuity.," A lightest supersymmetric particle (LSP), such as the neutralino, is the favourite SUSY particle among the particle physics community."
 The LSP belongs to a generic family of neutral massive outicles. usually known as Weally Iuteractiug Massive Particles (WIMPs). that are by definition the best DM uticle candidates.," The LSP belongs to a generic family of neutral massive particles, usually known as Weakly Interacting Massive Particles (WIMPs), that are by definition the best DM particle candidates."
 WIMPs interact through eravity aud xossiblv through the weak unclear force. and very likely hrough no other interactions stronger than the weal “ORCC.," WIMPs interact through gravity and possibly through the weak nuclear force, and very likely through no other interactions stronger than the weak force."
 Despite their weak interactions. WIMDPs can load to sienificant changes in the formation and evolution of stars. provided they have a sizeable scattering cross section with barvous.," Despite their weak interactions, WIMPs can lead to significant changes in the formation and evolution of stars, provided they have a sizeable scattering cross section with baryons."
 Coucermme WIMPs interaction with barvous. the consequence is twofold: WIMPs cau affect a star by annihilatiung :unong themselves iuto standard model particles iu its core. providing a source of enerev additional to standard unclear energy. (2)...," Concerning WIMPs' interaction with baryons, the consequence is twofold: WIMPs can affect a star by annihilating among themselves into standard model particles in its core, providing a source of energy additional to standard nuclear energy \citep{art-SalatiSilk1989}."
 A second wav WIMPS can influence stellar structure is by providing an additional nieclhiauisui of heat transport inside the star (2).., A second way WIMPS can influence stellar structure is by providing an additional mechanism of heat transport inside the star \citep{art-BouquetSalati1989}.
 This can reduce the local temperature eracieut. potentially iuhibitiug convection aud eublauciug the pulsation of horizontal brauch stars (7)..," This can reduce the local temperature gradient, potentially inhibiting convection and enhancing the pulsation of horizontal branch stars \citep{art-Dearbornetal1990}."
 In the case of the Sun. the current values favoured by WIMP selt-aunililation cross section. WIMP-uucleus scattering cross sections aud local DAL deusity indicate that this effect is not significant for the evolution of our star.," In the case of the Sun, the current values favoured by WIMP self-annihilation cross section, WIMP-nucleus scattering cross sections and local DM density indicate that this effect is not significant for the evolution of our star."
 The study of the effects of DAL particles accretion on stars is an alternative approach to investigate the properties of such particles., The study of the effects of DM particles accretion on stars is an alternative approach to investigate the properties of such particles.
 These effects were first studied in the Sun by ? aud later ou by ? aud ο., These effects were first studied in the Sun by \citet{art-SpergelPress1985} and later on by \citet{art-LopesBS2002} and \citet{art-Bottinoetal2002}.
 Recently. ? for white dwarfs. ?. for low-niass stars. aud," Recently, \citet{art-MoskalenkoWai2007} for white dwarfs, \citet{art-Scottetal2007} for low-mass stars, and"
The dotted line on the left-hancl panel of Fig.,The dotted line on the left-hand panel of Fig.
 5. shows the redshift-space correlation function for the entire population of 2dECGIUS galaxies. derived. hy Hawkins et al. (," \ref{fig:xi_s} shows the redshift-space correlation function for the entire population of 2dFGRS galaxies, derived by Hawkins et al. ("
2003): the similarity between this measurement and the one for local raclio-sources is remarkable.,2003); the similarity between this measurement and the one for local radio-sources is remarkable.
" This can be understood because the ELIST-2dECGIS catalogue probes radio Iluxes down to Siacgs= domJy. which results in a mixture of ""classical"" ACN-fuelled sources. generally hosted by elliptical galaxies. and star-forming objects such as spirals and. irregulars (see Section 2)."," This can be understood because the FIRST-2dFGRS catalogue probes radio fluxes down to $S_{\rm 1.4
GHz}=1$ mJy, which results in a mixture of “classical” AGN-fuelled sources, generally hosted by elliptical galaxies, and star-forming objects such as spirals and irregulars (see Section 2)."
 This mix of carly and late tvpe galaxies makes the dataset look similar to a fair (even though very. sparse) sample of the whole population of 20GINS galaxies., This mix of early and late type galaxies makes the dataset look similar to a fair (even though very sparse) sample of the whole population of 2dFGRS galaxies.
 The situation however looks very cdillerent if. one considers only ACN-fuellecl sources., The situation however looks very different if one considers only AGN-fuelled sources.
 In this case the sample is much more strongly correlated: the correlation length is higher. and also £68) has a steeper slope.," In this case the sample is much more strongly correlated; the correlation length is higher, and also $\xi(s)$ has a steeper slope."
 We will discuss the implications of these findings in Section 3.8 when dealing with the real-space correlation function., We will discuss the implications of these findings in Section 3.3 when dealing with the real-space correlation function.
 As a final step. we are interested. in investigating whether there is any dependence of the clustering signal on racio Luminosity.," As a final step, we are interested in investigating whether there is any dependence of the clustering signal on radio luminosity."
" We divided the radioAGN sample into two distinct subsets depending on whether the sources have racio uminosity brighter or fainter than log,07=22.0.", We divided the radio-AGN sample into two distinct subsets depending on whether the sources have radio luminosity brighter or fainter than ${\rm log_{10}}{\cal P}=22.0$.
 There are 260 objects in the faint sample. and their average radio uminosityv is οσο.=22.9.," There are 260 objects in the faint sample, and their average radio luminosity is ${\rm log_{10}}{\cal P}=22.9$."
 There are 276 objects in the right sample. with average racio Luminosity οσο=21.6.," There are 276 objects in the bright sample, with average radio luminosity ${\rm log_{10}}{\cal P}=21.6$."
 The redshift-space correlation functions for the two samples are plotted in Fig. 6:, The redshift-space correlation functions for the two samples are plotted in Fig. \ref{fig:xi_type};
 the fainter sample is plotted as illecl circles. and the brighter sample as open squares.," the fainter sample is plotted as filled circles, and the brighter sample as open squares."
 Even hough the small number of sources in the subsets lead to arge uncertainties in the measurements. it is clear that the wo £(5)'s are entirely compatible with each other.," Even though the small number of sources in the subsets lead to large uncertainties in the measurements, it is clear that the two $\xi(s)$ 's are entirely compatible with each other."
 The best-it parameters are sy=12c3 Alpe and ος=1.5d0.15 for xighter ACGNs and sj=132:3 Alpe and ος=14d0.1 for he fainter ones.," The best-fit parameters are $s_0 = 12\pm
3$ Mpc and $\gamma_s = 1.5\pm 0.15$ for brighter AGNs and $s_0 = 13 \pm 3$ Mpc and $\gamma_s = 1.4 \pm 0.1$ for the fainter ones."
 This result shows no evidence for luminosity dependence in the clustering amplitude. and shows that the amplitude of the correlation function at 10 Alpe cannot diller w more much than a factor of 2 even though the two samples ciller by a factor of 20 in luminosity.," This result shows no evidence for luminosity dependence in the clustering amplitude, and shows that the amplitude of the correlation function at 10 Mpc cannot differ by more much than a factor of 2 even though the two samples differ by a factor of 20 in luminosity."
 This is consistent with he results of Peacock Nicholson (1991) who analysed an all-sky sample of radio galaxies at z£50.1. and. found no evidence for any dillerence in clustering amplitude for samples 22.5«logivP23.5 and 23.5«logiwP24.5.," This is consistent with the results of Peacock Nicholson (1991) who analysed an all-sky sample of radio galaxies at $z \simlt 0.1$, and found no evidence for any difference in clustering amplitude for samples $22.5
< {\rm log_{10}}{\cal P} < 23.5$ and $23.5 < {\rm log_{10}}{\cal P} < 24.5$."
 These results imply that the correlation amplitude of radio galaxies is independent of their radio luminosity. at least in the power range 107<P£z1077.," These results imply that the correlation amplitude of radio galaxies is independent of their radio luminosity, at least in the power range $10^{20}\simlt {\cal P} \simlt 10^{25}$."
 The previous Section has shown that the redshift-space correlation function is extremely useful for characterizing the main properties of the clustering of Iow-redshift. racio sources., The previous Section has shown that the redshift-space correlation function is extremely useful for characterizing the main properties of the clustering of low-redshift radio sources.
 Llowever. £(8) differs from the real-space correlation function because of peculiar velocities that [ead to redshilt-space distortions (see e.g. Llawkins et al.," However, $\xi(s)$ differs from the real-space correlation function because of peculiar velocities that lead to redshift-space distortions (see e.g. Hawkins et al."
 2003 and Madgwick et al., 2003 and Madgwick et al.
 2003)., 2003).
 Lt follows that both the amplitude and the slope of the real-space correlation function €(7) will diller (rom the values measured in Section 3.2., It follows that both the amplitude and the slope of the real-space correlation function $\xi(r)$ will differ from the values measured in Section 3.2.
 The standard. way to recover £(r) is to first compute the two-dimensional correlations as a function of separation parallel ancl transverse to the line of sight. ἐνri) and then integrate it along the à direction in order to obtain the projected. correlation function = as: We estimate £(rp.i) by means of equation (1)) where this time pairs are counted in a grid of bins Ary. Ary and derive Z bv means of equation (2)).," The standard way to recover $\xi(r)$ is to first compute the two-dimensional correlations as a function of separation parallel and transverse to the line of sight, $\xi(\rp,\rt)$ and then integrate it along the $\rp$ direction in order to obtain the projected correlation function $\Xi$ as: We estimate $\xi(\rp,\rt)$ by means of equation \ref{eq:xiest}) ) – where this time pairs are counted in a grid of bins $\Delta \rp$, $\Delta \rt$ – and derive $\Xi$ by means of equation \ref{eq:projxi}) )."
 We set the upper limit for the integral to r7=60 Alpe as the best compromise between a large enough. value to produce stable results and a small enough value to avoid extra noise added to =., We set the upper limit for the integral to $\rp^{\rm max}=60$ Mpc as the best compromise between a large enough value to produce stable results and a small enough value to avoid extra noise added to $\Xi$.
 As in the previous subsection. = has been evaluated both using the whole spectroscopic sample and the sample of objects showing signatures of AGN in. their spectra.," As in the previous subsection, $\Xi$ has been evaluated both using the whole spectroscopic sample and the sample of objects showing signatures of AGN in their spectra."
 Once again. the errors were calculated (rom 20 jack-knife resamplings of the datasets uncer consideration.," Once again, the errors were calculated from 20 jack-knife resamplings of the datasets under consideration."
 The resulting measurements on scales. 1-30 Alpe are shown by the solid points in the two panels of Fig. (7)):, The resulting measurements on scales 1-30 Mpc are shown by the solid points in the two panels of Fig. \ref{fig:proj_xi}) ):
 the eft. panel shows the results for whole spectroscopic sample. and right panel show the results for AGN sample.," the left panel shows the results for whole spectroscopic sample, and right panel show the results for AGN sample."
 The open squares in Fig. (7)), The open squares in Fig. \ref{fig:proj_xi}) )
 show the projected correlation functions rom corresponding optical 2dGIU samples: in the left xiuiel they show the results for the entire population of 2dE ealaxies (Hawkins et al., show the projected correlation functions from corresponding optical 2dFGRS samples: in the left panel they show the results for the entire population of 2dF galaxies (Hawkins et al.
 2003): in the right panel they show he results for earlv-ty 2dECGIUS galaxies (Alaclewick et al., 2003); in the right panel they show the results for early-type 2dFGRS galaxies (Madgwick et al.
 2003)., 2003).
 From these comparisonspe we see that the clustering xoperties of the whole spectroscopic sample are remarkably similar to those of “normal” galaxies. but the projected correlation function of radio AXGNs has an amplitude that is roughly twice as large as that of local ellipticals.," From these comparisons we see that the clustering properties of the whole spectroscopic sample are remarkably similar to those of “normal” galaxies, but the projected correlation function of radio AGNs has an amplitude that is roughly twice as large as that of local ellipticals."
 From the measurements presented in Fig., From the measurements presented in Fig.
 7 it is then possible to estimate the real-space correlation function £(r) via (Davis Pecbles. 1983) which. if we assume the power-law [orm," \ref{fig:proj_xi} it is then possible to estimate the real-space correlation function $\xi(r)$ via (Davis Peebles, 1983) which, if we assume the power-law form"
the long-slit spectrum. (see. Fig.,the long-slit spectrum (see Fig.
 2 and 3)., 2 and 3).
 This and the similar ratios between the fluxes of the knot and the stars in the intermediate anc the broad band. images suggest that it is dominated by continuum emission., This and the similar ratios between the fluxes of the knot and the stars in the intermediate and the broad band images suggest that it is dominated by continuum emission.
 This feature appears very prominently in the rest frame V. band ACS UST image (Zakamska ct al., This feature appears very prominently in the rest frame V band ACS HST image (Zakamska et al.
 2006)., 2006).
 It shows knotty internal substructure and it seems to be part of the complex svstem of knots ancl filaments associated with the quasar., It shows knotty internal substructure and it seems to be part of the complex system of knots and filaments associated with the quasar.
 This confirms that the knot belongs to the quasar system., This confirms that the knot belongs to the quasar system.
 Dased on these results. we propose that SDSS 2358-00 is interacting with a companion star forming galaxy. whose nuclear gas is photoionized by voung stars possibly formed as a consequence of the interaction.," Based on these results, we propose that SDSS J2358-00 is interacting with a companion star forming galaxy whose nuclear gas is photoionized by young stars possibly formed as a consequence of the interaction."
 The quasar is associated with an extended ionized nebula of maximum extension 64 kpe., The quasar is associated with an extended ionized nebula of maximum extension $\sim$ 64 kpc.
 Phe nuclear gas and the extended: adjacent gaseous regions are preferentially photoionized by the quasar., The nuclear gas and the extended adjacent gaseous regions are preferentially photoionized by the quasar.
 The VLT-FODBS2 images of this quasar show two nuclei Cone hosts the quasar) separated in projection by Ll” or ~5 kpe and two tidal tails extending North and South (Fig 4)., The VLT-FORS2 images of this quasar show two nuclei (one hosts the quasar) separated in projection by $\arcsec$ or $\sim$ 5 kpc and two tidal tails extending North and South (Fig 4).
 ‘These are clear signatures of an ongoing merger., These are clear signatures of an ongoing merger.
 Two knots are also detected to the East (Anofl in the figure) ancl to the West (&nol2)., Two knots are also detected to the East $knot1$ in the figure) and to the West $knot2$ ).
 knoll appears much more prominently in the intermediate band image. which contains the OL line. while it is undetected in the broad band image.," $knot1$ appears much more prominently in the intermediate band image, which contains the [OII] line, while it is undetected in the broad band image."
 This suggests knollisan emission line object at similar z as the quasar., This suggests $knot1$ is an emission line object at similar $z$ as the quasar.
 Hs compact appearance is reminiscent of a star forming knot., Its compact appearance is reminiscent of a star forming knot.
 The opposite happens with &nof2., The opposite happens with $knot2$.
 It appears much. more prominently relative to other features in the broad. band image and thus it is most probably a continuum source of unknown z., It appears much more prominently relative to other features in the broad band image and thus it is most probably a continuum source of unknown $z$.
 We show in Fig., We show in Fig.
 5 the OLLI] 2D spectra for the two slit PAs., 5 the $\beta$ -[OIII] 2D spectra for the two slit PAs.
 PX 0 goes through the quasar and. the northern tical tail (fa@7/1) and PA 60 &oes through the quasar nucleus and the nucleus of the companion (nauc2. Pig.," PA 0 goes through the quasar and the northern tidal tail $tail1$ ) and PA 60 goes through the quasar nucleus and the nucleus of the companion $nuc2$, Fig."
 4)., 4).
 The visual inspection of both spectra shows that the tidal tail and the companion nucleus emit strong continuum and emission lines. which are much narrower than those of the quasar.," The visual inspection of both spectra shows that the tidal tail and the companion nucleus emit strong continuum and emission lines, which are much narrower than those of the quasar."
 nuc2 presents a shift in velocity relative to the quasar of O+70 km Í (slit effects are also accounted for. see 2)," $nuc2$ presents a shift in velocity relative to the quasar of $\pm$ 70 km $^{-1}$ (slit effects are also accounted for, see $\delta$ 2)."
 The velocity blueshift of the tidal tail relative to the quasar is also small (-1L5+70 kms 13., The velocity blueshift of the tidal tail relative to the quasar is also small $\pm$ 70 km $^{-1}$ ).
 The OU) line was outside the observed spectral range and no diagnostic diagram is presented., The [OII] line was outside the observed spectral range and no diagnostic diagram is presented.
 Lhe detection of strong Hell (Lable 2) is consistent with values measured in tvpe 2 AGNs. which implies that ACN photoionization is the dominant mechanisms responsible for the ionization of the nuclear gas.," The detection of strong HeII (Table 2) is consistent with values measured in type 2 AGNs, which implies that AGN photoionization is the dominant mechanisms responsible for the ionization of the nuclear gas."
 This is further confirmed by the detection of NeV]A3426 in the SDSS spectrum., This is further confirmed by the detection of $\lambda$ 3426 in the SDSS spectrum.
 This. as for the rest of the sample. is to be expected since one of the selection criteria applied hy Zakamska et al. (2003))," This, as for the rest of the sample, is to be expected since one of the selection criteria applied by Zakamska et al. \citeyear{zak03}) )"
 was an emission line spectrum typical of type 2 AGNs., was an emission line spectrum typical of type 2 AGNs.
 The spectra of the companion nucleus and the tidal tail are more reminiscent of LEE galaxies than ACGNs (see Fig., The spectra of the companion nucleus and the tidal tail are more reminiscent of HII galaxies than AGNs (see Fig.
 5. bottom).," 5, bottom)."
 Phe /LL2 values (1.264002 and. 40.08 respectively) are very low compared: with typical tvpe 2 AGNs ancl similar to values frequently. measured. in. LLL ealaxies (e.g. Lamareille ct al. 2004))., The $\beta$ values $\pm$ 0.02 and $\pm$ 0.08 respectively) are very low compared with typical type 2 AGNs and similar to values frequently measured in HII galaxies (e.g. Lamareille et al. \citeyear{lam04}) ).
 Well is undetected in ΕΠΟΣ and the tidal tail with η «0.02. and <0.05 respectively.," HeII is undetected in $nuc2$ and the tidal tail, with $\beta<$ 0.02 and $<$ 0.05 respectively."
 Phese low values are consistent with LIL, These low values are consistent with HII
 Phese low values are consistent with LILE, These low values are consistent with HII
Alaxwell’s equations in free space are: Potentials and a gauge. condition will be introduced later.,Maxwell's equations in free space are: Potentials and a gauge condition will be introduced later.
 We start. from the simple. and at first. sight pointless. observation that. the kinetic-cnerey term of the Wlein-Gordon equation for a charged. scalar field. in. Minkowski space. Φ0ρqAYd. when expanded. gives the term Q'qATP.," We start from the simple, and at first sight pointless, observation that the kinetic-energy term of the Klein-Gordon equation for a charged scalar field in Minkowski space, $\Phi^{*} ({\mathbf p} - q{\mathbf A})^2 \Phi$, when expanded, gives the term $\Phi^{*} q^2 {\mathbf A}^2 \Phi$."
 This has the same sign as the mass term Qm7. suggesting that in some circumstances. such as in a plasma. (qA75 might play the role of the square of an elective thermal mass.," This has the same sign as the mass term $\Phi^{*} m^2 \Phi$, suggesting that in some circumstances, such as in a plasma, $\langle q^2 {\mathbf A}^2 \rangle$ might play the role of the square of an effective thermal mass."
 £A7) is the sum of. contributions from particles in the immediate neighborhood. roughly. those within the Dehve sphere (?).. and should therefore be written (M.A; ," $\langle {\mathbf A}^2 \rangle$ is the sum of contributions from particles in the immediate neighborhood, roughly, those within the Debye sphere \citep{stur}, and should therefore be written $\langle (\sum_i {\mathbf A_i})^2 \rangle$."
When we sum over all contributions. the A; potentials will be randomly. oriented. and. will ace according to the theory of random Lliehts (?)..," When we sum over all contributions, the ${\mathbf A_i}$ potentials will be randomly oriented, and will add according to the theory of random flights \citep{hugh1}."
" SO,A will then be zero. but (M.A;Y5 will not."," $\langle \sum_i {\mathbf A_i} \rangle$ will then be zero, but $\langle (\sum_i {\mathbf A_i})^2 \rangle$ will not."
 In a proper quantum mechanical treatment we have to represent the source particles by means of a density matrix., In a proper quantum mechanical treatment we have to represent the source particles by means of a density matrix.
 This is not important for a plasma in. Minkowski space. but will be essential when we come to curved. space. so we introduce the idea here.," This is not important for a plasma in Minkowski space, but will be essential when we come to curved space, so we introduce the idea here."
 The density matrix. provides a wav of including all possible configurations of source particles. which are not. of course. individually observed.," The density matrix provides a way of including all possible configurations of source particles, which are not, of course, individually observed."
 Instead of A; we should write Ajj. where jr specifies a particular configuration.," Instead of ${\mathbf A_i}$ we should write ${\mathbf A_{\mu i}}$, where $\mu$ specifies a particular configuration."
 (A7) is then a double sum. over the particles within a configuration. and over the various possible configurations: up to a normalization factor. S(NDAnil?.," $\langle {\mathbf A}^2 \rangle$ is then a double sum, over the particles within a configuration, and over the various possible configurations; up to a normalization factor, $\langle \sum_{\mu} ( \sum_i {\mathbf A_{\mu i}})^2 \rangle$."
 Dimensional considerations indicate that in the conditions of the carly Universe this should have a value of order 27. where Tis the temperature of the plasma.," Dimensional considerations indicate that in the conditions of the early Universe this should have a value of order $T^2$, where $T$ is the temperature of the plasma."
" We are free to make an overall gauge transformation with an arbitrary function (μή),", We are free to make an overall gauge transformation with an arbitrary function $\psi (x^{\mu})$.
 Phe various A; become A;|Vo. and the source particles acquire corresponcing phases.," The various ${\mathbf A_i}$ become ${\mathbf A_i} + {\mathbf \nabla} \psi$, and the source particles acquire corresponding phases."
 But we should note that this freedom. is not the same as [freedom to choose any gauge we wish to describe the propagation of the potentials., But we should note that this freedom is not the same as freedom to choose any gauge we wish to describe the propagation of the potentials.
 For example. we might decide to switeh from Lorenz gauge (2). to Coulomb gauge.," For example, we might decide to switch from Lorenz gauge \citep{jack2} to Coulomb gauge."
 This would introduce a separate gauge function. for each Αι. and there would be no single gauge function. that could be used to generate a compensating phase for any chosen interacting particle.," This would introduce a separate gauge function for each ${\mathbf A_{\mu i}}$, and there would be no single gauge function that could be used to generate a compensating phase for any chosen interacting particle."
 Lowe are concerned. with the propagation of potentials we have to choose a gauge from he beginning that is suitable for that purpose. as cliscussed in section 7..," If we are concerned with the propagation of potentials we have to choose a gauge from the beginning that is suitable for that purpose, as discussed in section \ref{sec:dipot}."
 This choice is not altered by an overall gauge ransformation., This choice is not altered by an overall gauge transformation.
 We can argue. of course. that in Minkowski space we are not really dealing with a cirect effect of the vector potential. »ecause electric ancl magnetic fields are also present.," We can argue, of course, that in Minkowski space we are not really dealing with a direct effect of the vector potential, because electric and magnetic fields are also present."
 and hey are the actual physical agents., and they are the actual physical agents.
 This is true. but. as we will see in section 9.. it is no longer true in à curvecl space. where we have potentials without fields.," This is true, but, as we will see in section \ref{sec:FRW}, it is no longer true in a curved space, where we have potentials without fields."
 We will need to know the potential due to a single particle in the plasma at distances larger than the Debve length., We will need to know the potential due to a single particle in the plasma at distances larger than the Debye length.
 Lf the particle is stationary. the potential declines exponentially.," If the particle is stationary, the potential declines exponentially."
 Surprisingly. however. starting in the 1950s several authors (222). discovered that a test charge is not exponentially screened. but gencrates the field of a quadrupole in a collisionless plasma.," Surprisingly, however, starting in the 1950's several authors \citep{neuf,tapp1,mont1} discovered that a test charge is not exponentially screened, but generates the field of a quadrupole in a collisionless plasma."
 Phe restriction to a collisionless plasma was lifted. in later papers (??).. where it was shown that the far field of a moving test charge is that ofa dipole with strength of order qr. where q is the charge. 7; the collision time as measured by /. and V the velocity.," The restriction to a collisionless plasma was lifted in later papers \citep{yu,schr}, where it was shown that the far field of a moving test charge is that of a dipole with strength of order $q\tau_t V$, where $q$ is the charge, $\tau_t$ the collision time as measured by $t$, and $V$ the velocity."
 This dipole form ensures that in Minkowski space the contribution of particles to the ellective mass falls olf rapidlv with distance bevond the Dehve raclius., This dipole form ensures that in Minkowski space the contribution of particles to the effective mass falls off rapidly with distance beyond the Debye radius.
 We shall sec. however. that this is no longer the case in a curved space.," We shall see, however, that this is no longer the case in a curved space."
 ‘Lo studs the propagation of fields and potentials in a curved ERA space. we first need a model of the motion of the source xwiicles that produce them.," To study the propagation of fields and potentials in a curved FRW space, we first need a model of the motion of the source particles that produce them."
 We are concerned. with the early Universe. before any svmmetrv-breaking transitions hat may generate particle masses as we know them.," We are concerned with the early Universe, before any symmetry-breaking transitions that may generate particle masses as we know them."
 The »operties of the plasma are therefore determined by a single number. the temperature.," The properties of the plasma are therefore determined by a single number, the temperature."
 Phe photons will have the familiar απο. distribution., The photons will have the familiar Planck distribution.
 For simplicity. we assume the charged xuticles are associated with a single massless scalar. Ποιά.," For simplicity, we assume the charged particles are associated with a single massless scalar field."
 'Fhis field will have an elective thermal mass. mig. due to its interaction with the photons. so that migz2.," This field will have an effective thermal mass, $m_{\mathrm{th}}$, due to its interaction with the photons, so that $m_{\mathrm{th}} \approx T$."
 Phe charged xwlicleswill have a thermal distribution appropriate to his mass and temperature., The charged particleswill have a thermal distribution appropriate to this mass and temperature.
 Phe plasma will therefore. be weakly relativistic: for simplicitv. however. we will carry over some results from. non-relativistic plasmas.," The plasma will therefore be weakly relativistic; for simplicity, however, we will carry over some results from non-relativistic plasmas."
 Other plasma xwanmeters are determined by 7: for example. the plasma requeney. oy. will be of order 1.," Other plasma parameters are determined by $T$; for example, the plasma frequency, $\omega_p$, will be of order $T$."
 A charge that is part of the plasma. rather than xung a test charge constrained to move in a certain wav. will itself experience collisions.," A charge that is part of the plasma, rather than being a test charge constrained to move in a certain way, will itself experience collisions."
 We can picture such a xwticle as describing Brownian motion. with its screening cloud. sometimes closer. sometimes farther. but never Cully established.," We can picture such a particle as describing Brownian motion, with its screening cloud sometimes closer, sometimes farther, but never fully established."
 We will model the most important aspect. of a single step of this process by setting up a local set of Cartesian coordinates ancl placing a stationary screening charge —q at the origin., We will model the most important aspect of a single step of this process by setting up a local set of Cartesian coordinates and placing a stationary screening charge $-q$ at the origin.
 A charge q is initially at rest on the zoaxis at 2Vor. then begins to move with uniform velocity V. along the z axis. starting at /—τι and ending abf—n. when it again comes to rest.," A charge $q$ is initially at rest on the $z$ axis at $z = -V \tau_t$, then begins to move with uniform velocity $V$ along the $z$ axis, starting at $t = -\tau_t$ and ending at $t = \tau_t$, when it again comes to rest."
 Note that this choice of origin for / dilfers [rom that of the cosmic time used in section η. defined below. will diller in a similar wav.," Note that this choice of origin for $t$ differs from that of the cosmic time used in section \ref{sec:notation}; $\eta$ , defined below, will differ in a similar way."
 We reconcile these cdillerences later. in section 10.," We reconcile these differences later, in section \ref{sec:mass_1}."
. We are now going to take the result. for a uniformly moving test charge and use it to caleulate the field around our model charge that is subject to Brownian motion., We are now going to take the result for a uniformly moving test charge and use it to calculate the field around our model charge that is subject to Brownian motion.
 We justify this step as follows., We justify this step as follows.
 Imagine that the test charge. instead. of moving uniformly [rom an indefinite time in the past. is actually stationary until time /= 0. and then starts moving uniformly.," Imagine that the test charge, instead of moving uniformly from an indefinite time in the past, is actually stationary until time $t=0$ , and then starts moving uniformly."
 There will be transient. fields. but after a [ew collision times the final field of a moving dipole will," There will be transient fields, but after a few collision times the final field of a moving dipole will"
Initial attempts to fit the data showed that the model does not generally constrain the gravitating matter density tightly for individual shells.,Initial attempts to fit the data showed that the model does not generally constrain the gravitating matter density tightly for individual shells.
 This is because the gravitational potential is governed by the accumulated mass within any radius and variations of the gas density depend on changes in the potential., This is because the gravitational potential is governed by the accumulated mass within any radius and variations of the gas density depend on changes in the potential.
" Since there are two integrations between the mass density and changes in the potential, the gas density, hence the spectra, are only affected at second order by local changes in the gravitating matter density 3))."," Since there are two integrations between the mass density and changes in the potential, the gas density, hence the spectra, are only affected at second order by local changes in the gravitating matter density (equation \ref{eqn:dphi}) )."
" Splitting the gravitating matter from one shell into the two adjacent shells, in suitable proportions, has little (equationimpact on the fit."," Splitting the gravitating matter from one shell into the two adjacent shells, in suitable proportions, has little impact on the fit."
" In the presence of noise, this freedom to exchange mass from shell to shell results in large shell to shell variations of gravitating mass density, producing noisy best fitting mass profiles like that for Abell 907 in Fig. 2.."," In the presence of noise, this freedom to exchange mass from shell to shell results in large shell to shell variations of gravitating mass density, producing noisy best fitting mass profiles like that for Abell 907 in Fig. \ref{fig:a907mass}."
 'The freedom of gravitating mass to shift between adjacent shells can be limited to some extent by constraining the gravitating matter density to be a monotonically decreasing function of the radius., The freedom of gravitating mass to shift between adjacent shells can be limited to some extent by constraining the gravitating matter density to be a monotonically decreasing function of the radius.
 This constraint improves model behaviour with a relatively minor impact on the goodness of fit (Table 2))., This constraint improves model behaviour with a relatively minor impact on the goodness of fit (Table \ref{tab:mass}) ).
" In practice, the constraint requires gravitating mass densities to be linked for groups of adjacent shells where the unconstrained density would otherwise increase with radius."," In practice, the constraint requires gravitating mass densities to be linked for groups of adjacent shells where the unconstrained density would otherwise increase with radius."
" Mass profiles for Abell 907, with the gravitating matter density forced to be monotonic, are shown in Fig. 3.."," Mass profiles for Abell 907, with the gravitating matter density forced to be monotonic, are shown in Fig. \ref{fig:a907cons}."
" Evidently, the monotonic constraint makes the matter density profile considerably smoother."," Evidently, the monotonic constraint makes the matter density profile considerably smoother."
" Although this condition is not required of the gravitating matter density distribution, it is simple, physically reasonably and relatively weak, while it reduces the noise in the mass profiles significantly."," Although this condition is not required of the gravitating matter density distribution, it is simple, physically reasonably and relatively weak, while it reduces the noise in the mass profiles significantly."
" As a consequence, we prefer results for “monotonic” mass profiles in the following, although some results for unconstrained mass profiles are also given for comparison."," As a consequence, we prefer results for “monotonic” mass profiles in the following, although some results for unconstrained mass profiles are also given for comparison."
In order to build a database as complete as possible we started from Acker οἱ αἱ.,In order to build a database as complete as possible we started from Acker et al.
5 (1994) catalog of Galactic PNe and include all confirmed PN therein.,'s (1994) catalog of Galactic PNe and include all confirmed PN therein.
 The catalog offers the Galactie coordinates and basic data for most nebulae., The catalog offers the Galactic coordinates and basic data for most nebulae.
 The nebular optical diameters. essential for determining the distances. have been taken [rom Calin et al," The nebular optical diameters, essential for determining the distances, have been taken from Cahn et al."
s (1992. CINS) studs; which takes into account (he acquisition aperture. and. ib not available (herein. from Acker et al. (,"'s (1992, CKS) study, which takes into account the acquisition aperture, and, if not available therein, from Acker et al. ("
1994).,1994).
 Furthermore. for extended Northern Galactic PNe the diameters have been (aken [rom Manchado et al. (," Furthermore, for extended Northern Galactic PNe the diameters have been taken from Manchado et al. ("
1996).,1996).
 The nebular flix at 5 GlIz has been taken again [rom CIXS preferentially. otherwise [rom Acker et al. (," The nebular flux at 5 GHz has been taken again from CKS preferentially, otherwise from Acker et al. ("
1994).,1994).
 If not available. the 5 Gllz flix has been approximated by its relation to the IL? flux (see CINS).," If not available, the 5 GHz flux has been approximated by its relation to the $\beta$ flux (see CKS)."
 As mention in the introduction the major reason for the reanalvsis of the metallicity eradients is the advent of the new distance scale by SSV. which has been calibrated on the Magellanic Cloud PNe.," As mention in the introduction the major reason for the reanalysis of the metallicity gradients is the advent of the new distance scale by SSV, which has been calibrated on the Magellanic Cloud PNe."
 In this paper we preferentially use the best. newly calibrated distance scale. which is the re-calibration of the CIS scale (eq.," In this paper we preferentially use the best, newly calibrated distance scale, which is the re-calibration of the CKS scale (Eq."
 8a and Sb in SSV). but we also compare to other scales that use the ionized mass. the briehtness temperature. and the surface brightness relations to the nebular radii (Eq.," 8a and 8b in SSV), but we also compare to other scales that use the ionized mass, the brightness temperature, and the surface brightness relations to the nebular radii (Eq."
 5. 6. ancl 7 in SSV) to study (the impact of different (but equally well-calibrated) scales on the metallicity gradients and the Galactic distributions.," 5, 6, and 7 in SSV) to study the impact of different (but equally well-calibrated) scales on the metallicity gradients and the Galactic distributions."
 It is worth noting that the choice of Magellanic-Cloud calibrated. distance scales is based on the fact that these calibrations give (he best results when compared to known individual PN distances. and (hey represent an improvement with respect to the old Galactic-calibrated scales (see Table 3 in SSY).," It is worth noting that the choice of Magellanic-Cloud calibrated distance scales is based on the fact that these calibrations give the best results when compared to known individual PN distances, and they represent an improvement with respect to the old Galactic-calibrated scales (see Table 3 in SSV)."
The map is self calibrated to the strong compact feature at —37.5s. and this then falls at the origin.,"The map is self calibrated to the strong compact feature at $-37.5$, and this then falls at the origin."
 We find the lowest absolute velocity. and weakest. spot positions to the orth.," We find the lowest absolute velocity, and weakest, spot positions to the North."
 These run from -28 to. with most negitive velocities furthest from the centre.," These run from -28 to, with most negitive velocities furthest from the centre."
 This ts also the brightest feature peaking at at 9 Jy/beam., This is also the brightest feature peaking at at 9 Jy/beam.
 The Western cluster starts at. and runs further westwards with velocity until," The Western cluster starts at, and runs further westwards with velocity until."
 After which the spots track back across the same positions in the sky., After which the spots track back across the same positions in the sky.
 There is some further emission in the extreme West around —36.5., There is some further emission in the extreme West around $-36.5$.
 The Eastern cluster appear at about —36.5 aand run in a easterly direction until around —38. after which the components appear to the South of the starting point.," The Eastern cluster appear at about $-36.5$ and run in a easterly direction until around $-38$, after which the components appear to the South of the starting point."
 Figure 3 plots the velocities of the features as a function of their distance along the major axis (shown as the line in Figure 2)) from the centre of the emission along this line. the velocities are along the y-axis.," Figure \ref{fig:vma} plots the velocities of the features as a function of their distance along the major axis (shown as the line in Figure \ref{fig:pos}) ) from the centre of the emission along this line, the velocities are along the y-axis."
 Emission from a thin ring in a disk would produce a linear distribution., Emission from a thin ring in a disk would produce a linear distribution.
 The detailed mapping of spot position against velocity is difficult to reconcile with that expected from an edge-on Keplerian rotating disk model. as there is not a simple two sided structure let alone a monotonic ncrease in velocity along the main axis.," The detailed mapping of spot position against velocity is difficult to reconcile with that expected from an edge-on Keplerian rotating disk model, as there is not a simple two sided structure let alone a monotonic increase in velocity along the main axis."
 But other models are eas difficult to construct., But other models are as difficult to construct.
" If the emission delineates an entire ""Sisk. gravitationally bound by à massive central object. at a ""Sistance of kkpe. the implied enclosed mass is."," If the emission delineates an entire disk, gravitationally bound by a massive central object, at a distance of kpc, the implied enclosed mass is."
 However. in this source the spots are extended across the major axis. as discussed in Dodsonetal.(2004).. and neonsistent with the disk-model.," However, in this source the spots are extended across the major axis, as discussed in \cite{dodson_04}, and inconsistent with the disk-model."
 Similar structures are seen in the observations of water maser by Torrellesetal.(2001).. on both the small and the large scale.," Similar structures are seen in the observations of water maser by \cite{torrelles_02}, on both the small and the large scale."
 Water masers unquestionably form in shocked out-flows., Water masers unquestionably form in shocked out-flows.
 These facts combine to argue strongly against the disk-based models for the majority of the emission., These facts combine to argue strongly against the disk-based models for the majority of the emission.
 From the polarised images we present fluxes and polarisatior angles for all the spots. defined às regions of contiguous emission in space and velocity. in tabular form.," From the polarised images we present fluxes and polarisation angles for all the spots, defined as regions of contiguous emission in space and velocity, in tabular form."
 Figures are also presented. showing the arrangement of the emission anc the magnetic fields that this represents.," Figures are also presented, showing the arrangement of the emission and the magnetic fields that this represents."
 The Northern region. being very weak. has no identifible polarised flux.," The Northern region, being very weak, has no identifible polarised flux."
 The Wester has rapidly varying linear polarisation angles (y) which tenc to follow the ridge of emission., The Western has rapidly varying linear polarisation angles $\chi$ ) which tend to follow the ridge of emission.
 Interestingly the directio undergoes a swap across the brightest point. changing by 90< going North to South.," Interestingly the direction undergoes a swap across the brightest point, changing by $90^o$ going North to South."
 Across the North-Eastern region. at the phase centre. y is similar.," Across the North-Eastern region, at the phase centre, $\chi$ is similar."
 In the most Eastern region y Is agal variable., In the most Eastern region $\chi$ is again variable.
 In the South-Eastern region y the flux emitting regio is continuous and y is constant across this., In the South-Eastern region $\chi$ the flux emitting region is continuous and $\chi$ is constant across this.
 To relate y to magnetie field direction is not. simple., To relate $\chi$ to magnetic field direction is not simple.
 The dominant maser emission will either. be parallel. or perpendicular to the magnetic. field lines. depending on the angle between the magnetic field and line of sight.," The dominant maser emission will either be parallel or perpendicular to the magnetic field lines, depending on the angle between the magnetic field and line of sight."
" If it is greater (less) than ~55"" the vectors are perpendicular (parallel) to the magnetic field (Goldreichetal...1973).", If it is greater (less) than $\sim 55^o$ the vectors are perpendicular (parallel) to the magnetic field \citep{gold_73}.
. Also when the masers are highly saturated there are further complications. but as the polarisation vectors are similar from all components. weak and strong. one can deduce that the emission is never sufficiently saturated to change the emitting regime.," Also when the masers are highly saturated there are further complications, but as the polarisation vectors are similar from all components, weak and strong, one can deduce that the emission is never sufficiently saturated to change the emitting regime."
 Furthermore. the source is extended on the sky. being over aacross.," Furthermore, the source is extended on the sky, being over across."
 It is unlikely. therefore. that the field is pointing towards us.," It is unlikely, therefore, that the field is pointing towards us."
 The one region where this may not be correct is around the brightest spot in the Western cluster. where the polarisation vectors rapidly change by 90° across it. yet the polarisation ts zero at the centre.," The one region where this may not be correct is around the brightest spot in the Western cluster, where the polarisation vectors rapidly change by $90^o$ across it, yet the polarisation is zero at the centre."
 Very similar behaviour is also seen in the strongest feature reported on the mmasers discussed in Vlemmings&Diamond(2006)., Very similar behaviour is also seen in the strongest feature reported on the masers discussed in \cite{vlem_06}.
. For our source better data is needed. in particular the magnetic field magnitudes. to solve for the full field behaviour using Stokes V. (As Methanol and OH masers are often found co-located (as in W3(OH) Vlemmingsetal. (2006))) we could expect the," For our source better data is needed, in particular the magnetic field magnitudes, to solve for the full field behaviour using Stokes V. (As Methanol and OH masers are often found co-located (as in W3(OH) \citet{vlemmings_06}) ) we could expect the"
the importance of obtaining photometric limits al or bevond the actual turnover to avoid svstematic errors.,the importance of obtaining photometric limits at or beyond the actual turnover to avoid systematic errors.
 The WF data have limiting magnitudes similar to those of Lauer et al..," The WF data have limiting magnitudes similar to those of Lauer et al.,"
 and the turnover magnitudes we deduced from the WF data alone are generally closer to those deduced by Lauer et al..," and the turnover magnitudes we deduced from the WF data alone are generally closer to those deduced by Lauer et al.,"
 as are those from the total (PC+WF) dataset., as are those from the total (PC+WF) dataset.
 These latter fils are certainly to be preferred over the PCI data alone., These latter fits are certainly to be preferred over the PC1 data alone.
 We note that the datapoints in the laintest bin for A262. A3560 ancl ÀA3742 in Figure 3 and in the WF Figure 4. fall clearly below the fitted GCLF curve.," We note that the datapoints in the faintest bin for A262, A3560 and A3742 in Figure \ref{gclf_plot} and in the WF Figure \ref{gclf_comp}
 fall clearly below the fitted GCLF curve."
 This does not appear to be due to an incorrect completeness correction at that level., This does not appear to be due to an incorrect completeness correction at that level.
 The only other obvious possibility is (hat our empirical background has been overestimated in (he last bin. but it is unclear whether (hat is the case without deeper data to draw on.," The only other obvious possibility is that our empirical background has been overestimated in the last bin, but it is unclear whether that is the case without deeper data to draw on."
 The luminosity distribution function (LDF). or number of clusters per unit./ninosity GUN dL). is the visible signature of the cluster mass distribution and is a more physically oriented representation of the GCLE.," The luminosity distribution function (LDF), or number of clusters per unit $dN/dL$ ), is the visible signature of the cluster mass distribution and is a more physically oriented representation of the GCLF."
" In this plane it usually appears as a rough power law. ΝαονL""*."," In this plane it usually appears as a rough power law, $dN/dL \sim L^{-\alpha_L}$."
" By adopting a mass-to-light ratio one can also immediately obtain (he mass cistvibution function d.N/dM~M.""9, where a,7aa; as long as (he M/L ratio is roughly independent of cluster mass (see Mandushevetal.(1991) and MeLaughlin. (2000)))."," By adopting a mass-to-light ratio one can also immediately obtain the mass distribution function $dN/dM \sim M^{-\alpha_M}$, where $\alpha_L
\simeq \alpha_M$ as long as the $M/L$ ratio is roughly independent of cluster mass (see \citet{Man91} and \citet{McL00}) )."
 It has been noted many times that within observational uncertainty. the globular cluster mass distribution follows a simple power law relation which has the same shape as the mass distribution of giant molecular clouds (GAICs) in large spirals. cloud cores embedded. in GAICs. and giant LIT regions in large spirals (e.g. Harris&Pudiitz(1994) aud subsequent," It has been noted many times that within observational uncertainty, the globular cluster mass distribution follows a simple power law relation which has the same shape as the mass distribution of giant molecular clouds (GMCs) in large spirals, cloud cores embedded in GMCs, and giant HII regions in large spirals (e.g. \citet{HaPu94} and subsequent"
detailed description of the halo finders and their cllectiveness we refer the reader toGKGI.,detailed description of the halo finders and their effectiveness we refer the reader to.
. 1n we summarise the relevant characteristics of the eight host halos., In we summarise the relevant characteristics of the eight host halos.
 “Phe derivation of these properties 1s detailed in Sections 3.1--3.4.., The derivation of these properties is detailed in Sections \ref{Canon}- \ref{Supply}.
 quantities presented. discussed in this Section., quantities presented discussed in this Section.
 A simple aanalvsis of the simulationat redshift Ξ0 provides us with the relevant information for the host halo., A simple analysis of the simulationat redshift $z=0$ provides us with the relevant information for the host halo.
 At z=0 the halo masses range [rom 13. lott wwhere mass here was defined to be that within the virial radiusf, At $z=0$ the halo masses range from 1–3 $ \times 10^{14}$ where mass here was defined to be that within the virial radius.
é Phe virial radii in turn at which defined to be the point where the mean averaged density of the host (measured in terms of the cosmological background density po) drops below Avy=340 with bbeing the mass enclosed by that sphere., The virial radii in turn at which defined to be the point where the mean averaged density of the host (measured in terms of the cosmological background density $\rho_b$ ) drops below $\Delta_{\rm vir}=340$ with being the mass enclosed by that sphere.
 “Phe formation redshift) iis defined here as the redshift where the halo contains half ol its present day mass (Lacey Cole 1994)., The formation redshift is defined here as the redshift where the halo contains half of its present day mass (Lacey Cole 1994).
 Applying this criterion to our data we find that the ages of our host halos range from 8.3 Civrs to 3.4 Gives., Applying this criterion to our data we find that the ages of our host halos range from 8.3 Gyrs to 3.4 Gyrs.
 In other words. while the masses of our systems are comparable. they are dynamically cilferent.," In other words, while the masses of our systems are comparable, they are dynamically different."
 In1.. as in all following figures. the halos are ordered. 1-8 in age.," In, as in all following figures, the halos are ordered 1-8 in age."
" The appropriate coordinate system to investigate the orbits of the satellite galaxies is given. by the eigenvectors Eja (with E, being the major axis) of the inertia tensor of the respective host. halo."," The appropriate coordinate system to investigate the orbits of the satellite galaxies is given by the eigenvectors $\vec{E}_{\rm 1,2,3}$ (with $\vec{E}_{\rm 1}$ being the major axis) of the inertia tensor of the respective host halo."
 Moreover. the eigenvalues (tbc can be used to describe the shape of the hos and define its triaxialitv T2(αλα.c7) (rans. Hlngworth Zeeuw. 1991).," Moreover, the eigenvalues $a>b>c$ can be used to describe the shape of the host and define its triaxiality $T=(a^2-b^2)/(a^2-c^2)$ (Franx, Illingworth Zeeuw 1991)."
 The calculation of the inertia tensor is based upon the “core” region of the host as define by the 6 refinement level in MLAPM:: ic. the boundary of this refinement level is an isodensity contour., The calculation of the inertia tensor is based upon the “core” region of the host as defined by the $6^{\rm th}$ refinement level in ; i.e. the boundary of this refinement level is an isodensity contour.
 Phe 6 refinemen level surrounds material about 3000 times denser than pi. or 9 times denser than the material at the virial racius.," The $6^{\rm th}$ refinement level surrounds material about 3000 times denser than $\rho_b$, or 9 times denser than the material at the virial radius."
 The density profiles of our host halos are well described - at leas in the range [rom oout to the virial radius - by the functional form advocate by Navarro. Frenk White (1997) with concentration in the range ez4+9.," The density profiles of our host halos are well described - at least in the range from out to the virial radius - by the functional form advocated by Navarro, Frenk White (1997) with concentration in the range $c\approx 4-9$."
 Therefore. a density of roughly 95plvin) corresponds to about the hall-mass radius of the host.," Therefore, a density of roughly $9\times \rho(R_{\rm vir})$ corresponds to about the half-mass radius of the host."
 As we are interested. in investigating the inlluence of host halo formation history and environment on the orbital and internal properties of the satellites galaxies living within its virial radius. it is important to understand how the host halos actuallv formed.," As we are interested in investigating the influence of host halo formation history and environment on the orbital and internal properties of the satellites galaxies living within its virial radius, it is important to understand how the host halos actually formed."
 As incieated bv Tormen. (1997) the formation of dark matter halos can be characterised. by two clilferent phases: one corresponding to à rapid increase in halo mass. representative of a major merger.," As indicated by Tormen (1997) the formation of dark matter halos can be characterised by two different phases: one corresponding to a rapid increase in halo mass, representative of a major merger."
 We refer to this phase as a violent (V)) period., We refer to this phase as a violent ) period.
 The second phase is one of relaxation in which the halo processes the merger ancl settles toward virial equilibrium., The second phase is one of relaxation in which the halo processes the merger and settles toward virial equilibrium.
 A halo may continue to accrete smaller jalos during this phase., A halo may continue to accrete smaller halos during this phase.
 We refer to this phase as a quiet (QU) period., We refer to this phase as a quiet ) period.
 The history of cach halo is brielly outlined below using he simplified kevs V or OQ to signify violent or quiet episodes., The history of each halo is briefly outlined below using the simplified keys V or Q to signify violent or quiet episodes.
" For example. halo 3£11 has a history “OVQQ"". that is. a quiet. period. around. the time of formation zp44,. followed o» à violent. period of merging of about the same length and completed by quiet evolution for the remainder of the evolution. which lasts for twice as long as either of the wo earlier episodes."," For example, halo 1 has a history “QVQQ”, that is, a quiet period around the time of formation $z_{\rm form}$ followed by a violent period of merging of about the same length and completed by quiet evolution for the remainder of the evolution, which lasts for twice as long as either of the two earlier episodes."
 The coding chain splits the evolution since formation up into more-or-less equal segments. but has nothing to sav about the absolute timescales. which cdiller widely from halo to halo.," The coding chain splits the evolution since formation up into more-or-less equal segments, but has nothing to say about the absolute timescales, which differ widely from halo to halo."
 A qualitative summary of the eight halos follows: A reasonably quiet history with no major violent encounters. save for a medium one at z=0.7.," A qualitative summary of the eight halos follows: A reasonably quiet history with no major violent encounters, save for a medium one at $z=0.7$ ."
 A generally quiet history with a medium size merger one quarter of the way through its evolution at 2=0.53. quickly settling for the rest of its formation.," A generally quiet history with a medium size merger one quarter of the way through its evolution at $z=0.53$, quickly settling for the rest of its formation."
 An initial short. quiet period. followed. by a long and violent interaction that takes essentially the rest. of. its formation time to settle., An initial short quiet period followed by a long and violent interaction that takes essentially the rest of its formation time to settle.
 An initially violent merger which quickly settles for the rest of its formation., An initially violent merger which quickly settles for the rest of its formation.
 AO very violent formation history with a strongly oscillating potential., A very violent formation history with a strongly oscillating potential.
 AX steady. vet violent. formation history.," A steady, yet violent, formation history."
 A formation history quite similar to that of halo #266., A formation history quite similar to that of halo 6.
 A rapid formation history: constantly interacting with two other large halos., A rapid formation history; constantly interacting with two other large halos.
 In this sense. à unique system.," In this sense, a unique system."
 While useful. such a qualitative description needs to be augmented. with a quantitative one.," While useful, such a qualitative description needs to be augmented with a quantitative one."
 In order to do so. we use the dispersion of the rate of relative mass change of the host halos: where Now ds the number of available outputs from formation tto redshift z= 0. AA;=Mz)AM(z;1) the change in the mass of the hosthalo. and Af; the respective changein time.," In order to do so, we use the dispersion of the rate of relative mass change of the host halos: where $N_{\rm out}$ is the number of available outputs from formation to redshift $z=0$ , $\Delta M_i = M(z_i)-M(z_{i-1})$ the change in the mass of the hosthalo, and $\Delta t_i$ the respective changein time."
 Phe mean growth rate at time 7 , The mean growth rate at time $i$ 
In the current picture of hierarchical structure formation clusters of galaxies grow mainly by the merging of smaller and moderately sized. sub-elusters.,In the current picture of hierarchical structure formation clusters of galaxies grow mainly by the merging of smaller and moderately sized sub-clusters.
 During such merger events a significant fraction of the kinetic energy of the inter galactic medium. (LGAL) is dissipated in. \Ipe-sizecl shock waves., During such merger events a significant fraction of the kinetic energy of the inter galactic medium (IGM) is dissipated in Mpc-sized shock waves.
 Phe shock waves are responsible for heating the IGM to temperatures of several keV. Moreover. they are likely to inject and accelerate relativistic particle populations on cluster scales.," The shock waves are responsible for heating the IGM to temperatures of several keV. Moreover, they are likely to inject and accelerate relativistic particle populations on cluster scales."
 Cluster-wide relativistic electron populations are indeed observed in several merging or post-mereing clusters., Cluster-wide relativistic electron populations are indeed observed in several merging or post-merging clusters.
 These electrons reveal their presence. by. emitting. svnchrotron emission in the magnetic fields of the IGM to form the so- halos., These electrons reveal their presence by emitting synchrotron emission in the magnetic fields of the IGM to form the so-called .
 Cluster radio halos have steep radio spectra (spectral index ax1 1.5): they are unpolarised. and their diffuse morphologies are often similar to those of the thermal X-ray. emission of the cluster. gas (Govoni et al. 2001).," Cluster radio halos have steep radio spectra (spectral index $\alpha \approx
1-1.5$ ); they are unpolarised, and their diffuse morphologies are often similar to those of the thermal X-ray emission of the cluster gas (Govoni et al. \nocite{govoni2001}."
.. comparison of the typical radiative lifetime of the radio emitting electrons. which is of the order oEO.1 Give. to the tvpical dynamical timescale of the cluster merger. which is of the order of 1 Civr. shows that. the electron. population of a halo cannot be produced. directly bv a merger shock.," A comparison of the typical radiative lifetime of the radio emitting electrons, which is of the order of 0.1 Gyr, to the typical dynamical timescale of the cluster merger, which is of the order of 1 Gyr, shows that the electron population of a halo cannot be produced directly by a merger shock."
 Either these electrons have been re-accelerated. more recently. or they have been injected. by a long-lived. shock-accelerated proton population via the haclronie charged. pion production.," Either these electrons have been re-accelerated more recently, or they have been injected by a long-lived shock-accelerated proton population via the hadronic charged pion production."
 For reviews on recent observations ofcliffuse cluster radio sources see Leretti (1999).. Ciovannini. Tordi. Exο (1999). and Ixempner Sarazin (2001) .. ," For reviews on recent observations ofdiffuse cluster radio sources see Feretti \nocite{Feretti.Pune99}, Giovannini, Tordi, Feretti \nocite{1999NewA....4..141G}, and Kempner Sarazin (2001) \nocite{2001ApJ...548..639K}. ."
Unlike the racio halos. the so-called," Unlike the radio halos, the so-called"
Unlike the racio halos. the so-called.," Unlike the radio halos, the so-called"
"wind or inhomogeneities (i.e., stellar super-granulation) in the photosphere.","wind or inhomogeneities (i.e., stellar super-granulation) in the photosphere."
 0.2 cm The abundance analysis was performed using the local thermodynamic equilibrium (LTE) stellar line analysis program (Sneden 2002)., 0.2 cm The abundance analysis was performed using the local thermodynamic equilibrium (LTE) stellar line analysis program (Sneden 2002).
 Model atmospheres were obtained by interpolating in the ATLAS9 model atmosphere grid (Kurucz 1993)., Model atmospheres were obtained by interpolating in the ATLAS9 model atmosphere grid (Kurucz 1993).
 The models are line-blanketed plane-parallel uniform atmospheres in LTE and hydrostatic equilibrium with flux (radiative plus convective) conservation., The models are line-blanketed plane-parallel uniform atmospheres in LTE and hydrostatic equilibrium with flux (radiative plus convective) conservation.
" A model is defined by an effective temperature Τομ, surface gravity g, chemical composition as represented by metallicity [Fe/H] and a microturbulence velocity £ of2kms""!."," A model is defined by an effective temperature $T_{\rm eff}$, surface gravity $g$, chemical composition as represented by metallicity [Fe/H] and a microturbulence velocity $\xi$ of 2 km $^{-1}$."
 0.2 cm Several of the assumptions adopted in the construction. and application of the model atmospheres are of uncertain validity when considering post-AGB stars and supergiants in general., 0.2 cm Several of the assumptions adopted in the construction and application of the model atmospheres are of uncertain validity when considering post-AGB stars and supergiants in general.
 The presence of supersonic levels of macroturbulence and hints of a stellar wind seem incompatible with the assumption of hydrostatic equilibrium., The presence of supersonic levels of macroturbulence and hints of a stellar wind seem incompatible with the assumption of hydrostatic equilibrium.
 Departures from LTE are probable for these low density atmospheres., Departures from LTE are probable for these low density atmospheres.
 The real atmosphere is likely to depart from the uniform plane-parallel layered theoretical construction., The real atmosphere is likely to depart from the uniform plane-parallel layered theoretical construction.
 These qualifying remarks should be borne in mind when interpreting the derived abundances., These qualifying remarks should be borne in mind when interpreting the derived abundances.
" 0.2 cm A standard spectroscopic method of determining the effective temperature, surface gravity, and the microturbulence using and was applied."," 0.2 cm A standard spectroscopic method of determining the effective temperature, surface gravity, and the microturbulence using and was applied."
 Application of strict in the selection of suitable lines provided a list of 31 lines with lower excitation potentials (LEP) ranging from 0.9 to 4.5 eV and EWs of up to 224 aand 11 lines with excitation potentials of 2.8 to 3.9 eV and EWs of up to 154mA., Application of strict in the selection of suitable lines provided a list of 31 lines with lower excitation potentials (LEP) ranging from 0.9 to 4.5 eV and EWs of up to 224 and 11 lines with excitation potentials of 2.8 to 3.9 eV and EWs of up to 154.
. Only six lines have EW greater than 150mA., Only six lines have EW greater than 150.
. These lines are listed in Table 2., These lines are listed in Table 2.
 The gf-values are taken from Fühhr Wiese (2006)., The $gf$ -values are taken from Fühhr Wiese (2006).
 0.2 cm One estimate of the temperature is found from lines by excitation balance., 0.2 cm One estimate of the temperature is found from lines by excitation balance.
 The value for Teg is chosen so that the abundance is independent of a line's lower level excitation potentials (LEP)., The value for $T_{\rm eff}$ is chosen so that the abundance is independent of a line's lower level excitation potentials (LEP).
 The microturbulence is determined by adjusting the € so that the abundances were independent of reduced equivalent width (W/A)., The microturbulence is determined by adjusting the $\xi$ so that the abundances were independent of reduced equivalent width $W/\lambda$ ).
" For our sample of lines, these two conditions are imposed simultaneously (see Figure 5)."," For our sample of lines, these two conditions are imposed simultaneously (see Figure 5)."
 The microturbulence may also be determined from the lines as they are numerous and of suitable strength., The microturbulence may also be determined from the lines as they are numerous and of suitable strength.
" For a given model, we compute the dispersion in the Fe (or Ti) abundances over a range in the £ from 2 to 10 km s!"," For a given model, we compute the dispersion in the Fe (or Ti) abundances over a range in the $\xi$ from 2 to 10 km $^{-1}$."
" In Figure 6,, the dispersion o for Fe and Ti lines is displayed."," In Figure \ref{f_micro}, the dispersion $\sigma$ for Fe and Ti lines is displayed."
 The .dispersion c values for the and lines are computed for two different effective temperature values: Tig = 5750 K (e.g. green curve for Fe) and 6500 K (e.g. blue curve for Ti)., The dispersion $\sigma$ values for the and lines are computed for two different effective temperature values: $T_{\rm eff}$ = 5750 K (e.g. green curve for Fe) and 6500 K (e.g. blue curve for Ti).
" From the dispersion σ vs microturbulence velocity € plots for the Fe lines, the microturbulence velocity is found to be in the range 4.7<€<6.0 km s!."," From the dispersion $\sigma$ vs microturbulence velocity $\xi$ plots for the Fe lines, the microturbulence velocity is found to be in the range $\leq$$\xi$$\leq$ 6.0 km $^{-1}$."
 A minimum value of c for the Ti lines is reached at £ ~ 5.0 km s!., A minimum value of $\sigma$ for the Ti lines is reached at $\xi$ $\approx$ 5.0 km $^{-1}$.
 We adopt 4.7--0.5 km s!., We adopt $\pm$ 0.5 km $^{-1}$.
 The solutions for £ are not particularly dependent on the chosen Tig of the model., The solutions for $\xi$ are not particularly dependent on the chosen $T_{\rm eff}$ of the model.
 0.2 cm Imposition of ionization equilibrium for an element represented by, 0.2 cm Imposition of ionization equilibrium for an element represented by
"The second moment of the conditional velocity is given by (8b) of 2: hence the variance is equal {ο The presence of the factor /(£,,) in ((19)) (20)) aud the fact that we also have to include biasing > mean (hat in order to properly compare (he conditional velocity ος given by ((18)) with the dipole d measured from the data. ((13)). the latter has to be rescaled. using a best-lit 5 parameter. as in Eq. (11)).","The second moment of the conditional velocity is given by (8b) of \cite{JVW}: hence the variance is equal to The presence of the factor $f(\Omm)$ in \ref{eq:v_m}) \ref{eq:sigma_m}) ) and the fact that we also have to include biasing $b$ mean that in order to properly compare the conditional velocity $v_\mrc$ given by \ref{eq:v_cond}) ) with the dipole $d$ measured from the data, \ref{eq:g_v}) ), the latter has to be rescaled, using a best-fit $\beta$ parameter, as in Eq. \ref{eq:v_s}) )."
 In fact. this rescaling enables us (o estimate ;2 in a straightforweaad wav: we come back to (his point a few paragraphs later.," In fact, this rescaling enables us to estimate $\beta$ in a straightforward way; we come back to this point a few paragraphs later."
 In this subsection we discuss (he proper observational window [or our measurement., In this subsection we discuss the proper observational window for our measurement.
 We start bv noüng that when calculating the peculiar gravitational acceleration of the Local Group from the dipole of the all-sky galaxy distribution. in general (here are (wo schemes (o postulate a relation between this distribution and that of the underlving mass (see citealt Erdogdu)).," We start by noting that when calculating the peculiar gravitational acceleration of the Local Group from the dipole of the all-sky galaxy distribution, in general there are two schemes to postulate a relation between this distribution and that of the underlying mass (see \\citealt{Erdogdu}) )."
 The first scheme. calledweighting. assumes (hat the mass is distributed in the Universe as a continuous density field. which is sampled by galaxies in a Poissonian wav.," The first scheme, called, assumes that the mass is distributed in the Universe as a continuous density field, which is sampled by galaxies in a Poissonian way."
 The second prescription. namelyweighting.. uses the assumption that all the mass in the Universe is locked to the mass of the halos of luminous galaxies.," The second prescription, namely, uses the assumption that all the mass in the Universe is locked to the mass of the halos of luminous galaxies."
 The 2\LASS dipole as caleuated in is of the [lux-weighted (wpe., The 2MASS dipole as calculated in \\ref{Sec:Growth} is of the flux-weighted type.
predominantly stars and hence have high star probabilities) among the generated data.,predominantly stars and hence have high star probabilities) among the generated data.
 This means that for equal sample sizes there will be more sources with low star probabilities in the simulated sample when compared to the original data sample., This means that for equal sample sizes there will be more sources with low star probabilities in the simulated sample when compared to the original data sample.
" The increase in sources with less definite classifications is due to the fact that, as acknowledged in Section 3.1,, our model is not designed to take inter-band photometric noise correlations into account."," The increase in sources with less definite classifications is due to the fact that, as acknowledged in Section \ref{section:stargalclass}, our model is not designed to take inter-band photometric noise correlations into account."
 Thus the simulated data sample contains more sources with seemingly contradicting ddata in the different bands than a sample of real data., Thus the simulated data sample contains more sources with seemingly contradicting data in the different bands than a sample of real data.
" Both of these differences have only a small effect on the simulated data, and should affect the classification of a negligible number of real sources."," Both of these differences have only a small effect on the simulated data, and should affect the classification of a negligible number of real sources."
" The Bayesian method of cclassification described above was applied to the sample of UKIDSS sources in the SDSS Stripe 82 region, giving single-band star probabilities for every source detected (in each band in which the source was detected), as well as combined probabilities."," The Bayesian method of classification described above was applied to the sample of UKIDSS sources in the SDSS Stripe 82 region, giving single-band star probabilities for every source detected (in each band in which the source was detected), as well as combined probabilities."
" The general properties of the classifier are discussed in6.1,, and then compared to the UKIDSS classifications (in 6.2)) and the SDSS classifications (in 6.3))."," The general properties of the classifier are discussed in, and then compared to the UKIDSS classifications (in ) and the SDSS classifications (in )."
 shows the single-band posterior star probabilities in Y—cy space., shows the single-band posterior star probabilities in $Y-\stat_Y$ space.
 These can be compared with the probabilities obtained by using the full multi-band model (Fig. 12))., These can be compared with the probabilities obtained by using the full multi-band model (Fig. \ref{figure:PostClassProbasUKIDSSus-pipe}) ).
 The, The
 Young pulsars. neutron stars in supernova remnants (SNRs) and cooling neutron stars make up a subset of rotation-powered radio pulsars thal can be observable αἱ shorter wavelengths.," Young pulsars, neutron stars in supernova remnants (SNRs) and cooling neutron stars make up a subset of rotation-powered radio pulsars that can be observable at shorter wavelengths."
 Measurements of the high energy radiation are crucial as they provide important insights into the emission processes and the neutron star physics., Measurements of the high energy radiation are crucial as they provide important insights into the emission processes and the neutron star physics.
" ""Through observation and theoretical modeling it is generally accepted (hat a combination of emission mechanisms are responsible for the detected. X-ray [αν from rotation-powered pulsars (Lorareviewseee.g.Becker&Pavlov2001:Aschenbach2002)."," Through observation and theoretical modeling it is generally accepted that a combination of emission mechanisms are responsible for the detected X-ray flux from rotation-powered pulsars \citep[for a review see e.g.][]{bec01,bec02}."
. Soft thermal raciation is produced by cooling of the surface of the neutron star (cf.Greenstein&IHartkeRomani1987:Pavlovetal. 1995).. while (he acceleration of particles in the neutron star magnetosphere generates non-thermal radiation (cl.Michel1991:Beskin.Gurevich&Istomin1993.anclreferences therein)...," Soft thermal radiation is produced by cooling of the surface of the neutron star \citep[cf.][]{gre83,rom87,pav95}, while the acceleration of particles in the neutron star magnetosphere generates non-thermal radiation \citep[cf.][and references 
therein]{mic91,bes93}."
 A hirder thermal component can be produced by hot spots at the polar reeions (Ixundt&Schaal1993:Zavlin.ShibanovPavlov1995).. ancl the presence of a svnchrotron nebula may. contribute another source of non-thermal radiation (ef)Arons&Tavani1993).," A harder thermal component can be produced by hot spots at the polar regions \citep{kun93,zav95}, and the presence of a synchrotron nebula may contribute another source of non-thermal radiation \citep[cf.][]{aron93}."
. The dominant emission mechanism is related to the age of the pulsar (seee.g.Beckeral. 2002).," The dominant emission mechanism is related to the age of the pulsar \citep[see 
e.g.][]{bec96,pa02}."
. In pulsars older than 109 vr standard cooling scenarios predict that the temperature of the neutron star surface will be too low to generate detectable thermal X-ray emission (Nomoto&Tsuruta1937)., In pulsars older than $10^{6}$ yr standard cooling scenarios predict that the temperature of the neutron star surface will be too low to generate detectable thermal X-ray emission \citep{nom87}.
. ILowever. (he source may be observable if reheating via rotational energy loss or heating of the polar caps takes place (Drinkman. 1985).," However, the source may be observable if reheating via rotational energy loss or heating of the polar caps takes place \citep{brin85}."
. The middle-aged pulsars (104—10° vr) exhibit spectra that can be described by thermal emission from (he surface of the neutron star., The middle-aged pulsars $10^4-10^6$ yr) exhibit spectra that can be described by thermal emission from the surface of the neutron star.
 In some cases a power-law component is also detected (e.g.Becker&Aschenhbach2002:Pavlovetal.2002).," In some cases a power-law component is also detected \citep[e.g.][]{bec02,pa02}."
. In pulsars vounger than LO! vr the strong magnetospheric emission prevails over the weaker thermal radiation., In pulsars younger than $10^{4}$ yr the strong magnetospheric emission prevails over the weaker thermal radiation.
 By comparing measurements of the soft ταν [lux emitted [rom the, By comparing measurements of the soft X-ray flux emitted from the
"spectroscopic measurement (Kessleretal.2009a),, so any tthat may have occurred should have been detected in this once the host is subtracted from the image.","spectroscopic measurement \citep{kes09a}, so any that may have occurred should have been detected in this subsample once the host is subtracted from the image."
" subsampleApplying the method used on the full sample to the complete subsample reveals that the trend of HR with mass persists, with a slightly increased significance of 3.40."," Applying the method used on the full sample to the complete subsample reveals that the trend of HR with mass persists, with a slightly increased significance of $3.4 \sigma$."
" However, the HR trend with age is not statistically significant (1.20) for the complete subsample."," However, the HR trend with age is not statistically significant $1.2 \sigma$ ) for the complete subsample."
"Where Lis the lrequency dependent Compton luuinositv. L,; is the frequency dependent svuchrotron luminosity.","Where $L _{\nu c}$ is the frequency dependent Compton luminosity, $L_{\nu s}$ is the frequency dependent synchrotron luminosity."
 e; is a function of spectral index. tabulated in \larscher(1937)... Ne is (he normalization [actor of the energv dependent electron density distribution. aud A is (he radius of a spherical source.," $c_3$ is a function of spectral index, tabulated in \citet{mar87}, $N_O$ is the normalization factor of the energy dependent electron density distribution, and $R$ is the radius of a spherical source."
" 7, refers to the spectral turnover frequency in a plot of fux density versus frequency. and νο is the upper frequency eutolf in a similar plot."," $\nu_m$ refers to the spectral turnover frequency in a plot of flux density versus frequency, and $\nu_2$ is the upper frequency cutoff in a similar plot."
 A correction to this formula needs {ο be applied if the observed gaaima-rays are al a frequency bevond the hieh end spectral cutoff for Compton scattering. or if the svuchrotron photons are observed al a frequency at which the source is believed to be optically (hick or partially opaque.," A correction to this formula needs to be applied if the observed gamma-rays are at a frequency beyond the high end spectral cutoff for Compton scattering, or if the synchrotron photons are observed at a frequency at which the source is believed to be optically thick or partially opaque."
 The logarithmic term only varies a small amount for large changes in (hie parameters. so this term can usually be neglected relative to the others.," The logarithmic term only varies a small amount for large changes in the parameters, so this term can usually be neglected relative to the others."
 The function of a can vary over several orders of magnitude. but can be roughly constant if the optically thin spectral index of the sample is narrowly distributed.," The function of $\alpha$ can vary over several orders of magnitude, but can be roughly constant if the optically thin spectral index of the sample is narrowly distributed."
 The [actor of NeR. proportional to the Thomson optical depth. would also have to be tightly constrained.," The factor of ${N_O \,R}$, proportional to the Thomson optical depth, would also have to be tightly constrained."
 Using a somewhat different. formulation. Ghiselliniοἱ(1998). calculate a particle injection compactuess parameter. which is also proportional to the Thompson optical depth.," Using a somewhat different formulation, \citet{ghi98} calculate a particle injection compactness parameter, which is also proportional to the Thompson optical depth."
 They show that this parameter. though distributed over 4 orders of magnitude for a sample of 51 EGRET blazars. has a clear peak value (over half of the blazars with a value within 1 order of magnitude of the peak).," They show that this parameter, though distributed over 4 orders of magnitude for a sample of 51 EGRET blazars, has a clear peak value (over half of the blazars with a value within 1 order of magnitude of the peak)."
 Thus. in adopting a linear model [ον use in the following Monte Carlo analvsis. this parameter can be drawn randomly from a sharply peaked distribution.," Thus, in adopting a linear model for use in the following Monte Carlo analysis, this parameter can be drawn randomly from a sharply peaked distribution."
" It is not as evident that these arguments can be extended to a relationship such as that observed. L.xL,5**, "," It is not as evident that these arguments can be extended to a relationship such as that observed, ${L_{\gamma}} \propto {{L_r}^{0.77}} $."
We explore this possibility below., We explore this possibility below.
 Alternatively. the gamma-ray luminosity can be produced by an external Compton scattering process (ECS)(Dermer&Schlickeiser1993:Lister1999).," Alternatively, the gamma-ray luminosity can be produced by an external Compton scattering process \citep{der93,lis99a}."
. In (his particular model the source of the soft photons is the accretion disk. and (hese photons scatter off of à plasma Οἱ relativistic electrons in a blob.," In this particular model the source of the soft photons is the accretion disk, and these photons scatter off of a plasma of relativistic electrons in a blob."
 Adapting the formulas of to our notation: llere. the Iuminositv ratio is between the observed Compton Iuminosity in the range and the observed accretion Iuminositv.," Adapting the formulas of \citet{der92} to our notation: Here, the luminosity ratio is between the observed Compton luminosity in the gamma-ray range and the observed accretion luminosity."
 2 refers to the radius of the blob. assuming ibis spherical. and i refers to the distance between the blob aud the accretion disk.," $R$ refers to the radius of the blob, assuming it is spherical, and $r$ refers to the distance between the blob and the accretion disk."
 op refers to the Thomson scattering cross-section. πο refers to the electron rest mass. Vy has the salle meaning as above.," $\sigma_T$ refers to the Thomson scattering cross-section, ${m_e}c^2$ refers to the electron rest mass, $N_0$ has the same meaning as above."
 ὁ is the Doppler factor to correct for bulk relativistic motion of the emitting plasma and is defined by:, $\delta$ is the Doppler factor to correct for bulk relativistic motion of the emitting plasma and is defined by:
"Since 1572, when Tycho's nova was first observed, the astronomical community has come a long way in our search and understanding of stellar cycles and processes.","Since 1572, when Tycho's nova was first observed, the astronomical community has come a long way in our search and understanding of stellar cycles and processes."
" Still at magnitude 12, it is estimated that at least 90 per cent of the variables are unknown ∥"," Still at magnitude 12, it is estimated that at least 90 per cent of the variables are unknown \citep{Eyer}."
" Since began the multi-epoch photometric survey, there have been many ground based projects like the All-Sky Automated Survey (Pojmaniski,||2000),, Hungarian Automated Telescope (HATnet; 2002)), Wide Angle Search for Planets (WASP/SuperWASP; 2006)) as well as the space missions like (Baglin,Vauclair&TheCOROTTeam, |2000),, Micro-variability and Oscillations of STars (MOST;; [etaL. ⊓ Solar Mass Ejection 2000)),Imager(SMETI;; 2008)) which are dedicated to different types of variability studies and many of them have been hugely successful in not only discovering new exoplanets but also unravelling the stellar variability mysteries fal.,] 010), In this paper, we present the use of twin Solar TErrestrial RElations Observatory (STEREO)) for the study of stellar variability and Exoplanetary transits."," Since began the multi-epoch photometric survey, there have been many ground based projects like the All-Sky Automated Survey \citep{Pojmanski}, Hungarian Automated Telescope (HATnet; \citealt{Bakos}) ), Wide Angle Search for Planets (WASP/SuperWASP; \citealt{Pollacco}) ) as well as the space missions like \citep{Baglin}, , Micro-variability and Oscillations of STars ; \citealt{Matthews}) ), \citep{Blomme}, Solar Mass Ejection Imager; \citealt{Spreckley}) ) which are dedicated to different types of variability studies and many of them have been hugely successful in not only discovering new exoplanets but also unravelling the stellar variability mysteries \citealt{Michel, Pribulla, Basri}, In this paper, we present the use of twin Solar TErrestrial RElations Observatory ) for the study of stellar variability and Exoplanetary transits."
" The STRESS project occupies a very interesting position in this scenario in terms of the location of its field of view, size of the field and magnitude coverage."," The STRESS project occupies a very interesting position in this scenario in terms of the location of its field of view, size of the field and magnitude coverage."
" The spacecraft covers a portion of the sky classically avoided for these type of studies, i.e., in the zodiacal path."," The spacecraft covers a portion of the sky classically avoided for these type of studies, i.e., in the zodiacal path."
" As to the planetary transit searches, all of the dedicated space-based projects are concentrating away from this region."," As to the planetary transit searches, all of the dedicated space-based projects are concentrating away from this region."
" Hence this leaves a gap in the science for this particular sky region, which we are trying to fill in this project."," Hence this leaves a gap in the science for this particular sky region, which we are trying to fill in this project."
" Also, the pass band of this instrument lies very close to the magnitude of the stellar intensity spectrum."," Also, the pass band of this instrument lies very close to the magnitude of the stellar intensity spectrum."
" Hence we find that many of our tracked objects have actually no literature or very little basic In Section 2, we describe the spacecraft and the instrumental characteristics, in Section 3, the data reduction pipeline and then the general characteristics of the data in Section 4 and some earlyresult in Section 5 andsummarising in Section"," Hence we find that many of our tracked objects have actually no literature or very little basic In Section 2, we describe the spacecraft and the instrumental characteristics, in Section 3, the data reduction pipeline and then the general characteristics of the data in Section 4 and some earlyresult in Section 5 andsummarising in Section"
to derive analytical expressions for the Fisher matrix if we focus ou the parameter (IT(2)) as a sin of step functions.,to derive analytical expressions for the Fisher matrix if we focus on the parameter $H(z)$ ) as a sum of step functions.
 The reader should realize throughout this work that our procedure is mostly driven by the data. although there is a weak dependence of the componcuts on our starting choices of parameter values.," The reader should realize throughout this work that our procedure is mostly driven by the data, although there is a weak dependence of the components on our starting choices of parameter values."
 Iu other words. the functional form of cach cigeuvector is not of primary dmportauce. we are more interested in how they are linearly. combined.," In other words, the functional form of each eigenvector is not of primary importance, we are more interested in how they are linearly combined."
 This approach allows us to avoid many interpretation problems pointed out by ?.., This approach allows us to avoid many interpretation problems pointed out by \citet{kitching09}.
 Our only assumption is that the Universe is spatially homogencous aud isotropic aud can be described by Friccuaun-Robertsou-Walker (FRW) metric., Our only assumption is that the Universe is spatially homogeneous and isotropic and can be described by Friedmann-Robertson-Walker (FRW) metric.
 The paper is organized as follows., The paper is organized as follows.
 Iu section 2.. we briefly review our knowledge of PCA and demonstrate low it can be applied to a parameter analysis using type Ia supernova observatious.," In section \ref{sec:PCA}, we briefly review our knowledge of PCA and demonstrate how it can be applied to a parameter analysis using type Ia supernova observations."
 Section 3 shows the results obtained with a simulated supernova data set. following the standard procedure for dealing with the linear combination cocfiicicuts.," Section \ref{sec:application} shows the results obtained with a simulated supernova data set, following the standard procedure for dealing with the linear combination coefficients."
 We demoustrate that the quality of our results derived from the simulated data are greatly improved if we consider the paraiucter value in the upper redshift bound as a free parameter., We demonstrate that the quality of our results derived from the simulated data are greatly improved if we consider the parameter value in the upper redshift bound as a free parameter.
 We apply the same procedure to real type Ia supernova data compiled by the Sloan Digital Sky Survey team (?).., We apply the same procedure to real type Ia supernova data compiled by the Sloan Digital Sky Survey team \citep{kessler09}.
 The results are shown iu section l.., The results are shown in section \ref{sec:current_data}.
 Finally. iu section 5.. we present our conclusions.," Finally, in section \ref{sec:conclusions}, we present our conclusions."
 The procedure used to &ud the principal commponcuts (PCs) begius with the definition of the Fisher iuforiiation matrix (F3)., The procedure used to find the principal components (PCs) begins with the definition of the Fisher information matrix ).
 Owine to its relation to the covariauce matrix Ny at can be shown that the PCs aud their associated uncertainties are related to the eigenvectors and eigenvalues of the Fisher matrix. respectively.," Owing to its relation to the covariance matrix $^{-1}$ ), it can be shown that the PCs and their associated uncertainties are related to the eigenvectors and eigenvalues of the Fisher matrix, respectively."
 We consider that our data set is formed by NV independent observations. cach oue. characterized by a Cassia probability density function. f;6e;:0;:.3).," We consider that our data set is formed by $N$ independent observations, each one characterized by a Gaussian probability density function, $f_{i}(x_i,\sigma_{i};\pmb{\beta})$."
 Iu our notation. ον represents the /9ff measurement. σ; the uncertainty associated with if. aud ο) is the vector of pazaincters of our theoretical model.," In our notation, $x_i$ represents the $i-th$ measurement, $\sigma_{i}$ the uncertainty associated with it, and $\pmb{\beta}$ is the vector of parameters of our theoretical model."
 In other words. we investigate a specific quantity. c. which can be written as a function of the parameters ον 6C063)).," In other words, we investigate a specific quantity, $x$, which can be written as a function of the parameters $\beta_i$, $x(\pmb{\beta})$ )."
 In this context. the likelihood function is ⋅⋅given by £=[TNfs aud the Fisher matrix is defined as The brackets in equation (1)) represents the expectation value.," In this context, the likelihood function is given by $L=\prod_{i=1}^{N}f_i$ and the Fisher matrix is defined as The brackets in equation \ref{eq:FMdefinicao}) ) represents the expectation value."
 We cau write F22DZAD.. where the rows of the decorrelation matrix (D)) are the cigenvectors (6;) of Ε.. aud Ais a diagonal matrix whose non-zero elements are the cigeuvalues (A;) ofF.," We can write $^T \pmb{\Lambda}$, where the rows of the decorrelation matrix ) are the eigenvectors $\pmb{e_i}$ ) of , and $\pmb{\Lambda}$ is a diagonal matrix whose non-zero elements are the eigenvalues $\lambda_i$ ) of."
. Choosiug tobe orthogonal. with det((D))—1. e; forms an orthonormal basis of decorrclated vectors (or modes).," Choosing tobe orthogonal, with )=1, $\pmb{e_i}$ forms an orthonormal basis of decorrelated vectors (or modes)."
" After finding the cigenvectors and cleenvalues ofF.. we rewrite «as a linear combination of ο,"," After finding the eigenvectors and eigenvalues of, we rewrite $x$ as a linear combination of $\pmb{e_i}$."
" Our ability to determine cach coefficieut of this linear expansion (0;) is givou bv o,,=A;uz", Our ability to determine each coefficient of this linear expansion $\alpha_{i}$ ) is given by $\sigma_{\alpha_i}=\lambda_i^{-1/2}$.
 Following the standard conveution. we enunmerate e; from the larger to the siialler associated eigenvalue.," Following the standard convention, we enumerate $\pmb{e_i}$ from the larger to the smaller associated eigenvalue."
 The main goal of PCA is the dimensionality reduction of our initial parameter space., The main goal of PCA is the dimensionality reduction of our initial parameter space.
 This arises in the nuuber of PCs we use to rewrite ανν, This arises in the number of PCs we use to rewrite $x$.
" The most accurately determined modes (sinaller 0,,,) correspond. to directions of high", The most accurately determined modes (smaller $\sigma_{\alpha_i}$ ) correspond to directions of high
although the electrons efficiently destroy molecular hydrogen. electron discrete interactions only provide excitations in the II» vibrational ladder up to 0=2 1999).,"although the electrons efficiently destroy molecular hydrogen, electron discrete interactions only provide excitations in the $_2$ vibrational ladder up to $v = 2$ \citep{D99}."
. The radiative decavs of the electronically excited HE and LH» produces FUV photons. LH» Werner photons and II Lya photons.," The radiative decays of the electronically excited H and $_2$ produces FUV photons, $_2$ Werner photons and H $\alpha$ photons."
" We can estimate the impact of electron induced UV radiation in the following wav: assuming electrons of mean energy 30 eV (as in Tinéetal. 1997)). the number of excitations to the states BIN and CT"". including the contribution of cascading from higher singlet states. ave approximately 0.6. auc 0.4. respectivelv (Dalearno.Yan&Liu 1999)."," We can estimate the impact of electron induced UV radiation in the following way: assuming electrons of mean energy 30 eV (as in \citealt{T97}) ), the number of excitations to the states $B^1\Sigma_u^+$ and $C^1\Pi^u$, including the contribution of cascading from higher singlet states, are approximately 0.6 and 0.4, respectively \citep{D99}. ."
 The excitation rate to the excited electronic states is thus ~Cy. where Cy is the total rav ionization rate.," The excitation rate to the excited electronic states is thus $\sim \zeta_X$, where $\zeta_X$ is the total ray ionization rate."
 The radiative excitation of Lyman and Werner bands is roughly 5x10.y ! (Draine&Bertoldi1996).," The radiative excitation of Lyman and Werner bands is roughly $5 \times 10^{-10} \, 
\chi$ $^{-1}$ \citep{DB96}."
. We obtain the equivalent UV field scaling [actor by means of the relation \=(y/5x10.I., We obtain the equivalent UV field scaling factor by means of the relation $\chi = \zeta_X / 5 \times 10^{-10}$.
" Thus. the most prominent feature in (he IR spectrum generated using our formation pumping model. namely the transition 4—2 O(3). would be minimally affected. by ravs. as long as the ionization rale is Cy«5x10.Ms !,"," Thus, the most prominent feature in the IR spectrum generated using our formation pumping model, namely the transition $4-2$ O(3), would be minimally affected by rays, as long as the ionization rate is $\zeta_X \ll 
5 \times 10^{-10}$ $^{-1}$."
 In Fig. 8..," In Fig. \ref{fig8},"
 we report the intensity of the line 4-2 O(3) as a function of the Hs ionization rate in the RCM., we report the intensity of the line $4-2$ O(3) as a function of the $_2$ ionization rate in the RCM.
 It is evident that the transition 4—2 O(3) might be observed if the Is ionizalion rale is CZ1xLO! I; in agreement with LeBourlotetal.(1995).," It is evident that the transition $4-2$ O(3) might be observed if the $_2$ ionization rate is $\zeta
\ga 1 \times 10^{-14}$ $^{-1}$, in agreement with \citet{LB95}."
 In this case. since (he line intensity scales approximately with the ionization rate. the line would be lugelv dominated by formation pumping rather (han radiative pumping.," In this case, since the line intensity scales approximately with the ionization rate, the line would be largely dominated by formation pumping rather than radiative pumping."
 The crucial point is that NDRs may mantain large ionization rates up to hydrogen column densities of NyoLom—1071 7 for ray energies larger than 1: keV (CecchiPestellinietal.2009).," The crucial point is that XDRs may mantain large ionization rates up to hydrogen column densities of $N_{\rm H}\sim 10^{23} - 
10^{24}$ $^{-2}$ for ray energies larger than 1 keV \citep{CP09}."
. In conclusion. we model Ils formation punpine in standard dense clouds. taking into account (he IL/Ils transition zone.," In conclusion, we model $_2$ formation pumping in standard dense clouds, taking into account the $_2$ transition zone."
 The model. which includes recent laboratory data. on ll. formation. as well as the effects of the interstellar UV. field. predicts the populations of phase Ils molecules and their IH. emission spectra.," The model, which includes recent laboratory data on $_2$ formation, as well as the effects of the interstellar UV field, predicts the populations of phase $_2$ molecules and their IR emission spectra."
 Calculations suggest (hat some vibrationally excited states of Is might be detectable (towards lines of sight where significant destruction of H» occurs. such as X-ray sources.," Calculations suggest that some vibrationally excited states of $_2$ might be detectable towards lines of sight where significant destruction of $_2$ occurs, such as X-ray sources."
 These results also provide a possible explanation of the lack of detection to date of Hà» formation pumping in dark clouds., These results also provide a possible explanation of the lack of detection to date of $_2$ formation pumping in dark clouds.
 CCP. SV and SC would like to thank the Roval Society forfinding an exchange proeramme between UCL and Cagliari Observatory.," CCP, SV and SC would like to thank the Royal Society forfunding an exchange programme between UCL and Cagliari Observatory."
 We also would like to (hank (he anonvmous releree for Περί] comments and suggestions that improved the clarity of the paper., We also would like to thank the anonymous referee for hepful comments and suggestions that improved the clarity of the paper.
The implication is that if a supernova does not succeed on a time scale of ~100 ms. deleptonization is likely to cause the PNS to contract and spin up and amplify the driving and magnetic dissipation of nonaxisvinmetric modes that could pump energy into ihe environment of the neutron star. potentially energizing the explosion if T7πο0.01 during (he evolution.,"The implication is that if a supernova does not succeed on a time scale of $\sim 100$ ms, de–leptonization is likely to cause the PNS to contract and spin up and amplify the driving and magnetic dissipation of non–axisymmetric modes that could pump energy into the environment of the neutron star, potentially energizing the explosion if $\tw \gtrsim 0.01$ during the evolution."
 Even if an explosion has been launched on a (time scale of ~100 us. the infall will not have declined to zero in the early part of the contraction process.," Even if an explosion has been launched on a time scale of $\sim 100$ ms, the infall will not have declined to zero in the early part of the contraction process."
 The ambient density. will still eive a mecium in which to produce and dissipate magnetoacoustic waves generated by nonaxisvmmetrie instabilities., The ambient density will still give a medium in which to produce and dissipate magnetoacoustic waves generated by non–axisymmetric instabilities.
 The contraction phase could thus be important for both the energetics of the explosion and the rotational period of the contracted neutron star. so it is important to understand this phase.," The contraction phase could thus be important for both the energetics of the explosion and the rotational period of the contracted neutron star, so it is important to understand this phase."
 We have made some estimates of the energy that could be deposited by magnetoacoustic waves. but caution that this will depend on the actual free energy. of differential rotation. the details of the change of structure and hence binding energv during contraction and the mode of (he magnetoacoustic flux.," We have made some estimates of the energy that could be deposited by magnetoacoustic waves, but caution that this will depend on the actual free energy of differential rotation, the details of the change of structure and hence binding energy during contraction and the mode of the magnetoacoustic flux."
 If the latter were to emerge up the axis as Povnting flux. it might not contribute to the kinetic energy budget of the expanding ejecta.," If the latter were to emerge up the axis as Poynting flux, it might not contribute to the kinetic energy budget of the expanding ejecta."
 The contraction could lead to a rapidly rotating neutron star., The contraction could lead to a rapidly rotating neutron star.
 As we show here. however. a plausible result is a rather rapid spin down prior to substantial contraction lollowed by contraction at roughly constant T/|W|~0.01 corresponding to the threshold for NANI.," As we show here, however, a plausible result is a rather rapid spin down prior to substantial contraction followed by contraction at roughly constant $\tw \sim 0.01$ corresponding to the threshold for NAXI."
 That would correspond to a post-contraction rotational period of ~ 3 ms prior to any final spin clown., That would correspond to a post-contraction rotational period of $\sim$ 3 ms prior to any final spin down.
 The evolution during the deleptonization phase will depend on Che physics ancl time scales of the dissipation of the Iree energy of differential rotation., The evolution during the de–leptonization phase will depend on the physics and time scales of the dissipation of the free energy of differential rotation.
 We noted that in our simple model for the time scale associated with the magnetoacoustic [ux generated by NAXI. Eqn. 4..," We noted that in our simple model for the time scale associated with the magnetoacoustic flux generated by NAXI, Eqn. \ref{tau-mhd},"
 the time scale could be rather short compared to the contraction time., the time scale could be rather short compared to the contraction time.
" μι,", Eqn.
 4. depends on the rotation frequency implicitly through T/|W|x0? and àr/r., \ref{tau-mhd} depends on the rotation frequency implicitly through $\tw \propto \Omega^2$ and $\delta r/r$.
 This is in contrast. to (he dissipation timescale in a model in which the magnetic field serves to provide a magnetic viscosity (Thompsonetal.2005;Wilson2005:Ott2006).. for which the dissipation power scales as Q* and hence the time scale as O.!.," This is in contrast to the dissipation timescale in a model in which the magnetic field serves to provide a magnetic viscosity \citep{tho05,wil05,ott06}, for which the dissipation power scales as $\Omega^{3}$ and hence the time scale as $\Omega^{-1}$."
 We note that the time scale associated with this process is still model dependent with Thompsonetal.(2005) and Ottetal. adopting a dissipation power per unit mass of eaiO(dO/dlir)?oliQO* and hence a time scale of Tye.~(AQ)F(r/hp)., We note that the time scale associated with this process is still model dependent with \citet{tho05} and \citet{ott06} adopting a dissipation power per unit mass of $\sim \alpha h_P^2\Omega(d\Omega/d ln r)^2 \sim \alpha h_P^2\Omega^3$ and hence a time scale of $\tau_{diss} \sim (\alpha \Omega)^{-1}(r/h_P)^2$.
" Wilsonetal.(2005) invoke a threshold magnetic field but effectively adopt a dissipation power per unit mass of L/2077? and hence a time scale of ~Q!, ", \citet{wil05} invoke a threshold magnetic field but effectively adopt a dissipation power per unit mass of $1/2 \Omega^3 r^2$ and hence a time scale of $\sim \Omega^{-1}$.
While both of these time scales vary as Q!. that of Wilsonetal.(2005). is shorter by a factor of e(hp/r)?.," While both of these time scales vary as $\Omega^{-1}$, that of \citet{wil05} is shorter by a factor of $\sim (h_P/r)^2$."
 Another important difference between the dissipation by NANI and magnetoacoustic fhix ancl clissipation bv magnetic viscosity is Chat the magnetic viscosity is. bv. assumption.," Another important difference between the dissipation by NAXI and magnetoacoustic flux and dissipation by magnetic viscosity is that the magnetic viscosity is, by assumption,"
al. (,al. (
2007).,2007).
 We thus obtain the fraction of flux. say at IOum. IN {θμπι). due to dusty circumstellar envelopes. and. from the distance of the galaxy. the corresponding “dust” luminosity sampled by the slit. 4xDf«lit (10pm).," We thus obtain the fraction of flux, say at $\mu$ m, $f_d^{\rm slit}$ $\mu$ m), due to dusty circumstellar envelopes, and, from the distance of the galaxy, the corresponding “dust” luminosity sampled by the slit, $4\,\pi D^{2}f_d^{\rm slit}$ $\mu$ m)."
 Surprisingly. though ETGs contain a mixture of evolved stars of different metallicity and age. a single dusty envelope is typically enough for a good fit to the MIR spectrum.," Surprisingly, though ETGs contain a mixture of evolved stars of different metallicity and age, a single dusty envelope is typically enough for a good fit to the MIR spectrum."
" The shape of the broad feature near lOum in general requires τι~ 2-4. and so the envelopes are optically thin at IOjtm. From the of the I0jim feature we thus derive the optical depth of the ""average"" AGB star."," The shape of the broad feature near $\mu$ m in general requires $\tau_1\sim\,$ 2–4, and so the envelopes are optically thin at $\mu$ m. From the of the $\mu$ m feature we thus derive the optical depth of the “average” AGB star."
 To compute its dust mass-loss rate through Eq. (4)), To compute its dust mass-loss rate through Eq. \ref{MD}) )
 we need to assume a bolometric luminosity and wind velocity., we need to assume a bolometric luminosity and wind velocity.
 Typical values for evolved. old stars are Ly «0.2204 and v~5—I5kms.," Typical values for evolved, old stars are $L_4\sim$ 0.2–0.4 and $v_\infty\sim 5-15\;\rm km\,s^{-1}$."
" The total dust mass-loss sampled by the slit is. finally obtained by multiplying the value for the ""average"" AGB star by the number of dusty AGB stars sampled by the slit.", The total dust mass-loss sampled by the slit is finally obtained by multiplying the value for the “average” AGB star by the number of dusty AGB stars sampled by the slit.
" This is given by the ratio of the dust luminosity of the galaxy to that of the ""average"" AGB star. LU IOum)."," This is given by the ratio of the dust luminosity of the galaxy to that of the “average” AGB star, $L_d^{CE}$ $\mu$ m)."
 Thus. the total dust sampled by the slit is. Summarizing. the spectral fit provides τι and £F 10pm).," Thus, the total dust mass-loss sampled by the slit is, Summarizing, the spectral fit provides $\tau_1$ and $f_d^{\rm slit}$ $\mu$ m)."
" From τι. which characterizes the dusty envelope. and the assumed bolometric stellar luminosity. we obtain LU 10pm) and finally MY"". for a specified value of v."," From $\tau_1$, which characterizes the dusty envelope, and the assumed bolometric stellar luminosity, we obtain $L_d^{CE}$ $\mu$ m) and finally $\dot{M}_d^{\rm slit}$, for a specified value of $v_\infty$."
 We note that. since LOE (Oum) scales approximately with the bolometric lumimosity of the star. the total mass-loss has only a weak dependence on the assumed luminosity of the typical AGB star.," We note that, since $L_d^{CE}$ $\mu$ m) scales approximately with the bolometric luminosity of the star, the total mass-loss has only a weak dependence on the assumed luminosity of the typical AGB star."
 We finally note that recent work (Boyer et al., We finally note that recent work (Boyer et al.
 2010) has shown dust to be released into the ISM only by AGB stars. contrary to some claims that RGB stars also contribute.," 2010) has shown dust to be released into the ISM only by AGB stars, contrary to some claims that RGB stars also contribute."
 Dust mass-loss rates were derived from Spitzer-IRS. spectra that were taken through a slit of dimensions 18x centred on the galaxy., Dust mass-loss rates were derived from -IRS spectra that were taken through a slit of dimensions $18^{\prime\prime} \times$ centred on the galaxy.
 In order to compare these values with the dust masses within one 250pm beam we assume that the light distribution in the mid and far-infrared are similar. and. that both are similar to that at K-band.," In order to compare these values with the dust masses within one $250\;\rm \mu m$ beam we assume that the light distribution in the mid and far-infrared are similar, and that both are similar to that at K-band."
 For each galaxy. we use the 2MASS K-band image. smoothed to the Spitzer-IRS spatial resolution. to determine the flux within the IRS slit.," For each galaxy, we use the 2MASS K-band image, smoothed to the -IRS spatial resolution, to determine the flux within the IRS slit."
 We then smooth the K-band image to the 250pm resolution and calculate the flux within one beam., We then smooth the K-band image to the $250\;\rm \mu m$ resolution and calculate the flux within one beam.
 We use the ratio of these two fluxes to derive the mass-loss rate from the area of oneHerschel beam., We use the ratio of these two fluxes to derive the mass-loss rate from the area of one beam.
" We derive dust grain lifetimes simply as the ratio of dust mass detection limit to dust mass-loss rate. Mj/M,."," We derive dust grain lifetimes simply as the ratio of dust mass detection limit to dust mass-loss rate, $M_{\rm d}/\dot{M}_d$."
 Our dust mass detection limit of My<8.7x10°M for silicate grains results m grain lifetimes as given in Table ].., Our dust mass detection limit of $M_{\rm d} \leq 8.7 \times 10^3\;\rm M_{\odot}$ for silicate grains results in grain lifetimes as given in Table \ref{table:1}.
 The tightest constraint. of <46+25Myr. is provided by NGC 4473.," The tightest constraint, of $<46\pm 25\;\rm Myr$, is provided by NGC 4473."
 The error reflects the uncertainties in v and L4., The error reflects the uncertainties in $v_\infty$ and $L_4$.
 In Table 2. we provide the values used to arrive at this grain lifetime and their dependencies., In Table \ref{table:3} we provide the values used to arrive at this grain lifetime and their dependencies.
 For dust temperatures in the range 20—40K. for example. the grain lifetime lies in the range 69—31Myr.," For dust temperatures in the range $20-40\;\rm K$, for example, the grain lifetime lies in the range $69-31\;\rm Myr$."
 If dust grains are destroyed via sputtering in the 109—107K gas in ETGs then the theoretically. dust grain lifetime in years 18f=Ayr«/ng (e.g.. Tielens et al.," If dust grains are destroyed via sputtering in the $10^6 - 10^7\,\rm K$ gas in ETGs then the theoretically, dust grain lifetime in years is $t = k_i\, r_{\rm g}/n_{\rm H}$ (e.g., Tielens et al."
" 1994). where r, is the grain radius in nm. 7j is the gas density in οι) and &=310 for silicate dust (210 for amorphous carbon. 1500 for graphite) so the grain lifetime should be longer in galaxies with à lower density hot ISM."," 1994), where $r_{\rm g}$ is the grain radius in nm, $n_{\rm H}$ is the gas density in $\rm cm^{-3}$ and $k_{\rm i} = 310$ for silicate dust (210 for amorphous carbon, 1500 for graphite) so the grain lifetime should be longer in galaxies with a lower density hot ISM."
 Of our sample. NGC 4371 and NGC 4474 both lie in the least X-ray luminous category as defined by Irwin Sarazin (1998).," Of our sample, NGC 4371 and NGC 4474 both lie in the least X-ray luminous category as defined by Irwin Sarazin (1998)."
 NGC 4564 has been observed by Chandra. and the central hot gas density estimated to be 0.011+0.006cm? by Soria et al. (," NGC 4564 has been observed by Chandra, and the central hot gas density estimated to be $0.011\pm0.006\;\rm cm^{-3}$ by Soria et al. ("
2006).,2006).
 These authors analyzed a sample of “quiescent” galaxies and found central gas densities in. the range 0.011-0.03em7*., These authors analyzed a sample of `quiescent' galaxies and found central gas densities in the range $0.03\;\rm cm^{-3}$.
 These values overlap with the low end of estimates from Chandra data of more general ETG samples (Pellegrini. 2005).," These values overlap with the low end of estimates from Chandra data of more general ETG samples (Pellegrini, 2005)."
 We thus assume a hot gas density of 0.02em7* for all our ΕΤΟΣ., We thus assume a hot gas density of $0.02\;\rm cm^{-3}$ for all our ETGs.
 The expected dust grain lifetime. for “typical” 100.nm silicate. grains is 1.55Myr (1.05 for," The expected dust grain lifetime, for “typical” $100\;\rm nm$ silicate grains is $1.55\;\rm Myr$ (1.05 for"
corrected images.,corrected images.
 Fig., Fig.
" 1 shows the X-ray image in the 0.6—2.0 keV band divided by the best-fit, double- and smoothed with a 2 arcsec filtered Gaussian."," \ref{fig:sb} shows the X-ray image in the $0.6-2.0$ keV band divided by the best-fit, $\beta$ and smoothed with a 2 arcsec filtered Gaussian."
 This image spans the entire region covered by ACIS-I observations taken in 2005., This image spans the entire region covered by ACIS-I observations taken in 2005.
 The white circle (r~8.5 arcmin) denotes the outer extent of the data used for the spectral analysis reported here., The white circle $r\sim8.5$ arcmin) denotes the outer extent of the data used for the spectral analysis reported here.
 The cool X-ray arms are readily apparent in the image., The cool X-ray arms are readily apparent in the image.
 An extensive imaging analysis of these data is presented by Forman (2007)., An extensive imaging analysis of these data is presented by Forman (2007).
limit of MOTD turbulence.,limit of MHD turbulence.
 This paper is organized as follows: In 82. we provide the details of our computational scheme aud problem setup., This paper is organized as follows: In \ref{sec:methods} we provide the details of our computational scheme and problem setup.
 Ins 3 we report on the saturation of magnetic energy and provide power of spectra various quantities of mterest., In \ref{sec:results} we report on the saturation of magnetic energy and provide power of spectra various quantities of interest.
 We also investigate the scaling of various one and two dimensional structure functions of velocity field., We also investigate the scaling of various one and two dimensional structure functions of velocity field.
 In 81 we sumunarize our findings., In \ref{sec:conclusions} we summarize our findings.
 We lave cuploved Alara. a new musplit. second-order Godunov code which has been written to achieve robust and accurate evolution of the RMIID equations ou threc-dimensional rectilinear grids.," We have employed Mara, a new unsplit, second-order Godunov code which has been written to achieve robust and accurate evolution of the RMHD equations on three-dimensional rectilinear grids."
 Mara solves the system of ideal RAUID cquatious in couservation law fori., Mara solves the system of ideal RMHD equations in conservation law form.
" The covariant formumlation for RAQID can be expressed as a system of coupled couscrvation laws for particle uunber NW—pel and the energy-momentum of the fluid denoted by T""*=ph?ul'u""|pegl®—DFDÀ, where pis the restanass deusity of the fluid aud « is its four- and we use units for which the speed of light c=1l as follows. Tere, δήFu"" js the inaguetie field four-vector. and P=1|οἳpep is the total specific cuthalpy. where p=py|ooDf2 is the total pressure. py is the eas pressure and €=eg,|05/2p5 is the total specific energv density with ον being the thermal part."," The covariant formulation for RMHD can be expressed as a system of coupled conservation laws for particle number $N^\mu = \rho u^\mu$ and the energy-momentum of the fluid denoted by $T^{\mu \nu} = \rho h^* u^\mu
u^\nu + p^* g^{\mu \nu} - b^\mu b^\nu$, where $\rho$ is the rest-mass density of the fluid and $u$ is its four-velocity and we use units for which the speed of light $c=1$ as follows, Here, $b^\mu = F^\mu_{\ \nu} u^\nu$ is the magnetic field four-vector, and $h^* = 1+e^*+p^*/\rho$ is the total specific enthalpy, where $p^*
= p_g + b^2/2$ is the total pressure, $p_g$ is the gas pressure and $e^* = e_{th} + b^2/2\rho$ is the total specific energy density with $e_{th}$ being the thermal part."
 Iu this study System Lois closed by the adiabatic equation of state. py=pe;(D.1) with P—1/3.," In this study System \ref{eqn:rmhd-system} is closed by the adiabatic equation of state, $p_g = \rho e_{th} (\Gamma-1)$ with $\Gamma = 4/3$."
 Since our equation of state is not isothermal are are those used in most oevious studies( include 72)). thermalization | the kinetic cnerey mto (exceptionsinternal energv results in a uarginal decline of the sonic Mach umber throughout he run.," Since our equation of state is not isothermal are are those used in most previous studies (exceptions include \cite{Porter:2002p4511}) ), thermalization of the kinetic energy into internal energy results in a marginal decline of the sonic Mach number throughout the run."
 This is discussed in more detail iu 83.1.., This is discussed in more detail in \ref{sec:startup}.
" The fact that ph aud p and 5"" directly effect all aspects of the enerevauomoeutuim dynamics of the fluid hrough their coutributions to T"" means that RMIEID urbuleuce dynamics will contain mode couplings not xeseut in the non-relativistic case.", The fact that $\rho h^*$ and $p^*$ and $b^\mu$ directly effect all aspects of the energy-momentum dynamics of the fluid through their contributions to $T^{\mu \nu}$ means that RMHD turbulence dynamics will contain mode couplings not present in the non-relativistic case.
 This is because acoustic and RMIID: waves will alter eddy dyiiuaules via their modifications to fluid inertia. as mentioned above.," This is because acoustic and RMHD waves will alter eddy dynamics via their modifications to fluid inertia, as mentioned above."
" Iuthis study. fluctuations in the thermal energy and pressure due to compressive waves will dominate naenetic fluctuations in Z7"" since we consider the case with relativistic thermal pressure. p/p1. but sub-dominant maesnetie field."," Inthis study, fluctuations in the thermal energy and pressure due to compressive waves will dominate magnetic fluctuations in $T^{\mu \nu}$ since we consider the case with relativistic thermal pressure, $p/\rho
\sim 1$, but sub-dominant magnetic field."
 Alfvénnic RMIID. turbulence or which inagnetie energev density is significant or dominant (0502/2~ p) is also of interest ancl will form he basis for a future study.," Alfvénnic RMHD turbulence for which magnetic energy density is significant or dominant $b^2/2
\sim \rho$ ) is also of interest and will form the basis for a future study."
 The ideal RMITID. equations cau also be expressed iu flux conservative fori amenable to ασΊσα] solution as where the couserved quautities represent the lab frame particle nuniber. total euerev. (excluding rest mass). 1iomoeutunm. aud magnetic induction respectively. and the correspondiug fixes are By introducing the volume averaged conserved quantities. and rewriting Equation 2 using the cdivereeuce theorem. we obtain volune averaged time derivatives iu cach zone. where FU). are the fluxes of conserved quautitics evaluated at the interfaces between cell voliunes.," The ideal RMHD equations can also be expressed in flux conservative form amenable to numerical solution as where the conserved quantities represent the lab frame particle number, total energy (excluding rest mass), momentum, and magnetic induction respectively, and the corresponding fluxes are By introducing the volume averaged conserved quantities, and rewriting Equation \ref{eqn:diff-cons-law} using the divergence theorem, we obtain volume averaged time derivatives in each zone, where $\hat{\vct{F}}^j$, are the fluxes of conserved quantities evaluated at the interfaces between cell volumes."
 Equation 6 would iu principle complete the integration scheme for advancing the solution iu time., Equation \ref{eqn:method-of-lines} would in principle complete the integration scheme for advancing the solution in time.
 However. iu oxactiee an expression which is higher order iu time is desirable to maintain accuracy.," However, in practice an expression which is higher order in time is desirable to maintain accuracy."
 In this study; Mara las 2001 configured to use a second order uusplit MUSCL- type integration scheme sinuibku to the one described in ?.. and differs mostly iu that maguetic fields are volume iustead of arca-averaged.," In this study, Mara has been configured to use a second order unsplit MUSCL-Hancock type integration scheme similar to the one described in \cite{Mignone:2006p2905}, and differs mostly in that magnetic fields are volume instead of area-averaged."
 The sclicie is parameterized around an approximate Reimann solver or obtaining the iutercell fluxes F7. aud a recoustruction algoritlin for interpolating primitive quantities to the gone interfaces.," The scheme is parameterized around an approximate Reimann solver for obtaining the intercell fluxes $\hat{\vct{F}}^j$ , and a reconstruction algorithm for interpolating primitive quantities to the zone interfaces."
 For completeness. the full scheme is described below.," For completeness, the full scheme is described below."
We inject clectrous aud protous with different euergies aud augular distributions into our model Sun aud track them as well as their secoudaries.,We inject electrons and protons with different energies and angular distributions into our model Sun and track them as well as their secondaries.
 The tracking stops if the particles leave the Sun or if their energy. falls below 50 keV. ILowever. because positrons seldom auuihilate uutil they thermalize. the 50 keV cutoff does not apply to them: we track them until they aumililate or leave the Sun.," The tracking stops if the particles leave the Sun or if their energy falls below 50 keV. However, because positrons seldom annihilate until they thermalize, the 50 keV cutoff does not apply to them; we track them until they annihilate or leave the Sun."
 We also track pious to their decay., We also track pions to their decay.
 Tade L shows all the different models of injected electrons used in the simulations., Table \ref{tab:e} shows all the different models of injected electrons used in the simulations.
 For the dowinward-beamed aud dowmward-isotropic distributions. the clectrous are iuitialized just above the model solar atmosphliere.," For the downward-beamed and downward-isotropic distributions, the electrons are initialized just above the model solar atmosphere."
 For the isotropic and pancake distributions. they are injected at au iutegrated column depth of &«10πο e 2.," For the isotropic and pancake distributions, they are injected at an integrated column depth of $8
\times 10^{-5}$ g $^{-2}$."
 The results are not sensitive to this xuineter as long as it is not verv deep iu the atinosphere., The results are not sensitive to this parameter as long as it is not very deep in the atmosphere.
 As the electrons have to experience murroring to eive these distrinitions. they are confined in the region aud refiected. artificially iu the simulation.," As the electrons have to experience mirroring to give these distributions, they are confined in the region and reflected artificially in the simulation."
 We do not invoke rea magnetic mirroring because the evration radius is too s1uall compared to other leugt1 scales in the simulation aud includiug the maenetic feld would make the ruus inpracticallv slow., We do not invoke real magnetic mirroring because the gyration radius is too small compared to other length scales in the simulation and including the magnetic field would make the runs impractically slow.
" Iu Table Ἐν, columns LE7 slrow the ratio between 511 keV line flux and the coutimmaun in two places: the energy flux per keV at 200 keV. aud he integrated contiuuun from δ15 MeV. The simulation marked with cashes gave no photons from 5.15 MeV. The coluuus marked ""(siuij"," In Table \ref{tab:e}, columns 4–7 show the ratio between 511 keV line flux and the continuum in two places: the energy flux per keV at 200 keV and the integrated continuum from 8–15 MeV. The simulation marked with dashes gave no photons from 8–15 MeV. The columns marked “(sim.)”"
 are the ratios from the direct output of the sinumations., are the ratios from the direct output of the simulations.
" To ect the ratios marked ""(envlv.)."," To get the ratios marked “(cnvlv.),”"
 we convolved our simulated spectra with the mstriuneuta response matrix ofRHESST. so we could compare the simulations with the ratio of counts iu a flare observed with tat spacecraft.," we convolved our simulated spectra with the instrumental response matrix of, so we could compare the simulations with the ratio of counts in a flare observed with that spacecraft."
 The last three colunuus give the production cficiency for photous in each baud exiting the Sum per iu]mit particle iu the simulation., The last three columns give the production efficiency for photons in each band exiting the Sun per input particle in the simulation.
 The first half of Table 1 represents a disk flare (cosine of the viewing angle 20.8) arc he last half represents a lab flare (cosine of the viewing anele between 0.2 iux 10.1).," The first half of Table \ref{tab:e}
 represents a disk flare (cosine of the viewing angle $>0.8$ ) and the last half represents a limb flare (cosine of the viewing angle between 0.2 and 0.4)."
 The electron angular distribution affects the ougoing photons in several wavs., The electron angular distribution affects the outgoing photons in several ways.
 First. the broeiisstralilung photons are lighly beamed in the direction of the electrous notion.," First, the bremsstrahlung photons are highly beamed in the direction of the electrons' motion."
 The more t1e primary elecrons are beamed downward. the fewer plotous cau escape to be observed.," The more the primary electrons are beamed downward, the fewer photons can escape to be observed."
 Secouc. the more the primary electrons arο beamed downward. the deeper positrons are produced aud the fewer aunibilation photons escape without being scatcred or absorbed.," Second, the more the primary electrons are beamed downward, the deeper positrons are produced and the fewer annihilation photons escape without being scattered or absorbed."
 Therefore. the escaping flux aud the annihilation line to contiutuui ratio depends oi the injected aieular distribution.," Therefore, the escaping flux and the annihilation line to continuum ratio depends on the injected angular distribution."
 Not all the photons recorded come to the detector directly after tLOW are produced., Not all the photons recorded come to the detector directly after they are produced.
 Some of them may have been Compton scattered. changing both their energy aud direction.," Some of them may have been Compton scattered, changing both their energy and direction."
 Compton scattering becomes very important when the aneular distribution of injected electrous is most vodoscuscard., Compton scattering becomes very important when the angular distribution of injected electrons is mostly downward.
" In this case. since most direct bremsstralluue photons head iuto the Sun. Compton ""albedo cau coutribute a significant par of the observed spectruii. aud may even become dominant at lower energies (Ioutar&Brown20¢1G:IKotokuetal.20WT)."," In this case, since most direct bremsstrahlung photons head into the Sun, Compton “albedo” can contribute a significant part of the observed spectrum, and may even become dominant at lower energies \citep{kontar06,kotoku07}."
 Iu paucls A aud B of Figure 3.. we plot the outeoing eamuna-rav spectra for different piriuneters of injected clectrous. collected for cos.)>0.8.," In panels A and B of Figure \ref{fig:e_all}, we plot the outgoing gamma-ray spectra for different parameters of injected electrons, collected for $\cos \beta > 0.8$."
 The spectra are normalized to outgoing plotous per MeV. per incoming electron., The spectra are normalized to outgoing photons per MeV per incoming electron.
 As expected. the harder the spectral iudex. the higher the production rate. s;nce lighl-cucrey electrons are more efficient for bremsstraliluug.," As expected, the harder the spectral index, the higher the production rate, since high-energy electrons are more efficient for thick-target bremsstrahlung."
 It cau also be seen that the production rate decreases with more cowuward beaming (panel €, It can also be seen that the production rate decreases with more downward beaming (panel C
12.3«logN<12.6 ? for both Mgtr aud Fe 11. with 1.1c22kn«s 1,"$12.3 < \log N < 12.6$ $^{-2}$ for both Mg and Fe , with $1.4 < b < 2.2$ km $^{-1}$."
" We assumed the cloud is hermatlv broadened aud used the curve of erowtl to estiniate 11.2logNVa1)16.5Γ 2,", We assumed the cloud is thermally broadened and used the curve of growth to estimate $14.2 < \log N(\hbox{H~{\sc i}}) < 16.5$ $^{-2}$.
 We then used CLOUDY η. once wit havt? UV couui slope and ouce with Fox5000 I& blackbody sSpectruni [cool stars are slTeecster by (Τομ)/N(A\Ieu)~ 1]. to explore the cloud clienucal aud ionizaion conditions.," We then used CLOUDY \cite{ferland}, once with a $\nu ^{-1.5}$ UV continuum slope and once with $T\approx 5000$ K blackbody spectrum [cool stars are suggested by $N(\hbox{Fe~{\sc ii}})/N(\hbox{Mg~{\sc
ii}}) \sim 1$ ], to explore the cloud chemical and ionization conditions."
" Forthe powerlaw UX""D with Jx,=0.2. the cloud properties are UDc5 pec ane AM1JO NL wit Lionization parameter logC~ 3.5."," For the power–law UVB with $J_{-21} = 0.2$, the cloud properties are $n_H \sim 0.05$ $^{-3}$, $D \sim 5$ pc, and $M \sim
10^{-3}$ $_{\odot}$, with ionization parameter $\log U \sim
-3.5$ ."
 This cloud is iuferec to have supersolar netallicity. 0.5<|ZZ.|«1.5!," This cloud is inferred to have super–solar metallicity, $0.5 <
[Z/Z_{\odot}] < 1.5$!"
 Tua F702W WEPC/IIST imageof the 01511039 field |5] there are a few diffuse extender LSB galaxies over tje liupact paramecr range 20«Dh60 kpe. if they |jnve =(0.93.," In a F702W WFPC/HST imageof the $0454+039$ field \cite{lebrun} there are a few diffuse extended LSB galaxies over the impact parameter range $20 < Dh^{-1} < 60$ kpc, if they have $z=0.93$."
 However. it is difficult to wnderstand how extended supersolay gas could arise fiom such diffuse galaxies.," However, it is difficult to understand how extended super–solar gas could arise from such diffuse galaxies."
 Fort16 blackbody “coolsars UV coutiuuuui. the inferred clou properties are yp~0.1 cia5. D—100 pe. and AL~6 OAL... with logC|1.," For the blackbody “cool stars” UV continuum, the inferred cloud properties are $n_H \sim 0.1$ $^{-3}$, $D \sim 100$ pc, and $M
\sim 600$ $_{\odot}$, with $\log U \sim +1$."
 The interred uctallicity is |Z/Z..]1.2., The inferred metallicity is $[Z/Z_{\odot}] \sim - 1.2$.
 This scenario models a dwarflike ealaxy with a latetype stellar popuation., This scenario models a dwarf–like galaxy with a late–type stellar population.
 The value of C implies au extrene number of stars: Us sce14110 ls astroslivsically implausible [2].., The value of $U$ implies an extreme number of stars; this scenario is astrophysically implausible \cite{cwc}.
 We thus coiclude that the aSC)rher is metal reli and ionized bv the UVB., We thus conclude that the absorber is metal rich and ionized by the UVB.
 It leWw be that svsteis lise the one preseuted here are fairlycommon aud contLINC5 a vetobe explored class of absorber., It may be that systems like the one presented here are fairlycommon and comprise a yet–to–be explored class of absorber.
 A scusitive scare1 for Me Svstenis i the fwests along the lines of sieht to other QSOs is in progress., A sensitive search for Mg systems in the forests along the lines of sight to other QSOs is in progress.
"source to be approximately 1.5κρό (Steeleetal.1998).. we find the intrinsic luminosity to be Lc5xIO""eres| when the hydrogen deusity is of the order of ~5x10cm7.","source to be approximately $1.8\,\rm{kpc}$ \citep{Steele}, we find the intrinsic luminosity to be $L\approx5\times10^{37}\rm{erg\,s^{-1}}$ when the hydrogen density is of the order of $\sim5\times 10^{13}\rm{cm}^{-3}$."
 This intrinsic luminosity is Comparable to that suggested by Bottcher(2007) (or5039.. the ouly other kuowu TeV binary thougit to contain a black It is interesting to Compare this intrinsic luminosity to the Edcdiugton Lpag£1.3x107(Ma/AL.)ergs|. which is comparable to L. and implies that radiation may ye beaiued in our direction.," This intrinsic luminosity is comparable to that suggested by \citet{Bottcher} for, the only other known TeV binary thought to contain a black It is interesting to compare this intrinsic luminosity to the Eddington $L_{Edd}\approx1.3\times10^{39}(M_2/M_\odot)\rm{erg\,s^{-1}}$, which is comparable to $L$, and implies that radiation may be beamed in our direction."
 It is also interestiug to calculate the accretion rate that would be needed in order to obtain the intrinsic luminosity: By taking £LzzολοHI. where 2 is of the order of he Schwarzschild radius (26M2/c). we find Moz9x10.7M.vr.1.," It is also interesting to calculate the accretion rate that would be needed in order to obtain the intrinsic luminosity: By taking $L\approx GM_2\dot{M_2}/R$, where $R$ is of the order of the Schwarzschild radius $2GM_2/c^2$ ), we find $\dot{M_2}\approx 2\times 10^{-8}M_\odot \rm{yr}^{-1}$."
 This rate is comparable with he observed inass loss rate of 10.A.vr.4., This rate is comparable with the observed mass loss rate of $\sim 10^{-8}M_\odot \rm{yr}^{-1}$.
 The fact that the accretion rate is comparable to the ueasured mass loss rate. suggests that the [low of matter cau be quite complicated. e.g. an iucrease in the accretion rate would strip most of the circumstellar mass. leadiug to time variability.," The fact that the accretion rate is comparable to the measured mass loss rate, suggests that the flow of matter can be quite complicated, e.g. an increase in the accretion rate would strip most of the circumstellar mass, leading to time variability."
 This uay explain the fact that no VHE cletectious have been reported since Still asstuning the intrinsic luminosity to be constant iu time. we cau estimate the amount of hydrogen needed to attenuate the source to below the cletectability threshold.," This may explain the fact that no VHE detections have been reported since Still assuming the intrinsic luminosity to be constant in time, we can estimate the amount of hydrogen needed to attenuate the source to below the detectability threshold."
 We find that the deusity must increase from ~5xI0Pem* to ~5x10en7 at the characteristic distance of 1004.., We find that the density must increase from $\sim5\times10^{13}\rm{cm}^{-3}$ to $\sim5\times10^{14}\rm{cm}^{-3}$ at the characteristic distance of $100R_{\odot}$.
 This amount of hydrogen in turn leads to much higher mass loss rates than those observed. aud it may also imply a strouger activity of the ]t is worth mentioning that the attenuation moclel is not the only. possible way to account [or the moclulation.," This amount of hydrogen in turn leads to much higher mass loss rates than those observed, and it may also imply a stronger activity of the It is worth mentioning that the attenuation model is not the only possible way to account for the modulation."
 For example. there is also the possibility of the emission being anisotropic. aid the moclulation resulting [rom a geometrical ellect.," For example, there is also the possibility of the emission being anisotropic, and the modulation resulting from a geometrical effect."
 This possibility is described iu detail by (2010).. were a shocked pulsar wind with a large Lorentz [actor is thought to be the cause of elulssion.," This possibility is described in detail by \citet{Neronov}, were a shocked pulsar wind with a large Lorentz factor is thought to be the cause of emission."
 For the case of LS2+617303. we Bud that attenuation due to ++ interactions with the background radiation does not account for the observed high euergy flux modulation as a function oL the orbital phase. namely a uarrow peak near apastrou.," For the case of $LS\,I\,+61^\circ303$, we find that attenuation due to $\gamma\gamma$ interactions with the background radiation does not account for the observed high energy flux modulation as a function of the orbital phase, namely a narrow peak near apastron."
 This eflect leads us to investigate soie properties of the ejectecl material [rom the Be star. aud the inclination auele of the orbit.," This effect leads us to investigate some properties of the ejected material from the Be star, and the inclination angle of the orbit."
 We [iuc the angle of the orbit to be 7<31° (AL> 2.5M..) at the 99% confidence level. suggesting that the compact object is a black hole rather than a neutrou star.," We find the angle of the orbit to be $i<34^\circ$ $M>2.5M_\odot$ ) at the $99\%$ confidence level, suggesting that the compact object is a black hole rather than a neutron star."
 We also find the density of, We also find the density of
"while using expression (5)). Le. a blackbodyv as the thermal component. expression (2)) cau be written as where np;=Of, ad sq;=sd.","while using expression \ref{ec5.15}) ), i.e., a blackbody as the thermal component, expression \ref{ec5.2}) ) can be written as where $n_{Tt} = {\beta_t / \beta_{t_0}}$ and $n_{nt} = {A_t / A_{t_0}}$."
 Th this wav. changes iu amplitude are casily obtained by varving the values of these ratios from unity. at ty. to their final values at f.," In this way, changes in amplitude are easily obtained by varying the values of these ratios from unity, at $t_0$, to their final values at $t$."
 Once we ect Ty. og. and ess. changes of T; and/or wpe. or o; and/or με. du expression (2)). eenerate the trajectories in the wy:cp plaue (seo Figures 2—-6)).," Once we get $T_{t_0}$ $\alpha_{t_0}$ , and $a_{\nu t_0}$, changes of $T_t$ and/or $n_{Tt}$, or $\alpha_t$ and/or $n_{nt}$, in expression \ref{ec5.2}) ), generate the trajectories in the $\varpi_{V, R}: \varpi_B$ plane (see Figures \ref{pks15vardos}- \ref{pks15z}) )."
" Siuultaneous changes in T; and sm. or αγ and 54, can seuerate diaguosis trajectories with a returning behavior (see Figure 2j)."," Simultaneous changes in $T_t$ and $n_{T_t}$, or $\alpha_t$ and $n_{n_t}$ can generate diagnosis trajectories with a returning behavior (see Figure \ref{pks15vardos}) )."
 A similar case can happen iu an expansion of the thermal component with a decrease in its temperature., A similar case can happen in an expansion of the thermal component with a decrease in its temperature.
 Untortunately. for the data presented in PII it is not possible to establish a unique set of initial parameters. due to the lack of data iu more bands.," Unfortunately, for the data presented in PII it is not possible to establish a unique set of initial parameters, due to the lack of data in more bands."
 Figure 1. shows this problem., Figure \ref{pks15dos} shows this problem.
 Iu this figure. we preseut three reasonable fits for disk temperatures of 26.000 Ik. 20.000 I& aud 30.000 I& for the first data set of PISS 1510-089.," In this figure, we present three reasonable fits for disk temperatures of $26,000$ K, $20,000$ K and $30,000$ K for the first data set of PKS 1510-089."
 For this reason. we iust select the nios appropriate values for μι. T; and αι. based ou the typical values found in the literature for simular objects.," For this reason, we must select the most appropriate values for $\alpha_{t_0}$, $T_{t_0}$, and $a_{\nu t_0}$, based on the typical values found in the literature for similar objects."
 Some investigations sugecst tha the typical maxima disk temperature. close to the central object. should be between 20.000 Ts and 30.000 Is. although temperatures outside of this range are not discarded (e.g... Malan&Sm-gout 1982: Malkau&Moore.1986: Czoruv&Elvis 1987: Perevraetal. 2006)).," Some investigations suggest that the typical maximum disk temperature, close to the central object, should be between $20,000$ K and $30,000$ K, although temperatures outside of this range are not discarded (e.g., \citealt{Malkan82}; ; \citealt{Malkan86}; \citealt{Czerny87}; \citealt{Pereyra06}) )."
 The spectra iudex of the uon-thermal component might be around —1 (e.g. Malkau&Sarecut1982: ctal. 1986: Brownotal. 1989a: Brownctal. 198953).," The spectral index of the non-thermal component might be around $-1$ (e.g., \citealt{Malkan82}; \citealt{Elvis86}; \citealt{Brown89a}; ; \citealt{Brown89b}) )."
 On the other haud. for blazars. the non-thermal component coutributes with most of the flux (e.g...Malkan&Sarecnt19521). and at low brightness levels. it is expected that both components coutribute the same (e.g.Caretal. 20063).," On the other hand, for blazars, the non-thermal component contributes with most of the flux (e.g.,\citealt{Malkan82})), and at low brightness levels, it is expected that both components contribute the same (e.g.,\citealt{Gu06}) )."
 Nevertheless. reeardlessοι the exact value for these parameters atf= ty. we can discern the OM origin analwzing the spectral variations.," Nevertheless, regardless the exact value for these parameters at$t=t_0$ , we can discern the OM origin analyzing the spectral variations."
Classical novae are ai subset of cataclysmic variables which are interacting binary svstems hosting a main-sequence secondary (sometimes a slightly evolved star) and a collapsed primary component. a white cdwarl (Warner 1995),"Classical novae are a subset of cataclysmic variables which are interacting binary systems hosting a main-sequence secondary (sometimes a slightly evolved star) and a collapsed primary component, a white dwarf (Warner 1995)."
 An ouburst on the surface of the white cwarlas a result ofa thermonuclear runaway in the aceretecl material causes the jectionof 5to ΤΝ. of material at. velocities up to severa thousand kilometers per second(Shara 1989:> Warner , An outburst on the surface of the white dwarf as a result of a thermonuclear runaway in the accreted material causes the ejectionof $^{-3}$ to $^{-7}$ $_{\odot}$ of material at velocities up to several thousand kilometers per second (Shara 1989; Warner 1995).
V2215 Cve (Nova Cvg 2001. No.2) was discovered a magnitude 7.0-8.8 on 2001 August LS simultaneously by Nakamura ct al. (, V2275 Cyg (Nova Cyg 2001 No.2) was discovered at a magnitude 7.0-8.8 on 2001 August 18 simultaneously by Nakamura et al. (
2001) and Nakano et al. (,2001) and Nakano et al. (
2001).,2001).
 Early spectroscopy showed hydrogen. Balmer lines with P ‘ven profies and tla lines indicating expansion velocities Q: 1700 km (Avani 2001), Early optical spectroscopy showed hydrogen Balmer lines with P Cygni profiles and $\alpha$ lines indicating expansion velocities of 1700 km $^{-1}$ (Ayani 2001).
 At later stages. high energy coronal lines were found to dominate the spectrum (e... hi N]. Si IN] and Ad IND.," At later stages, high energy coronal lines were found to dominate the spectrum (e.g., [Si X], [Si IX] and [Al IX])."
 The nova was found to belong to the Πο subclass of novae defined by Williams (1992) because of the broad lines of HH. He and NN in its spectrum (Ixiss et al.," The nova was found to belong to the ""He/N"" subclass of novae defined by Williams (1992), because of the broad lines of H, He and N in its spectrum (Kiss et al."
 2002)., 2002).
 In addition. Ixiss et al. (," In addition, Kiss et al. ("
"20€)2) measured t2=?.9+0.5 d. t4— T4 d and Aly = -9"".7 L0.""7 which were used to derive a cistance of 3-8 kpc for the nova.","2002) measured $_2$ $\pm$ 0.5 d, $_3$ $\pm$ 1 d and $_V$ = $^{m}$ $\pm$ $^{m}$ 7 which were used to derive a distance of 3-8 kpc for the nova."
" A USNO star of Z/— 18.8 and D—19""'.6 was suggested as a possible progeniOr star (Schmoeer et al.", A USNO star of $R$ $^{m}$ .8 and $B$ $^{m}$ .6 was suggested as a possible progenitor star (Schmeer et al.
 2)01)., 2001).
 This paper is on the CCD photometry of V2215 (νο Covering vears 2002 and 2003 obtained with the 1.5 m Russian-Purkish joint telescope (UET150) at the ΡΕΙΤΑΛ National Observatory (PUG) in Antalya. Turkey.," This paper is on the CCD photometry of V2275 Cyg covering years 2002 and 2003 obtained with the 1.5 m Russian-Turkish joint telescope (RTT150) at the TUBITAK National Observatory (TUG) in Antalya, Turkey."
 We present the discovery of clistinet period re»orted by Zalman et al. (, We present the discovery of a distinct period reported by Balman et al. (
2003) (which we mark as Du) and the detection. of a highly coherent OPO (Quasi-periodic oscillations) on 6 clillerent nichts in 2003 (using V. 2. { filters).,"2003) (which we mark as $_1$ ) and the detection of a highly coherent QPO (Quasi-periodic oscillations) on 6 different nights in 2003 (using $V$, $R$ , $I$ filters)."
 Fast variations from V2275 (νο similar to this second period (which we mark as P2) were also reported by, Fast variations from V2275 Cyg similar to this second period (which we mark as $_2$ ) were also reported by
The 100 Myr cluster Iuminosity function has a feature which is not present in the 10 Alvr luminosity function: a sharp spike (D) between peaks A and C. By 100 Myr. nearly all brown dwarf deuterium burning has ceased. and these higher-mass brown clwarls join (heir lower-lass cousins in rapid cooling.,"The 100 Myr cluster luminosity function has a feature which is not present in the 10 Myr luminosity function: a sharp spike (D) between peaks A and C. By 100 Myr, nearly all brown dwarf deuterium burning has ceased, and these higher-mass brown dwarfs join their lower-mass cousins in rapid cooling."
 This leads to the formation of the second peak/tiroush feature (D and IE) as brown clwarls separate from hyvdrogen-burning stars., This leads to the formation of the second peak/trough feature (D and E) as brown dwarfs separate from hydrogen-burning stars.
 To verily that peak D objects correspond (o higher-mass brown cwarls. we segregate (he 100 Myr sample bv mass.," To verify that peak D objects correspond to higher-mass brown dwarfs, we segregate the 100 Myr sample by mass."
 Figure 4 confirms that peak D includes only brown clwarls that have finished (heir deuterium burning phase., Figure 4 confirms that peak D includes only brown dwarfs that have finished their deuterium burning phase.
 Finally. the bottom panel in Figure 3 shows our prediction for a 1 Gyr cluster.," Finally, the bottom panel in Figure 3 shows our prediction for a 1 Gyr cluster."
 The evolution of peak A has halted. since nearly all stars are stabilized on the main sequence and all brown dwarls (hat burned deuterium have separated from (his group.," The evolution of peak A has halted, since nearly all stars are stabilized on the main sequence and all brown dwarfs that burned deuterium have separated from this group."
 Peak D has broadened since brown dwarls cool al mass-dependent rates., Peak D has broadened since brown dwarfs cool at mass-dependent rates.
 A new trough (F) lies in the midst of this peak. reflecting (he onset of dust cloud. formation and dust rainout in the Burrows models (see 53.2).," A new trough (F) lies in the midst of this peak, reflecting the onset of dust cloud formation and dust rainout in the Burrows models (see $\S$ 3.2)."
 Note that peak C spans roughly the same magnitude range al each age (all panels of Figure 3)., Note that peak C spans roughly the same magnitude range at each age (all panels of Figure 3).
 In general. the cooling rates of substellar objects are mass dependent. but the cooling rates of the lowest mass («13 Mj) brown cdwarfs are similar to each other between 5 Myr and 1 Gyr.," In general, the cooling rates of substellar objects are mass dependent, but the cooling rates of the lowest mass $< 13~M_J$ ) brown dwarfs are similar to each other between 5 Myr and 1 Gyr."
 This leads to the uniform behavior of peak C members over time., This leads to the uniform behavior of peak C members over time.
 We do not include dynamical evolution effects in our models., We do not include dynamical evolution effects in our models.
 While these effects are not hugely important for the vounger clusters considered here (he effects on old clusters. e-] Gyr. may be important.," While these effects are not hugely important for the younger clusters considered here the effects on old clusters, $\sim$ 1 Gyr, may be important."
 Overall. (he bolometric cluster laminosity Iunction exhibits complicated time dependent behavior that depends on both the interior aud a(imospheric evolution of brown chiwarls.," Overall, the bolometric cluster luminosity function exhibits complicated time dependent behavior that depends on both the interior and atmospheric evolution of brown dwarfs."
 llowever. the features iclentifiecdl in Figure 3 are dependent mostly on the evolution of the total emereent luminosity interior evolution).," However, the features identified in Figure 3 are dependent mostly on the evolution of the total emergent luminosity interior evolution)."
 Therefore. since the interior plvsics of {hese models is relatively well understood. we believe that the locations of the major features. peak D and troughs D and IE. are defined robustly.," Therefore, since the interior physics of these models is relatively well understood, we believe that the locations of the major features, peak D and troughs B and E, are defined robustly."
 We note that the normalization of the model luminosity functions ultimately is arbitrary. and that only the relative heights. and locations of (ποσο features are important., We note that the normalization of the model luminosity functions ultimately is arbitrary and that only the relative heights and locations of these features are important.
 Droad-band Iuminosity Iuictions are constructed using the BC's discussed in 62.2., Broad-band luminosity functions are constructed using the BCs discussed in $\S$ 2.2.
 Figure 5 displavs the evolution of {- and A-band cluster huninositv functions from 10 Myr to 900 Myrt., Figure 5 displays the evolution of $I$ - and $K$ -band cluster luminosity functions from 10 Myr to 900 .
. The morphological features discussed in 53.1 and labeled in Figure 3 are also, The morphological features discussed in $\S$ 3.1 and labeled in Figure 3 are also
include the dwarls within 50 kpc of the galactic center the case is no longer clear cut.,include the dwarfs within $50$ kpc of the galactic center the case is no longer clear cut.
" If the satellite count from 50—100 kpe increases to greater than 25, there is a case for fossils even using the most conservative epi=20 kms !"," If the satellite count from $50-100$ kpc increases to greater than 25, there is a case for fossils even using the most conservative $v_{filt}=20$ km $^{-1}$."
 For Όρη=30 Kms 1 the number of non-fossils available from 50—100 kpe drops to e»]8., For $v_{filt}=30$ km $^{-1}$ the number of non-fossils available from $50-100$ kpc drops to $~\sim18$.
" For luminosities at which the observational sample 1s complete, to the right of the dashed lines, we see too many bright (L4:>104L.. ) objects, even in this inner most radial bin."," For luminosities at which the observational sample is complete, to the right of the dashed lines, we see too many bright $L_V > 10^4
L_\odot$ ) objects, even in this inner most radial bin."
" In addition, as our simulations do not account [or post-reionization star formation, it is likely that the overabundance of bright objects is worse than shown in Figure 5.."," In addition, as our simulations do not account for post-reionization star formation, it is likely that the overabundance of bright objects is worse than shown in Figure \ref{LF.pristine}."
" Unless all of the non-fossils have accreted no gas and formed no additional stars alter reionization, the simulated curve must lie the observations."," Unless all of the non-fossils have accreted no gas and formed no additional stars after reionization, the simulated curve must lie the observations."
" This allows these star forming halos to increase in luminosity, shifting the luminosity function of the non-fossils to the right."," This allows these star forming halos to increase in luminosity, shifting the luminosity function of the non-fossils to the right."
" In this bin, we probe the outer reaches of the Milky Way's virial halo and there are a [ew notable characterisucs of the luminosity functions."," In this bin, we probe the outer reaches of the Milky Way's virial halo and there are a few notable characteristics of the luminosity functions."
" First, with the addition of the observed dwarls in this bin, the total number of known satellites around the Milky Way increases to ~65. ~[5 not including the inner ultra-faints."," First, with the addition of the observed dwarfs in this bin, the total number of known satellites around the Milky Way increases to $\sim 65$, $\sim 45$ not including the inner ultra-faints."
 The sample at these larger radii is only complete for Li:>101 L.., The sample at these larger radii is only complete for $L_V > 10^4$ $_\odot$ .
" For 100—200 kpc, with aeyy,=20 kms! and the less conservative epi;=30 km ! there are ~60 and ~10 simulated respectively."," For $100-200$ kpc, with a $v_{filt}=20$ km $^{-1}$ and the less conservative $v_{filt}=30$ km $^{-1}$ there are $\sim 60$ and $\sim 40$ simulated non-fossils respectively."
" Second, the presence of undetected dwarts 1s corroborated by the shape of the observed luminosity function around 10! L..."," Second, the presence of undetected dwarfs is corroborated by the shape of the observed luminosity function around $10^4$ $_\odot$."
" Not only is it rising steeply to the detection limit at /?=100 kpe, but its shape 1s similar to the simulated primordial luminosity funcuion for the true fossils."," Not only is it rising steeply to the detection limit at $R=100$ kpc, but its shape is similar to the simulated primordial luminosity function for the true fossils."
" In the outer virial halo, we once again overproduce the number of bright satellites."," In the outer virial halo, we once again overproduce the number of bright satellites."
 At these radii the discrepancy between theory and observation is more severe than for 50 kpe<£2<100 kpe since for these radii there is only one observed satellite with Ly>3x10! L...," At these radii the discrepancy between theory and observation is more severe than for $50$ $<R<100$ kpc since for these radii there is only one observed satellite with $L_V > 3
\times10^4$ $_\odot$."
" For 2>200 kpe. we can only make observational comparisons for L4:>10"" L..."," For $R>200$ kpc, we can only make observational comparisons for $L_V > 10^5$ $_\odot$."
" Beyond the virial radius the discrepancy between the observed number of satellites and our simulations is up to ~1.5 orders of magnitude, compared with factors of 2 and ~10 for the 50kpe«&<100 kpe and 100 kpe bins, respectively."," Beyond the virial radius the discrepancy between the observed number of satellites and our simulations is up to $\sim1.5$ orders of magnitude, compared with factors of $\sim 2$ and $\sim 10$ for the $50~{\rm kpc}<R<100$ kpc and $100$ $<R<200$ kpc bins, respectively."
" Our simulations of the fossils of the first galaxies are consistent with the observed Milky Way satellite galactocentric radial distribunons (Section 4.1). primordial cumulative luminosity l'unctions(Figure 6)), and internal stellar properties (see Paper D."," Our simulations of the fossils of the first galaxies are consistent with the observed Milky Way satellite galactocentric radial distributions (Section \ref{RDs}) ), primordial cumulative luminosity functions(Figure \ref{LF.fossil}) ), and internal stellar properties (see Paper I)."
" More intriguing, is that at first glance the model appears to fail"," More intriguing, is that at first glance the model appears to fail"
"We rescale the scale factor a and the radius of the overdense region R by their values at turn-around, ai, and Ra, respectively, defining the parameters In addition, we introduce the dimensionless time τ and the overdensity at turn-around 6 by with the Hubble parameter at turn-around H.","We rescale the scale factor $a$ and the radius of the overdense region $R$ by their values at turn-around, $a_\mathrm{ta}$ and $R_\mathrm{ta}$, respectively, defining the parameters In addition, we introduce the dimensionless time $\tau$ and the overdensity at turn-around $\hat{\zeta}$ by with the Hubble parameter at turn-around $H_\mathrm{ta}$."
" In the following, we will sketch the most important steps to consider cosmologies like EdS, ACDM, and OCDM."," In the following, we will sketch the most important steps to consider cosmologies like EdS, $\Lambda$ CDM, and OCDM."
" Our consideration is based on ?,, but simplified because we ignore dynamical dark energy for now."," Our consideration is based on \cite{Bartelmann2006}, but simplified because we ignore dynamical dark energy for now."
 This extends the work by ? towards cosmologies with non-vanishing curvature., This extends the work by \cite{Wang1998} towards cosmologies with non-vanishing curvature.
" Spherical collapse is then described by the differential equations with the matter and dark-energy densities at turn around, Om and Qnta, respectively."," Spherical collapse is then described by the differential equations with the matter and dark-energy densities at turn around, $\Omega_\mathrm{m,ta}$ and $\Omega_\mathrm{\Lambda,ta}$, respectively."
 Primes denote derivatives with respect to the dimensionless time τ., Primes denote derivatives with respect to the dimensionless time $\tau$ .
" Equations (38)) and (89)) can be solved numerically using the boundary conditions y=0 at x=O and y'= Oat x=1, meaning that the overdensity starts with zero radius and reaches its maximal extent at turn-around."," Equations \ref{eq:SCMI}) ) and \ref{eq:SCMII}) ) can be solved numerically using the boundary conditions $y=0$ at $x=0$ and $y^\prime=0$ at $x=1$, meaning that the overdensity starts with zero radius and reaches its maximal extent at turn-around."
 The requirement y=1 at turn-around then uniquely determines é., The requirement $y=1$ at turn-around then uniquely determines $\hat{\zeta}$.
 The overdensity inside a halo with respect to the at any time is A=(αν)., The overdensity inside a halo with respect to the at any time is $\Delta=(x/y)^3 \hat{\zeta}$.
" Assuming that the collapsing halo virialises at the collapse redshift σε, which corresponds to the normalised scale factor x; when it would ideally collapse to zero radius, the virial overdensity is The redshifts at collapse and turn-around, z, and Za, are related by f(Zta)=itc)."," Assuming that the collapsing halo virialises at the collapse redshift $z_\mathrm{c}$, which corresponds to the normalised scale factor $x_\mathrm{c}$ when it would ideally collapse to zero radius, the virial overdensity is The redshifts at collapse and turn-around, $z_\mathrm{c}$ and $z_\mathrm{ta}$, are related by $t(z_\mathrm{ta})=\frac{1}{2}t(z_\mathrm{c})$."
" Later, we shall need the overdensity with respect to the rather than the background density, Ay=Og(z.)A,."," Later, we shall need the overdensity with respect to the rather than the background density, $\tilde{\Delta}_\mathrm{v}=\Omega_\mathrm{m}(z_\mathrm{c})\Delta_\mathrm{v}$."
" The ratio between the radii at turn-around and at collapse is 2 in an EdS universe because of virialisation, but slightly different in more general cosmologies."," The ratio between the radii at turn-around and at collapse is 2 in an EdS universe because of virialisation, but slightly different in more general cosmologies."
" Due to an additional contribution of dark energy to the potential, denoted by (Eae), the virial theorem is modified to (Ey)=--ᾱ(Εροι)+(Ege)."," Due to an additional contribution of dark energy to the potential, denoted by $\langle E_\mathrm{de}\rangle$, the virial theorem is modified to $\langle E_\mathrm{kin}\rangle=-\frac{1}{2}\langle E_\mathrm{pot}\rangle+\langle E_\mathrm{de}\rangle$."
" This leads to the following approximation for the ratio of the two radii (?):: As the density perturbations evolve linearly at very early times, the density contrast expected from linear theory at collapse, δε(ας). is simply given by In an EdS universe, 6.=1.686 and A,=178, both independent of the collapse redshift."," This leads to the following approximation for the ratio of the two radii \citep{Wang1998}: As the density perturbations evolve linearly at very early times, the density contrast expected from linear theory at collapse, $\delta_\mathrm{c}(x_\mathrm{c})$, is simply given by In an EdS universe, $\delta_\mathrm{c}=1.686$ and $\Delta_\mathrm{v}=178$, both independent of the collapse redshift."
" We shall use the potential in the centre of a spherical and homogeneous overdensity, Eq. (30)),"," We shall use the potential in the centre of a spherical and homogeneous overdensity, Eq. \ref{eq:centralPot}) ),"
 to relate the linear and non-linear potential depths., to relate the linear and non-linear potential depths.
" During the following calculation, we will denote quantities at an initial scale factor a; with the subscript ‘i’ and quantities at the collapse scale factor ae with the subscript ‘c’."," During the following calculation, we will denote quantities at an initial scale factor $a_\mathrm{i}$ with the subscript `i' and quantities at the collapse scale factor $a_\mathrm{c}$ with the subscript `c'."
 The potentials at the initial time and at collapse are respectively., The potentials at the initial time and at collapse are respectively.
" Their ratio is where 6,=,— 1.", Their ratio is where $\delta_\mathrm{v}=\Delta_\mathrm{v}-1$ .
" We have used here that the densities at the initial time and at collapse time are p;=vod;754 and pod. 36,, respectively."," We have used here that the densities at the initial time and at collapse time are $\bar{\rho}_\mathrm{i}=\rho_\mathrm{b0}a_\mathrm{i}^{-3}\delta_\mathrm{i}$ and $\bar{\rho}_\mathrm{c}=\rho_\mathrm{b0}a_\mathrm{c}^{-3}\delta_\mathrm{v}$ , respectively."
" Using Eq. ᾷ0),"," Using Eq. \ref{eq:defDelta}) ),"
 we can write (y;/x)?Σ/Δι and y;~£!?x; since Δι«1 for early times., we can write $(y_c/x_c)^3=\hat{\zeta}/\Delta_\mathrm{v}$ and $y_\mathrm{i}\approx\hat{\zeta}^{1/3}x_\mathrm{i}$ since $\Delta_\mathrm{i}\approx 1$ for early times.
" This yields We have neglected the difference between ó, and A, in the last step, which is a good approximation since A,=O(10?)."," This yields We have neglected the difference between $\delta_\mathrm{v}$ and $\Delta_\mathrm{v}$ in the last step, which is a good approximation since $\Delta_\mathrm{v}=\mathcal{O}(10^2)$."
 The ratio ó;/x;=:C is given by (?).., The ratio $\delta_\mathrm{i}/x_\mathrm{i}=:C$ is given by \citep{Bartelmann2006}.
 Since Eqs. (45] 46) ," Since Eqs. \ref{eq:nonLinEvolution}, \ref{eq:nonLinRatio}) )"
"describe the non-linear evolution between scale factors a; and ας, the linear and non-linear potential depths are related by where Φις is the potential evolved linearly from αι to dg."," describe the non-linear evolution between scale factors $a_\mathrm{i}$ and $a_\mathrm{c}$, the linear and non-linear potential depths are related by where $\Phi_\mathrm{l,c}$ is the potential evolved linearly from $a_\mathrm{i}$ to $a_\mathrm{c}$."
" For an EdS universe, we have ®,)/®,=n, independent of the collapse redshift because the potential growth factor G.,(a) is constant and y,— but for more general cosmological models, it depends on the collapse3, redshift."," For an EdS universe, we have $\Phi_\mathrm{nl}/\Phi_\mathrm{l}=\frac{10}{3}$, independent of the collapse redshift because the potential growth factor $G_+(a)$ is constant and $y_\mathrm{c}=\frac{1}{2}$, but for more general cosmological models, it depends on the collapse redshift."
" We show ®,)/@; for three different cosmological models in Fig. D].", We show $\Phi_\mathrm{nl}/\Phi_\mathrm{l}$ for three different cosmological models in Fig. \ref{fig:linNonlinGrowth}.
" We arbitrarily choose the initial scale factor to be five times the scale factor at matter-radiation equality because this is early enough for the potential not to have begun developing since we are in the matter dominated era, and late enough for ignoring any evolution of the transfer function T(k,a) with time."," We arbitrarily choose the initial scale factor to be five times the scale factor at matter-radiation equality because this is early enough for the potential not to have begun developing since we are in the matter dominated era, and late enough for ignoring any evolution of the transfer function $T(k,a)$ with time."
 While the ratio Eq. re, While the ratio Eq. \ref{eq:linNonLin}) )
"aches the constantD expected in an EdS model relatively (pquickly in the ACDM case as the redshift increases, its evolution is much slower for OCDM."," reaches the constant$\frac{10}{3}$ expected in an EdS model relatively quickly in the $\Lambda$ CDM case as the redshift increases, its evolution is much slower for OCDM."
" Wepoint out that the difference between the linear and the potential evolution in the centre is by far not as large as for the density contrast, where it is of order 103-4,"," Wepoint out that the difference between the linear and the non-linear potential evolution in the centre is by far not as large as for the density contrast, where it is of order $10^{3\ldots4}$ ."
respectively.,respectively.
 If the emission region is really LOpe. then the diffusion coefficient of Terzan 5 is much smaller than that of 47 Tuc.," If the emission region is really 10pc, then the diffusion coefficient of Terzan 5 is much smaller than that of 47 Tuc."
 According to Eq.(20) it gives D10ος!., According to Eq.(20) it gives $D\sim 10^{25}cm^2 s^{-1}$.
 The locations of 47 Tuc and Terzan 5 are very much different. the former is above the galactic plane and the latter is in the galactic plane.," The locations of 47 Tuc and Terzan 5 are very much different, the former is above the galactic plane and the latter is in the galactic plane."
 This factor may cause the difference in the diffusion coefficient., This factor may cause the difference in the diffusion coefficient.
 According to Fig., According to Fig.
" 1. éseiefere©0.3 and rcfic/Copricat00.05. bv using Eq.(24) the predicted X-ray energy fluxes ~7x10.LiMereem7s band ~10.Merecm7sH respectively,"," 1, $\epsilon_{relic}/\epsilon_{IR}\sim 0.3$ and $\epsilon_{relic}/\epsilon_{optical}\sim 0.05$, by using Eq.(24) the predicted X-ray energy fluxes $\sim 7\times 10^{-14}\rm erg ~cm^{-2} s^{-1}$ and $\sim 10^{-13}\rm erg ~cm^{-2} s^{-1}$ respectively."
 These predicted. values are about a factor of 3-4 lower than (hat of the observed value., These predicted values are about a factor of 3-4 lower than that of the observed value.
 However in Fie.2 of Eger. Domainko Clapson (2010) we can see that if (he unresolved X-ray point-source can contribute to the diffuse X-ray. (hen alter subtracting this contribution (the green solid curve) the real diffuse X-ray Παν is actually reduced significantlv.," However in Fig.2 of Eger, Domainko Clapson (2010) we can see that if the unresolved X-ray point-source can contribute to the diffuse X-ray, then after subtracting this contribution (the green solid curve) the real diffuse X-ray flux is actually reduced significantly."
 Again we can use Eq.(27) to estimate the predicted radio energy. flix. which gives ~5x10Mereem7s! for the IR model and ~3.4x10.ergem7s! for the Optical model (5 Jv and 3.4 Jv).," Again we can use Eq.(27) to estimate the predicted radio energy flux, which gives $\sim 5\times 10^{-14}\rm erg ~cm^{-2} s^{-1}$ for the IR model and $\sim 3.4\times 10^{-14}\rm erg ~cm^{-2} s^{-1}$ for the Optical model (5 Jy and 3.4 Jy)."
 We don't have radio data lor 3° region around. Terzan 5., We don't have radio data for 3' region around Terzan 5.
 Η observations show the lower values of radio flux [rom the corresponding region (then radio enission. eamiuna-ray enussion and X-rav emission should occupy more extended region.," If observations show the lower values of radio flux from the corresponding region then radio emission, gamma-ray emission and X-ray emission should occupy more extended region."
 In that case the observed diffuse X-ray emission [rom 3° region should not be related to IC model aud should have different nature., In that case the observed diffuse X-ray emission from 3' region should not be related to IC model and should have different nature.
 The more detailed observations including spatial and spectral information by Fermi ancl other higher energy detectors. like IIESS. MAGIC. VERITAS ete.," The more detailed observations including spatial and spectral information by Fermi and other higher energy detectors, like HESS, MAGIC, VERITAS etc."
 as well as radio observations can provide better constraints for the models., as well as radio observations can provide better constraints for the models.
 We have calculated GeV gamma-ray spectrum produced by inverse Compton scattering between (he relativistic ἐπ pairs of the pulsar wind and the background soft. photons. which include the relic photons. the star lights of the cluster. the infrared photons and the," We have calculated GeV gamma-ray spectrum produced by inverse Compton scattering between the relativistic $e^{\pm}$ pairs of the pulsar wind and the background soft photons, which include the relic photons, the star lights of the cluster, the infrared photons and the"
is consistent with neutral iron.,is consistent with neutral iron.
 Addition of an absorption edee at 7.1keV does not lead to a sgguificaut innproveraent in the fit. aud the upper limit to the optical depth is fouud to be r«0.03.," Addition of an absorption edge at $7.1\kev$ does not lead to a significant improvement in the fit, and the upper limit to the optical depth is found to be $\tau < 0.03$."
 We have also tested the observed ion Ίνα emission profile of MCCC-5-2:-16 against that expected from) an accretion disk around a rotating (ντ) black hole 1991)., We have also tested the observed iron $\alpha$ emission profile of MCG-5-23-16 against that expected from an accretion disk around a rotating (Kerr) black hole \citep{Laor91}.
". We fixed the iuner radius at 1.2274. the minima radius allowed for a ery black hole. aud outer radius at 1007, which is the inaxinnun radius allowed bv the model."," We fixed the inner radius at $1.23r_g$, the minimum radius allowed for a Kerr black hole, and outer radius at $400r_g$ which is the maximum radius allowed by the model."
 As before. the disk οιαν is a power-law in radius (xr. 7).," As before, the disk emissivity is a power-law in radius $\propto r^{-q}$ )."
 The variable parameters were Epp... fy. and the line normalization.," The variable parameters were $E_{FeK\alpha}$, $i$, $q$, and the line normalization."
 We used an absorbed aud red-shifted power-law model for the coutimmun., We used an absorbed and red-shifted power-law model for the continuum.
 The bottom two panels in Fie., The bottom two panels in Fig.
 E. show the ratio of the data aud best-fit disk-line models for a err black hole., \ref{f4} show the ratio of the data and best-fit disk-line models for a Kerr black hole.
 Without a narrow Gaussian conrponent. the fit is acceptable (47=251.7 for 235) dof} but the best-fit inclination angle is ~lsdee.," Without a narrow Gaussian component, the fit is acceptable $\chi^2 = 251.7$ for 235) dof) but the best-fit inclination angle is $\sim 18\deg$."
 Tuclusion of a narrow Gaussian component (0=0.01 keV) resulted in a significant improvement (A47=60.5 for oue additional paraincter) and in the best-fit iuclination angle of ~L7.ldee (see Table 2))., Inclusion of a narrow Gaussian component $\sigma=0.01\kev$ ) resulted in a significant improvement $\Delta \chi^2 = 60.5$ for one additional parameter) and in the best-fit inclination angle of $\sim47.4\deg$ (see Table \ref{tab2}) ).
 Addition of an absorption οσο at τι]keV does uot improve the fit significautlv (NA?=0.9 for oue additional dof, Addition of an absorption edge at $7.1\kev$ does not improve the fit significantly $\Delta \chi^2 = 0.9$ for one additional dof).
 Iu re 5. we have plotted the final|restLit models for the Fit observediron I&o line profile of MCG-5-23-16.," In Figure \ref{f5}, we have plotted the final best-fit models for the observed iron $\alpha$ line profile of MCG-5-23-16."
--. The three models (1) a combination of a narrow and broad Caussian. (i) a disk line for a Scluwarzsclild or (111) a Werr black hole all describe the observed. data equally well.," The three models – (i) a combination of a narrow Gaussian and broad Gaussian, (ii) a disk line for a Schwarzschild or (iii) a Kerr black hole all describe the observed data equally well."
 Iu order to look for any variations in the streneth of the Έσνα emission. we have also analyzed the observed Felka profiles from the two observations.," In order to look for any variations in the strength of the $\alpha$ emission, we have also analyzed the observed $\alpha$ profiles from the two observations."
 We used both PN and MOS data for this purpose., We used both PN and MOS data for this purpose.
 We fitted combination of a broad and a narrow Gaussian profile to the PN and MOS data jointly for each observation., We fitted a combination of a broad and a narrow Gaussian profile to the PN and MOS data jointly for each observation.
 The 2.510keV contiuuuni was fixed as determined earlier (see Table 1))., The $2.5-10\kev$ continuum was fixed as determined earlier (see Table \ref{tab1}) ).
 The rest-frame line energies of both the narrow and broad components were fixed at 6.1keV., The rest-frame line energies of both the narrow and broad components were fixed at $6.4\kev$.
 The results of these fits are listed in Table 3 for both the observations., The results of these fits are listed in Table \ref{tab3} for both the observations.
 It appears that the streneth of the broad component of the Έσνα line decreased by about a factor of two between the two observations taken six mouths apart. while the narrow conrponeut did not vary significantly.," It appears that the strength of the broad component of the $\alpha$ line decreased by about a factor of two between the two observations taken six months apart, while the narrow component did not vary significantly."
 Under certain conditions. the Compton reflection Cluission can be muportaut even below ~10keV (see section [.2)).," Under certain conditions, the Compton reflection emission can be important even below $\sim 10\kev$ (see section \ref{orig_feka}) )."
 Tf the onset of the reflection compoucut is at 5keV. the presence of a stroug Fe [shell edee at FLkeV inav artificially Πο a broad endssion line feature at ~6.1keV.," If the onset of the reflection component is at $5\kev$, the presence of a strong Fe K-shell edge at $\sim 7.1\kev$ may artificially mimic a broad emission line feature at $\sim 6.4\kev$."
" This artificial""broad liue"" is likely to if the observed continua is flatter andis dominated by usthe COMM ", This artificial “broad line” is likely to arise if the observed continuum is flatter and is dominated by the reflection component.
The 2.5—10keV. photon index of reflection.MCG-5-23-16Buren« derived fro the combined PN data (Ty~ 1.7) is than the average 2.010keV photon index of Sevfert galaxies (<Py>~1.9: Mushotzkv L997))., The $2.5-10\kev$ photon index of MCG-5-23-16 derived from the combined PN data $\Gamma_X \sim 1.7$ ) is flatter than the average $2-10\kev$ photon index of Seyfert galaxies $<\Gamma_X>\sim 1.9$; \citealt{Mushotzky97}) ).
 flatter and strong iron hea line of MCGmoilu6 could thenbe empartly duc to the contribution of a C reflection process in a geometry where the primary N-rav source is partially covered by cold matter e.g. a torus., This flatter spectrum and strong iron $\alpha$ line of MCG-5-23-16 could then be partly due to the contribution of a Compton reflection process in a geometry where the primary X-ray source is partially covered by cold matter e.g. a torus.
 The reflection enission las been detected frou MCG-5-23-16 with observations in L995 (Weaver.Ixrolik.&Pier1998)., The reflection emission has been detected from MCG-5-23-16 with observations in 1995 \citep{WKP98}.
. To test whether the broad feature near 6.1keV could be due to reflection aud ion 1ν-edee absorption of the primary cussion. we have fitted Compton reflection model to the combined PN data inthe 2.5.12keV band.," To test whether the broad feature near $6.4\kev$ could be due to reflection and iron K-edge absorption of the primary emission, we have fitted a Compton reflection model to the combined PN data in the $2.5-12\kev$ band."
" We used the reflection model ""pexrav (Maedziuz&Zdziarski1995) available withXSPEC.", We used the reflection model ” \citep{MZ95} available with.
 This model calculates the reflected spectra from a neutral disk exposed to an exponentially cut-off law spectrum (Maedziarz&Zdziarski1995)., This model calculates the reflected spectrum from a neutral disk exposed to an exponentially cut-off power-law spectrum \citep{MZ95}.
. Since does not cover the expected peak (~810keW) of the reflection component. it is not possible to coustrain all the parameters of the reflection model using data alone.," Since does not cover the expected peak $\sim30-40\kev$ ) of the reflection component, it is not possible to constrain all the parameters of the reflection model using data alone."
 Iustead we fx the cut-off energy of the primary power-law at 200keV. disk inclination at 5Odee. aud the abundance of heavy clements at the solar value.," Instead we fix the cut-off energy of the primary power-law at $200\kev$, disk inclination at $50\deg$, and the abundance of heavy elements at the solar value."
 The free parameters are the photon iudex of the primary power-law. the power-law normalization. and the relativo amount of reflection compared to the directly viewed primary spectrun C2).," The free parameters are the photon index of the primary power-law, the power-law normalization, and the relative amount of reflection compared to the directly viewed primary spectrum $R$ )."
 We also included a warow Caussianu liue model to describe the Felk&o emission., We also included a narrow Gaussian line model to describe the $\alpha$ emission.
 The results of this fit are listed in Table L., The results of this fit are listed in Table \ref{tab4}.
 The best- photon iudex of the incident power-law contiuuun is Ls aud is consistent with the mean photon iudex for Seyfert 1 galaxies., The best-fit photon index of the incident power-law continuum is $\sim1.8$ and is consistent with the mean photon index for Seyfert 1 galaxies.
 The ratio ofthe observed data to he best-fit model is shown in Figure 6.., The ratio ofthe observed data to the best-fit model is shown in Figure \ref{f6}.
" Although the fit ix acceptable (\7,;,=2211 for 269 dof). there is weak excess cussion ucar 6keV suggestive of the possible xesence of a weak broad cussion liue."," Although the fit is acceptable $\chi^2_{min}=224.4$ for $269$ dof), there is weak excess emission near $6\kev$ suggestive of the possible presence of a weak broad emission line."
 To investigate urther. we included au additional Gaussian compoucut in our reflection model aud carried out the fitting.," To investigate further, we included an additional Gaussian component in our reflection model and carried out the fitting."
 This resulted in an nprovonient in the fit (AX?=20.1 at the cost of 2 dof)., This resulted in an improvement in the fit $\Delta \chi^2=20.1$ at the cost of 2 dof).
 This is an improvement at a significance level of 99% according to the maxima likelihood test., This is an improvement at a significance level of $99\%$ according to the maximum likelihood test.
 The best-fit paraicters are listed in Table [.., The best-fit parameters are listed in Table \ref{tab4}.
 The relative normalization of the reflection emission derived from the PN data is much higher than the value of R=0.51Contime inferred from the observations of AIC (Risaliti2002)., The relative normalization of the reflection emission derived from the PN data is much higher than the value of $R=0.54_{-0.17}^{+0.26}$ inferred from the observations of MCG-5-23-16 \citep{Risaliti02}.
. Thüs is due to the excess enission above 10keV which amounts ~20% above 10keV (see Fie. 1))., This is due to the excess emission above $\sim10\kev$ which amounts $\sim20\%$ above $10\kev$ (see Fig. \ref{f1}) ).
 Such a large discrepancy in the reflection emission interred from the PN and Bepposax data could be due to calibration uncertainties., Such a large discrepancy in the reflection emission inferred from the PN and Bepposax data could be due to calibration uncertainties.
 This view is supported by MOS data. albeit lower signal-to-noise. which do not show a clear excess emission above 10keV.," This view is supported by MOS data, albeit lower signal-to-noise, which do not show a clear excess emission above $10\kev$."
 To test the reliabilitv of the excess cussion above 10keV iu the PN data. we have analyzed he EPIC PN spectrum of a well known BL Lac. Mku 121.," To test the reliability of the excess emission above $10\kev$ in the PN data, we have analyzed the EPIC PN spectrum of a well known BL Lac, Mkn 421."
 The BL Lac type ACGNs do not show the Compton reflection component. just a smooth coutimmun.," The BL Lac type AGNs do not show the Compton reflection component, just a smooth continuum."
 Therefore. μον are good targets check the reliability of spectral eatures in other ACN toN-rav spectra.," Therefore, they are good targets to check the reliability of spectral features in other AGN X-ray spectra."
 We retrieved the data correspouding to the observation. of Alku 121 on 1 May 2002 for au exposure time of ~LOks roni the public archive maintained at TEASARC., We retrieved the data corresponding to the observation of Mkn 421 on 4 May 2002 for an exposure time of $\sim40\ks$ from the public archive maintained at HEASARC.
 The data were processed in a similar way as described above for AICC-5-2:-16., The data were processed in a similar way as described above for MCG-5-23-16.
" The source spectruu was extracted from au aunular region with inuer aud outer radii of 10” aud S0"", respectively aud ceutered at the observed source position."," The source spectrum was extracted from an annular region with inner and outer radii of $10\arcsec$ and $80\arcsec$ , respectively and centered at the observed source position."
 Due to the lieh flux of Mku 121. the eveuts from the core of the point spread function were excluded to avoid possible pile-up which results iu artificial hardening of the," Due to the high flux of Mkn 421, the events from the core of the point spread function were excluded to avoid possible pile-up which results in artificial hardening of the"
 In parallel to the structure scaling analysis. clump with the spectral index y in a relatively narrow range between 1.7 to 1.9 (Krameretal..1998:Heithausen1998).," In parallel to the structure scaling analysis, clump with the spectral index $\gamma$ in a relatively narrow range between 1.7 to 1.9 \citep{Kramer, Heithausen98}."
. Stutzkietal.(1998) demonstrated that a clump ensemble with such a mass spectrum and with a power-law mass-size scaling relation results in à cloud image with the A-variance scaling index From these results it is obvious that there is a strong interest in studying the spatial scaling behaviour of observed maps of the interstellar medium via the A-variance analysis., \citet{Stutzki} demonstrated that a clump ensemble with such a mass spectrum and with a power-law mass-size scaling relation results in a cloud image with the $\Delta$ -variance scaling index From these results it is obvious that there is a strong interest in studying the spatial scaling behaviour of observed maps of the interstellar medium via the $\Delta$ -variance analysis.
and repeated the same procedure at the new eyating setting.,and repeated the same procedure at the new grating setting.
 Occasionally. if two or thDree target stars were available nearby ou the sky. we increased the observing effücienev by using the sale tellure staudax for all of them.," Occasionally, if two or three target stars were available nearby on the sky, we increased the observing efficiency by using the same telluric standard for all of them."
 The spectra were reduced using. LRA tasks written specifically for FSpec., The spectra were reduced using $IRAF$ tasks written specifically for FSpec.
 An average of the sky backgrounds taken inunediately before and after cach object was subtracted to remove simauultaneouslv the sky emission lines. aud the dark current and bias level.," An average of the sky backgrounds taken immediately before and after each object was subtracted to remove simultaneously the sky emission lines, and the dark current and bias level."
 Darlk-subtracted iluninated dome flats tale4 atf the same ceutral wavelengths as the science exposures were applied to correct for pixel-to-pixel variations., Dark-subtracted illuminated dome flats taken at the same central wavelengths as the science exposures were applied to correct for pixel-to-pixel variations.
 The known bad pixels were masked out., The known bad pixels were masked out.
 Object Inages were shifted (uxing ceutrok fitting across the confinmun). and median combined to produce a singlea two-dimieusioual spectrum.," Object images were shifted (using centroid fitting across the continuum), and median combined to produce a single two-dimensional spectrum."
 The large uunber of object images allowed us to reject any remaining bad pixels and cosmic rave., The large number of object images allowed us to reject any remaining bad pixels and cosmic rays.
 Onc-dimensional spectra were extracted by fitting a polvnomial of order 3-5 to the coutimmiuu in the two-dimensional image with the JRAF task epall., One-dimensional spectra were extracted by fitting a polynomial of order 3-5 to the continuum in the two-dimensional image with the $IRAF$ task $apall$.
 The spatial width of the extraction apertures weS usually 3-5 pixels. depending on the scale aud the secle.," The spatial width of the extraction apertures was usually 3-5 pixels, depending on the scale and the seeing."
 Iu inuost cases the object spectra were divided bv spectra of solar analog stars observed at tle same πο απ. hen multiplied by the solar spectra. (Livineston&Wallace1991) to remove the effects of the photospheric absorption (Maiolino.Rieke&Ricke 1996).," In most cases the object spectra were divided by spectra of solar analog stars observed at the same airmass, and then multiplied by the solar spectrum \citep{liv91} to remove the effects of the photospheric absorption \citep{mai96}."
. The standard stars were not always exactly C2 chwarts (usually raneing from VV to G3BVV). aud the true shape of the coutim§£n had to be restored by multiphiug the spectra by the ratio of lack bodies with the standard star and solar effective teiiperatures.," The standard stars were not always exactly G2 dwarfs (usually ranging from V to V), and the true shape of the continuum had to be restored by multiplying the spectra by the ratio of black bodies with the standard star and solar effective temperatures."
 Iu the cases we chose nearby A stars for telluric staucdards as an alternative of the solar analogs. we multiplied. by another A star spectrui already corrected for tlic photospheric absorption wi ha VV stir.," In the cases we chose nearby A stars for telluric standards as an alternative of the solar analogs, we multiplied by another A star spectrum, already corrected for the photospheric absorption with a V star."
 If an A type standard was used to correct only a A-baud spectrum. we removed the Drs feature by interactively fitting and sibtractiug a Cassia with the tasksplot.," If an A type standard was used to correct only a $K$ -band spectrum, we removed the $\rm Br\gamma$ feature by interactively fitting and subtracting a Gaussian with the task."
 We carried out the wavelength calibration using ΟΠ airglow lines (Oliva&Origlia1992) complemented if necessary with Ne-EKr lamp spectra., We carried out the wavelength calibration using OH airglow lines \citep{oli92} complemented if necessary with Ne-Kr lamp spectra.
 The spectrum at cach individual setting was divided bv second ox third order polvnonual continuum fits and combined with the rest of he settings to construct a single {111 spectre., The spectrum at each individual setting was divided by second or third order polynomial continuum fits and combined with the rest of the settings to construct a single $HK$ spectrum.
" Finally, we multiplied the spectra wea black )ody with stellar effective temperature correspoudine o the spectra type (Schinidt-haler1982:Straizvs1992)."," Finally, we multiplied the spectrum by a black body with stellar effective temperature corresponding to the spectral type \citep{sch82,str92}."
. Unfortunately. the normalizationprocedure removes the woad vapor absorption features iu he coolest stars but this loss 1s unavoidable )ocase the spectral extent of a single setting is onlv 10750.095ia. and does not provide sufficieu coverage for a reliable estimate of the coutimmun shape.," Unfortunately, the normalization procedure removes the broad vapor absorption features in the coolest stars but this loss is unavoidable because the spectral extent of a single setting is only $0.075-0.095\,\mu$ m and does not provide sufficient coverage for a reliable estimate of the continuum shape."
 Furthermore. im many cases he true continuum shape was distorted bv the inperfect spectral type match of the telluric standards. as discussed above.," Furthermore, in many cases the true continuum shape was distorted by the imperfect spectral type match of the telluric standards, as discussed above."
 The deviation vetween the constructed continui shape aud the real one ds most severe for late M stars. where the nolecular absorption is the strongest.," The deviation between the constructed continuum shape and the real one is most severe for late M stars, where the molecular absorption is the strongest."
 A possible wav fo alleviate this problemi completely is to inpose on our spectra enipirical continui shapes aken from lower resolution spectra (Laucoun&Rocca-Volincranee1992:Lancgon&Wood 2000).," A possible way to alleviate this problem completely is to impose on our spectra empirical continuum shapes taken from lower resolution spectra \citep{lan92,lan00}."
. We inten to explore this avem5 oe1i the future., We intend to explore this avenue in the future.
" The eror analysis of spectra that consist of ""pieces taken at different funes. auk ofteu ou different niehts. is particularly coniplicated because of the large variations of the signal-to-noise ratio (S/N) across the individual spectra."," The error analysis of spectra that consist of “pieces” taken at different times, and often on different nights, is particularly complicated because of the large variations of the signal-to-noise ratio (S/N) across the individual spectra."
 The uucertaünuties are dominated by systematic errors due to: (1) sky cussion and transparency variations with waveleneth. aud (d) temporal changes iu the observing conditions.," The uncertainties are dominated by systematic errors due to: (i) sky emission and transparency variations with wavelength, and (ii) temporal changes in the observing conditions."
" An cxample 1s Given in refFiela.. where the difference between the ""fSiunal spectra of two different TTD stars with near solu auactallicity is shown."," An example is given in \\ref{Fig1a}, where the difference between the “final” spectra of two different III stars with near solar metallicity is shown."
 The cliffercuce A i been divided by the average of the two spectra., The difference $\Delta$ has been divided by the average of the two spectra.
 The inset shows the distribution of ese) differences., The inset shows the distribution of these differences.
 Their average difference <A> is statistically iudistinguishable from zero. and ie value of the standard deviation σ suggests jit each spectirmm has an average S/N50.," Their average difference $<$$\Delta$$>$ is statistically indistinguishable from zero, and the value of the standard deviation $\sigma$ suggests that each spectrum has an average $\sim$ 50."
 At 10 sane time. the photon statistics suggests S/N~1L50.," At the same time, the photon statistics suggests $\sim$ 150."
 The inconsistency is lavecly due to the variation of the sky backeround aud transmission., The inconsistency is largely due to the variation of the sky background and transmission.
mas/yr and pipe.=—15.34+1.2 mas/yr. source 185 ts unlikely to be a member of NGC 752. whose typical proper motion 1s Hea=7.5 mas/yr and up=—11.5 mas/vr.,"mas/yr and $\mu_{\rm Dec}=-15.3 \pm 1.2$ mas/yr, source 185 is unlikely to be a member of NGC 752, whose typical proper motion is $\mu_{\rm RA}= 7.5$ mas/yr and $\mu_{\rm Dec}= -11.5$ mas/yr."
 No counterpart is found for the fainter source 182 in the studies of NGC 752. however. its counterpart in the catalogue has pra=8.2+9.0 mas/yr and fips.=—88.5+9.0 mas/yr. implying that also this star is very unlikely to be a member of the cluster.," No counterpart is found for the fainter source 182 in the studies of NGC 752, however, its counterpart in the catalogue has $\mu_{\rm RA}=8.2 \pm 9.0$ mas/yr and $\mu_{\rm Dec}=-88.5 \pm 9.0$ mas/yr, implying that also this star is very unlikely to be a member of the cluster."
 Away from the Galactic plane. the 2MASS Point Source Catalogue (PSC) is complete down to K=14.3 mag. in the absence of confusion. which corresponds to M.~0.45Me for this cluster.," Away from the Galactic plane, the 2MASS Point Source Catalogue (PSC) is complete down to $K = 14.3$ mag, in the absence of confusion, which corresponds to $M \sim 0.45~M_{\sun}$ for this cluster."
 Nevertheless. for K«12.5 that is M>0.8Mo. cross-matching with the 2MASS catalogue allowed only one extra X-ray source to be identified with respect to the studies by DLM94 and Platais(1991) (source 182). and. in particular. no potential new cluster member was identified with respect to DLM?94.," Nevertheless, for $K < 12.5$ that is $M \ge 0.8~M_{\sun}$, cross-matching with the 2MASS catalogue allowed only one extra X-ray source to be identified with respect to the studies by DLM94 and \cite{platais91} (source 182), and, in particular, no potential new cluster member was identified with respect to DLM94."
 The sensitivity of the ddata does not appear to be the limiting factor in identifying new potential members with M.»0.8Mo; within 2MASS. since the X-ray detection rate of cluster members is around for this mass range.," The sensitivity of the data does not appear to be the limiting factor in identifying new potential members with $M > 0.8~M_{\sun}$ within 2MASS, since the X-ray detection rate of cluster members is around for this mass range."
 This indicates that the list by DLM94 is à complete census of cluster members within the FFOV. for M>0.8Mc. and confirms the cluster to be deficient in solar-mass starswith respect to the number of more massive members.," This indicates that the list by DLM94 is a complete census of cluster members within the FOV, for $M >
0.8~M_{\sun}$, and confirms the cluster to be deficient in solar-mass starswith respect to the number of more massive members."
 In the CMD of reffig:colmagIR.— (right. panel). one can also see 11 objects fainter than K=12.5. not too far displaced from the isochrones and thus with colours compatible with being members of the cluster (Ids 21. 24. 35. 44. 87. 107. 136. 151. 223. 245. and 246).," In the CMD of \\ref{fig:colmagIR} (right panel), one can also see 11 objects fainter than $K=12.5$, not too far displaced from the isochrones and thus with colours compatible with being members of the cluster (Ids 21, 24, 35, 44, 87, 107, 136, 151, 223, 245, and 246)."
 To establish whether these sources could be possible members of the cluster we checked their proper motion in the catalogue., To establish whether these sources could be possible members of the cluster we checked their proper motion in the catalogue.
 Only sources 21. 44. 107. 136. 223. and 246 have proper motion values compatible (within 4r) with membership of NGC 752.," Only sources 21, 44, 107, 136, 223, and 246 have proper motion values compatible (within $\sigma$ ) with membership of NGC 752."
 There is 10 counterpart in for source 87 (within 3 aresec)., There is no counterpart in for source 87 (within 3 arcsec).
" In the CMD of reffig:colmagIRxmm.. there are 9 objects not too far displaced from the isochrones ssources ids: 2. 5. 11. 35. 58. 65. 95. 121. and 127). but only 2, 35. 58 and 127 have proper motion compatible with cluster membership."," In the CMD of \\ref{fig:colmagIRxmm}, there are 9 objects not too far displaced from the isochrones sources ids: 2, 5, 11, 35, 58, 65, 95, 121, and 127), but only 2, 35, 58 and 127 have proper motion compatible with cluster membership."
 Of the ssources with a 2MASS counterpart 12 have enough source counts across the entire bbandwidth for their spectra to be analysed (count rate > 0.3 ks! )., Of the sources with a 2MASS counterpart 12 have enough source counts across the entire bandwidth for their spectra to be analysed (count rate $>$ 0.3 ${\rm ks}^{-1}$ ).
 The results of the spectral and timing analysis for these 12 ssourees are presented in reftab:psfit.. with the possible or likely members of the cluster in the first half of the Table.," The results of the spectral and timing analysis for these 12 sources are presented in \\ref{tab:psfit}, with the possible or likely members of the cluster in the first half of the Table."
 We inspected the light curve of all these sources and performed a Kolmogorov-Smirnov test. which measures the maximum deviation of the integral photon arrival times from a constant source model.," We inspected the light curve of all these sources and performed a Kolmogorov-Smirnov test, which measures the maximum deviation of the integral photon arrival times from a constant source model."
 The results. in terms of constaney probability. are also given in the Table.," The results, in terms of constancy probability, are also given in the Table."
 All the spectral fits were performed using an absorbed one-temperature plasma model., All the spectral fits were performed using an absorbed one-temperature plasma model.
 Initially. we performed the fits with N(H) as a free parameter.," Initially, we performed the fits with $N({\rm H})$ as a free parameter."
 All 12. fits. however. resulted in an essentially unconstrained value for the absorbing column densities. so the fits were repeated fixing N(H) to its optically determined value of 2x10-°em7*.," All 12 fits, however, resulted in an essentially unconstrained value for the absorbing column densities, so the fits were repeated fixing $N({\rm H})$ to its optically determined value of $2 \times
10^{20}{\rm cm}^{-2}$."
 The inability to tightly constrain the value of NCH) with these ACIS-I data is not unexpected. since the instrument’s energy band extends only to 0.2 keV at the low energies. and the values of N(H) here are rather low.," The inability to tightly constrain the value of $N({\rm H})$ with these ACIS-I data is not unexpected, since the instrument's energy band extends only to 0.2 keV at the low energies, and the values of $N({\rm
H})$ here are rather low."
 As shown in reftab:psfit.. all the four established cluster members have temperature AT around 0.5 — 0.7 keV; indeed. all the sources except 180 and 223 have a similar (relatively) low plasma temperature. consistent with being stellar sources.," As shown in \\ref{tab:psfit}, all the four established cluster members have temperature $kT$ around 0.5 $-$ 0.7 keV; indeed, all the sources except 180 and 223 have a similar (relatively) low plasma temperature, consistent with being stellar sources."
 Source 223 has AT=1.9 keV. however. this source underwent a strong flare during the observation: its count rate increased impulsively by more than a factor of 30 and then decreased exponentially over 18 ks.," Source 223 has $kT = 1.9$ keV, however, this source underwent a strong flare during the observation: its count rate increased impulsively by more than a factor of 30 and then decreased exponentially over 18 ks."
 A spectral fit to the source data during the quiescent time yields AT=0.6+0.2 keV. similar to the value of the other sources.," A spectral fit to the source data during the quiescent time yields $kT = 0.6 \pm 0.2$ keV, similar to the value of the other sources."
 The spectrum of source 180 is too hard for a normal star. thus this source is very likely a background AGN.," The spectrum of source 180 is too hard for a normal star, thus this source is very likely a background AGN."
 Indeed its spectrum can be equally well fitted with an absorbed power law with a spectral index y=1.9+0.1 (null-hypothesis probability P= 0.96)., Indeed its spectrum can be equally well fitted with an absorbed power law with a spectral index $\gamma = 1.9 \pm 0.1$ (null-hypothesis probability $P=0.96$ ).
 Its 2MASS colours are consistent with this source being in the background., Its 2MASS colours are consistent with this source being in the background.
 Source 185 underwent a flare at about 30 ks from the start of the observations: during the flare. the source's count rate increased by a factor ~5.," Source 185 underwent a flare at about 30 ks from the start of the observations; during the flare, the source's count rate increased by a factor $\sim 5$."
 The spectrum of this source integrated over the entire exposure is not well modeled by an absorbed one-temperature plasma model., The spectrum of this source integrated over the entire exposure is not well modeled by an absorbed one-temperature plasma model.
 We subdivided the spectral data for this source in two time intervals. one during the flare and one during the star's quiescent activity.," We subdivided the spectral data for this source in two time intervals, one during the flare and one during the star's quiescent activity."
" During the quiescent phase the spectrum is well fitted (P= 0.14) by an absorbed two-temperature model with «Τι=0.35+0.04 keV. KT;=0.97+0.05 keV. EM,=0.7xI07 cm. EM:=0.53x10? em7. and Z=0.22+0.05Zo: the value of N(H) is also in this case not well constrained: (0.0+0.7)x107em7?.."," During the quiescent phase the spectrum is well fitted $P = 0.14$ ) by an absorbed two-temperature model with $kT_1 =
0.35 \pm 0.04$ keV, $kT_2=0.97\pm 0.05$ keV, $EM_1=0.7 \times
10^{52}$ $^{-3}$, $EM_2=0.53\times 10^{52}$ $^{-3}$, and $Z=0.22
\pm 0.05 Z_{\sun}$; the value of $N({\rm H})$ is also in this case not well constrained: $(0.0 \pm 0.7) \times 10^{20}$."
 During the flare. the value of NOH). ΤΙ. ΕΛΠ. and Z remain essentially unchanged. but «Τὸ increases to 1.920.2 and EM? to 1.3x107 em? (null-hypothesis probability of the fit P= 0.35).," During the flare, the value of $N({\rm H})$, $kT_1$, $EM_1$, and $Z$ remain essentially unchanged, but $kT_2$ increases to $1.9 \pm 0.2$ and $EM_2$ to $1.3 \times 10^{52}$ $^{-3}$ (null-hypothesis probability of the fit $P = 0.35$ )."
" In reftab:xmm,s Fittheresultsof thespectralanalysisforXMM ssourceswitha2MASS counter partandacountrategreaterthan| Scts/ksa", In \\ref{tab:xmm_psfit} the results of the spectral analysis for sources with a 2MASS counterpart and a count rate greater than 1.5 cts/ks are presented (these are also 12 sources).
i aandX d," For each source, the fit was performed jointly to PN, MOS1, and MOS2 spectral data."
dataareavailable. thebest fitvalue sof the plasmatemperatureandtheent: ," As in the table, for the stellar sources for which both and data are available, the best fit values of the plasma temperature and the emission measure are in good agreement between the two data sets."
The typical value of the plasma temperature for the possible or likely members of NGC 752 ts 0.7 keV. This value is similar to the plasma temperatures derived for members of the (0.8 Gyr old) Hyades cluster and somewhat lower than the typical plasma temperature for the much younger Pleiades ( 0.08 Gyr)., The typical value of the plasma temperature for the possible or likely members of NGC 752 is 0.7 keV. This value is similar to the plasma temperatures derived for members of the (0.8 Gyr old) Hyades cluster and somewhat lower than the typical plasma temperature for the much younger Pleiades $\sim$ 0.08 Gyr).
 Sternetal.(1994) report the results of 2T temperaturefits to the spectral data of 1] members of the Hyades., \cite{ssp+94} report the results of 2T temperaturefits to the spectral data of 11 members of the Hyades.
 The, The
"The galaxy luminosity finelion (P) remains at the core of both galaxy evolution and cosmology,",The galaxy luminosity function $\Phi$ ) remains at the core of both galaxy evolution and cosmology.
 By integrating ᾧ over space and time. various observable distributions can be obtained.," By integrating $\Phi$ over space and time, various observable distributions can be obtained."
 In particular. differential number counts of galaxies as a function of apparent," In particular, differential number counts of galaxies as a function of apparent"
and evolution.,and evolution.
" Observationally, probing the inner profiles of dark matter halos with rotation curve data is difficult due to the disk-halo degeneracy (e.g.,??).."," Observationally, probing the inner profiles of dark matter halos with rotation curve data is difficult due to the disk-halo degeneracy \citep[e.g.,][]{vanAlbadaSancisi86, Dutton++05}."
" Since the rotation curve primarily depends on the enclosed mass within spherical radii, a heavy disk with a light halo and a light disk with a heavy halo can both be fit to the rotation curve."," Since the rotation curve primarily depends on the enclosed mass within spherical radii, a heavy disk with a light halo and a light disk with a heavy halo can both be fit to the rotation curve."
" The degeneracy is prominent in models where the disk and halos have fixed parametric forms, and is reduced in self-consistent models where the halo shape changes in response to the presence of the disk (?).."," The degeneracy is prominent in models where the disk and halos have fixed parametric forms, and is reduced in self-consistent models where the halo shape changes in response to the presence of the disk \citep{AmoriscoBertin10}."
" To circumvent the disk-halo degeneracy, some studies have assumed that the disk contributes maximally to the circular velocity."," To circumvent the disk-halo degeneracy, some studies have assumed that the disk contributes maximally to the circular velocity."
" However, studies based on the Tully-Fisher relation or the central vertical velocity dispersion of disk stars have shown that disks tend to be submaximal (e.g.,???).."," However, studies based on the Tully-Fisher relation or the central vertical velocity dispersion of disk stars have shown that disks tend to be submaximal \citep[e.g.,][]{CourteauRix99, Bottema93, Bershady++11}."
" To break the disk-halo degeneracy without resorting to maximal-disk assumptions, one needs to measure independently the relative mass contribution of the disk and the dark matter halo, or equivalently, the mass-to-light ratio (M/L) of the disk."," To break the disk-halo degeneracy without resorting to maximal-disk assumptions, one needs to measure independently the relative mass contribution of the disk and the dark matter halo, or equivalently, the mass-to-light ratio $M/L$ ) of the disk."
 Stellar population synthesis (SPS) models allows estimations of the stellar mass and hence the M/L of the disk., Stellar population synthesis (SPS) models allows estimations of the stellar mass and hence the $M/L$ of the disk.
" However, uncertainties in the stellar mass due to, for example, the unknown stellar initial mass function (IMF), limits the accuracy of this approach (e.g.,?).."," However, uncertainties in the stellar mass due to, for example, the unknown stellar initial mass function (IMF), limits the accuracy of this approach \citep[e.g.,][]{Conroy++09}."
" Therefore, disentangling the contributions of the disk and the halo to the rotation curve is key in understanding both the inner halo profile and the stellar IMF."," Therefore, disentangling the contributions of the disk and the halo to the rotation curve is key in understanding both the inner halo profile and the stellar IMF."
 An effective way to overcome the disk-halo degeneracy is to combine rotation curves with strong gravitational lensing., An effective way to overcome the disk-halo degeneracy is to combine rotation curves with strong gravitational lensing.
" If a spiral galaxy lies along the line of sight between the observer and a background source, the source can be strongly lensed into multiple images by the spiral galaxy (e.g.,"," If a spiral galaxy lies along the line of sight between the observer and a background source, the source can be strongly lensed into multiple images by the spiral galaxy \citep[e.g.,][]{Treu10}."
" While kinematics probe mass within spheres, strong ?)..lensing probes mass enclosed within cylinders (within the “Einstein radius”, which is roughly the radial distance of the multiple images from the lens galaxy "," While kinematics probe mass within spheres, strong lensing probes mass enclosed within cylinders (within the “Einstein radius”, which is roughly the radial distance of the multiple images from the lens galaxy center)."
The combination of the two methods with different center).mass dependence breaks the disk-halo degeneracy., The combination of the two methods with different mass dependence breaks the disk-halo degeneracy.
" Spectroscopic and imaging surveys in recent years have substantially enlarged the sample of spiral lenses, totaling more than 20 now (e.g., T"," Spectroscopic and imaging surveys in recent years have substantially enlarged the sample of spiral lenses, totaling more than $20$ now \citep[e.g.,][]{Feron++09, Sygnet++10, Treu++11}."
he first few analyses of spiral lenses are already ???)..informing us about disk-maximality and the stellar IMFs in these ," The first few analyses of spiral lenses are already informing us about disk-maximality and the stellar IMFs in these systems \citep[e.g.,][]{Koopmans++98,
 Maller++00, Trott++10, Dutton++11}. ."
"In this paper, we studyB1933+503,, a spiral gravitational lens at z;=0.755 with 10 radio lensed images that was discovered by ? in the Cosmic Lens All-Sky Survey (CLASS;??).."," In this paper, we study, a spiral gravitational lens at $z_{\rm l}=0.755$ with 10 radio lensed images that was discovered by \citet{Sykes++98} in the Cosmic Lens All-Sky Survey \citep[CLASS;][]{Myers++03, Browne++03}."
 Previous modeling of the radio data by ? tested power-law models for the combined dark and baryonic mass distribution of the lens., Previous modeling of the radio data by \citet{Cohn++01} tested power-law models for the combined dark and baryonic mass distribution of the lens.
" Here, we obtain new radio, infrared and spectroscopic observations, and construct a 3-component mass model (for the disk, bulge and dark matter halo) that is simultaneously fitted to both the kinematics and lensing data."," Here, we obtain new radio, infrared and spectroscopic observations, and construct a 3-component mass model (for the disk, bulge and dark matter halo) that is simultaneously fitted to both the kinematics and lensing data."
" The analysis is very similar in spirit to the one presented by ? on the lens JJ2141—0001, except we use an NFW instead of an isothermal profile to describe the dark matter halo."," The analysis is very similar in spirit to the one presented by \citet{Dutton++11} on the lens $-$ 0001, except we use an NFW instead of an isothermal profile to describe the dark matter halo."
" The aims of our study are (1) measure the inner shape and profile of the dark matter halo, determine the relative contributions of the disk, bulge (2)and halo, and (3) place constraints on the stellar IMF."," The aims of our study are (1) measure the inner shape and profile of the dark matter halo, (2) determine the relative contributions of the disk, bulge and halo, and (3) place constraints on the stellar IMF."
 The paper is organized as follows., The paper is organized as follows.
" In Section 2, we present observations of the radio lensB19334-503."," In Section \ref{sec:obs}, we present observations of the radio lens."
". The alignment of the radio and near-infrared images is described in Section 3,, and the lens light profile in the near-infrared image is measured in Section 4.."," The alignment of the radio and near-infrared images is described in Section \ref{sec:align}, and the lens light profile in the near-infrared image is measured in Section \ref{sec:lenslight}."
" The 3-component mass model is outlined in Section 5,, and the statistical framework for the analysis is described in Section 6.."," The 3-component mass model is outlined in Section \ref{sec:mass-model}, and the statistical framework for the analysis is described in Section \ref{sec:Bayes}."
" We present the kinematics-only and lensing- results in Sections 7 and 8,, respectively."," We present the kinematics-only and lensing-only results in Sections \ref{sec:kinematics}
 and \ref{sec:lensing}, respectively."
" We discuss the results and implications of the joint kinematics and lensing analysis in Section 9,, before concluding in Section 10.."," We discuss the results and implications of the joint kinematics and lensing analysis in Section \ref{sec:L+D}, before concluding in Section \ref{sec:conclude}."
" Throughout the paper, we assume a flat A-CDM cosmology with Ho=70kms~!Mpc7!, Q4—1—=0.73."," Throughout the paper, we assume a flat $\Lambda$ -CDM cosmology with $H_0=70\,{\rm km\,s^{-1}\,Mpc^{-1}}$, $\Omega_{\Lambda}=1-\Omega_{\rm m}=0.73$ ."
" In this cosmology, 1"" corresponds to 7.5kpc at the lens redshift and 8.7kpc at the source redshift, which is measured in Section 2.5.."," In this cosmology, $1''$ corresponds to $7.5\kpc$ at the lens redshift and $8.7\kpc$ at the source redshift, which is measured in Section \ref{sec:obs:spec:z}."
 Images of the lens system are north up and east left., Images of the lens system are north up and east left.
 Parameter constraints are given as the median values with uncertainties given by the 16th and 84th percentiles to credible intervals (CI)) unless otherwise(corresponding stated., Parameter constraints are given as the median values with uncertainties given by the 16th and 84th percentiles (corresponding to credible intervals (CI)) unless otherwise stated.
 We obtained both lensing and kinematic observations of ffor constraining the lens mass distribution., We obtained both lensing and kinematic observations of for constraining the lens mass distribution.
" We present the global VLBI observations of the lensed radio source in Section 2.1,, near-infrared imaging of the lens system in Sections 2.2 and 2.3,, and spectroscopic data sets for obtaining the rotation curve of the lens galaxy and the source redshift in Sections 2.4 and 2.5.."," We present the global VLBI observations of the lensed radio source in Section \ref{sec:obs:radio}, , near-infrared imaging of the lens system in Sections \ref{sec:obs:AO} and \ref{sec:obs:nirc}, and spectroscopic data sets for obtaining the rotation curve of the lens galaxy and the source redshift in Sections \ref{sec:obs:spec:ESI} and \ref{sec:obs:spec:z}."
 We describe the archival (HST)) images in Section 2.6.., We describe the archival ) images in Section \ref{sec:obs:HST}.
 We observed wwith the global Very Long Baseline Interferometry array on 1998 November 27 at GGHz with a (VLBI)bandwidth of MMHz., We observed with the global Very Long Baseline Interferometry (VLBI) array on 1998 November 27 at GHz with a bandwidth of MHz.
 We used 17 telescopes with 10 from the Very Long Baseline Array (VLBA) and 7 from the European VLBI Network (EVN)., We used 17 telescopes with 10 from the Very Long Baseline Array (VLBA) and 7 from the European VLBI Network (EVN).
 We adopt the center of component 4 of the lensed images as the phase center for the observations., We adopt the center of component 4 of the lensed images as the phase center for the observations.
" Observations were conducted on a cycle of 6.5 minutes, with 1.5 minutes on a phase calibrator (B19544-51—J19554-5131) followed by 5 minutes on the target sourceB1933--503."," Observations were conducted on a cycle of 6.5 minutes, with 1.5 minutes on a phase calibrator $+$ $+$ 5131) followed by 5 minutes on the target source."
". T'he exception was the Lovell telescope, which has a slower slew rate and for which every other observation of the phase calibrator was omitted, yielding a 1.5-minute+11.5-minute cycle on the phase reference and target."," The exception was the Lovell telescope, which has a slower slew rate and for which every other observation of the phase calibrator was omitted, yielding a $+$ 11.5-minute cycle on the phase reference and target."
" The total observing time was 9 hours, providing the good u-v coverage required for high dynamic range imaging and image fidelity."," The total observing time was 9 hours, providing the good $u$ $v$ coverage required for high dynamic range imaging and image fidelity."
 A single observation of 3C345 was obtained for fringe finding and flux calibration., A single observation of 3C345 was obtained for fringe finding and flux calibration.
 We reduce the data with theAstronomical Image Processing System (AIPS!4)) package using standard procedures., We reduce the data with theAstronomical Image Processing System ) package using standard procedures.
" The images are iteratively CLEANed and self-calibrated (phase-only), before a single amplitude self-calibration solution is performed, to removeresidual phase and amplitude errors."," The images are iteratively CLEANed and self-calibrated (phase-only), before a single amplitude self-calibration solution is performed, to removeresidual phase and amplitude errors."
 The final maps are produced using natural-weighting of the visibilities and with a 10, The final maps are produced using natural-weighting of the visibilities and with a 10
∙⊥⊐ ∙ ∙⊺≺≻↕≺∏∐⋅↑∐∪↥⋅≼∐∖↥⋅↕∐∫⋮⋝↑∐↸∖∐⋜⋯∐↕↑∪↕∐⋜⋯↴⋝↸∖≼⊳∪⋯↸∖↴∖↴ which is independent of 05 so that £4 is a conserved quautity aud we find that we have successfully transtered the ILuniltonian iuto action angle variables.,To fourth order in $I_3^{1/2}$ the Hamiltonian becomes which is independent of $\theta_3$ so that $I_3$ is a conserved quantity and we find that we have successfully transfered the Hamiltonian into action angle variables.
 Via a similar canonical trausforiiation the tei) proportional to (rDe):oc du EquationB (5))5 disappears+ but the term proportional. to οτς2.02 remains: vielding: the additional∙∙ term (#723093)opitaη which: we have included: im: Equ. (7))., Via a similar canonical transformation the term proportional to $(r-r_c ) z^2$ in Equation \ref{Hz}) ) disappears but the term proportional to $(r - r_c)^2 z^2$ remains yielding the additional term $ (\kappa^2 - 3\Omega^2) {\nu I_1 I_3 \over 4\kappa }$ which we have included in Eqn. \ref{Hz_can}) ).
 Via a similar canonical trausforiiation the tei) proportional to (rDe):oc du EquationB (5))5 disappears+ but the term proportional. to οτς2.02 remains: vielding: the additional∙∙ term (#723093)opitaη which: we have included: im: Equ. (7)).-, Via a similar canonical transformation the term proportional to $(r-r_c ) z^2$ in Equation \ref{Hz}) ) disappears but the term proportional to $(r - r_c)^2 z^2$ remains yielding the additional term $ (\kappa^2 - 3\Omega^2) {\nu I_1 I_3 \over 4\kappa }$ which we have included in Eqn. \ref{Hz_can}) ).
between intrinsic radio core luminosity and Kinetic. luminosity given by Eq. (55).,between intrinsic radio core luminosity and kinetic luminosity given by Eq. \ref{eq:lkin_int}) ).
 In order to do that we have assumed distribution distances. black hole masses radio and X-ray core flux limits that closely resemble the observed ones.," In order to do that we have assumed distribution distances, black hole masses radio and X-ray core flux limits that closely resemble the observed ones."
" We then Doppler-boost the intrinsic radio core luminosity picking E from a normal distribution with mean DL, and variance ep= 0.1L.", We then Doppler-boost the intrinsic radio core luminosity picking $\Gamma$ from a normal distribution with mean $\Gamma_{\rm m}$ and variance $\sigma_{\Gamma}=0.1\Gamma_{\rm m}$ .
" Fits of the ντ {νεο correlation for the LO! simulated samples result in a distribution of slopes Bon. as a function of Py, (shaded areas in the lower panels figure 3))."," Fits of the $L_{\rm kin}$ $L_{\rm R,obs}$ correlation for the $10^4$ simulated samples result in a distribution of slopes $B_{\rm obs}$ as a function of $\Gamma_{\rm m}$ (shaded areas in the lower panels figure \ref{fig:bobs}) )."
 We can now assess the probability of observing Bor.=(0.54+0.09) for any value of Εμ. by simply integrating these (properly normalized) distributions in the range 0.544-0.09.," We can now assess the probability of observing $B_{\rm obs}=(0.54 \pm 0.09)$ for any value of $\Gamma_{\rm m}$, by simply integrating these (properly normalized) distributions in the range $\pm$ 0.09."
 The result of such an integration is shown in the upper panel of Figure 3.., The result of such an integration is shown in the upper panel of Figure \ref{fig:bobs}.
 The distribution of the simulated sources in the LposLn vs. Lian plane shows tantalizing evidence of a discrepancy with the observed sample. with a slight deticit of luminous. de-boosted (i.e. seen at large angles with respect to the line of sight) objects.," The distribution of the simulated sources in the $L_{\rm R,obs}/L_{\rm
R}$ vs. $L_{\rm kin}$ plane shows tantalizing evidence of a discrepancy with the observed sample, with a slight deficit of luminous, de-boosted (i.e. seen at large angles with respect to the line of sight) objects."
" Statistically. we found that this diserepaney mainly effects the normalization of the intrinsic Lyy,-L relation. rather than its slope."," Statistically, we found that this discrepancy mainly effects the normalization of the intrinsic $L_{\rm
kin}$ $L_{\rm R}$ relation, rather than its slope."
 The reason for such a discrepancy is not clear at this point. but we believe it may signal a problem in the modellization of the selection criteria of the sample. rather than a problem with the FP scaling.," The reason for such a discrepancy is not clear at this point, but we believe it may signal a problem in the modellization of the selection criteria of the sample, rather than a problem with the FP scaling."
 This is by no means surprising. in particular given the lack of any realistic constraint on the distribution and selection functions of the kinetic power measurements.," This is by no means surprising, in particular given the lack of any realistic constraint on the distribution and selection functions of the kinetic power measurements."
 From this Monte Carlo test. we can reach the following conclusions: Interestingly. the relationship between kinetic power and radio luminosity gets tighter if one uses the FP relation as an estimator of the un-boosted radio flux. as shown in Figure 4: the intrinsic scatter is reduced from 0.47 dex to 0.37 dex.," From this Monte Carlo test, we can reach the following conclusions: Interestingly, the relationship between kinetic power and radio luminosity gets tighter if one uses the FP relation as an estimator of the un-boosted radio flux, as shown in Figure \ref{fig:pboth}: the intrinsic scatter is reduced from 0.47 dex to 0.37 dex."
 This is expected if this steeper correlation reflects more directly the intrinsic relation between jet kinetic and radiative power. and lends support to our statistical method to correct for the bias induced by relativistic beaming.," This is expected if this steeper correlation reflects more directly the intrinsic relation between jet kinetic and radiative power, and lends support to our statistical method to correct for the bias induced by relativistic beaming."
 Finally. we note that the slope of the correlation between Lyyp and Lj isconsistent with the predictions of synchrotron models for the flat spectrum jet cores according to which," Finally, we note that the slope of the correlation between $L_{\rm R,FP}$ and $L_{\rm kin}$ isconsistent with the predictions of synchrotron models for the flat spectrum jet cores according to which"
emission in the two transitions are shown in Figure 10..,emission in the two transitions are shown in Figure \ref{nh3masers}.
 We also detect maser emission at this position. as detailed in Fable 2. and shown in Figure 6..," We also detect maser emission at this position, as detailed in Table \ref{330masers} and shown in Figure \ref{spectra}."
 However. we note that he emission of the NIL; transitions at approximately is on the edge of the extent of the maser emission and about ollset from the strongest maser spot.," However, we note that the emission of the $_3$ transitions at approximately is on the edge of the extent of the maser emission and about offset from the strongest maser spot."
 We cannot confirm that these two emission lines are due o masers with the current data. but the fact that the lines are tvpically narrow (1.5 and for (11.9) and (8.6). respectively) and that these ransitions have only been previously detected: as masers. suggests that a maser origin is more likely than a thermal origin.," We cannot confirm that these two emission lines are due to masers with the current data, but the fact that the lines are typically narrow (1.5 and for (11,9) and (8,6), respectively) and that these transitions have only been previously detected as masers, suggests that a maser origin is more likely than a thermal origin."
 €119.61-0.23 is a well known region of high mass star ormation in the Galaxy. containing OLL (Caswell1983) and ΟΙ masers (Caswelletal.1995:Walshetal. 1998)... including therare ClIz ΟΙ maser (Voronkovetal.2010).. cold. dust. continuum emission (Walshctal.2003:Thompson2006).. molecular line emission (Santangeloetal.2010) and multiple ultracompact (UC) regions (Garayetal.1998).," G19.61-0.23 is a well known region of high mass star formation in the Galaxy, containing OH \citep{caswellandhaynes83} and $_3$ OH masers \citep{caswell95,walsh98}, including therare GHz $_3$ OH maser \citep{voronkov10}, cold dust continuum emission \citep{walsh03,thompson06}, molecular line emission \citep{santangelo10} and multiple ultracompact (UC) regions \citep{garay98}."
 IxXolpaketal.(2003) determine a distance to C19.61-0.23 of kkpe.. based on observations.," \citet{kolpak03}
 determine a distance to G19.61-0.23 of kpc, based on observations."
" It is surprising that one of only two known sources of emission in these NLL, lines is at such a arge distance.", It is surprising that one of only two known sources of emission in these $_3$ lines is at such a large distance.
 This suggests G19.61-0.23 may be an unusual region of maser activity in the Galaxy otherwise we would expect to detect other maser sites closer to us., This suggests G19.61-0.23 may be an unusual region of maser activity in the Galaxy otherwise we would expect to detect other maser sites closer to us.
 Garayctal.(1998) concluded that in this region an ionisation front is driven bv an expanding region into a molecular cloud., \citet{garay98} concluded that in this region an ionisation front is driven by an expanding region into a molecular cloud.
 ‘Together with the presence of the rare CIIz ΟΙ maser. which is known to trace strong shocks. it is possible that the NIL; masers are createcd in the shock interface between region and molecular cloud.," Together with the presence of the rare GHz $_3$ OH maser, which is known to trace strong shocks, it is possible that the $_3$ masers are created in the shock interface between region and molecular cloud."
 We finc widespread thermal NIL; (3.3) emission throughout the LLOPS region.," We find widespread thermal $_3$ (3,3) emission throughout the HOPS region."
 However. here we report on the possible detection of a maser in this transition.," However, here we report on the possible detection of a maser in this transition."
 The possible maser is located: at. G23.33-0.30., The possible maser is located at G23.33-0.30.
 The spectra of NIL; (1.1). (2.2) ancl (3.3) emission at the position of C123.33-0.30 are shown in Figure 11..," The spectra of $_3$ (1,1), (2,2) and (3,3) emission at the position of G23.33-0.30 are shown in Figure \ref{nh333}."
 We suspect that the narrow-Iined emission peak at ds a maser because this feature is not seen in either of he (1.1)or (2.2) spectra.," We suspect that the narrow-lined emission peak at is a maser because this feature is not seen in either of the (1,1)or (2,2) spectra."
 I also shows an unusually narrow ine F'WILM ofkms. je.," It also shows an unusually narrow line FWHM of, ie."
 much narrower than the tvpical (1.1) and (2.2) hermal linewidths (Longmoreetal.2007).," much narrower than the typical (1,1) and (2,2) thermal linewidths \citep{longmore07}."
 We await urther. observations to confirm. or otherwise. the maser nature of this emission. feature. as it is not possible to conclude given the current data.," We await further observations to confirm, or otherwise, the maser nature of this emission feature, as it is not possible to conclude given the current data."
 The NIL; (3.3) transitionms previously been detected. as a maser in 221COLLD (Mangum&Wooten 1994).. W51 (Zhang&Lo 1995).. 1E Csracmer&Jackson1995) and €15.89-0.39 (Llunteretal. 2008)..," The $_3$ (3,3) transitionhas previously been detected as a maser in 21(OH) \citep{mangum94}, , W51 \citep{zhang95}, , I \citep{kraemer95} and G5.89-0.39 \citep{hunter08}. ."
 Llowever. in all previous detections. the," However, in all previous detections, the"
obtained by direct integration: II qxzs. lor p2» pu. where r=min(q.s).,"obtained by direct integration: If $q\ne s$, for $p\gg p_{\rm inj}$ , where $r=\min(q,s)$."
 That is. if (he spectral slope of pre-existing CRs is softer (han the Lest-particle slope (s> q). the re-accelerated CR spectrum gets flattened to p* by DSA: in the opposite case (s <q). the re-accelerated CR. spectrum is simply amplifiecl by the factor ol q/(q—s) and retains the same slope as the slope of pre-existing CRs.," That is, if the spectral slope of pre-existing CRs is softer than the test-particle slope $s>q$ ), the re-accelerated CR spectrum gets flattened to $p^{-q}$ by DSA; in the opposite case $s<q$ ), the re-accelerated CR spectrum is simply amplified by the factor of $q/(q-s)$ and retains the same slope as the slope of pre-existing CRs."
 Figure 2 shows (he re-accelerated CW distribution given in Equation (7)) for a M=3 shock in the presence of (he pre-existing power-law CR spectrum with the slope s=4 and 4.5 Gight panel) and s=5 (left panel)., Figure 2 shows the re-accelerated CR distribution given in Equation \ref{f2p}) ) for a $M=3$ shock in the presence of the pre-existing power-law CR spectrum with the slope $s= 4$ and 4.5 (right panel) and $s=5$ (left panel).
 The Allvénnie drift is ignored (0=0). so the test-particle slope is q=4.5.," The Alfvénnic drift is ignored $\delta=0$ ), so the test-particle slope is $q=4.5$."
" Here. we adopted the following parameters: the upstream eas temperature Ti,=10* IX and the injection parameter ej;=0.25. resulting in Di=8.0XxLO?mye (see the next subsection lor details of our injection mocdel)."," Here, we adopted the following parameters: the upstream gas temperature $T_0 = 10^7$ K and the injection parameter $\epsilon_B = 0.25$, resulting in $p_{\rm inj} = 8.0 \times 10^{-3} m_p c$ (see the next subsection for details of our injection model)."
" The figure illustrates that [orp2 pi. tbe CR amplification factor. f5(p)/fo(p). approaches a constant. q/(q—5)= 9.in the case of s=4. increases as In(p/piy) in Lhe case of q=s4.5. and scales as (p/pig."" in the case of s—5."," The figure illustrates that for $p\gg p_{\rm inj}$ , the CR amplification factor, $f_2(p)/f_0(p)$, approaches a constant, $q/(q-s)=9$, in the case of $s=4$, increases as $\ln(p/p_{\rm inj})$ in the case of $q=s=4.5$, and scales as $(p/p_{\rm inj})^{s-q}$ in the case of $s=5$."
 So. for instance. the [actor becomes [5/f=32 and 310 at p/myc=10 lor s=45 and 5. respectively.," So, for instance, the factor becomes $f_2/f_0=32$ and $310$ at $p/m_p c=10$ for $s=4.5$ and 5, respectively."
 We point that these values of the CHR. amplification [actor are substantially larger than those expected for the adiabatic compression across (he shock., We point that these values of the CR amplification factor are substantially larger than those expected for the adiabatic compression across the shock.
 With pre-existing C'Rs of fyxp. the amplification factor due to the adiabatic compression is given by in the test-particle regime.," With pre-existing CRs of $f_0 \propto p^{-s}$, the amplification factor due to the adiabatic compression is given by in the test-particle regime."
 So the adiabatic amplification factor is [3/fy=4.3. 5.2. and 6.2 and for s=4. 4.5 and 5. respectively. al a Mach 3 shock.," So the adiabatic amplification factor is $f_2^{\rm adb} / f_0 = 4.3$, 5.2, and 6.2 and for $s=4$, 4.5 and 5, respectively, at a Mach 3 shock."
 Note that the adiabatic compression does not change the slope of the CR. spectrum., Note that the adiabatic compression does not change the slope of the CR spectrum.
 The left panel of Figure 2 also shows the time evolution of the CR distribution at the shock location. f.(p./). from a DSA simulation for (he same set οἱ parameters (see section 4 lor details of DSA simulations).," The left panel of Figure 2 also shows the time evolution of the CR distribution at the shock location, $f_s(p,t)$, from a DSA simulation for the same set of parameters (see Section 4 for details of DSA simulations)."
 The CR. injection was turned olf for thisparticular simulation in order to compare the analvtic and numerical solutions only [or pre-existing CRs., The CR injection was turned off for thisparticular simulation in order to compare the analytic and numerical solutions only for pre-existing CRs.
 This demonstratesthat the time-dependent. solution asvimptotes to the steady-state solution in Equation (7))., This demonstratesthat the time-dependent solution asymptotes to the steady-state solution in Equation \ref{f2p}) ).
with z=0.04 has o(AMs3))>| and we prefer to eliminate 1t. (,with $z=0.04$ has $\sigma(\Delta M_{570})>1$ and we prefer to eliminate it. (
"In fact. this event is a spectroscopic outlier with z;,4.=0.247.)","In fact, this event is a spectroscopic outlier with $z_{spec}=0.247$.)"
 With the 75:5 and redshift cuts. we are left with 177 events. 60 of which are spectroscopically or photometrically identified SNIa.," With the $m_{570}$ and redshift cuts, we are left with 177 events, 60 of which are spectroscopically or photometrically identified SNIa."
 From these numbers. we will derive the SNee rate as follows.," From these numbers, we will derive the SNcc rate as follows."
 We first assign. weights to the observed events that take into account detection efficiency and the volume over which the event could be detected by SNLS., We first assign weights to the observed events that take into account detection efficiency and the volume over which the event could be detected by SNLS.
 Because of their intrinsic faintness. this will significantly increase the number of SNee candidates to 287.," Because of their intrinsic faintness, this will significantly increase the number of SNcc candidates to 287."
 We next evaluate two effects that can change the number of SNee candidates relative to SNla candidates., We next evaluate two effects that can change the number of SNcc candidates relative to SNIa candidates.
 The first is simple spectral or photometric misidentification., The first is simple spectral or photometric misidentification.
 The second comes from the use of host photometric redshifts which. we will see. has a slight tendency to Increase the number of SNIa candidates relative to SNee candidates.," The second comes from the use of host photometric redshifts which, we will see, has a slight tendency to increase the number of SNIa candidates relative to SNcc candidates."
 Using the corrected number of candidates. we then calculate the SNee rate relative to the SNIa rate.," Using the corrected number of candidates, we then calculate the SNcc rate relative to the SNIa rate."
 By adopting the previously measured SNIa rate. we then derive the SNee rate for luminosities within 4.5mag of normal SNIa.," By adopting the previously measured SNIa rate, we then derive the SNcc rate for luminosities within $4.5\,{\rm mag}$ of normal SNIa."
 Finally. we estimate the total SNee rate taking into account the decrease in the number of observed supernovae due to extinction by dust in the host galaxy.," Finally, we estimate the total SNcc rate taking into account the decrease in the number of observed supernovae due to extinction by dust in the host galaxy."
 The observed distribution of AMs;o is the histogram shown in Fig., The observed distribution of $\Delta M_{570}$ is the histogram shown in Fig.
 |] for the 177 events with z:«0.4 and το« 24.1.," \ref{ratefig}
 for the 177 events with $z<0.4$ and $m_{570}<24.1$ ."
" In order to derive the true distribution of AMaso for events with =<04. this distribution must be corrected for the /-dependent detection efficiency and. more importantly. for the fact that an event with absolute magnitude AMs7) can be seen only up to a redshift. z,,, defined by where d(z) is defined by (4)) and zis;g4;=24-1 1s the maximum accepted magnitude."," In order to derive the true distribution of $\Delta M_{570}$ for events with $z<0.4$, this distribution must be corrected for the $i^\prime$ -dependent detection efficiency and, more importantly, for the fact that an event with absolute magnitude $\Delta M_{570}$ can be seen only up to a redshift, $z_{max}$ defined by where $d(z)$ is defined by \ref{ddefeq}) ) and $m_{570max}=24.1$ is the maximum accepted magnitude."
 Events with ων«0.4 (re. Αλάτι> 1.7) must be given a weight. W>|.," Events with $z_{max}<0.4$ (i.e. $\Delta M_{570}>1.7$ ) must be given a weight, $W>1$."
 The weight takes into account. most importantly. the fact that SNLS detects them over a smaller volume.," The weight takes into account, most importantly, the fact that SNLS detects them over a smaller volume."
" Of secondary but non negligible importance ts the fact that the SNee rate is believed to increase with redshift. Λα«(14+2)"" with a~3.6 to reflect the increasing star-formation rate with redshift."," Of secondary but non negligible importance is the fact that the SNcc rate is believed to increase with redshift, $R_{cc}\propto (1+z)^\alpha$ with $\alpha\sim3.6$ to reflect the increasing star-formation rate with redshift."
 We are therefore sensitive to intrinsically faint supernovae only in a redshift range where rate is small., We are therefore sensitive to intrinsically faint supernovae only in a redshift range where rate is small.
" We correct for this with a=3.6 appropriate for SNec because our SNIa candidates are all bright enough to have z,4,> O.4.", We correct for this with $\alpha=3.6$ appropriate for SNcc because our SNIa candidates are all bright enough to have $z_{max}>0.4$ .
 Finally. because of cosmological time dilation. the SNLS observing time is proportional to (ILzr!," Finally, because of cosmological time dilation, the SNLS observing time is proportional to $(1+z)^{-1}$."
 The total weight. W(AMsso.7). is therefore given by where εί) is the event detection efficiency.," The total weight, $W(\Delta M_{570},i^\prime)$, is therefore given by where $\epsilon(i^\prime)$ is the event detection efficiency."
" The factor of proportionality is chosen so that W(z,,,=OAL21)Ι."," The factor of proportionality is chosen so that $W(z_{max}=0.4,i^\prime=21)=1$."
" Without the factors of (1+2) in (4)) and (7)). the weight would be simply the product of e(=21)/e(//) and the euclidean volume ratio (0.4/2,,5."," Without the factors of $(1+z)$ in \ref{ddefeq}) ) and \ref{weightdefeq}) ), the weight would be simply the product of $\epsilon(i^\prime=21)/\epsilon(i^\prime)$ and the euclidean volume ratio $(0.4/z_{max})^3$."
 The factors of (1+2) correct for the redshift evolution of the volume element. the exposure time. and the ρου rate.," The factors of $(1+z)$ correct for the redshift evolution of the volume element, the exposure time, and the SNcc rate."
 Weighting individual events gives the corrected AMao distribution shown by the data points and error bars in Fig. 11.., Weighting individual events gives the corrected $\Delta M_{570}$ distribution shown by the data points and error bars in Fig. \ref{ratefig}.
 All of the 60 SNla candidates have weights near unity., All of the 60 SNIa candidates have weights near unity.
 Because of their faintness. many of the 117 SNee candidates have W>| and the corrected number of SNee candidates is 287+40 (statistical error only).," Because of their faintness, many of the 117 SNcc candidates have $W>1$ and the corrected number of SNcc candidates is $287\pm40$ (statistical error only)."
 In this section we correct the raw number of SNla and SNee candidates for two effects that can affect their numbers: type misidentification (summarized in Table 2)) and redshift migration due to the use of photometric redshifts., In this section we correct the raw number of SNIa and SNcc candidates for two effects that can affect their numbers: type misidentification (summarized in Table \ref{correctiontab}) ) and redshift migration due to the use of photometric redshifts.
 The first shift in the SNla-SNee ratio is due to SNIa that are incorrectly identified as SNec., The first shift in the SNIa-SNcc ratio is due to SNIa that are incorrectly identified as SNcc.
" We divided this correction into that for ""sub-Iuminous"" SNIa and normal SNla.", We divided this correction into that for “sub-luminous” SNIa and normal SNIa.
 Sub-luminous SNIa (Lietal.2001) have a mean magnitude l.5mag below the mean magnitude for normal SNla and account for 16+6% of SNIa., Sub-luminous SNIa \citep{sublum} have a mean magnitude 1.5mag below the mean magnitude for normal SNIa and account for $16\pm6\%$ of SNIa.
 None are found in our sample since both selection for spectroscopy and photometric selection aimed at finding normal SNIa., None are found in our sample since both selection for spectroscopy and photometric selection aimed at finding normal SNIa.
 We therefore add (subtract) 9+Sevents to the SNla (from the SNec) samples.," We therefore add (subtract) $9\pm5\,{\rm events}$ to the SNIa (from the SNcc) samples."
 For normal SNIa. we must correct for events that were neither spectroscopically nor photometrically selected.," For normal SNIa, we must correct for events that were neither spectroscopically nor photometrically selected."
 From Table 1.. of the 46 spectroscopically confirmed events. only 7 were not photometrically selected.," From Table \ref{classificationtab}, of the 46 spectroscopically confirmed events, only 7 were not photometrically selected."
 This gives an inefficieney. of 7/46=0.15 for photometric identification of spectroscopically confirmed SNIa., This gives an inefficiency of $7/46=0.15$ for photometric identification of spectroscopically confirmed SNIa.
 To the 14 5la candidates relying solely on photometric selection. we can therefore add 0.152events and subtract the same number from the SNec.," To the 14 SNIa candidates relying solely on photometric selection, we can therefore add $0.15\times14=2\,{\rm events}$ and subtract the same number from the SNcc."
 As discussed in Section 4.. we make no correction forSNee incorrectly identified as Sla but assign a systematic one standard deviation upper limit of 7eventsto contamination of the SNIa sample with SNec.," As discussed in Section \ref{classificationsec}, , we make no correction forSNcc incorrectly identified as SNIa but assign a systematic one standard deviation upper limit of $7\,{\rm events}$to contamination of the SNIa sample with SNcc."
 Contamination with non-supernova events is expected to be unimportant., Contamination with non-supernova events is expected to be unimportant.
 The scan of events resulted in the elimination, The scan of events resulted in the elimination
A 5.9!x5.2’ region toward the IC 318 cluster was mosaicked in the A31 continuum using the OVRO millimeter-wave interferomieter between September 2001 and January 2002.,A $5.2'\times5.2'$ region toward the IC 348 cluster was mosaicked in the $\lambda$ 3mm continuum using the OVRO millimeter-wave interferometer between September 2001 and January 2002.
 Continuum data were recorded simultaneously in four. 1 GHz wide continuum chanuels centered at 96.18 GHz. 97.98 GHz. 100.98 GHz. aud 102.18 GHz.," Continuum data were recorded simultaneously in four, 1 GHz wide continuum channels centered at 96.48 GHz, 97.98 GHz, 100.98 GHz, and 102.48 GHz."
 The phase aud amplitude calibrator was JO336+323 (a.6 = 03:36:30.10.4-32:18:39.3 J2000). which is located {from the cluster center.," The phase and amplitude calibrator was J0336+323 $\alpha$ $\delta$ = 03:36:30.10,+32:18:29.3 J2000), which is located from the cluster center."
 The data were c:ibrated using the OVRO MALA data reduction package (Scovilleetal.1993)., The data were calibrated using the OVRO MMA data reduction package \citep{Scoville93}.
. The adopted continuum flux for J03364-323. calibrated by observing Neptune and/or Uranus. was 1.60 Jy.," The adopted continuum flux for J0336+323, calibrated by observing Neptune and/or Uranus, was 1.60 Jy."
 The RAIS dispersion in the measured flux for J03364-323 is 0.10 Jy as computed from observations ou 12 separate nights in which both the calibrator aud the planets were observed., The RMS dispersion in the measured flux for J0336+323 is 0.10 Jy as computed from observations on 12 separate nights in which both the calibrator and the planets were observed.
 The mosaic consists of 61 pointinge centers arrangedOm ii a 8x8 eerkd as shown in Figuree 1.., The mosaic consists of 64 pointing centers arranged in a $8\times8$ grid as shown in Figure \ref{fig:gain}.
" The pointing centers along a row are separated by 10"" (compared to the primary FWHM beam size of 72"").", The pointing centers along a row are separated by $''$ (compared to the primary FWHM beam size of $''$ ).
" Adjacent rows are also separated by LO” but with pointing centers shifted by 20"" in right ascensiou.", Adjacent rows are also separated by $''$ but with pointing centers shifted by $''$ in right ascension.
 The mosaicking sequeuce consisted of obtaining a 3 münuute integration ou the phase calibrator followed by observing 5 positions iu the mosaic for 3 minutes each., The mosaicking sequence consisted of obtaining a 3 minute integration on the phase calibrator followed by observing 5 positions in the mosaic for 3 minutes each.
 This sequence was repeated uutil all 61 positious iu tle mosaic were observed., This sequence was repeated until all 64 positions in the mosaic were observed.
 The mosaic was observed iu tle OVRO compact. low. equatorial. and hieh configurations both to increase the UV sunpliug aid to decrease the RMS noise.," The mosaic was observed in the OVRO compact, low, equatorial, and high configurations both to increase the UV sampling and to decrease the RMS noise."
 The top few rows iu the mosaic were often observed at high airmass with lower sensitivity., The top few rows in the mosaic were often observed at high airmass with lower sensitivity.
 Additional observations of these rows were obtained to provide more uniform sensitivity across tlie mosaic., Additional observations of these rows were obtained to provide more uniform sensitivity across the mosaic.
 The 61 individual poiuts were formed iuto an image using the mosaicking routines in MIRIAD., The 64 individual points were formed into an image using the mosaicking routines in MIRIAD.
" The data were averaged using natural weighting to tanimize seusitivity. resulting ina beam size of LO""xL9""."," The data were averaged using natural weighting to maximize sensitivity, resulting ina beam size of $4.0''\times 4.9''$."
 Unit gain. was achieved over a 2.27x5.2) area as shown by the dotted curve in Figure 1.., Unit gain was achieved over a $5.2'\times5.2'$ area as shown by the dotted curve in Figure \ref{fig:gain}.
 The average RMS noise within the unit gain region is 0.75 aalid is spatially uniform over the mosaic to withinLOY., The average RMS noise within the unit gain region is 0.75 and is spatially uniform over the mosaic to within.
. Belore using the OVRO observations to coustraiu the circumstellar disk masses in the IC 315 cluster. I review the stellar properties of the IC 318 cluster members located within the mosaic jo»uncdaries.," Before using the OVRO observations to constrain the circumstellar disk masses in the IC 348 cluster, I review the stellar properties of the IC 348 cluster members located within the mosaic boundaries."
 The stellar aud substellar membership list of the IC 318 cluster was compiled frou the spectroscopic observations by Herbie(1098)... Lulimanetal. (1998).. aud Luhinan(1999).. and the narrow band. imagiug survey by Najita.Tiede.&Carr(2000).," The stellar and substellar membership list of the IC 348 cluster was compiled from the spectroscopic observations by \citet{Herbig98}, \citet{Luhman98}, and \citet{Luhman99}, and the narrow band imaging survey by \citet{Najita00}."
. To ensure a reliable list of cluster members. only. sources brighter than /y;—1L5 were considered. cluster inembers for this studs. as the field star contamination becomes appreciable at [alnter maguituces (Luhimau 2000)..," To ensure a reliable list of cluster members, only sources brighter than $K_s$ =14.5 were considered cluster members for this study, as the field star contamination becomes appreciable at fainter magnitudes \citep{Luhman98,Najita00}. ."
 In total. 95 cluster members brighter than J. =1L5 have been," In total, 95 cluster members brighter than $K_s$ =14.5 have been"
Alultifttequeucy studies of CamunaRav Durst (CRB) afterelows at late times (2 10 days) can be used to test some predictions of the standard. as well as alternative. models.,"Multifrequency studies of Gamma–Ray Burst (GRB) afterglows at late times $\gsim$ 10 days) can be used to test some predictions of the standard, as well as alternative, models."
 This has been doue so far for a haudful of bursts (0.8... Frail. Waxiuan Ixullauni 2000: Frail ct al.," This has been done so far for a handful of bursts (e.g., Frail, Waxman Kulkarni 2000; Frail et al."
 2001)., 2004).
 Thauks to its high fix and low redshift (:—0.1685. Cereiner et al.," Thanks to its high flux and low redshift $z$ =0.1685, Greiner et al."
 2003: Caldwell et al., 2003; Caldwell et al.
 2003). CRB 030329 is an ideal target or such kiud of investigations.," 2003), GRB 030329 is an ideal target for such kind of investigations."
 Tn fact had a very laree fluence of 10. ! 7? (30100 keV. Ricker ot al.," In fact had a very large fluence of $\sim$ $^{-4}$ erg $^{-2}$ (30–400 keV, Ricker et al."
 2003). iu the top of all detected CRBs. aud its optical transient had magnitude 13 one hour after the explosion (Peterson Price 2003: Tori 2003).," 2003), in the top of all detected GRBs, and its optical transient had magnitude 13 one hour after the explosion (Peterson Price 2003; Torii 2003)."
 is also the first CRB unuubieuouslv associated with a superuova (SN2003ch. Stauck ot al.," is also the first GRB unambiguously associated with a supernova (SN2003dh, Stanek et al."
 2003: Tjorth et al., 2003; Hjorth et al.
 2003)., 2003).
 Systematic uultiwaveleneth iuonitoriug of its afterglow (c.e.. Lipkiu (t al," Systematic multiwavelength monitoring of its afterglow (e.g., Lipkin et al."
 2001 Alatheson et al., 2004; Matheson et al.
 2003: Tieugo et al., 2003; Tiengo et al.
 2003: Sheth et al., 2003; Sheth et al.
 2003) is vieldiug important information for he understandingC» of the jet structure. CRB enerecticsOo aud circunburst environment.," 2003) is yielding important information for the understanding of the jet structure, GRB energetics and circumburst environment."
 Tere we report on a new observation oorforiued 258 davs after the burst in order to study the ate evolution of the Xταν afterglow., Here we report on a new observation performed 258 days after the burst in order to study the late evolution of the X–ray afterglow.
 We also re.analvsed he previous observations to derive im a cousisteut wav all he Xrav fluxes iu the 0.5-2 keV energy rauge., We also re–analysed the previous observations to derive in a consistent way all the X–ray fluxes in the 0.5-2 keV energy range.
 This is the range where the effective area of the EPIC iustruinenut is hiehest aud the correspoucing fluxes are less affected by uncertainties in the afterglow spectral shape., This is the range where the effective area of the EPIC instrument is highest and the corresponding fluxes are less affected by uncertainties in the afterglow spectral shape.
 observed the position of starting on December 12. 2003 at 7:30 UT. for an observation leusth of —21 hours," observed the position of starting on December 12, 2003 at 7:30 UT, for an observation length of $\sim$ 24 hours."
 After excludiug the time intervals affected by high particle backerouud. the net exposure times were 68 and 73 ks. respectively in the PN and MOS cameras of the EPIC inustrunent (Styüdder et al.," After excluding the time intervals affected by high particle background, the net exposure times were 68 and 73 ks, respectively in the PN and MOS cameras of the EPIC instrument (Strüdder et al."
 2001: Turner ct al., 2001; Turner et al.
 2001)., 2001).
 All the cameras operated in Full Frame mode aud with the thin optical focking filter., All the cameras operated in Full Frame mode and with the thin optical blocking filter.
 The data were processed using SAS version 5.1.1., The data were processed using SAS version 5.4.1.
 A faint source at the GRD position is visible. albeit xwelv. in the 0.510 keV nuages.," A faint source at the GRB position is visible, albeit barely, in the 0.5–10 keV images."
 The previous Xταν observations (Tiengo et al., The previous X–ray observations (Tiengo et al.
 2003) indicated a rather soft spectrum anda low absorption. which. combined with the ugh effective area of the PN camera at very low enereies. results in a significaut fraction of the source counts iu he 0.20.5 keV baud.," 2003) indicated a rather soft spectrum and a low absorption, which, combined with the high effective area of the PN camera at very low energies, results in a significant fraction of the source counts in the 0.2–0.5 keV band."
 To increase the sigual to noise ratio we therefore analyzed the data over the larecr 10 keV range., To increase the signal to noise ratio we therefore analyzed the data over the larger 0.2--10 keV range.
 This required. au additional cleaning to reduce the instrmmental noise. which in the PN detector increases very rapidly below ~0. Ll keV. The resulting nuage is shown in Fie.l. where the siall solid circle indicates the position.," This required an additional cleaning to reduce the instrumental noise, which in the PN detector increases very rapidly below $\sim$ 0.4 keV. The resulting image is shown in Fig.1, where the small solid circle indicates the position."
" The estimate of the afterglow fux requires particular care. due to the proxtuity (~307) of an N-ray cmittine AGN, which in this observation was much brighter than the CRB afterglow."," The estimate of the afterglow flux requires particular care, due to the proximity $\sim$ $''$ ) of an X-ray emitting AGN, which in this observation was much brighter than the GRB afterglow."
 For this reason we followed differeut methods to estimate the backeround and the fraction of AGN counts falling in the source extraction region., For this reason we followed different methods to estimate the background and the fraction of AGN counts falling in the source extraction region.
" For the afterglow counts we used a circular region with radius of 15"" ceutered at the accurately known CRB vosition (Tavlor et al.", For the afterglow counts we used a circular region with radius of $''$ centered at the accurately known GRB position (Taylor et al.
 2003)., 2003).
 The total uuuber of counts (ie. background. ACN contamination. aud afterglow) contained in this region is Lis for the PN and 171 for he stun of the two MOS.," The total number of counts (i.e. background, AGN contamination, and afterglow) contained in this region is 148 for the PN and 174 for the sum of the two MOS."
 With the first method. we estimated separately the vackeround aud the ACN contamination.," With the first method, we estimated separately the background and the AGN contamination."
 The former was derived from a source free region (a circle of radius 107) in the same CCD chip. while our estinate of he latter was based on the well known model of the instrumental Pout Spread Function (PSF. Chizzarci 2002).," The former was derived from a source free region (a circle of radius $''$ ) in the same CCD chip, while our estimate of the latter was based on the well known model of the instrumental Point Spread Function (PSF, Ghizzardi 2002)."
" We measured the net ACN counts within 15"" frou he ACN position (572426 iu the PN and 15625 in he two MOS sununed).", We measured the net AGN counts within $''$ from the AGN position $\pm$ 26 in the PN and $\pm$ 25 in the two MOS summed).
 The PSF model predicts that a iuuber of counts corresponding to aud of these values (for the PN aud MOS cameras. respectively) will," The PSF model predicts that a number of counts corresponding to and of these values (for the PN and MOS cameras, respectively) will"
as sniall as 0.8 (Boruckietal.2011)..,as small as $\sim$ 0.8 \citep{Borucki}.
" The distribution with 7i, peaks near and al (he completeness limit ofAepler (Howardetal.2011).", The distribution with $R_p$ peaks near and at the completeness limit of \citep{Howard2011}.
". In principle. the mass M, of a transiting planet can be uniquely determined by Doppler observations and mass and radii compared with theoretical relationships."," In principle, the mass $M_p$ of a transiting planet can be uniquely determined by Doppler observations and mass and radii compared with theoretical relationships."
 The mean density of scores of giant planets and a handful of objects between the size of Earth and Neptune orbiting nearby stars have been determined in this manner (Gillonetal.2007:Charbonneauetal.2009:Hartman2011:WinnDemoryοἱ 2011).," The mean density of scores of giant planets and a handful of objects between the size of Earth and Neptune orbiting nearby stars have been determined in this manner \citep{Gillon2007,Charbonneau2009a,Hartman2011,Winn2011,Demory2011}."
. This technique has also successfully confirmed. candidate planets around (he brightest ColtoT and.Kepler stars. including two with masses only a few times that of Earth (Datalhaetal.2011: 2011).," This technique has also successfully confirmed candidate planets around the brightest CoRoT and stars, including two with masses only a few times that of Earth \citep{Batalha2011,Hatzes2011}."
". Comparison with a mass-radius relationship (MIR) can discriminate between denser planets composed of silicates ancl metal (~super-Earths”). and less dense planets wilh substantial envelopes of ices ancl hyvdrogen-helium gas (ocean planets or ""mini-Neptunes"") (Seagerelal.2007)."," Comparison with a mass-radius relationship (MRR) can discriminate between denser planets composed of silicates and metal (“super-Earths”), and less dense planets with substantial envelopes of ices and hydrogen-helium gas (“ocean planets” or “mini-Neptunes”) \citep{Seager2007}."
. Llowever. the Doppler signal expected from manyKepler candidate planets is comparable (o total instrument noise and stellar “jitter” (2-9mI.. Figure 1)).," However, the Doppler signal expected from many candidate planets is comparable to total instrument noise and stellar “jitter” (2-3, Figure \ref{fig.koi}) )."
" RV measurements can be ""phased"" to the transit-determined orbit. achieving greater sensitivitv."," RV measurements can be “phased” to the transit-determined orbit, achieving greater sensitivity."
" Unfortunately. the ereat majority of coolKepler stars are too faint (A,> 13) to achieve the required high SNR even using 10-1 telescopes."," Unfortunately, the great majority of cool stars are too faint $K_p > 13$ ) to achieve the required high SNR even using 10-m telescopes."
 Instead. Doppler observations of a sample ofnearby. brighter stars can constrain (he nmasses and mean densiües of planets around correspondingAepler stars. assuming both samples host the same planet population.," Instead, Doppler observations of a sample of, brighter stars can constrain the masses and mean densities of planets around corresponding stars, assuming both samples host the same planet population."
 Every planet will contribute to BV. variance and the aggregate effect in excess of instrument errors and the noise from the stellar ablmosphere (“jitter”) can be detected., Every planet will contribute to RV variance and the aggregate effect in excess of instrument errors and the noise from the stellar atmosphere (“jitter”) can be detected.
 Given. Aeplerdetermined orbits and planet raclii and a hypothetical MR. the cumulative distribution of RV variation can be predicted ancl compared to that [from the nearby population.," Given -determined orbits and planet radii and a hypothetical MRR, the cumulative distribution of RV variation can be predicted and compared to that from the nearby population."
 For a given distribution of observed. τας. deuser. rocky planets will generate greater RV variation. while less dense. ice- or gas-rich," For a given distribution of observed radii, denser, rocky planets will generate greater RV variation, while less dense, ice- or gas-rich"
uake a fine erid in the disk orientation parameter space.,make a fine grid in the disk orientation parameter space.
" For every combination of cos/ aud 2. we determine the A, iuninositv of the disk at the epochs when $2 was actually observed by ?.."," For every combination of $\cos{i}$ and $\beta$, we determine the $K_s$ luminosity of the disk at the epochs when S2 was actually observed by \cite{Schoedel03}."
 We then pick the πακαι of these values., We then pick the maximum of these values.
" The disk A, Iuniuosityv found in this way is the niaxinua unmiuositv that should have been observed by ? for given cos/ aud 2j.", The disk $K_s$ luminosity found in this way is the maximum luminosity that should have been observed by \cite{Schoedel03} for given $\cos{i}$ and $\beta$.
 The result is displaved in Figure 10. where we show the ratio of the disk flux to that of the star for the hree NIR frequencies. averaged over JJ.," The result is displayed in Figure \ref{fig:disklum} where we show the ratio of the disk flux to that of the star for the three NIR frequencies, averaged over $\beta$."
 Except for ucarly edee-on disks. the reprocessed emission should have been detected by now.," Except for nearly edge-on disks, the reprocessed emission should have been detected by now."
 Since this effect has not been observed. we can rule out the existeuce of an optically thick disk with no inner hole in Ser A.," Since this effect has not been observed, we can rule out the existence of an optically thick disk with no inner hole in Sgr $^*$."
" We now perform similar calculations but allowing the disk to have au inner hole of a given size Ry,40.", We now perform similar calculations but allowing the disk to have an inner hole of a given size $R_{\rm in}\ne 0$.
 Figure 1l shows the lisht curves in the three frequency. bands for the disk inclined at /=60° aad 3=S007. with B;=0.057.," Figure \ref{fig:lightcurvehole05} shows the light curves in the three frequency bands for the disk inclined at $i=60$ and $\beta=300$, with $R_i=0.05$."
. Comparing the lielt curves with those shown in Fig. 7..," Comparing the light curves with those shown in Fig. \ref{fig:lightcurvenohole},"
" the most striking difference is the absence of the second maxima in the II aud AK, bauds.", the most striking difference is the absence of the second maximum in the $H$ and $K_s$ bands.
 This is due to the fact that there is now ouly one crossing of the disk with the star πι 2001.5 while the second crossing shown in Fig., This is due to the fact that there is now only one crossing of the disk with the star – in 2001.8 – while the second crossing shown in Fig.
 7 does uot occur because there is no mnuer disk for P<Rin., \ref{fig:lightcurvenohole} does not occur because there is no inner disk for $R < R_{\rm in}$.
 Nevertheless the streneth of the first πλακα is such that such a disk is still ruled out., Nevertheless the strength of the first maximum is such that such a disk is still ruled out.
" We hen repeated the same calculation (same / aud 7) ut with a larger inner hole radius. Ry,=0.1""."," We then repeated the same calculation (same $i$ and $\beta$ ) but with a larger inner hole radius, $R_{\rm in}=0.1$."
.. The result is shown in Fie. 12., The result is shown in Fig. \ref{fig:lightcurvehole1}.
. Since the star is relatively fay from 1e disk surface for all of its orbit for these particulardisk xuaneters. there are no eclipses or detectable mucreases πι the Z7 or Wy biuds.," Since the star is relatively far from the disk surface for all of its orbit for these particulardisk parameters, there are no eclipses or detectable increases in the $H$ or $K_s$ bands."
 Further. until 2002. the $2 star has rot been detected in the £7 baud. herefore the ποτ curves oe1 Fig.," Further, until 2002, the S2 star has not been detected in the $L'$ band, therefore the light curves in Fig."
 12 appear to be consistent with the observations.," \ref{fig:lightcurvehole1}
 appear to be consistent with the observations."
 Iu fact. we feel that by adjusting the disk parameters it is yossible to obtain the L’ band spectral excess simular to iat observed by ?..," In fact, we feel that by adjusting the disk parameters it is possible to obtain the $L'$ band spectral excess similar to that observed by \cite{Genzel03}. ."
 We shall explore this iu detail in the ture papers., We shall explore this in detail in the future papers.
acquired prior to this.,acquired prior to this.
 A similar GPS-based PWV monitor operated bv is located at White Sands (WS). New Mexico. 50 km southwest of APO at an elevation of 1200 m (1580 m below APO).," A similar GPS-based PWV monitor operated by is located at White Sands (WS), New Mexico, 50 km southwest of APO at an elevation of 1200 m (1580 m below APO)."
 We interpolated the PWV estimates from. WS during 2009 to the times of those from APO having PWV<LO mm. only considering APO measurements within 30 minutes of a WS measurement.," We interpolated the PWV estimates from WS during 2009 to the times of those from APO having $<10$ mm, only considering APO measurements within 30 minutes of a WS measurement."
 We found that the APO and WS PWY measurements are highly correlated. (Pearsons r=0.85). though with significant deviations [rom linearity at PWV< 1mm.," We found that the APO and WS PWV measurements are highly correlated (Pearson's r=0.85), though with significant deviations from linearity at $<1$ mm."
 We adopt an empirical relation between WS and APO by interpolating the average PWY data given in Table 2.., We adopt an empirical relation between WS and APO by interpolating the average PWV data given in Table \ref{table1}.
 While the scatter in this relation is large. particularly al low PWV. it is sullicient for considering the relationship between the overall statistical properties of SDSS z-band photometry and PWV.," While the scatter in this relation is large, particularly at low PWV, it is sufficient for considering the relationship between the overall statistical properties of SDSS z-band photometry and PWV."
 The photometric measurements in the SDSS DR& database have undergone the calibration procedure described in ?.. which has been shown to achieve global photometric precision of ~2% ing band. and —1 in g. r. andi bands.," The photometric measurements in the SDSS DR8 database have undergone the calibration procedure described in \citet{padmanabhan2008}, which has been shown to achieve global photometric precision of $\sim2\%$ in z band, and $\sim1\%$ in g, r, and i bands."
" In z band. in addition to the components of atmospheric extinction (hat vary smoothly wilh wavelength. such as Ravleigh scattering by molecules. Mie scattering by aerosols. and ""grav absorption by Chin clouds. line absorption bv TO becomes important."," In z band, in addition to the components of atmospheric extinction that vary smoothly with wavelength, such as Rayleigh scattering by molecules, Mie scattering by aerosols, and “gray” absorption by thin clouds, line absorption by $_2$ O becomes important."
 This means that (he extinction for a given object depends on the SED of the object. which is not the ease for the other bands.," This means that the extinction for a given object depends on the SED of the object, which is not the case for the other bands."
 is funclamentally a. differential approach. where flux is calibrated relative to a large ensemble of objects having a vide range of SEDs that. when averaged. al NIB. wavelengths have à smooth SED like a solar ivpe star.," is fundamentally a differential approach, where flux is calibrated relative to a large ensemble of objects having a wide range of SEDs that, when averaged, at NIR wavelengths have a smooth SED like a solar type star."
 Given (liis. we expect svstematic residuals in the SDSS z-band measurements for objects wilh complex NIB. SEDs. such as M stars. that will correlate wilh PWV.," Given this, we expect systematic residuals in the SDSS z-band measurements for objects with complex NIR SEDs, such as M stars, that will correlate with PWV."
 We selected two samples of M stars [rom the SDSS DIS to investigate this effect., We selected two samples of M stars from the SDSS DR8 to investigate this effect.
 The first sample is based on the spectroscopicallvy-classilied catalog of M stars produced bv ?.., The first sample is based on the spectroscopically-classified catalog of M stars produced by \citet{west2011}.
 We selected 7.300 objects having spectral twpes from MY {ο MA and brighter (han i=17.0 and retrieved the CLEAN photometric measurements of these objects Irom the STAR view in (he DRS context.," We selected 7,300 objects having spectral types from M7 to M4 and brighter than i=17.0 and retrieved the CLEAN photometric measurements of these objects from the STAR view in the DR8 context."
 We estimated PWV at the tme of each observation based on the WS data and rejected epochs where no WS data was available., We estimated PWV at the time of each observation based on the WS data and rejected epochs where no WS data was available.
 We also rejected outliers in (1) vs.(r-z) color space by excluding objects with (1-z) colors falling more (han 0.2 mag from a linear fit to the stellar locus and caleulated AG—z). the color of each object relative to the stellar locus for a given (2-1).," We also rejected outliers in (r-i) vs.(r-z) color space by excluding objects with (r-z) colors falling more than 0.2 mag from a linear fit to the stellar locus and calculated $\Delta (r-z)$, the color of each object relative to the stellar locus for a given (r-i)."
 We also caleulated the mean. with outlier rejection. of A(r—z) in each of the six eamcols and found significant offsets which we subtracted off.," We also calculated the mean, with outlier rejection, of $\Delta(r-z)$ in each of the six camcols and found significant offsets which we subtracted off."
" The relation between ,N(r—2) and PWV is shown in Figure 6..", The relation between $\Delta(r-z)$ and PWV is shown in Figure \ref{fig5}.
 The best fit linear relation between change in (1-z) color and PWY is ACr—2)=(720.0019&0.0002)x(PIV3.3mm) mag., The best fit linear relation between change in (r-z) color and PWV is $\Delta(r-z)=(-0.0019\pm0.0002)\times(PWV-3.3~\rm{mm})$ mag.
elluric lines becomes worse Lf we take into cousideration other gas molecules such as MoO aud C'Os.,telluric lines becomes worse if we take into consideration other gas molecules such as $H_2O$ and $CO_2$.
 We assume different levels of RV fluctiation due to atinospherie behaviors deypar (5 ms1. 10 nes land 20115 4).," We assume different levels of RV fluctuation due to atmospheric behaviors $\delta v_{N,ATM}$ (5 $\rm{m\cdot s}^{-1}$ , 10 $\rm{m\cdot s}^{-1}$ and 20 $\rm{m\cdot s}^{-1}$ )."
 The uucertaiutvy iuduced by atinospherie tellurie lines is transferred to 0644 via Equation (22)) without the ellort of diseutareliug stellar aud telluric lines as if he uncertainty is due to plioton-nolse of By., The uncertainty induced by atmospheric telluric lines is transferred to $\delta v_{rms}$ via Equation \ref{eq:simple_example_tulleric_2}) ) without the effort of disentangling stellar and telluric lines as if the uncertainty is due to photon-noise of $B_S$.
 Telluric lines witli he largeste slope are masked at the ughest priority jecause they cause the most RV uucertainty iu the measurement., Telluric lines with the largest slope are masked at the highest priority because they cause the most RV uncertainty in the measurement.
 Fig., Fig.
 18. shows the results of telluric liue 1asking lor au M9 dwarf uuder diTerent levels of elluric line masking., \ref{fig:RV_Un_Mask} shows the results of telluric line masking for an M9 dwarf under different levels of telluric line masking.
" Alter masking a certait j»ortion of the most severely contaninated. stellar spectrum. optimal RV. uncertainty vcj4,; is 3.3 insI 3.6 esH aud 3.9 in:sH respectively [or Sexpay OLS mossIF 10 mes band 20m-s J|."," After masking a certain portion of the most severely contaminated stellar spectrum, optimal RV uncertainty $v_{rms}$ is 3.3 $\rm{m\cdot s}^{-1}$ , 3.6 $\rm{m\cdot s}^{-1}$ and 3.9 $\rm{m\cdot s}^{-1}$ respectively for $\delta v_{N,ATM}$ of 5 $\rm{m\cdot s}^{-1}$, 10 $\rm{m\cdot s}^{-1}$ and 20 $\rm{m\cdot s}^{-1}$."
" They aο 2.6. 2.5 and 3.0 times worse compared to the faudamental photou-limited RV uncertainv of the stellar spectrum 9,44,9. Le.. 1.3 byesloo "," They are 2.6, 2.8 and 3.0 times worse compared to the fundamental photon-limited RV uncertainty of the stellar spectrum $\delta v_{rms,S}$, i.e., 1.3 $\rm{m\cdot s}^{-1}$."
we co not apply telluric liue masking at all. RV uucertaiuy is dominated by atmospheric behaviors. δρα.," If we do not apply telluric line masking at all, RV uncertainty is dominated by atmospheric behaviors, $\delta v_{N,ATM}$."
 HC ds expected that μη Increases as we nask more of the stellar spectrum because less photon flux is available to calculate RV., It is expected that $\delta v_{rms}$ increases as we mask more of the stellar spectrum because less photon flux is available to calculate RV.
 Depending οἱ values of deapar. the optimal spectrum fraction used in RV measurement lies in between aud50%.," Depending on values of $\delta v_{N,ATM}$, the optimal spectrum fraction used in RV measurement lies in between and."
. Higher value of deyapa; requires masking aud removing larger fraction of stellar spectruu.," Higher value of $\delta v_{N,ATM}$ requires masking and removing larger fraction of stellar spectrum."
 It is noted that we would have expected δρ Lo be only L.1 times worse than ομεις after ~50% oL the spectrum ΠΠ for pure concern of phoon flux.," It is noted that we would have expected $\delta v_{rms}$ to be only $\sim$ 1.4 times worse than $\delta v_{rms,S}$ after $\sim$ of the spectrum is masked for pure concern of photon flux."
" However. 944 Is 3 times worse than ομις because not only N, bu also Q is reduced after telluric line masking."," However, $\delta v_{rms}$ is $\sim$ 3 times worse than $\delta v_{rms,S}$ because not only $N_{e^-}$ but also $Q$ is reduced after telluric line masking."
 Iu principle. the telluric lines can be modeled. aud ‘feoved using a telluric line spectrum templae.," In principle, the telluric lines can be modeled and removed using a telluric line spectrum template."
 This kiud of template cau ye Obtained by observing fast rotating early type stars since the προςttur of an early type star (early A type in particular) ls nearly featureless aud a good approxinatlon o ‘a blackbody spectr min NIR except [or broad ivcdrogen absorption ures(?).., This kind of template can be obtained by observing fast rotating early type stars since the spectrum of an early type star (early A type in particular) is nearly featureless and a good approximation of a blackbody spectrum in NIR except for broad hydrogen absorption \citep{Vacca2003}.
 However. the nuuber of available telULIG staidarcd stars Liuits the application of this method.," However, the number of available telluric standard stars limits the application of this method."
 Iu addition. the spectruin of a telluric sandar star is not eitively featureless. which results tu some residuas tlal uLdenines precision RV measremetts.," In addition, the spectrum of a telluric standard star is not entirely featureless, which results in some residuals that undermines precision RV measurements."
 Asi first orcler estimation. we coisider t1e simplest case in which we assume that the spectrum . a tellwic statdarc star is a perfect black)ody s;»ectrum. with no spectral features which may hierwise be pe‘fectM7 modeled aud. removect.," As a first order estimation, we consider the simplest case in which we assume that the spectrum of a telluric standard star is a perfect blackbody spectrum with no spectral features which may otherwise be perfectly modeled and removed."
 Since the spectrum of a science target and. the spectrur rofateluric line standard star are ιοί taken simultaneously. the telluric lines. centroids xd dephs may changee over time.," Since the spectrum of a science target and the spectrum of a telluric line standard star are not taken simultaneously, the telluric lines' centroids and depths may change over time."
 We assuiue that he centroids of telluric lines remain uushiltec., We assume that the centroids of telluric lines remain unshifted.
 As aresut. the only uncertainty is the depth ofa teluric line.," As a result, the only uncertainty is the depth of a telluric line."
 Equation (13)) aud (20)) offer insight ist uucerstandiug the process of telluric line mocleliig., Equation \ref{eq:overall_Doppler_2d}) ) and \ref{eq:B_atm}) ) offer insight in understanding the process of telluric line modeling.
 Iu the telluric line ruodeliug. we model the telluric ines by observinga standard star or by forward modeling using a listof telluric lines.," In the telluric line modeling, we model the telluric lines by observinga standard star or by forward modeling using a listof telluric lines."
 We remove telluric lines (rom the observed spectrum of a science target., We remove telluric lines from the observed spectrum of a science target.
 The deptis of tlie telluric, The depths of the telluric
first bound. state becomes monotonically more bound and pressure ionization never occurs.,first bound state becomes monotonically more bound and pressure ionization never occurs.
 The free electrons are able to prevent ionization exactly like the Saha equation with electron. degeneracy. which vields that the free electrons recombine as the density increases.," The free electrons are able to prevent ionization exactly like the Saha equation with electron degeneracy, which yields that the free electrons recombine as the density increases."
 7? applied the Neutral-Pseudo Atom. (NPA) method to evaluate. the equation of state anc the degree of ionization of pure Be metal under normal conditions (p—1.85gem5 and 7= 0) and at high densities. keeping 2=0.," \citet{Per90} applied the Neutral-Pseudo Atom (NPA) method to evaluate the equation of state and the degree of ionization of pure ${\rm Be}$ metal under normal conditions $\rho=1.85~{\rm g~cm}^{-3}$ and $T=0$ ) and at high densities, keeping $T=0$."
 The results are not directly applicable to the Sun because Perrot discusses pure metallic Bervilium while we are interested in à trace Be atom embedded in a sea of protons and à particles., The results are not directly applicable to the Sun because Perrot discusses pure metallic Beryllium while we are interested in a trace ${\rm Be}$ atom embedded in a sea of protons and $\alpha $ particles.
 Yet. the results are instructive for the comparison of the present method with others. especially because they serve as a consistency check.," Yet, the results are instructive for the comparison of the present method with others, especially because they serve as a consistency check."
 The applicability of the NPA method (7). is limited to compression ratios e below 40 (see fie., The applicability of the NPA method \citep{Per90} is limited to compression ratios $c$ below 40 (see fig.
 5 in the ?. and the explanation therein) while Be becomes fully ionized at compression ratio of e=50., 5 in the \citealt{Per90} and the explanation therein) while Be becomes fully ionized at compression ratio of $c=50$.
 At high compressions. band caleulations show that the gap between the Is band and the upper one close (2)..," At high compressions, band calculations show that the gap between the 1s band and the upper one close \citep{MZ88}."
 Phe normal density of BervlIlium is 1.85οem and hence a compression ratio of 50 corresponds to a density of 02.5οem 7., The normal density of Beryllium is $1.85~{\rm g~cm^{-3}}$ and hence a compression ratio of 50 corresponds to a density of $92.5~{\rm g~cm^{-3}}$ .
 Consequently. Aletallic Bervllium: is fully pressure ionized at 7=0 and a density of 92.5gem 7.," Consequently, Metallic Beryllium is fully pressure ionized at $T=0$ and a density of $92.5~{\rm g~cm^{-3}}$ ."
 2. presents an extrapolation between the end point of his results (e= 40) and the band calculations (e= 50)., \citet{Per90} presents an extrapolation between the end point of his results $c=40$ ) and the band calculations $c=50$ ).
 We note that when the density or temperature (or both) are increased starting [rom p=92.5οem. and T=0 no bound state can re-appear., We note that when the density or temperature (or both) are increased starting from $\rho=92.5~{\rm g~cm^{-3}}$ and $T=0$ no bound state can re-appear.
 There is simply no bound state at higher densities and/or higher temperatures if it docs not exist lor 7=0 and à given density., There is simply no bound state at higher densities and/or higher temperatures if it does not exist for $T=0$ and a given density.
 Our calculations of the pressure ionization assume that the heavy elements ander considerations are trace elements., Our calculations of the pressure ionization assume that the heavy elements under considerations are trace elements.
 Yet. it is of interest to compare the present. method. with others.," Yet, it is of interest to compare the present method with others."
 Ehe above results for metallic BeryIHlium provide such an opportunity., The above results for metallic Beryllium provide such an opportunity.
 When the specie under consideration is à trace element. the electrons are contributed by the Hydrogen and Llelium and there is no connection between the number of electrons in a unit cell and the charge of the ion. C," When the specie under consideration is a trace element, the electrons are contributed by the Hydrogen and Helium and there is no connection between the number of electrons in a unit cell and the charge of the ion. ("
Pheore is no condition of charge neutrality per cach ion sphere.,There is no condition of charge neutrality per each ion sphere.
 The number of electrons in the Bervllium ion sphere is not necessarily 4)., The number of electrons in the Beryllium ion sphere is not necessarily 4).
 In the pure Bervllium case. when we search for the density of complete ionization. we assume that the free electrons are the the first three electrons of Beryllium and that the forth one is bound.," In the pure Beryllium case, when we search for the density of complete ionization, we assume that the free electrons are the the first three electrons of Beryllium and that the forth one is bound."
 Thus the exchange terni is evaluated on the basis of Bervllium ionized three times., Thus the exchange term is evaluated on the basis of Beryllium ionized three times.
 As can be deduced. from. the previous caleulation. a critical factor is the packing of the specie.," As can be deduced from the previous calculation, a critical factor is the packing of the specie."
 Lf spherical packing is assumed. then the INS equation predicts complete ionization al p2:56&em.7.," If spherical packing is assumed, then the KS equation predicts complete ionization at $\rho\approx 56~{\rm g~cm}^{-3}$."
 On the other hand. 2 quotes that complete ionization is reached. at 92.5οem.7.," On the other hand, \citet{Per90} quotes that complete ionization is reached at $92.5~{\rm g~ cm}^{-3}$."
 The exact lattice structure of Bervllium at very high densities is not known and Be apparently undergoes a structural change at a compression ratio of about 3., The exact lattice structure of Beryllium at very high densities is not known and Be apparently undergoes a structural change at a compression ratio of about 3.
 However. if we assume an [cc lattice structure and resort to the appendix in ?. to find the relation between the lattice structure and the radius of the atomic cell (5;= (2/4)a) we find complete ionization al a density of 80.3&em7. in good agreement with ?..," However, if we assume an fcc lattice structure and resort to the appendix in \citet{Lai91} to find the relation between the lattice structure and the radius of the atomic cell $r_{i}=(\sqrt{2}/4)a$ ) we find complete ionization at a density of $89.3 ~{\rm g~cm}^{-3}$, in good agreement with \citet{Per90}."
 This result reassures that our analvsis for De! as a trace element is valid. as well., This result reassures that our analysis for ${\rm Be}^7$ as a trace element is valid as well.
 When DBeryllium is completely pressure ionized in the core of the Sun. electron. capture by Be takes place via. the continuum only.," When Beryllium is completely pressure ionized in the core of the Sun, electron capture by Be takes place via the continuum only."
 Consequently. no corrections to the rate due to bound electrons should apply.," Consequently, no corrections to the rate due to bound electrons should apply."
 The elfect of the complete ionization of De* on the solar neutrino [lux can be easily. estimated without. recourse to detailed solar models because Bet is a trace element and the amount of energy released by its reactions is neeligible., The effect of the complete ionization of ${\rm Be}^{7}$ on the solar neutrino flux can be easily estimated without recourse to detailed solar models because ${\rm Be}^{7}$ is a trace element and the amount of energy released by its reactions is negligible.
 Pwo facts are relevant. (, Two facts are relevant. (
a) The De* electron capture neutrino Dux and the D7 flux are proportional to the abundance of Be! (,a) The ${\rm Be}^{7}$ electron capture neutrino flux and the ${\rm B}^{8}$ flux are proportional to the abundance of ${\rm Be}^{7}$. (
b) The rate of electron. capture is much larger than the rate of proton capture.,b) The rate of electron capture is much larger than the rate of proton capture.
 Consequently. a decrease of about in the rate of the Betο capture increases the abundance of Be* by the same factor and hence increases the D neutrino [lux by the same factor.," Consequently, a decrease of about in the rate of the ${\rm Be}^{7}+e^{-}$ capture increases the abundance of ${\rm Be}^{7}$ by the same factor and hence increases the ${\rm B}^{8}$ neutrino flux by the same factor."
 The [lux of the ο|e neutrinos is unchanged because the decrease in the rate is lly compensated for by the increase in the abundance.," The flux of the ${\rm 
 Be}^{7}+e^{-}$ neutrinos is unchanged because the decrease in the rate is fully compensated for by the increase in the abundance."
" As a matter of fact. the rate of ο|e is determined (under he condition that the rate of Be""|e. is much larger than he rate of De*|p ) only by the rate of He?|He!"," As a matter of fact, the rate of ${\rm Be}^{7}+e^{-}$ is determined (under the condition that the rate of ${\rm Be}^{7}+e^{-}$ is much larger than the rate of ${\rm Be}^{7}+p$ ) only by the rate of ${\rm He}^{3}+ {\rm He}^{4}$."
 The above treatment of the pressure ionization of Be applies ο all solar models irrespective of any other parameter., The above treatment of the pressure ionization of ${\rm Be}^{7}$ applies to all solar models irrespective of any other parameter.
 The elect. on the predicted Hux assuming few cdilferent sets of nuclear parameters is shown in Table 2.., The effect on the predicted flux assuming few different sets of nuclear parameters is shown in Table \ref{tbl:neut}.
 Phe four mocdels referred to in the table are the following., The four models referred to in the table are the following.
" C'est refers to ?.. 12900 refers to 2.. ΗΛΙΟΣ refers to? and NACTUS refers to ον,"," $Cas97$ refers to \citet{Cas97}, $DS96$ refers to \citet{DS96}, $RMP98$ refers to \citet{RMP98} and NACRE refers to \citet{NACRE}."
 The models ciffer mainly in the parameters for the rates of the nuclear reaction ancl slightly in the details of the equation of state., The models differ mainly in the parameters for the rates of the nuclear reaction and slightly in the details of the equation of state.
 In this work. we were interested in the internal structure of a trace ion in a high density plasma. and not in the general properties of the plasma.," In this work, we were interested in the internal structure of a trace ion in a high density plasma, and not in the general properties of the plasma."
 The relevant. physical quantity for the latter. is the elective charge ofan ionnot the electronic structure provided the elfective radius of the electronic wave function is much smaller than the Debye radius.," The relevant physical quantity for the latter, is the effective charge of an ion—not the electronic structure provided the effective radius of the electronic wave function is much smaller than the Debye radius."
 As to the structure of the ion itself. we distinguished: between two cases depending on whether the mean interparticle distance is smaller or larger than the Debve radius.," As to the structure of the ion itself, we distinguished between two cases depending on whether the mean interparticle distance is smaller or larger than the Debye radius."
 We found that throughout most of the Sun. the mean interparticle distance is slightly smaller than the Debye radius.," We found that throughout most of the Sun, the mean interparticle distance is slightly smaller than the Debye radius."
 Under such conditions. the ionization state of a given ion depends mostly on the distance to the nearest. neighbor rather than the distance scale of the screened. potential.," Under such conditions, the ionization state of a given ion depends mostly on the distance to the nearest neighbor rather than the distance scale of the screened potential."
 llence. we approximate the condition of the plasma hy a generalized Wiencr-Seitz cell around. cach ion plus the proper boundary condition on the surface of the cell.," Hence, we approximate the condition of the plasma by a generalized Wigner-Seitz cell around each ion plus the proper boundary condition on the surface of the cell."
 We then impose the Blochcondition on the boundary. of the ecncralizecdl Wiencr-Seitz cell., We then impose the Blochcondition on the boundary of the generalized Wigner-Seitz cell.
 Phe fact that the nearest neighbor is so close implies that the implementation of this condition has a major cllect on thepoint at which complete ionization takes place., The fact that the nearest neighbor is so close implies that the implementation of this condition has a major effect on thepoint at which complete ionization takes place.
The following notes are presented in RA order for the northern objects. then a few pertaining to the south are appenclect.,"The following notes are presented in RA order for the northern objects, then a few pertaining to the south are appended."
 WILL JOOQ044-5:Io: M-shaped Galactic nebulositv., WHI J0004+52: M-shaped Galactic nebulosity.
 WII J00184-65: Planetary nebula. confirmed by Ia image.," WHI J0018+65: Planetary nebula, confirmed by $\alpha$ image."
 WIII J0039466: Galactic nebula. with Ila emission that looks like a bow shock.," WHI J0039+66: Galactic nebula, with $\alpha$ emission that looks like a bow shock."
 WILL JOOL0+66: Galactic nebulositw., WHI J0040+66: Galactic nebulosity.
 ειν ill-defined. (to the point that the size is a guess. and the surlace brightness also.," Very ill-defined, to the point that the size is a guess, and the surface brightness also."
 WIL JOIJ4+17: A faint bit of galactic nebulositv., WHI J0144+17: A faint bit of galactic nebulosity.
 No apparent Ila., No apparent $\alpha$.
 WII JOL56+63: Arrowhead-shaped bit of Galactic nebulosity., WHI J0156+63: Arrowhead-shaped bit of Galactic nebulosity.
 WIL 0150-10: A reflection nebula in the glave of HD 11861. to whieh it max be related.," WHI J0156+13: A reflection nebula in the glare of HD 11861, to which it may be related."
 Blue in color wilh no apparent Ho., Blue in color with no apparent $\alpha$.
 We present an image below., We present an image below.
 ZOAG G133.63-03.62: Face-on spiral galaxy., ZOAG G133.63-03.62: Face-on spiral galaxy.
 WILL J0226--52: A verv large Galactie nebulosity. extending off the field to the north and east.," WHI J0226+52: A very large Galactic nebulosity, extending off the field to the north and east."
 ]xIx93-20: Galaxy. elliptical overall but showing a trace a spiral structure.," KK98-20: Galaxy, elliptical overall but showing a trace a spiral structure."
 reported a detection in HI at τοῦ mJy. with a svstemic velocity of -10 km/s. and concluded that it is à Galactic IHE cloud.," \citet{HKKE00} reported a detection in HI at 760 mJy, with a systemic velocity of -70 km/s, and concluded that it is a Galactic HI cloud."
 However. Rosenberg&Schneider(2000) found a sienal al 3.7 mJv showing 3994 km/s. The latter detection makes more sense together with the compact. spiral morphology that we see.," However, \citet{RS00} found a signal at 3.7 mJy showing 3994 km/s. The latter detection makes more sense together with the compact, spiral morphology that we see."
 Huchtmeieretal.(2000b) searched only. out to 3970 km/s. which would explain how thev missed the extragalactic signal.," \citet{HKKE00} searched only out to 3970 km/s, which would explain how they missed the extragalactic signal."
 What thev found al -70 km/s. however. is not explained: (here is no obvious Galactic object nearby. and Rosenbere&Schneicer(2000). did not report it.," What they found at -70 km/s, however, is not explained; there is no obvious Galactic object nearby, and \citet{RS00}
 did not report it."
 ZOAG GLI34.312-06.24: Bright face-on spiral., ZOAG G134.31+06.24: Bright face-on spiral.
 ZOAG 139.32+04.85: Cam C. identified as an emission nebula by (2003).," ZOAG 139.32+04.85: Cam C, identified as an emission nebula by \citet{KSD03}."
. The ZOAG catalog seems to have listed each of the two bright spots separately., The ZOAG catalog seems to have listed each of the two bright spots separately.
 Pretiv in H-alplia: probably a bipolar PN., Pretty in H-alpha; probably a bipolar PN.
 IXIXIIO1-20: Heavily extincted face-on spiral., KKH01-20: Heavily extincted face-on spiral.
 Identified as a possible dE by (1995).. from plate material which did not go deep enough to show the spiral aruis.," Identified as a possible dE by \citet{HFL95}, from plate material which did not go deep enough to show the spiral arms."
The shaded area indicates the absolute magnitude range where the UV high-z LF is currently well sampled.,The shaded area indicates the absolute magnitude range where the UV $z$ LF is currently well sampled.
 It is clear that the UV uminosity is practically not affected by dust. since the predicted extinction is low for galaxy ages less than ἑωμι.," It is clear that the UV luminosity is practically not affected by dust, since the predicted extinction is low for galaxy ages less than $t_{\rm crit}$."
 Fig., Fig.
 7 also shows the age dependence of the expected Lya uminosity at fixed halo mass., 7 also shows the age dependence of the expected $\alpha$ luminosity at fixed halo mass.
 At variance with respect to the behavior of the UV magnitude. the Lya luminosity of hosts in arger halos is already declining for ages less than for at ος6. since Lya emission is sensitive not only to dust but also to neutral ivdrogen absorption.," At variance with respect to the behavior of the UV magnitude, the $\alpha$ luminosity of hosts in larger halos is already declining for ages less than $t_{\rm crit}$ at $z\ga 6$, since $\alpha$ emission is sensitive not only to dust but also to neutral hydrogen absorption."
 Anyhow we expect a strict correlation between GRB hosts and Lyman Break Galaxies (LBG) and Lya emitters (LAE)., Anyhow we expect a strict correlation between GRB hosts and Lyman Break Galaxies (LBG) and $\alpha$ emitters (LAE).
 As he galaxy model here adopted reproduces the high-redshift UV LF of LBGs and LAEs (see Mao et al., As the galaxy model here adopted reproduces the high-redshift UV LF of LBGs and LAEs (see Mao et al.
" 2007). it is meaningful to estimate the UV LF expected for GRB hosts. namely by imposing he condition ZSZui,70.1Z.."," 2007), it is meaningful to estimate the UV LF expected for GRB hosts, namely by imposing the condition $Z\la Z_{\rm crit}\approx 0.1\, Z_{\odot}$."
 The result is shown in Fig., The result is shown in Fig.
 8., 8.
 In general the conditional UV LF depends on the ratio between μι and the time during which the host is brighter than a fixed absolute magnitude., In general the conditional UV LF depends on the ratio between $t_{\rm crit}$ and the time during which the host is brighter than a fixed absolute magnitude.
 As expected. the metallicity cut depresses the UV luminosity distribution. but this depression is minimal at the faint and bright ends. and maximum at intermediate values. as expected from the effects of the cut on M55 in individual systems.," As expected, the metallicity cut depresses the UV luminosity distribution, but this depression is minimal at the faint and bright ends, and maximum at intermediate values, as expected from the effects of the cut on $M_{1350}$ in individual systems."
 In particular. the time spent by galaxies in large halos as LBGs - before turning into strongly submm emitting galaxies because of dust attenuation - is short and comparable with foi.," In particular, the time spent by galaxies in large halos as LBGs - before turning into strongly submm emitting galaxies because of dust attenuation - is short and comparable with $t_{\rm crit}$."
 At the faint end the luminosity of small hosts can fall below a fixed magnitude in a relatively short time. as shown in Fig.," At the faint end the luminosity of small hosts can fall below a fixed magnitude in a relatively short time, as shown in Fig."
 8 for hosts in halos with AlyzcLOMAZ...," 8 for hosts in halos with $M_{\rm H}\approx
10^{10}\, M_{\odot}$."
 It is also apparent that intermediate mass halos and the corresponding intermediate UV luminosity objects are significantly more affected by the condition on metallicity., It is also apparent that intermediate mass halos and the corresponding intermediate UV luminosity objects are significantly more affected by the condition on metallicity.
 Obviously at high redshift. eg. 2cz10. the cut reduces the visibility timescale only by a small fraction.," Obviously at high redshift, e.g. $z\approx 10$, the cut reduces the visibility timescale only by a small fraction."
 We can conclude that GRB hosts should well reproduce the LBG LF at its faint and bright ends., We can conclude that GRB hosts should well reproduce the LBG LF at its faint and bright ends.
 Similar conclusions hold for LAE LF., Similar conclusions hold for LAE LF.
 The shortness of {οι750 Myr implies that the hosts must exhibit quite large [a/Fe] enhancement., The shortness of $t_{\rm crit}\approx 50$ Myr implies that the hosts must exhibit quite large $\alpha$ /Fe] enhancement.
 In fact. the cumulative fraction of SNIa explosions after an instantaneous burst of star formation (1 at 12 Gyr) is negligibly small for 50 Myr (corresponding to the lifetime of a 7AJ. star). for a wide class of progenitor models. i.e. Single Degenerates (SD). and Double Degenerates (DD) exploders (Greggio 2005).," In fact, the cumulative fraction of SNIa explosions after an instantaneous burst of star formation $1$ at $12$ Gyr) is negligibly small for $50$ Myr (corresponding to the lifetime of a $7\, M_\odot$ star), for a wide class of progenitor models, i.e. Single Degenerates (SD), and Double Degenerates (DD) exploders (Greggio 2005)."
 At 0.1 Gyr it reaches LO per cent in the most favorable case of close DD scheme., At $0.1$ Gyr it reaches $10$ per cent in the most favorable case of close DD scheme.
 Furthermore. the typical timescales required to. significantly decrease the [a/Fe] ratio from its initial value produced by a single generation of massive stars (approximately 0.0.6 depending on metallicity. IMF and stellar yields. Gibson et al.," Furthermore, the typical timescales required to significantly decrease the $\alpha$ /Fe] ratio from its initial value produced by a single generation of massive stars (approximately $0.4-0.6$ depending on metallicity, IMF and stellar yields, Gibson et al."
 2003). is 0.3. ] and 3 Gyr. for close DD. SD and WIDE DD progenitors. respectively.," 2003), is $0.3$, $1$ and $3$ Gyr, for close DD, SD and WIDE DD progenitors, respectively."
 Thus while in the most massive ellipticals the duration of the burst of star formation (around 0.8 Gyr) may be enough for a mild pollution by Fe-peak elements (depending on the assumed scenario for SNIa progenitors). the lower timescale required to reach the critical metallicity implies that GRB hosts should display the original pattern of heavy elements produced by massive star chemical evolution.," Thus while in the most massive ellipticals the duration of the burst of star formation (around $0.3$ Gyr) may be enough for a mild pollution by Fe-peak elements (depending on the assumed scenario for SNIa progenitors), the lower timescale required to reach the critical metallicity implies that GRB hosts should display the original pattern of heavy elements produced by massive star chemical evolution."
 Notice that the subsequent history of star formation decreases the initial a-enhancement more in smaller than in larger objects (see Fig., Notice that the subsequent history of star formation decreases the initial $\alpha$-enhancement more in smaller than in larger objects (see Fig.
 1)., 1).
 We conclude that at high redshift. GRB hosts (and the similarly young LAEs) exhibit the highest values of a-enhancement. even higher than those of high-z quasar hosts and of their descendents. the massive elliptical galaxies.," We conclude that at high redshift, GRB hosts (and the similarly young LAEs) exhibit the highest values of $\alpha$ -enhancement, even higher than those of $z$ quasar hosts and of their descendents, the massive elliptical galaxies."
 Finally. we can also estimate the distribution of intrinsic SFRs.," Finally, we can also estimate the distribution of intrinsic SFRs."
 It is worth stressing that generally the hosts with SFRs exceeding afew. 107AL. vr.+ are significantly less than the overall galaxy population.," It is worth stressing that generally the hosts with SFRs exceeding a few $\times 10^2\, M_{\odot}$ $^{-1}$ are significantly less than the overall galaxy population."
 This suppression reflects not only the steep halo mass function. but also the short duty cycle of GRB hosts following the rapid metal enrichment in the initial stages of star formation.," This suppression reflects not only the steep halo mass function, but also the short duty cycle of GRB hosts following the rapid metal enrichment in the initial stages of star formation."
 And again the effect gets more pronounced at decreasing 2 due to the increased fraction of observable hosts which are below threshold., And again the effect gets more pronounced at decreasing $z$ due to the increased fraction of observable hosts which are below threshold.
 On the other hand. the model allows for the existence of GRB hosts with SFRs exceeding a few «107AZ. vr.  within halos endowed with Ag—1077AL.: as shown in Fig.," On the other hand, the model allows for the existence of GRB hosts with SFRs exceeding a few $\times 10^2\,
M_{\odot}$ yr $^{-1}$ within halos endowed with $M_{\rm H}\ga
10^{12}\, M_{\odot}$: as shown in Fig."
 | and Fig., 1 and Fig.
 8. the fraction of these hosts should amount to a few per cent of the total.," 8, the fraction of these hosts should amount to a few per cent of the total."
 Nevertheless they should not have formed a large amount of stars ALAL. exhibit specific SER. AL/AL210~ + and should740! be rather extincted by dust (see Fig.," Nevertheless they should not have formed a large amount of stars $M_{\star}\la 10^{10}\, M_{\odot}$, exhibit specific SFR $\dot{M_{\star}}/M_{\star}\ga 10^{-8}$ $^{-1}$ and should be rather extincted by dust (see Fig."
 1)., 1).
 The adopted galaxy formation scenario coupled with the metal poor collapsar model suggested by stellar evolution have been exploited to infer the above results. which include GRB counts and redshift distribution and the complete deseription of the relevant properties of their hosts. such as SFR. mass in stars. chemical evolution in the cold star forming gas and in the stellar component within individual galaxy halos. with specified mass and formation redshift.," The adopted galaxy formation scenario coupled with the metal poor collapsar model suggested by stellar evolution have been exploited to infer the above results, which include GRB counts and redshift distribution and the complete description of the relevant properties of their hosts, such as SFR, mass in stars, chemical evolution in the cold star forming gas and in the stellar component within individual galaxy halos, with specified mass and formation redshift."
 In this 4 these results are discussed in the light of presently available observations and they are compared to previous studies., In this 4 these results are discussed in the light of presently available observations and they are compared to previous studies.
 The imposed metallicity threshold affects the GRB progenitor redshift distribution., The imposed metallicity threshold affects the GRB progenitor redshift distribution.
" Instead of peaking at around zz3 as in the case without metallicity constrain. the threshold Zoi,=Z./10 yields a broad peak at ς6 (Fig."," Instead of peaking at around $z\approx
3$ as in the case without metallicity constrain, the threshold $Z_{\rm crit}=Z_{\odot}/10$ yields a broad peak at $z\approx 6$ (Fig."
 2)., 2).
 A significant fraction of progenitors are expected at high redshift: approximately 60 per cent at +4 and approximately 30 per cent at 2=6 (see Fig., A significant fraction of progenitors are expected at high redshift: approximately $60$ per cent at $z\ga 4$ and approximately $30$ per cent at $z\ga 6$ (see Fig.
 3)., 3).
 This behavior is shared by all models which associate GRBs with metal poor progenitors (e.g. Natarajan et al., This behavior is shared by all models which associate GRBs with metal poor progenitors (e.g. Natarajan et al.
 2005: Langer orman 2006: Salvaterra Chincarini 2007)., 2005; Langer Norman 2006; Salvaterra Chincarini 2007).
" In particular, our findings are similar to those inferred by Langer Norman (2006). who explored the effect of a metallicity threshold in the environment of GRBs. by adopting a mass-stellar metallicity relation for galaxies and an average cosmic metallicity ‘Z| dependence on redshift dZ]/dzs—0.15 dex."," In particular, our findings are similar to those inferred by Langer Norman (2006), who explored the effect of a metallicity threshold in the environment of GRBs, by adopting a mass-stellar metallicity relation for galaxies and an average cosmic metallicity $[Z]$ dependence on redshift ${\rm
d}[Z]/{\rm d}z\approx -0.15$ dex."
 This law. derived to reproduce the metallicity of stars in galaxies. has been extrapolated to the ISM.," This law, derived to reproduce the metallicity of stars in galaxies, has been extrapolated to the ISM."
 This extrapolation implies that at zZ77 all cosmic star formation occurs in environments with Z]—0.1Z.. independently of the processes occurring in galaxy halos.," This extrapolation implies that at $z\ga 7$ all cosmic star formation occurs in environments with $[Z]\la 0.1\, Z_{\odot}$, independently of the processes occurring in galaxy halos."
 As a result the corresponding rate of low metallicity SNae peaks at 6., As a result the corresponding rate of low metallicity SNae peaks at $z\approx 6$ .
 In our model the combination of cooling and feedback processes implies that at +7 the SFR in cold gas with Z=0.1Z. amounts to about 40 per cent of the cosmic one. due to the short timescale for gas enrichment.," In our model the combination of cooling and feedback processes implies that at $z\approx 7$ the SFR in cold gas with $Z\la 0.1\, Z_{\odot}$ amounts to about $40$ per cent of the cosmic one, due to the short timescale for gas enrichment."
 Therefore. despite of the quite different approach. the redshift distributions of GRB progenitors found by Langer Norman (2006) and Yoon et al. (," Therefore, despite of the quite different approach, the redshift distributions of GRB progenitors found by Langer Norman (2006) and Yoon et al. ("
2006) are very similar to ours. since their assumed SER for metal poor stars peaks at ς=6. similarly to our SFR in cold gas environment (see Fig.,"2006) are very similar to ours, since their assumed SFR for metal poor stars peaks at $z\approx 6$, similarly to our SFR in cold gas environment (see Fig."
 2)., 2).
 The combination of the galaxy formation scenario with the low metallicity collapsar hypothesis for GRB events leads to a good agreement of the predicted and observed (bright. ο1 ph 1 7) counts (see Fig.," The combination of the galaxy formation scenario with the low metallicity collapsar hypothesis for GRB events leads to a good agreement of the predicted and observed (bright, $S\ga 1$ ph $^{-1}$ $^{-2}$ ) counts (see Fig."
 4)., 4).
 This naturally follows - without any tuning - from the derived number of GRB progenitors. under quite simple and plausible assumptions on the GRB jet opening," This naturally follows - without any tuning - from the derived number of GRB progenitors, under quite simple and plausible assumptions on the GRB jet opening"
the core-envelope boundary at the end of the main sequence in case 1 is around an order of magnitude lower than in case 3.,the core-envelope boundary at the end of the main sequence in case 1 is around an order of magnitude lower than in case 3.
 This is partially due to the core of the case-3 star rotating faster than in case 1 but is mostly due to the inclusion of the mean molecular weight gradient in the formulation for case 1., This is partially due to the core of the case-3 star rotating faster than in case 1 but is mostly due to the inclusion of the mean molecular weight gradient in the formulation for case 1.
 Frischknechtetal.(2010) (who use a model very similar to our case 1) predict a much greater decline in the mixing near the core but we have been unable to reproduce this., \citet{Frischknecht10} (who use a model very similar to our case 1) predict a much greater decline in the mixing near the core but we have been unable to reproduce this.
 It is likely that the difference is a result of the inhibiting effect of the mean molecular weight gradient on the rotational mixing., It is likely that the difference is a result of the inhibiting effect of the mean molecular weight gradient on the rotational mixing.
" Whilst it is included in our models, the results of Frischknechtetal.(2010) suggest that towards the end of the main-sequence its effect covers a much larger proportion of the radiative envelope than in our models."," Whilst it is included in our models, the results of \citet{Frischknecht10} suggest that towards the end of the main-sequence its effect covers a much larger proportion of the radiative envelope than in our models."
" As expected, the effects of rotation on the structure and chemical evolution of each star are significant across the HR diagram."," As expected, the effects of rotation on the structure and chemical evolution of each star are significant across the HR diagram."
 We have plotted the case 1 models in Fig 4.., We have plotted the case 1 models in Fig \ref{HR}.
 Centrifugal forces cause the star to expand making it dimmer and redder., Centrifugal forces cause the star to expand making it dimmer and redder.
" However, because of the additional chemical mixing, more hydrogen is made available during the main sequence so, by the main-sequence turn off, rotating stars are generally more luminous than similar mass non-rotating stars."," However, because of the additional chemical mixing, more hydrogen is made available during the main sequence so, by the main-sequence turn off, rotating stars are generally more luminous than similar mass non-rotating stars."
 This effect becomes more pronounced at higher rotation rates and is most apparent for stars with masses up to 20Mo., This effect becomes more pronounced at higher rotation rates and is most apparent for stars with masses up to $20$.
. There are clear differences between the predicted evolution of rotating stars in each of the three cases., There are clear differences between the predicted evolution of rotating stars in each of the three cases.
 Fig., Fig.
" 5 shows the evolution of five different stellar masses in the HR diagram for cases 1, 2 and 3 with an initial surface rotation of 300kms""!."," \ref{HRrad1} shows the evolution of five different stellar masses in the HR diagram for cases 1, 2 and 3 with an initial surface rotation of $300\,\rm{km}\,\rm{s}^{-1}$."
 These cases are the three different models of rotational mixing in radiative zones at solar metallicity., These cases are the three different models of rotational mixing in radiative zones at solar metallicity.
 Rotating case-l stars appear to be the most luminous at low masses but least luminous at high masses., Rotating case-1 stars appear to be the most luminous at low masses but least luminous at high masses.
 Case-2 stars are also consistently cooler than their case-1 and case-3 equivalents except below 10Mo.., Case-2 stars are also consistently cooler than their case-1 and case-3 equivalents except below $10$.
 This is because the strength of rotation-induced mixing increases rapidly, This is because the strength of rotation-induced mixing increases rapidly
work.,work.
 This research has made use of the NASA/IDAC Extragalactic Database (NIZD) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Acronautics ancl Space Aclniinistration.," 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."
It would be interesting to investigate the existence of a first-order differential equation associated with the colatitudinal gradient of the potential. complementary to the radial ODE reported here.,"It would be interesting to investigate the existence of a first-order differential equation associated with the colatitudinal gradient of the potential, complementary to the radial ODE reported here."
 This is the subject of ongoing work., This is the subject of ongoing work.
 Startingfrom Eq. 7.. ," Startingfrom Eq. \ref{eq:uofk}, ,"
and assuming @ constant. the derivative of it with respect to k is This derivative is therefore a function of only &.," and assuming $\theta$ constant, the derivative of $u$ with respect to $k$ is This derivative is therefore a function of only $k$."
 The potential in Eq., The potential in Eq.
" 2. ean then be written as the product of a function of the spherical radius + by an integral over &. namely where The new integral bounds. Ay, and Κομι. correspondto the disk edges diy and Coy. and they are found from Eq. 4.."," \ref{eq:psi} can then be written as the product of a function of the spherical radius $r$ by an integral over $k$, namely where The new integral bounds, $\kint$ and $\kout$, correspondto the disk edges $\ain$ and $\aout$, and they are found from Eq. \ref{eq:kmodulus}."
 In particular. we have anddo respectively.," In particular, we have and respectively."
 For constant colatitude &. the derivative of w with respect to the spherical radius is then given by This quantity is just the opposite of the radial acceleration due to the disk.," For constant colatitude $\theta$, the derivative of $\psi$ with respect to the spherical radius is then given by This quantity is just the opposite of the radial acceleration due to the disk."
 Using an elementary derivation rule (see Paper I). we can calculate the right hand-side of this equation.," Using an elementary derivation rule (see Paper I), we can calculate the right hand-side of this equation."
 We findwhere and similarly for αμ., We findwhere and similarly for $\kint$.
" When a is held constant. we have and|, so OrlyIt follows Okl, that where A is Fo.defined by: Moutdow/R and ttydiy/R."," When $a$ is held constant, we have and so It follows that where $\Lambda$ is defined by: $\uout=\aout/R$ and $\uin=\ain/R$."
 This ordinary differential equation (ODE) is the generalization to the whole space of the ODE reported in ?.. which was valid only 1n the disk plane (1.8. the case @= 4).," This ordinary differential equation (ODE) is the generalization to the whole space of the ODE reported in \cite{hh07}, which was valid only in the disk plane (i.e. the case $\theta=\frac{\pi}{2}$ )."
 This expression differs mainly by the presence of the spherical radius r (instead of R) and by the presence of the Z-dependent modulus & (instead of 71)., This expression differs mainly by the presence of the spherical radius $r$ (instead of $R$ ) and by the presence of the $Z$ -dependent modulus $k$ (instead of $m$ ).
 Asin Paper I. thesecond member A is an analytical function of à single spatial coordinate r.," Asin Paper I, thesecond member $\Lambda$ is an analytical function of a single spatial coordinate $r$ ."
 It now depends on the colatitude € and on the four parameters 5. do. di. and au.," It now depends on the colatitude $\theta$ and on the four parameters $s$ , $a_0$ , $\ain$ , and $\aout$ ."
energv.,energy.
 To be identified with the Crab's optical filaments. hese fingers protrude inward from the outer ejecta shell and eud in dense “heads” with slower expausion velocities han the pleriou. which cau eventually become decoupled youn the shell.," To be identified with the Crab's optical filaments, these fingers protrude inward from the outer ejecta shell and end in dense “heads” with slower expansion velocities than the plerion, which can eventually become decoupled from the shell."
 In αις simulations. the density of the icads was on average 10 times that of the rest of the SN ejecta. and the radial exteut of the fingers was ~0.2 nues that of the shell radius.," In Jun's simulations, the density of the heads was on average $\sim 10$ times that of the rest of the SN ejecta, and the radial extent of the fingers was $\sim 0.2$ times that of the shell radius."
 However. ax mentioned iu us discussion. the inclusion of radiative cooling should lucrease the density coutrast of the heads; aud both this and the radial extent of the finecrs should erow with inue.," However, as mentioned in his discussion, the inclusion of radiative cooling should increase the density contrast of the heads, and both this and the radial extent of the fingers should grow with time."
 These quantities could then be much larger for he supranova plerion. since the relative timescale of the instability here might be much shorter Lj}.," These quantities could then be much larger for the supranova plerion, since the relative timescale of the instability here might be much shorter \ref{eqn:trt}) )."
" Although a fru conclusion warrants Ligh resolution simulations of the relevant conditious. it is uot implausible that the pleriou can effectively shred a substautinal portionia of the SN ejecta into coudeused fragments aud eugulf them curing its lifetime f,."," Although a firm conclusion warrants high resolution simulations of the relevant conditions, it is not implausible that the plerion can effectively shred a substantinal portion of the SN ejecta into condensed fragments and engulf them during its lifetime $t_p$."
 Note that Arons (2002). iu a somewhat ciffereut context. has recently discussed —the issue of SNR fraeieutation by a powerful pulsar wind -iu greater depth.," Note that Arons (2002), in a somewhat different context, has recently discussed the issue of SNR fragmentation by a powerful pulsar wind in greater depth."
 If this is indeed the case (see 85 for conuueuts when this is not). there are important nuplicatious for the Fe line ciuission iu afterelows.," If this is indeed the case (see 5 for comments when this is not), there are important implications for the Fe line emission in afterglows."
 The simplest explauation for the lines is Fe Ίνα unultiple recombination radiation from Fe-vich matter photoionized bv the ταν afterglow contimmi on timescales of davs (Lazzati et al., The simplest explanation for the lines is Fe $\alpha$ multiple recombination radiation from Fe-rich matter photoionized by the X-ray afterglow continuum on timescales of days (Lazzati et al.
 1999. Weth et al.," 1999, Weth et al."
 2000. Paerels et al.," 2000, Paerels et al."
 2000)., 2000).
 Consistency with observations require that the material to be illuminated is very dense aud possesses a huge covering factor. and vet that the GRB line of sight is devoid of anv such matter so that the CRB blastwave will not be decelerated too quickly (Lazzati ct al.," Consistency with observations require that the material to be illuminated is very dense and possesses a large covering factor, and yet that the GRB line of sight is devoid of any such matter so that the GRB blastwave will not be decelerated too quickly (Lazzati et al."
 1999)., 1999).
 The flamenutary fragmentation of the SNR univ naturally account for such a eeouetry., The filamentary fragmentation of the SNR may naturally account for such a geometry.
 The condensation of the SNR aatter may also cuhauce the line enmüssvitv., The condensation of the SNR matter may also enhance the line emissivity.
" The cussion rate of line photous through recombination when a sufficient phlotoioniziug flux ivraciates amaterial with clectrou density nn.= aud temperature T=10Nv containing an Fe mass Mg.=0.1ΛουAL.. ds where NVR. is the total nuuber of Fe atoms and fi2aquaΊδηςTTS61""nj.ο locis the recombination: tine: for] ILlike. Fe (Paerels et al."," The emission rate of line photons through recombination when a sufficient photoionizing flux irradiates material with electron density $n_e = 10^9 n_{e,9} {\rm cm^{-3}}$ and temperature $T = 10^7 T_7 K$ containing an Fe mass $M_{\rm Fe} = 0.1 M_{\rm Fe, 0.1} {\rm M_\odot}$ is where $N_{\rm Fe}$ is the total number of Fe atoms and $t_{rec} \simeq 127 {\rm s} \ T_7^{3/4} n_{e,9}^{-1}$ is the recombination time for H-like Fe (Paerels et al."
 2000. ποσα et al.," 2000, Vietri et al."
 2001)., 2001).
" By the time of the GRB at £,,= (που roefsecioc)). a SNR. of 120f,459daysM,=10M.14M expanding af CQ=0.105940 will have reached a radius Roc34do&10156. τουσ. and ifodistrubuted m a spherical shell of width gat,AB,~OLR... its electron deusity would be Typically observed line fluxes can be obtained for ΔΑ{που= dP(Eq.5)). but oulv if the cutive spherical shell is nnracdiated and enmüts line photons cticicutly."," By the time of the GRB at $t_p = 120 t_{p,120} {\rm days}$ (see \\ref{sec:ec}) ), a SNR of $M_s = 10 M_{s,10} {\rm M_\odot}$ expanding at $v_s = 0.1 v_{s,0.1} c$ will have reached a radius $R_s \simeq 3.1 \times 10^{16} v_{s,0.1} t_{p,120} {\rm cm}$ , and if distributed in a spherical shell of width $\Delta R_s \sim 0.1 R_s$, its electron density would be Typically observed line fluxes can be obtained for $M_{\rm Fe, 0.1} \gtrsim 4$ \ref{eqn:nl}) ), but only if the entire spherical shell is irradiated and emits line photons efficiently."
 The CRB blast wave must then be isotropic and no beaming is allowed (Piro ct al., The GRB blast wave must then be isotropic and no beaming is allowed (Piro et al.
 2000: see however I&CO02). which is incongruous with recent evidence to the contrary (6.8. Frail et al.," 2000; see however KG02), which is incongruous with recent evidence to the contrary (e.g. Frail et al."
 2001. Panaitescu I&unar 2002).," 2001, Panaitescu Kumar 2002)."
" Iowever. if the SNR. ejecta can be condensed iuto filaments of much higher density. £,4 is shortened. aud irradiating a smaller fraction of material may suffice to produce the observed lines."," However, if the SNR ejecta can be condensed into filaments of much higher density, $t_{rec}$ is shortened, and irradiating a smaller fraction of material may suffice to produce the observed lines."
 For comparison. the density of the the Crab's optical filaments averaged over the volume of the whole nebula is vn~Lem°. whereas the actual deusity of the individual filaments is 56~LOcm (Davidson Fesen 1985).," For comparison, the density of the the Crab's optical filaments averaged over the volume of the whole nebula is $n \sim 10 {\rm cm^{-3}}$, whereas the actual density of the individual filaments is $n \sim 10^{3} {\rm cm^{-3}}$ (Davidson Fesen 1985)."
 Although detailed uuuerical nocdeling is necessary for quantitative predictions. we may speculate that the deusitv contrast cotld be even higher or the suprauova pleriou due to the instability beime more developed (see above). and beaming Yactions of order ~0.01 may be cutirely compatible wit1i the observed Fe ines.," Although detailed numerical modeling is necessary for quantitative predictions, we may speculate that the density contrast could be even higher for the supranova plerion due to the instability being more developed (see above), and beaming fractions of order $\sim 0.01$ may be entirely compatible with the observed Fe lines."
 Note that in explaining the trausieut Fe absorption eature in GRDB990705. Lazzati ct al. (," Note that in explaining the transient Fe absorption feature in GRB990705, Lazzati et al. ("
2001) have inferred he presence of chuupy SNR ejecta materal with density contrasts of order 100-1000. surromndiis the burst site (see also Botttcher. Dermer Fryer 202j.,"2001) have inferred the presence of clumpy SNR ejecta material with density contrasts of order 100-1000 surrounding the burst site (see also Bötttcher, Dermer Fryer 2002)."
 The observed iue cucrey in CRD991216 can also be consistent with )anuue if identified with bhlicshitted ciuission from Fe (for which the rest frame energyv is 6.7 keV. aud fag Us sudayr to I]Blke Fe at somewhat lower T) in uaterial approaching toward the observer with e;~0.le (Ballautvue Ramiurez-Ruiz 2001).," The observed line energy in GRB991216 can also be consistent with beaming if identified with blueshifted emission from He-like Fe (for which the rest frame energy is 6.7 keV, and $t_{rec}$ is similar to H-like Fe at somewhat lower $T$ ) in material approaching toward the observer with $v_s \sim 0.1c$ (Ballantyne Ramirez-Ruiz 2001)."
" We aneution that even when circumstances conducive o Fe line cussion cannot be realized. the action of the erion for f,>LOS aay expel nuch of the barvous surroundius the CRB site out to radii >LOcm and clear he path for the eusuiug fireball. which is a great advantage of the suprauova 1ος]."," We mention that even when circumstances conducive to Fe line emission cannot be realized, the action of the plerion for $t_p \gtrsim 10^3 {\rm s}$ may expel much of the baryons surrounding the GRB site out to radii $\gtrsim 10^{13} {\rm cm}$ and clear the path for the ensuing fireball, which is a great advantage of the supranova model."
 Another important implication of the precursor pleriou in the supranova inodel is that the GRB should be exploding iuto a radiation-dich! environment. ic. iuto the luminous radiation Seld of the pleriou. which cau constitute a laree fraction of the pulsar wind hnuninositv.," Another important implication of the precursor plerion in the supranova model is that the GRB should be exploding into a `radiation-rich' environment, i.e. into the luminous radiation field of the plerion, which can constitute a large fraction of the pulsar wind luminosity."
" Such ""external photons inpiugiug iuto the relativistically expanding GRB shock from outside would be seen lighly Doppler-boosted in the shock comoving frame. aud act as Cficicut seeds for iuverse Compton scattering (referred to as external Comptouization. or EC). with inportaut- observational consequences for tle afterglow cunissiou."," Such `external' photons impinging into the relativistically expanding GRB shock from outside would be seen highly Doppler-boosted in the shock comoving frame, and act as efficient seeds for inverse Compton scattering (referred to as external Comptonization, or EC), with important observational consequences for the afterglow emission."
 Since our focus here is on the possible manistestatious of the EC enüssiou process in the suprauova model. we do not attempt a detailed plivsical modeling of the the plerion dynamics. enploviusg iusteacd a simplific description for illustrative purposes.," Since our focus here is on the possible manisfestations of the EC emission process in the supranova model, we do not attempt a detailed physical modeling of the the plerion dynamics, employing instead a simplified description for illustrative purposes."
 As discussed by WO02. such modeling would eutail various uncertainties and requires a dedicated study by itself. which is out of our current scope.," As discussed by KG02, such modeling would entail various uncertainties and requires a dedicated study by itself, which is out of our current scope."
 Once a suitable dyxauuical model of the pleriou can be constructed. the formulation of this paper nav be used to make more reliable predictions of the afterglow eunission.," Once a suitable dynamical model of the plerion can be constructed, the formulation of this paper may be used to make more reliable predictions of the afterglow emission."
 Álternativelv. if an afterglow EC enüssion coniponeut is actually observed in the future. we may interpret the data with our formulation so tha the unknown properties of the supranova pleriou cau be probed.," Alternatively, if an afterglow EC emission component is actually observed in the future, we may interpret the data with our formulation so that the unknown properties of the supranova plerion can be probed."
related to the pressure gradients of (he gas as in r-direction and along the z-axis.,related to the pressure gradients of the gas as in $r$ -direction and along the $z$ -axis.
" In equations (1) and (2). o,(R) and P,(R) ave the density and pressure of the gas. respectively. wy is the angular velocity of the gas on a plane parallel to the midplane ab a height z. aud wy is ils corresponding Ixeplerian angular velocity. given by where G is the gravitational constant and A. is the mass of the central star."," In equations (1) and (2), ${\rho_g}({\bf R})$ and ${{\cal P}_g}({\bf R})$ are the density and pressure of the gas, respectively, $\omega_g$ is the angular velocity of the gas on a plane parallel to the midplane at a height $z$, and $\omega_K$ is its corresponding Keplerian angular velocity given by where $G$ is the gravitational constant and $M$ is the mass of the central star."
 The balance of the gravitational attraction of the central star by the pressure gradients in the vertical direction. as given by equation (2). determines (he distribution of the gas along the z-axis.," The balance of the gravitational attraction of the central star by the pressure gradients in the vertical direction, as given by equation (2), determines the distribution of the gas along the $z$ -axis."
 In the model nebula considered. here. the gas is pure molecular hydrogen and it. therefore. obevs the equation state of an ideal gas.," In the model nebula considered here, the gas is pure molecular hydrogen and it, therefore, obeys the equation state of an ideal gas."
 As a result. the pressure and densitv of the gas are related as where Aj is the Bollzmann constant. J is the temperature of the eas and rp is the molecular mass of hydrogen.," As a result, the pressure and density of the gas are related as where $K_{\rm B}$ is the Boltzmann constant, $T$ is the temperature of the gas and $m_0$ is the molecular mass of hydrogen."
" Substituting lor P,(R) [rom equation (4) in equation (2). the density of our model nebula will be given by In equation (5). pj(r.0) is the density of the gas on the midplane."," Substituting for ${{\cal P}_g}({\bf R})$ from equation (4) in equation (2), the density of our model nebula will be given by In equation (5), ${\rho_g}(r,0)$ is the density of the gas on the midplane."
 As mentioned in § 1. in order to focus attention on the clvnamics of solids. we consider a nebula wilh an azimuthallv symmetric density enhancement on its midplane.," As mentioned in $\S$ 1, in order to focus attention on the dynamics of solids, we consider a nebula with an azimuthally symmetric density enhancement on its midplane."
" Following IIDO03. we assume where pij.r4, and 9 are constant quantities."," Following HB03, we assume where ${\rho_0}\,,{r_m}$ and $\beta$ are constant quantities."
 Figure 1 shows an edge-on view of our model nebula with the line of sieht perpendicular to one of the midplane diameters., Figure 1 shows an edge-on view of our model nebula with the line of sight perpendicular to one of the midplane diameters.
" The central star in (his figure is solar-tvpe and the gas temperature is 300 Ix. The values of pp.;2 and r,, are equal to LO""σοι7.1 and 1 AU. respectively."," The central star in this figure is solar-type and the gas temperature is 300 K. The values of ${\rho_0}\,,\beta$ and ${r_m}$ are equal to ${10^{-9}}\,{\rm {g\,cm^{-3}}}\,,1$ and 1 AU, respectively."
redshifts.,redshifts.
" Assuming that only one supermassive Pop III star forms in unenriched minihalos, and that none form in protogalaxies, ? found the PISNe rate be ~0.34 deg? yr! at z~20."," Assuming that only one supermassive Pop III star forms in unenriched minihalos, and that none form in protogalaxies, \citet{Wise2005} found the PISNe rate be $\sim 0.34$ $^{-2}$ $^{-1}$ at $z\sim 20$."
" After our paper was submitted, ? presented a complimentary analysis of the source density of PISNe from pristine minihalos, and determined the observability of such events with the (JWST), finding approximately ~0.4 PISNe visible per JWST field of view at any given time."," After our paper was submitted, \citet{Hummel2011} presented a complimentary analysis of the source density of PISNe from pristine minihalos, and determined the observability of such events with the (JWST), finding approximately $\sim 0.4$ PISNe visible per JWST field of view at any given time."
" PISNe after the epoch of reionization were also considered; ? calculated a suite of PISNe model light curves with blackbody spectra, and analyzed the detectability and rates of PISNe from Pop III stars formed from leftover pristine gas at z<6."," PISNe after the epoch of reionization were also considered; \citet{Scannapieco2005a} calculated a suite of PISNe model light curves with blackbody spectra, and analyzed the detectability and rates of PISNe from Pop III stars formed from leftover pristine gas at $z \lesssim 6$."
" As for CCSNe during reionization, ? presented detailed predictions for the number of core collapse SNe that JWST could observe as a function of different survey parameters."," As for CCSNe during reionization, \citet{Mesinger2006} presented detailed predictions for the number of core collapse SNe that JWST could observe as a function of different survey parameters."
" In this paper, we present light curves and spectral time series for PISNe from our multi-wavelength radiation-hydrodynamics simulations."," In this paper, we present light curves and spectral time series for PISNe from our multi-wavelength radiation-hydrodynamics simulations."
" As the stellar population responsible for reionization is currently unknown, instead of predicting a fixed SNe rate, we normalize the star formation rate by requiring that enough ionizing photons must be produced by either Pop III or Pop II stars in protogalaxies to complete reionization by z~6, and calculate the rates of pair-instability, core-collapse, and Type Ia SNe and their detectability with JWST for these two scenarios; the actual SNe rates will be in between these limiting cases."," As the stellar population responsible for reionization is currently unknown, instead of predicting a fixed SNe rate, we normalize the star formation rate by requiring that enough ionizing photons must be produced by either Pop III or Pop II stars in protogalaxies to complete reionization by $z \sim 6$, and calculate the rates of pair-instability, core-collapse, and Type Ia SNe and their detectability with JWST for these two scenarios; the actual SNe rates will be in between these limiting cases."
" We show that using the observed rates of these SNe, it is possible to distinguish the contribution of Pop III and Pop II stars toward reionization by characterizing the IMF at that time."," We show that using the observed rates of these SNe, it is possible to distinguish the contribution of Pop III and Pop II stars toward reionization by characterizing the IMF at that time."
" The stellar evolution and explosion of PISN models, and the resulting broadband light curves and spectral time-series are described in detail in ?;; here we summarize the results."," The stellar evolution and explosion of PISN models, and the resulting broadband light curves and spectral time-series are described in detail in \citet{Kasen2011}; here we summarize the results."
" Models R150, R175, R200, R225, R250 represent explosions of 150-250 Mo red supergiant stars, respectively, each with their hydrogen envelope intact."," Models R150, R175, R200, R225, R250 represent explosions of 150-250 $M_{\odot}$ red supergiant stars, respectively, each with their hydrogen envelope intact."
" In principle, blue supergiants are also possible progenitors of PISNe, but convective mixing of metals into the hydrogen envelope makes it more likely that the progenitor dies as a red supergiant."," In principle, blue supergiants are also possible progenitors of PISNe, but convective mixing of metals into the hydrogen envelope makes it more likely that the progenitor dies as a red supergiant."
" Models He80, He100, He130 were explosions of 80, 100, 130 Mo bare helium cores."," Models He80, He100, He130 were explosions of 80, 100, 130 $M_{\odot}$ bare helium cores."
 Such models may represent stars that lost they hydrogen envelope due to a prior pulsational phase or through binary interactions., Such models may represent stars that lost they hydrogen envelope due to a prior pulsational phase or through binary interactions.
 Here we use an approximate empirical relation between the helium core mass and the progenitor main-sequence mass (?):: Properties of all presupernova stars and their explosions are given in Table 1.., Here we use an approximate empirical relation between the helium core mass and the progenitor main-sequence mass \citep{Heger2002}: Properties of all presupernova stars and their explosions are given in Table \ref{ProgenitorModelTable}.
" A few days after the explosion, hydrodynamical processes subside and the ejected material reaches a phase of nearly free expansion."," A few days after the explosion, hydrodynamical processes subside and the ejected material reaches a phase of nearly free expansion."
 The energy powering the subsequent light curve may derive from three possible sources: (i)) Lingering thermal energy from the explosion itself; (14)) The radioactive decay of synthesized ?9Ni; (iii)) The interaction of the ejecta with a dense circumstellar medium., The energy powering the subsequent light curve may derive from three possible sources: ) Lingering thermal energy from the explosion itself; ) The radioactive decay of synthesized $^{56}$ Ni; ) The interaction of the ejecta with a dense circumstellar medium.
" Thermal energy suffers adiabatic losses on the expansion timescale te;=Ro/v, and so source (7)) is only significant for stars with large initial radii Ro."," Thermal energy suffers adiabatic losses on the expansion timescale $t_{ex} = R_{0}/v$, and so source ) is only significant for stars with large initial radii $R_{0}$."
 Circumstellar interaction has not been included in the models discussed here., Circumstellar interaction has not been included in the models discussed here.
 We have computed light curves and spectral time series of the explosion models using the time dependent radiative transfer code SEDONA (?)., We have computed light curves and spectral time series of the explosion models using the time dependent radiative transfer code SEDONA \citep{Kasen2006}.
" All models shown here assume spherical symmetry, and calculations of atomic level populations assume local thermodynamic equilibrium."," All models shown here assume spherical symmetry, and calculations of atomic level populations assume local thermodynamic equilibrium."
" Using Monte Carlo methods, we solve the full multi-wavelength radiative transfer problem using realistic opacities as a function of wavelength, composition and temperature, over millions of line transitions."," Using Monte Carlo methods, we solve the full multi-wavelength radiative transfer problem using realistic opacities as a function of wavelength, composition and temperature, over millions of line transitions."
" Unlike previous blackbody models (??),, our results allow us to calculate more accurate light curves for any given color bands and to study the time evolution of the supernova colors and spectral features."," Unlike previous blackbody models \citep{Wise2005, Scannapieco2005a}, our results allow us to calculate more accurate light curves for any given color bands and to study the time evolution of the supernova colors and spectral features."
 'The shape and duration of PISN light curves depend on the mass and radius of their progenitors., The shape and duration of PISN light curves depend on the mass and radius of their progenitors.
 Model R250, Model R250
Corbetetal.(2005). found the 8.9640.01 dav orbital period by analyzing a Durst Alert Telescope 11-200 keV lieht curve. aud determined the epoch of maxima flux to be MJD 53507.1£0.1.,"\citet{corbetetal05} found the $8.96 \pm 0.01$ day orbital period by analyzing a Burst Alert Telescope 14-200 keV light curve, and determined the epoch of maximum flux to be MJD $53507.1 \pm 0.1$."
 Walteretal.(2006) usec observations with to measure the period. obtaining P=8.99X0.05 d. The orbital period is secu at a high level of significance in the ASM power spectrum shown in Figure 16..," \citet{walteretal06} used observations with to measure the period, obtaining $P =
8.99 \pm 0.05$ d. The orbital period is seen at a high level of significance in the ASM power spectrum shown in Figure \ref{fig:pds1632}."
 We use the ASM power spectrum to estimate that the period is 8.9901+0.0009[0.0081 d. is an N-rav source in the Galactic plane that was discovered using (Tousick.etal.," We use the ASM power spectrum to estimate that the period is $8.9901 \pm 0.0009\,[\pm 0.0081]$ d. is an X-ray source in the Galactic plane that was discovered using \citep{tomsicketal04}."
" 2001Y.. Corbetetal.(2006). found ancl measure the orbital period using both Swift/BAT aud ASA data and obtained the values 3.75340.001 days and 3.7389+0.0001 days respectively,"," \citet{corbetal06} found and measured the orbital period using both /BAT and ASM data and obtained the values $3.753 \pm 0.004$ days and $3.7389 \pm 0.0004$ days, respectively."
 Our curren ASAD power spectrum (Fie. 17)), Our current ASM power spectrum (Fig. \ref{fig:pds1641}) )
 shows a peak tha is moderatelv significant given prior kuowledee of the iod., shows a peak that is moderately significant given prior knowledge of the period.
 The frequency of this peak corresponds. to the veriod P23.73886c0.00028 davs.," The frequency of this peak corresponds to the period $P = 3.73886 \pm
0.00028\,[\pm 0.00140]$ days."
 This veriod is essentially identical to that [0.001determinedIu earlier roni the ASM databy Corbetetabral.(2006)., This period is essentially identical to that determined earlier from the ASM data by \citet{corbetal06}.
.. is an A-rvav in a highanass ynary system seen edec-ou (Thompsonetal.2007.andreferences therein)., is an X-ray pulsar in a high-mass binary system seen edge-on \citep[and references therein]{thompson07}.
 Eclipses were found im N-rav observations made in scaus of the Galactic plane with heRNTE PCA aud their temporal spacing was used to eot the first real mcasurement of the orbital period. 1.6.. P—9.71x0.001 davs (Corbetetal.," Eclipses were found in X-ray observations made in scans of the Galactic plane with the PCA and their temporal spacing was used to get the first real measurement of the orbital period, i.e., $P = 9.741 \pm
0.004$ days \citep{cms05}."
 2005).. Thompsonetal(2007) lave estimated the orbital parameters through a pulse timing analysis aud obtain a value for the period of P=9.71032:0.0001 days., \citet{thompson07} have estimated the orbital parameters through a pulse timing analysis and obtain a value for the period of $P = 9.7403 \pm 0.0004$ days.
One might expect a strong signal from an eclipsing svstem but the source,One might expect a strong signal from an eclipsing system but the source
Our strategy is motivated by two basic limitations in modeling star formation on cosmological scales.,Our strategy is motivated by two basic limitations in modeling star formation on cosmological scales.
 First. there is no fundamental theory of this process.," First, there is no fundamental theory of this process."
 Second. large-scale simulations lack the resolution that would be required to characterize the ISM in detail.," Second, large-scale simulations lack the resolution that would be required to characterize the ISM in detail."
 Our. statistical. method decouples our ignorance of star formation from its impact on galactic scales. by coarse-graining the physies of star-forming gas.," Our statistical method decouples our ignorance of star formation from its impact on galactic scales, by coarse-graining the physics of star-forming gas."
 In principle. this strategy could be applied to any model of star formation.," In principle, this strategy could be applied to any model of star formation."
 For a detailed deseription of our multiphase model we refer thereader to Springel&Hernquist(2003a)., For a detailed description of our multiphase model we refer thereader to \cite{sh03a}.
. For definiteness. we list in Table | the parameter values adopted in our simulations.," For definiteness, we list in Table 1 the parameter values adopted in our simulations."
 The parameters include the efficiency ofthe evaporation process Ag. the mass fraction of stars that are short-lived and die as supernovae .;. the cold gas cloud temperature Ίρμμι. the effective supernova temperature τον. and the gas consumption time-scale t5. As Sprin," The parameters include the efficiency ofthe evaporation process $A_{0}$, the mass fraction of stars that are short-lived and die as supernovae $\beta$, the cold gas cloud temperature $T_{\rm cloud}$, the effective supernova temperature $T_{\rm SN}$, and the gas consumption time-scale $t_0^\star$."
gel&Hern-quist(2003a) argue. all of these aside from one. e.g. fj. can be constrained by simple physical arguments.," As \cite{sh03a} argue, all of these aside from one, e.g. $t_0^\star$, can be constrained by simple physical arguments."
" We adjust 4, to match the Kennicutt Law which describes empirically observed star formation rates in nearby galaxies (e.g.Kenni-cutt1989, 1998)."," We adjust $t_0^\star$ to match the Kennicutt Law which describes empirically observed star formation rates in nearby galaxies \citep[e.g.][]{kennicutt89a,kennicutt98a}."
 On the surface. our description of star-forming gas appears complicated. with the properties of the different phases described by differential equations that include the various processes listed above.," On the surface, our description of star-forming gas appears complicated, with the properties of the different phases described by differential equations that include the various processes listed above."
 However. in the end. our model can be reduced to two main ingredients that make our results easier to interpret.," However, in the end, our model can be reduced to two main ingredients that make our results easier to interpret."
 Springel&Hernquist(2003a) showed that the star-forming gas quickly establishes a self-regulated cycle in which the mass and energy of the phases can be approximated by equilibrium solutions., \cite{sh03a} showed that the star-forming gas quickly establishes a self-regulated cycle in which the mass and energy of the phases can be approximated by equilibrium solutions.
 In this limit. the impact of star formation and feedback can be reduced to: 1) the rate at which gas Is converted into stars. and 2) the effective equation of state for star-forming σας.," In this limit, the impact of star formation and feedback can be reduced to: 1) the rate at which gas is converted into stars, and 2) the effective equation of state for star-forming gas."
" Here. as in Springel&Hernquist(2003a).. we choose to parameterize the star formation rate by where The free parameter £j is chosen to match the Kennicutt Law. fu isa threshold density above which gas ts subject to thermal instability and star formation. and p, is the density of clouds which. in equilibrium. is given by equation (18) of Springel&Hernquist (2003a)."," Here, as in \citet{sh03a}, we choose to parameterize the star formation rate by where The free parameter $t_0^\star$ is chosen to match the Kennicutt Law, $\rho_{\rm th}$ is a threshold density above which gas is subject to thermal instability and star formation, and $\rho_c$ is the density of clouds which, in equilibrium, is given by equation (18) of \cite{sh03a}."
". Springel&Hernquist(20034). showed that py, can be fixed by e.g. requiring the equation of state to be continuous.", \cite{sh03a} showed that $\rho_{\rm th}$ can be fixed by e.g. requiring the equation of state to be continuous.
 In our subresolution model. feedback from supernovae adds thermal energy to the ISM. pressurizing it and modifying its equation of state.," In our subresolution model, feedback from supernovae adds thermal energy to the ISM, pressurizing it and modifying its equation of state."
 On the scales relevant to the dynamics of the gas. this is described by an effective equation of state. which can be written where 5 is the ratio of specific heats. pis the total gas density. and ty is the effective specific thermal energy of the star-forming gas which. in equilibrium. is given by equation (19) of Springel&Hernquist (2003a)..," On the scales relevant to the dynamics of the gas, this is described by an effective equation of state, which can be written where $\gamma$ is the ratio of specific heats, $\rho$is the total gas density, and $u_{\rm eff}$ is the effective specific thermal energy of the star-forming gas which, in equilibrium, is given by equation (19) of \cite{sh03a}. ."
 The effective equation of state for the particular model parameters employed in our study is illustrated in Figure ].. in egs units.," The effective equation of state for the particular model parameters employed in our study is illustrated in Figure \ref{fig:eos}, in cgs units."
 Also shown 1a) Figure | is a simple fit to the equation of state. which 1 accurate to about 1% and is given by In the particular example shown in Figure l.. the gas is assumed to be isothermal for densities p—py.," Also shown in Figure \ref{fig:eos} is a simple fit to the equation of state, which is accurate to about $1\%$ and is given by In the particular example shown in Figure \ref{fig:eos}, the gas is assumed to be isothermal for densities $\rho \le \rho_{\rm th}$."
 In egs units. for the parameter choices adopted here. the critical density at which the gas begins to depart from isothermality ts ”y.)=0.128 em.," In cgs units, for the parameter choices adopted here, the critical density at which the gas begins to depart from isothermality is $n_{\rm H, th} = 0.128$ $^{-3}$."
 This choice ensures that the effective pressure is a continuous function of density., This choice ensures that the effective pressure is a continuous function of density.
" For the equation of state shown in Figure |. a different value of yy, would introduce an unphysical jump in pressure at the transition density where the gas is no longer isothermal."," For the equation of state shown in Figure 1, a different value of $n_{\rm H,
th}$ would introduce an unphysical jump in pressure at the transition density where the gas is no longer isothermal."
 Our implementation of feedback differs significantly from previous works (e.g.Sommer-Larsenetal.2003;Governatoetal. 2002).," Our implementation of feedback differs significantly from previous works \citep[e.g.][]{slgp03a,governato02a}. ."
". In our subresolution model. feedback energy is ""stored"" in the surrounding gas. adding pressure support to it."," In our subresolution model, feedback energy is “stored” in the surrounding gas, adding pressure support to it."
 As shown inFigure 1.. at densities p> py. the equation of state becomes stiffer than isothermal due to this feedback," As shown inFigure \ref{fig:eos}, , at densities $\rho > \rho_{\rm th}$ , the equation of state becomes stiffer than isothermal due to this feedback"
"the wide range of evolutionary phases pertaining outside the red clump, which certainly will cause a complex dependence of & with more parameters than just the large separation.","the wide range of evolutionary phases pertaining outside the red clump, which certainly will cause a complex dependence of $\varepsilon$ with more parameters than just the large separation."
 This disagreement reinforces the homogenous properties of red-giant stars., This disagreement reinforces the homogenous properties of red-giant stars.
" The clearly observed pattern confirms that, on average, the linewidths of the modes are significantly smaller than the separation of the even mode pairs and hence makes short mode lifetimes unlikely (?).."," The clearly observed pattern confirms that, on average, the linewidths of the modes are significantly smaller than the separation of the even mode pairs and hence makes short mode lifetimes unlikely \citep{2004SoPh..220..207S}."
" From the quasi-uniform width of the ridges (Fig. 3)),"," From the quasi-uniform width of the ridges (Fig. \ref{identi}) ),"
" we can see that the lifetimes of the modes increase significantly with decreasing large separation, contrary to ?.."," we can see that the lifetimes of the modes increase significantly with decreasing large separation, contrary to \cite{huber2010}."
 It also suggests that very complex oscillation spectra previously observed may be an artefact of noise., It also suggests that very complex oscillation spectra previously observed may be an artefact of noise.
" Finally, the better determination of the large separation Av helps us to enhance the accuracy of the estimates of the stellar mass and radius as done in ?,, with typical error-bars of 12 and 20 and without the need of stellar modeling (?), constitutes an important progress compared to the current photometric determination and demonstrates the power of asteroseismology."," Finally, the better determination of the large separation $\dnumoy$ helps us to enhance the accuracy of the estimates of the stellar mass and radius as done in \cite{2010A&A...517A..22M}, with typical error-bars of 12 and 20 and without the need of stellar modeling \citep{kallinger2010}, constitutes an important progress compared to the current photometric determination and demonstrates the power of asteroseismology."
 We have shown with CoRoT observations that the red-giant oscillation spectrum is very regular and can be described by its underlying universal pattern., We have shown with CoRoT observations that the red-giant oscillation spectrum is very regular and can be described by its underlying universal pattern.
 This was modelled in parallel by ?.., This was modelled in parallel by \cite{2010ApJ...721L.182M}.
" As a consequence, the precise measures of the large separation and the scaling relation of the parameter & allow us to provide an unambiguous detection of the radial orders and angular degrees of the modes."," As a consequence, the precise measures of the large separation and the scaling relation of the parameter $\varepsilon$ allow us to provide an unambiguous detection of the radial orders and angular degrees of the modes."
" Since the method is able to mitigate the realization noise, we consider it to give the most precise determination of the large separation available."," Since the method is able to mitigate the realization noise, we consider it to give the most precise determination of the large separation available."
 It remains important to interpret the physical meaning of the scaling law for the term e in the Tassoul expression., It remains important to interpret the physical meaning of the scaling law for the term $\varepsilon$ in the Tassoul expression.
 We will have to disentangle the contributions of the surface and of the inner region., We will have to disentangle the contributions of the surface and of the inner region.
 This will require an investigation of the term ε in the context of the second-order corrections of the Tassoul development., This will require an investigation of the term $\varepsilon$ in the context of the second-order corrections of the Tassoul development.
 Very long-duration observations with will help for this task., Very long-duration observations with will help for this task.
" Despite the uniform aspect of the oscillation spectra, many differences invisible in the global approach are revealed by a detailed analysis of each individual spectrum, as, for example, the modulation with frequency of the large separation (?).. (??).."," Despite the uniform aspect of the oscillation spectra, many differences invisible in the global approach are revealed by a detailed analysis of each individual spectrum, as, for example, the modulation with frequency of the large separation \citep{2010A&A...517A..22M}. \citep{2008Sci...322..558M,2008A&A...488..705A}."
In this equation the vector. of (physical) is defined as where eG=ο) is the Iuid 3-velocity. defined. as vímulfou!|d focwilh e;25:50.,"In this equation the vector of (physical) is defined as where $v_i (i=r,\theta,\phi)$ is the fluid 3-velocity, defined as $v^i=u^i/\alpha u^t + \beta^i/\alpha$ with $v_i=\gamma_{ij}v^j$."
 On the other hand. the state vector (evolved quantities) in Iq. (43))," On the other hand, the state vector (evolved quantities) in Eq. \ref{system}) )"
 is The explicit relations between the two sets of variables.U and w. are with L being the Lorentz factor. Lb—os!=(1.02)E? with p2sighe.," is The explicit relations between the two sets of variables,${\bf U}$ and ${\bf w}$, are with $\Gamma$ being the Lorentz factor, $\Gamma\equiv\alpha u^t =
(1-v^2)^{-1/2}$, with $v^2=\gamma_{ij}v^i v^j$."
 Phe specilie form of the Duxes. F'. and the source terms.S. read with with the definitions cs dn the above expressions clenotes partial differentiation and the D stand for the Christollel symbols (only the non-vanishing ones are displaved) which are obtained from the metric according to the usual definition The hvdrodynamics code used in our computations was originally developed for studies of relativistic wind accretion on to black holes (?22?7)).," The specific form of the fluxes, ${\bf F}^{i}$, and the source terms, read with with the definitions The `,' in the above expressions denotes partial differentiation and the $\Gamma^{\delta}_{\mu\nu}$ stand for the Christoffel symbols (only the non-vanishing ones are displayed) which are obtained from the metric according to the usual definition The hydrodynamics code used in our computations was originally developed for studies of relativistic wind accretion on to black holes \cite{font:98a,font:98b,font:98c,font:99}) )."
 Phis code performs the numerical integration of svstenmi (43)) using a so-called Ciodunov-type scheme., This code performs the numerical integration of system \ref{system}) ) using a so-called Godunov-type scheme.
" Such sehemes are specifically designed: to. solve nonlinear hyperbolic systems of conservation laws (sec. e.g. ""Toro 1999 for definitions)."," Such schemes are specifically designed to solve nonlinear hyperbolic systems of conservation laws (see, e.g. Toro 1999 for definitions)."
 In a Godunoy-tvpe method the knowledge of the characteristic structure of the equations is essential to design a solution. procedure. based: upon either exact or approximate Riemann solvers., In a Godunov-type method the knowledge of the characteristic structure of the equations is essential to design a solution procedure based upon either exact or approximate Riemann solvers.
 These solvers compute. at every. cell-cinterface of the numerical grid. the solution of local Ricmann problems (i.e. the simplest initial value problems with discontinuous initial data).," These solvers compute, at every cell-interface of the numerical grid, the solution of local Riemann problems (i.e., the simplest initial value problems with discontinuous initial data)."
 Therefore. they automatically guarantee the proper capturing of all discontinuities which may arise naturally in the solution space of a nonlinear hyperbolic svsten.," Therefore, they automatically guarantee the proper capturing of all discontinuities which may arise naturally in the solution space of a nonlinear hyperbolic system."
" Phe time update of system (43)) from /"" to £* is performed according to the following conservative algorithm: Index n represents the time level and the time (space) discretization interval is indicated by 2M. (Ar.A@)."," The time update of system \ref{system}) ) from $t^n$ to $t^{n+1}$ is performed according to the following conservative algorithm: Index $n$ represents the time level and the time (space) discretization interval is indicated by $\Delta t$ $\Delta r, \Delta\theta$ )."
 The numerical Luxes in the above equation. F'. F are computed bv means of the LILLE Biemann solver (??)..," The numerical fluxes in the above equation, $\widehat{{\bf F}}^{r}$, $\widehat{{\bf F}}^{\theta}$ are computed by means of the HLLE Riemann solver \citep{harten:83,einfeldt:88}."
 Phese fluxes are obtained. independentIs for cach direction and the time update of the state-vector. U is done simultaneously. using a method. of lines in combination with a second-order (in time) conservative Itunge-Ixutta scheme., These fluxes are obtained independently for each direction and the time update of the state-vector ${\bf U}$ is done simultaneously using a method of lines in combination with a second-order (in time) conservative Runge-Kutta scheme.
 Moreover. in order to set up a Family of local Riemann problems at every. cell-interface we use a piecewise linear reconstruction procedure (?) which provides second-order accuracy. in space.," Moreover, in order to set up a family of local Riemann problems at every cell-interface we use a piecewise linear reconstruction procedure \citep{vanleer:79} which provides second-order accuracy in space."
 We use à computational grid of 300.100 zones in the radial and angular clirection. respectively.," We use a computational grid of $300\times 100$ zones in the radial and angular direction, respectively."
 The ericl is logarithmically spaced in the radial direction., The grid is logarithmically spaced in the radial direction.
 The innermost raclius is located at rji=2.1., The innermost radius is located at $r_\mathrm{min}=2.1$.
 The location of the maximum radius ras depends on the particular model under study., The location of the maximum radius $r_\mathrm{max}$ depends on the particular model under study.
 bor the stationary models presented in Section 5.. we have Moa=35. Correspondingly. for the simulations of the runaway instability. the racial grid extends to a sulliciently large distance in order to ensure that the whole disc is included. within the computational domain.," For the stationary models presented in Section \ref{tests}, we have $r_\mathrm{max}=35.$ Correspondingly, for the simulations of the runaway instability, the radial grid extends to a sufficiently large distance in order to ensure that the whole disc is included within the computational domain."
 Phe particular values of rias are displaved in Table 3. below., The particular values of $r_\mathrm{max}$ are displayed in Table \ref{tab:ModelParameters} below.
 The typical width of the innermost cell. where we have the highest resolution.is Xe21910 7.," The typical width of the innermost cell, where we have the highest resolution,is $\Delta r \simeq 1.9\times 10^{-2}$ ."
 1n the angular clirection we use a finer ericl within the torus and a much coarser grid. outside., In the angular direction we use a finer grid within the torus and a much coarser grid outside.
 The angular zones are distributed according to the following law:, The angular zones are distributed according to the following law:
From the fact. that when normalised to the stellar nuass of a ealaxy the specific elobulay cluster (GC) frequency ToesSieNe‘ap . ba factor. of. ~x2 higherfl im+ ellipticals than in spirals. Zepf Ashman (1993) predict that if elliptical galaxies are formed from one major spiral spiral iiereer the number of GCs formed dunues the,"From the fact that $-$ when normalised to the stellar mass of a galaxy $-$ the specific globular cluster ) frequency $T_{GC} := {N_{GC} \over {M_{\ast} / 10^9~M_{\odot}}}$ is a factor of $\sim 2$ higher in ellipticals than in spirals, Zepf Ashman (1993) predict that if elliptical galaxies are formed from one major spiral $-$ spiral merger the number of GCs formed during the"
feature in the parsec-scale radio jet of 3345 is found.,feature in the parsec-scale radio jet of 345 is found.
 This stationary feature is located at a distance of ~0.1 mmas ( ppc) from the core., This stationary feature is located at a distance of $\sim$ mas $\sim$ pc) from the core.
" The kinematics of a large sample of relativistic jets, obtained through the MOJAVEsurvey*,, revealed stationary features as a frequent occurence (?).."," The kinematics of a large sample of relativistic jets, obtained through the MOJAVE, revealed stationary features as a frequent occurence \citep{2009AJ....138.1874L}."
" In particular, in the jets of y-ray blazars, observed at 22 and GGHz, stationary features within ppc (projected) from the core are commonly observed (?).."," In particular, in the jets of $\gamma$ -ray blazars, observed at 22 and GHz, stationary features within pc (projected) from the core are commonly observed \citep{2001ApJS..134..181J}."
" Stationary jet features were investigated in more detail in the cases of 3390.3 (?), a nearby double-peaked radio galaxy at z= 0.0561, and the Seyfert galaxy 1120 (z=0.033; ?))."," Stationary jet features were investigated in more detail in the cases of 390.3 \citep{2010MNRAS.401.1231A}, a nearby double-peaked radio galaxy at $z = 0.0561$ , and the Seyfert galaxy 120 $z = 0.033$; \citealt{2010ApJ...715..355L}) )."
" For these two sources, stationary features were found at distances of  ppc 3390.3) and ~ ppc 1120) from the core at GGHz."," For these two sources, stationary features were found at distances of $\sim$ pc 390.3) and $\sim$ pc 120) from the core at GHz."
 Their physical origin was associated with that of standing shocks., Their physical origin was associated with that of standing shocks.
" A more detailed investigation of the spectral evolution of a radio flare in 1102, a highly polarized quasar at z=1.037, provides supporting evidence for a shock- interaction scenario, providing a physical description for stationary features interacting with traveling shocks (?).."," A more detailed investigation of the spectral evolution of a radio flare in 102, a highly polarized quasar at $z$ =1.037, provides supporting evidence for a shock-shock interaction scenario, providing a physical description for stationary features interacting with traveling shocks \citep{2011A&A...531A..95F}."
" The moving plasma condensations (components) are most likely generated near the base of the jet of 3345, but can only be reliably monitored after they pass through the location of the stationary feature."," The moving plasma condensations (components) are most likely generated near the base of the jet of 345, but can only be reliably monitored after they pass through the location of the stationary feature."
 The nucleus of the jet lies at a distance of ~7 ppc upstream from the GGHz VLBI core (??).. ," The nucleus of the jet lies at a distance of $\sim$ pc upstream from the GHz VLBI core \citep{1998A&A...330...79L, PhD...Schinzel2011}."
"After the passage of the stationary feature, the superluminal components in 3345 undergoe an apparent acceleration from ~ 55 to ~ 115 c over a distance of mmas in extent (23 ppc deprojected)."," After the passage of the stationary feature, the superluminal components in 345 undergoe an apparent acceleration from $\sim$ 5 to $\sim$ 15 c over a distance of mas in extent $\sim$ pc deprojected)."
" This acceleration seems to be a commonly observed feature of many objects in the MOJAVE sample, where a statistically significant tendency for acceleration in the base of jets is found (?).."," This acceleration seems to be a commonly observed feature of many objects in the MOJAVE sample, where a statistically significant tendency for acceleration in the base of jets is found \citep{2009ApJ...706.1253H}."
" Previously, ? discussed the observed acceleration of a different component in 3345, testing the case of a substantially curved three-dimensional path, causing the observed dramatic change of the apparent component speed."," Previously, \citet{2005A&A...431..831L} discussed the observed acceleration of a different component in 345, testing the case of a substantially curved three-dimensional path, causing the observed dramatic change of the apparent component speed."
" They concluded that the observed acceleration is not likely to be a geometrical effect, but should reflect physical acceleration of plasma."," They concluded that the observed acceleration is not likely to be a geometrical effect, but should reflect physical acceleration of plasma."
 The possibility of intrinsic acceleration of jet features on parsec scales was discussed by ?.., The possibility of intrinsic acceleration of jet features on parsec scales was discussed by \citet{2004ApJ...605..656V}.
" There it was specifically argued that the acceleration observed in 3345 is not purely hydrodynamic, but can be attributed to magnetic driving."," There it was specifically argued that the acceleration observed in 345 is not purely hydrodynamic, but can be attributed to magnetic driving."
 They showed that the observed acceleration is consistent with an acceleration from DI—5toT ~10 over a linear distance of ~3 to ~20 ppc., They showed that the observed acceleration is consistent with an acceleration from $\Gamma\sim5$ to $\Gamma\sim10$ over a linear distance of $\sim$ 3 to $\sim$ pc.
 The results presented here are consistent with these findings., The results presented here are consistent with these findings.
" The times of passage of knots Q10, Q11, and Q12 through the GGHz VLBI core coincide with short-term increases in the y-ray flux (see Fig. 5,,"," The times of passage of knots Q10, Q11, and Q12 through the GHz VLBI core coincide with short-term increases in the $\gamma$ -ray flux (see Fig. \ref{fig:lightcurve},"
 with times listed in Table 2))., with times listed in Table \ref{tab:kinsummary}) ).
" In a similar case, 11510-089 showed, in addition to the appearance of a new VLBI component, a rapid rotation in the optical linear polarization just prior the components passage through the core."," In a similar case, 1510-089 showed, in addition to the appearance of a new VLBI component, a rapid rotation in the optical linear polarization just prior the components passage through the core."
 This was explained by the feature following a spiral path through a toroidal field until it crosses a standing shock in the GGHz core (?).., This was explained by the feature following a spiral path through a toroidal field until it crosses a standing shock in the GHz core \citep{2010ApJ...710L.126M}.
" A y-ray flare centered on 2009.4 may be related to the brightening of radio structure at distances of 0.12 — mmas from the core (0.8 — ppc), corresponding to a deprojected distance of ~ ppc."," A $\gamma$ -ray flare centered on 2009.4 may be related to the brightening of radio structure at distances of 0.12 – mas from the core (0.8 – pc), corresponding to a deprojected distance of $\sim$ pc."
" Interestingly, this includes the region for which the presence of a standing shock is suggested by the observations presented in Sec. 3.1.1.."," Interestingly, this includes the region for which the presence of a standing shock is suggested by the observations presented in Sec. \ref{sec:kinematic}."
" Radio flares in the compact jet downstream of the VLBI core are known to occur (e.g.,?).."," Radio flares in the compact jet downstream of the VLBI core are known to occur \citep[e.g., ][]{2001ApJS..133..297W}."
" Furthermore, ?? have found that y-ray flares often occur after superluminal knots have separated from the VLBI core."," Furthermore, \citet{2001ApJS..134..181J,
Jorstad_FmJ_2010} have found that $\gamma$ -ray flares often occur after superluminal knots have separated from the VLBI core."
" The results presented here support the inference that y-ray emission still occurs parsecs downstream of the central engine, contrary to conclusions based on theoretical arguments (e.g., ??))."," The results presented here support the inference that $\gamma$ -ray emission still occurs parsecs downstream of the central engine, contrary to conclusions based on theoretical arguments (e.g., \citealt{2010MNRAS.405L..94T, 2010ApJ...717L.118P}) )."
 These arguments place the y-ray emission zones within the broad-line region (BLR) at distances of <1 ppc from the central engine., These arguments place the $\gamma$ -ray emission zones within the broad-line region (BLR) at distances of $\lesssim$ pc from the central engine.
" Within this region a high number of optical-UV photons are produced (e.g.?),, providing ideal conditions for inverse Compton scattering with relativistic electrons from the jet (e.g.??).."," Within this region a high number of optical--UV photons are produced \citep[e.g.][]{2007ApJ...659..997K}, providing ideal conditions for inverse Compton scattering with relativistic electrons from the jet \citep[e.g.][]{2011arXiv1104.4946A, 1997ApJS..109..103D}."
" In addition, the observed variability time scales place constraints on the size of the emitting region due to causality arguments."," In addition, the observed variability time scales place constraints on the size of the emitting region due to causality arguments."
" Usually this size is related to the jet cross section, implying that the emission region is located close to the black hole."," Usually this size is related to the jet cross section, implying that the emission region is located close to the black hole."
" However, thesestandard assumptions do not necessarily need to be true."," However, thesestandard assumptions do not necessarily need to be true."
 In we have shown that long-term trends observed, In \\ref{sec:longterm} we have shown that long-term trends observed
"radio integrated emission from local starburst galaxies also holds for distant galaxies, the submm-to-radio flux ratio can be used as a measure of redshift (CarilliYun 1999). ","radio integrated emission from local starburst galaxies also holds for distant galaxies, the submm-to-radio flux ratio can be used as a measure of redshift \citep{Carilli1999}. ."
"Figure 3 shows the 890 jm to 20 cm flux ratio as a function of redshift for the prototypical starburst galaxy Arp220, and illustrates the uncertainties introduced by different dust temperatures."," Figure \ref{fig:fluxratio} shows the 890 $\mu$ m to 20 cm flux ratio as a function of redshift for the prototypical starburst galaxy Arp220, and illustrates the uncertainties introduced by different dust temperatures."
" From this, we derive a redshift of 4.513 for MM1, and a lower limit z>8.5 for MM14S. Given the lack of optical/IR photometric information for MM14S, we do not attempt to derive the redshift and dust properties of this source, and hereafter we focus on MM1 and MMIAN. We derived optical/IR photometric redshifts for MM1 and MMIAN using theHyperZ code (Bolzonellaetal."," From this, we derive a redshift of $_{-1.4}^{+2.5}$ for MM1, and a lower limit $z>3.5$ for MM14S. Given the lack of optical/IR photometric information for MM14S, we do not attempt to derive the redshift and dust properties of this source, and hereafter we focus on MM1 and MM14N. We derived optical/IR photometric redshifts for MM1 and MM14N using the code \citep{Bolzonella2000}."
" We allowed for a redshift range z—07, and 2000)..using a Calzettietal.(2000) extinction law with an extinction range Ay=0—4."," We allowed for a redshift range $z=0-7$, and using a \citet{Calzetti2000} extinction law with an extinction range $A_\mathrm{V}=0-4$."
" For comparison, we used two different set of templates libraries: 5 solar metallicity stellar population models from Bruzual&Charlot (2003),, similar to theHyperZ defaults; and 10 templates from the SWIRE library (Pollettaetal. including models for an elliptical, three spiral, four 2007),,starburst and three AGN dominated galaxies."," For comparison, we used two different set of templates libraries: 5 solar metallicity stellar population models from \citet{bc2003}, , similar to the defaults; and 10 templates from the SWIRE library \citep{Polletta2007}, including models for an elliptical, three spiral, four starburst and three AGN dominated galaxies."
" As shown in Fig. 4,,"," As shown in Fig. \ref{fig:sed},"
 the x? distribution and redshift solutions for MM1 and MM14N obtained using both set of templates are similar., the $\chi^2$ distribution and redshift solutions for MM1 and MM14N obtained using both set of templates are similar.
" Using the Bruzual&Charlot(2003) templates, the best fit for MMI is produced at z=3.1792 by a spiral galaxy model, with Ay=1.4 (black curve); while the best fit for MM14N is produced at z=3.7753 by a single burst model, with Ay=1.0."," Using the \citet{bc2003} templates, the best fit for MM1 is produced at $z=3.1_{-0.6}^{+0.5}$ by a spiral galaxy model, with $A_\mathrm{V}=1.4$ (black curve); while the best fit for MM14N is produced at $z=3.7_{-0.3}^{+0.3}$ by a single burst model, with $A_\mathrm{V}=1.0$."
" Using the SWIRE library, the best fits are produced by a late spiral galaxy at z=3.0703 and a QSO template at z=3.6702 for MM1 and MMAAN, respectively."," Using the SWIRE library, the best fits are produced by a late spiral galaxy at $z=3.0_{-0.9}^{+0.5}$ and a QSO template at $z=3.6_{-0.3}^{+0.2}$ for MM1 and MM14N, respectively."
 The quoted uncertainties correspond to the confidence level derived from the fitting routine., The quoted uncertainties correspond to the confidence level derived from the fitting routine.
 Each of the Bruzual&Charlot(2003) templates follow a prescription for the stellar mass to luminosity ratio (e.g. as a function of age)., Each of the \citet{bc2003} templates follow a prescription for the stellar mass to luminosity ratio (e.g. as a function of age).
" Using the best fits and assuming a Chabrier(2003) initial mass function, we find stellar masses of ~1.0x1011Μο and ~3.6x1019Mo, for MM1 and MM14N, respectively."," Using the best fits and assuming a \citet{Chabrier2003} initial mass function, we find stellar masses of $\sim1.0\times10^{11}\ M_\sun$ and $\sim3.6\times10^{10}\ M_\sun$, for MM1 and MM14N, respectively."
" We note, however, that these stellar mass estimates are rough given the large uncertainty in redshift."," We note, however, that these stellar mass estimates are rough given the large uncertainty in redshift."
" For MMI, we also computed redshifts by fitting templates to the UV-to-mm photometry."," For MM1, we also computed redshifts by fitting templates to the UV-to-mm photometry."
" We used the same SWIRE templates, redshift and extinction ranges."," We used the same SWIRE templates, redshift and extinction ranges."
" The best fit is produced by an Arp220 model, with 0.3 and z=4.5."," The best fit is produced by an Arp220 model, with $A_\mathrm{V}=0.3$ and $z=4.5$."
" The value of x? is dominated by the ratio between the submm to optical light, indicating a possible range of redshift from ~3.0 to 5.0."," The value of $\chi^2$ is dominated by the ratio between the submm to optical light, indicating a possible range of redshift from $\sim$ 3.0 to 5.0."
 Our redshift estimates are in good agreement with the redshift implied by the submm to radio flux ratio and supports a higher redshift than that obtained purely from the optical photometry., Our redshift estimates are in good agreement with the redshift implied by the submm to radio flux ratio and supports a higher redshift than that obtained purely from the optical photometry.
" As illustrated in Fig. 4,,"," As illustrated in Fig. \ref{fig:sed},"
 the far-IR SED of MMI can be described by a modified black body spectrum., the far-IR SED of MM1 can be described by a modified black body spectrum.
" We fitted a model of the form S,οςB,(Taust)(1—e~™), where B,(Taust) is the Planck function."," We fitted a model of the form $S_\nu\propto B_\nu (T_\mathrm{dust}) (1-e^{-\tau_\nu})$, where $B_\nu (T_\mathrm{dust})$ is the Planck function."
" The opacity, 7,, is proportional to the dust mass Maust and to pe, with the emissivity index @=1.5."," The opacity, $\tau_\nu$, is proportional to the dust mass $M_\mathrm{dust}$ and to $\nu^\beta$, with the emissivity index $\beta=1.5$."
" Given the large uncertainties in redshift, we consider a range of redshift z=3—5 to model the photometric data (70—1200um)."," Given the large uncertainties in redshift, we consider a range of redshift $z=3-5$ to model the photometric data $70-1200\mu$ m)."
 We find dust temperatures and masses in the range Taus=50—65 K and Maust=1.2—2.6x109Mo., We find dust temperatures and masses in the range $T_\mathrm{dust}=50-65$ K and $M_\mathrm{dust}=1.2-2.6\times10^{9}\ M_\sun$.
 These models imply far-IR luminosities La1000um=0.9—2.5x1015 Lo., These models imply far-IR luminosities $L_{8-1000\mu\mathrm{m}}=0.9-2.5\times10^{13}\ L_\sun$ .
" Using the computed IR luminosities and the Kennicutt(1998) empirical calibration, we compute star-formation rates (SFRs) of 1800—5000Mo yr-! for this source."," Using the computed IR luminosities and the \citet{Kennicutt1998} empirical calibration, we compute star-formation rates (SFRs) of $1800-5000\ M_\sun$ $^{-1}$ for this source."
 Our detection of two out of the five significant radio-faint sources discovered in the MAMBO survey of the COSMOS field supports the increasing evidence for a population of luminous SMGs at z>3., Our detection of two out of the five significant radio-faint sources discovered in the MAMBO survey of the COSMOS field supports the increasing evidence for a population of luminous SMGs at $z>3$.
" It has recently been suggested that these galaxies may be the progenitors of quiescent, massive galaxies at z~2 (Capaketal.2008;Coppin2009,2010)."," It has recently been suggested that these galaxies may be the progenitors of quiescent, massive galaxies at $z\sim2$ \citep{Capak2008, Coppin2009, Coppin2010}."
. The old stellar populations found in these z~2 quiescent galaxies require to have formed at z>3 in short bursts of star formation., The old stellar populations found in these $z\sim2$ quiescent galaxies require to have formed at $z>3$ in short bursts of star formation.
" If we assume that four of these five MAMBO sources with no radio significant radio counterparts are real and located at z>3 (e.g., we expect thatone of the five is a fake detection due to flux it implies that up to ~30% (4/15) of the Sosoquz>4 boosting),mJy detections are located at z>3."," If we assume that four of these five MAMBO sources with no radio significant radio counterparts are real and located at $z>3$ (e.g., we expect thatone of the five is a fake detection due to flux boosting), it implies that up to $\sim30\%$ (4/15) of the $S_\mathrm{250 GHz}>4$ mJy detections are located at $z>3$."
" This is well justified by the confirmation of MMI and tentative detection of MM14 with the SMA, and of two other MAMBO sources with LABOCA (Albrecht et al,"," This is well justified by the confirmation of MM1 and tentative detection of MM14 with the SMA, and of two other MAMBO sources with LABOCA (Albrecht et al.,"
 in preparation)., in preparation).
" Assuming that 2—4 of the MAMBO sources are uniformly distributed over the comoving volume spanned by z=3—5 within the area of the MAMBO survey, we find a surface density of ~13—30 deg? and a volume density of ~1—6x1076 Mpc-?."," Assuming that $2-4$ of the MAMBO sources are uniformly distributed over the comoving volume spanned by $z=3-5$ within the area of the MAMBO survey, we find a surface density of $\sim13-30$ $^{-2}$ and a volume density of $\sim1-6\times10^{-6}$ $^{-3}$ ."
 This is consistent with the upper limit of >1076 Mpc? (>6 from the spectroscopically confirmed z>4 $8MGs deg?)(Coppinetal.2009) and with the density of 2.»3—5 systems with baryonic masses >10!!Mo from predictions of theoreticalmodels (Baughetal. 2005).., This is consistent with the upper limit of $>10^{-6}$ $^{-3}$ $>6$ $^{-2}$ )from the spectroscopically confirmed $z>4$ SMGs \citep{Coppin2009} and with the density of $z\sim3-5$ systems with baryonic masses $>10^{11}\ M_\sun$ from predictions of theoreticalmodels \citep{Baugh2005}. .
"Το and large average electron Lorentz factor (e,2), both of which are proportional to «/σι.","$\Gamma_2$ and large average electron Lorentz factor $\left<\gamma_{e,2}\right>$, both of which are proportional to $\sqrt{\sigma_1}$."
" The latter requirement can be eased, noting that some sort of stochastic particle acceleration process is necessary in order to reproduce power-law spectral tails to fit observations."," The latter requirement can be eased, noting that some sort of stochastic particle acceleration process is necessary in order to reproduce power-law spectral tails to fit observations."
 Lower σι implies lower Το and thus a more compact minijet region for the same observed variability timescale., Lower $\sigma_1$ implies lower $\Gamma_2$ and thus a more compact minijet region for the same observed variability timescale.
 Reduced emitting volume would have a strong impact on the luminosity of both spectral components., Reduced emitting volume would have a strong impact on the luminosity of both spectral components.
" We study this effect in the class of models including opposite minijet radiation, trying to match the TeV luminosity of PKS 2155-304 or, if impossible, calculating a model of maximum luminosity."," We study this effect in the class of models including opposite minijet radiation, trying to match the TeV luminosity of PKS 2155-304 or, if impossible, calculating a model of maximum luminosity."
 In Fig. ," In Fig. \ref{fig10},"
we comparethe SEDs for three values of σι., we comparethe SEDs for three values of $\sigma_1$.
" The value σι[I0],=100 lines)) has been used in and in previous paragraphs.", The value $\sigma_1=100$ ) has been used in \cite{2009MNRAS.395L..29G} and in previous paragraphs.
" σι=50 lines)) corresponds to lz=6.4x1014cm and [2=7.1, while c;=25 lines)) to lz=4.5x1074cm and Τὸ=5."," $\sigma_1=50$ ) corresponds to $l_2=6.4\times 10^{14}\;{\rm cm}$ and $\Gamma_2=7.1$, while $\sigma_1=25$ ) to $l_2=4.5\times 10^{14}\;{\rm cm}$ and $\Gamma_2=5$."
" We were able to fit data for PKS 2155-304 for σι=50, but not for σι=25, where opacity limits TeV luminosity below the observed level."," We were able to fit data for PKS 2155-304 for $\sigma_1=50$, but not for $\sigma_1=25$, where opacity limits TeV luminosity below the observed level."
" Keeping ΤΓ]οι= 10, the last case corresponds to effective Lorentz factor of the minijet plasma Τ2Γ]οι~50, the minimum value derived by et [BegeImanal.|(2008).."," Keeping $\Gamma\jet=10$ , the last case corresponds to effective Lorentz factor of the minijet plasma $\Gamma_2\Gamma\jet\sim 50$, the minimum value derived by \cite{2008MNRAS.384L..19B}. ."
" Thus, our model confirms that prediction, even though it has been derived withina framework."," Thus, our model confirms that prediction, even though it has been derived withina single-zone framework."
"The high temperature of the host star places HAT-P-1I4b in the highly-irradiated ""pM"" category of ? and 15 a good candidate lor invesugaling temperature inversions and day/night contrasts.",The high temperature of the host star places HAT-P-14b in the highly-irradiated `pM' category of \citet{Fortney08} and is a good candidate for investigating temperature inversions and day/night contrasts.
 An observation of the secondary transit would be particularly interesüng to further constrain the low eccentricity., An observation of the secondary transit would be particularly interesting to further constrain the low eccentricity.
" However, the orbital geometry of the system means that HAT-P-14b is on the borderline of having no secondary eclipse."," However, the orbital geometry of the system means that HAT-P-14b is on the borderline of having no secondary eclipse."
 The results [rom the joint analysis predict that it will not occur with more than 3e confidence., The results from the joint analysis predict that it will not occur with more than $\sigma$ confidence.
" However, the fit to the data presented in this paper alone suggests that the secondary eclipse could be grazing."," However, the fit to the data presented in this paper alone suggests that the secondary eclipse could be grazing."
" Since these opposing secondary eclipse predictions arise [rom extremely small differences in orbital eccentricity, whether or not we observe such an transit will provide further constraints on the system geometry."," Since these opposing secondary eclipse predictions arise from extremely small differences in orbital eccentricity, whether or not we observe such an transit will provide further constraints on the system geometry."
 HAT-P-14 thus provides excellent opportuniues for future investigations and informative characterisation., HAT-P-14 thus provides excellent opportunities for future investigations and informative characterisation.
" The SuperWASP Consortium consists of astronomers primarily [rom QueenOs University Belfast, St Andrews, Keele, Leicester, The Open University, Isaac Newton Group La Palma and Insututo de Astrolosica de Canarias."," The SuperWASP Consortium consists of astronomers primarily from QueenÕs University Belfast, St Andrews, Keele, Leicester, The Open University, Isaac Newton Group La Palma and Instituto de Astrofõsica de Canarias."
 The SuperWASP-N camera is hosted by the Issac Newton Group on La Palma and we are grateful for their continuing support and assistance., The SuperWASP-N camera is hosted by the Issac Newton Group on La Palma and we are grateful for their continuing support and assistance.
 Funding for WASP comes from consortium universities and from the UK's Science and Technology Facilities Council., Funding for WASP comes from consortium universities and from the UK's Science and Technology Facilities Council.
" Based on observations made at Observatoire de Haute Provence (CNRS), France and at the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias."," Based on observations made at Observatoire de Haute Provence (CNRS), France and at the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias."
 The Liverpool Telescope is operated on the island of La Palma by Liverpool John Moores University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias with financial support from the UK Science and Technology Facilities Council., The Liverpool Telescope is operated on the island of La Palma by Liverpool John Moores University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias with financial support from the UK Science and Technology Facilities Council.
 We thank Tom Marsh for the use of the ULTRACAM pipeline., We thank Tom Marsh for the use of the ULTRACAM pipeline.
 FPK is grateful to AWE Aldermaston for the award of a William Penny Fellowship., FPK is grateful to AWE Aldermaston for the award of a William Penny Fellowship.
 EKS would like to thank R. M. Crockett [or his thorough prool-reading and excellent image-making., EKS would like to thank R. M. Crockett for his thorough proof-reading and excellent image-making.
for the YSO outflows of 30 and 3000ο 102 ergs). respectively. similar to those found: towards other massive and energetic molecular outllows driven bv high-mass YSOs. (,"for the YSO outflows of 30 and 3000 $6 \times 10^{46}$ ergs), respectively, similar to those found towards other massive and energetic molecular outflows driven by high-mass YSOs. ("
3) We discovered a clump towards E6035. supporting the presence of outllows in the region because it is known that such molecular species enhances in the boundary laver between the outllow jet and the surrounding molecular core.,"3) We discovered a $^{+}$ clump towards EGOg35, supporting the presence of outflows in the region because it is known that such molecular species enhances in the boundary layer between the outflow jet and the surrounding molecular core."
 The central spectra present an absorption dip at v ~54 due to selt-absorbed eas. which is probably. revealing the existence of a density eracient in the clump. ," The central $^{+}$ spectra present an absorption dip at v $\sim54$ due to self-absorbed gas, which is probably revealing the existence of a density gradient in the clump. ("
4) We discovered a CS clump towards ECGOe35.,4) We discovered a CS clump towards EGOg35.
 The CS J=76 emission maps the dense. envelope where the massive YSO is evolving. and its detection. implies the presence of molecular gas with temperatures anc densities above 40 Ix and ο105 7. respectively. ," The CS J=7–6 emission maps the dense envelope where the massive YSO is evolving, and its detection implies the presence of molecular gas with temperatures and densities above 40 K and $6 \times 10^{6}$ $^{-3}$, respectively. ("
5) The central and CS spectra. whieh survey the densest region where EGOe35 is embedded. show two velocity components with the closer one (blue component) stronger than the farthest one (rec component).,"5) The central $^{+}$ and CS spectra, which survey the densest region where EGOg35 is embedded, show two velocity components with the closer one (blue component) stronger than the farthest one (red component)."
 This signature suggests that these lines are mapping infalling eas. which is consistent with the presence of a YSO accreting ) mentco," This signature suggests that these lines are mapping infalling gas, which is consistent with the presence of a YSO accreting material. ("
linFrom the spectral energy. distribution (SED) study we that EGOe35 is a massive YSO at the earliest evolutionary stage (Le. a class | YSO). (,6) From the spectral energy distribution (SED) study we confirm that EGOg35 is a massive YSO at the earliest evolutionary stage (i.e. a class I YSO). (
7) Analysing radio continuum cmission towarcls EGOg35 we conclude that there is evidence of the presence of an UCI region and another source that could be either an LICLILE region or a constant-velocity ionized wind source.,7) Analysing radio continuum emission towards EGOg35 we conclude that there is evidence of the presence of an UCHII region and another source that could be either an HCHII region or a constant-velocity ionized wind source.
 The radio continuum analysis suggests the presence of several possible voung stellar. objects in the region., The radio continuum analysis suggests the presence of several possible young stellar objects in the region.
 Future multiwavelength observations with very high angular resolution will be of a great importance to go deeper in the study of this region., Future multiwavelength observations with very high angular resolution will be of a great importance to go deeper in the study of this region.
 We wish to thank the anonvmous referee whose Comments and suggestions have helped to improve the paper., We wish to thank the anonymous referee whose comments and suggestions have helped to improve the paper.
 S.I. ALO. E.G. and C.D. are members of thecicutilico of CONICET. Arecntina.," S.P., M.O., E.G. and G.D. are members of the of CONICET, Argentina."
 A.P. is a doctoral fellow of CONICET. Argentina.," A.P. is a doctoral fellow of CONICET, Argentina."
 This work was partially supported. by Arecntina grants awarded by Universidad de Buenos Aires. CONICET and ANPCY," This work was partially supported by Argentina grants awarded by Universidad de Buenos Aires, CONICET and ANPCYT."
 ALR. wishes to acknowledge support from FONDISCY T.(CLULE) erant Nol08033., M.R wishes to acknowledge support from FONDECYT (CHILE) grant No108033.
 She is supported. by the ChileanTAstroplivsics FONDAP No., She is supported by the Chilean FONDAP No.
 15010003., 15010003.
 S.I. ancl ALR. are erateful to Dr. Shinva Womugi for the support received during the observations., S.P. and M.R. are grateful to Dr. Shinya Komugi for the support received during the observations.
Observations of T Tauri Stars (LVS) have revealed the presence of magnetic structures much larger. than those seen on our Sun.,Observations of T Tauri Stars (TTS) have revealed the presence of magnetic structures much larger than those seen on our Sun.
 Indeed. analysis of these structures has invoked solar Hare-based models: to infer the length scales of confining loops. developed the uniform cooling loop (UCL) model. linking solar [are X-ray decay slopes to spatially resolved lengths of the loops confining the emitting eas.," Indeed, analysis of these structures has invoked solar flare-based models: to infer the length scales of confining loops, developed the uniform cooling loop (UCL) model, linking solar flare X-ray decay slopes to spatially resolved lengths of the loops confining the emitting gas."
 The UCL model was applied to data from the Chandra Orion Ultradeep Project 7). and it was discovered that evidently the post-Hare loops of TES can reach up to multiple stellar radii in extent 1)mainDBodvCitationEnd99]Favata:2005.," The UCL model was applied to data from the Chandra Orion Ultradeep Project , and it was discovered that evidently the post-flare loops of TTS can reach up to multiple stellar radii in extent ."
 This result is surprising: T ‘Tauri coronae are typically believed: to be compact. as evidenced by the common detection of rotationally moclulatecl coronal N-ray emission (?7).," This result is surprising: T Tauri coronae are typically believed to be compact, as evidenced by the common detection of rotationally modulated coronal X-ray emission ."
. N-rav bright regions are generally thought to be confined. within the corona. with loops generally not reaching more than a stellar radius in height.," X-ray bright regions are generally thought to be confined within the corona, with loops generally not reaching more than a stellar radius in height."
 In the mechanical equilibrium mocdel of ?.. prominences form after reconnection occurs in the open field. and it is à straightforward matter to show that cool. dense loops can reach heights well beyond. corotation (the radius at which the orbital velocity equals the stellar rotational velocity) and the closed stellar coronal field.," In the mechanical equilibrium model of , prominences form after reconnection occurs in the open field, and it is a straightforward matter to show that cool, dense loops can reach heights well beyond corotation (the radius at which the orbital velocity equals the stellar rotational velocity) and the closed stellar coronal field."
 Hot loops such as those inferred by the COUP. however. ap»ear to need the support of the stellar field. ancl thus shoud be limited to heights within the closed. coronal magnetic* field: a fraction of the wieghts inferred by UCL moclels.," Hot loops such as those inferred by the COUP, however, appear to need the support of the stellar field, and thus should be limited to heights within the closed coronal magnetic field: a fraction of the heights inferred by UCL models."
 1 was initially suggested hat perhaps these hot. large-scale' loops are anchored to circumstellar disc material for stajlitv.," It was initially suggested that perhaps these hot, large-scale loops are anchored to circumstellar disc material for stability."
 “Testing this idea. ollowup studies of the COUP objects that. searched. for discs were unable to find conclusive! evidence for clusty disc material within reach of the loops 22).," Testing this idea, followup studies of the COUP objects that searched for discs were unable to find conclusive evidence for dusty disc material within reach of the loops ."
. Furthermore. he apparent anti-correlation of large-scale loops and close-in disc material suggests it is the absence of inner disc material hat allows the loops to reach greater extents than they would were close-in disc material present ," Furthermore, the apparent anti-correlation of large-scale loops and close-in disc material suggests it is the absence of inner disc material that allows the loops to reach greater extents than they would were close-in disc material present ."
Potentially. this indicates some missing physics in earlier models. and it raises the question of how such large loops remain stable for the duration of the X-ray Hare decay. phase (in some cases. multiple rotation periods)," Potentially, this indicates some missing physics in earlier models, and it raises the question of how such large loops remain stable for the duration of the X-ray flare decay phase (in some cases, multiple rotation periods)."
 The potential ramifications of highly energetic events on stellar ancl circumstellar evolution are far-reaching: large-scale magnetic structures. in their formation and eventual disruption. could regulate stellar angular momentun evolution as well as circumstellar dise evolution. anc thus planet formation.," The potential ramifications of highly energetic events on stellar and circumstellar evolution are far-reaching: large-scale magnetic structures, in their formation and eventual disruption, could regulate stellar angular momentum evolution as well as circumstellar disc evolution, and thus planet formation."
 The combination of the high frequency, The combination of the high frequency
The main equations for the pair production process are briefly presented here.,The main equations for the pair production process are briefly presented here.
 Detailed calculations can be found in ?.. ? and 9," Detailed calculations can be found in \citet{1967PhRv..155.1408G}, , \citet{1971MNRAS.152...21B} and \citet{1997A&A...325..866B}."
" The interaction of a gamma-ray photon of energy ει and a soft photon of energy &j in the observer frame leads to the production of an electron-positron. pair if the total available energy in the center-of-mass (CM) frame is greater than the rest mass energy of the pair where 71, 1s the electron mass and ϐµ the angle between the two incoming photons in the observer frame.", The interaction of a gamma-ray photon of energy $\epsilon_1$ and a soft photon of energy $\epsilon_0$ in the observer frame leads to the production of an electron-positron pair if the total available energy in the center-of-mass (CM) frame is greater than the rest mass energy of the pair where $m_e$ is the electron mass and $\theta_0$ the angle between the two incoming photons in the observer frame.
 It 15 useful to define the Lorentz invariant s=ejeo(1—cos65)/2. Pairs are produced if s>acc and the velocity8 of the electron-positron pair in the CM frame is B=(1-micis)Io., It is useful to define the Lorentz invariant $s=\epsilon_1\epsilon_0\left(1-\cos\theta_0\right)/2$ Pairs are produced if $s\ge m_e^2 c^4$ and the velocity $\beta$ of the electron-positron pair in the CM frame is $\beta=(1-m_e^2 c^4/s)^{1/2}$.
" The differential cross-section dor,/d(cos0,) in the CM frame depends on B and the angle @, between the outcoming electron-positron pair and the incoming photons.", The differential cross-section $d\sigma_{\gamma\gamma}/d(\beta\cos\theta'_1)$ in the CM frame depends on $\beta$ and the angle $\theta'_1$ between the outcoming electron-positron pair and the incoming photons.
 The full expression can be found in ?.. Eq. (," The full expression can be found in \citet{1971MNRAS.152...21B}, , Eq. ("
2.7).,2.7).
 The differential cross-section presents a symmetric structure. peaked at cosÜ|=zl and minimum for cos@)=0.," The differential cross-section presents a symmetric structure, peaked at $\cos\theta'_1=\pm 1$ and minimum for $\cos\theta'_1=0$."
 Electrons are mostly created in the same and opposite direction with respect to the incoming hard photon direction in the CM frame., Electrons are mostly created in the same and opposite direction with respect to the incoming hard photon direction in the CM frame.
 The double peaked structure is enhanced with increasing energy (s29 mzc!) and becomes less pronounced close to the threshold (Μπο)., The double peaked structure is enhanced with increasing energy $s\gg m_e^2 c^4$ ) and becomes less pronounced close to the threshold $s\sim m_e^2 c^4$ ).
 The integration over the angles gives the total pair production cross-section c. naximum close to the threshold (see Eq.," The integration over the angles gives the total pair production cross-section $\sigma_{\gamma\gamma}$, maximum close to the threshold (see Eq."
 | in ?))., 1 in \citealt{1967PhRv..155.1408G}) ).
 The construction of the CM frame with respect to the observer frame can be simplified if one of the incoming photons carries most of the energy., The construction of the CM frame with respect to the observer frame can be simplified if one of the incoming photons carries most of the energy.
 This case is appropriate in the present context., This case is appropriate in the present context.
 For ει>>ε. the CM frame can be considered as propagating along the same direction as the high energy photon.," For $\epsilon_1\gg\epsilon_0$, the CM frame can be considered as propagating along the same direction as the high energy photon."
" The velocity of the CM frame in the observer frame can be expressed as The total energy of say the electron E, in the observer frame can then be formulated using the Lorentz transform from the CM to the observer frames providingg a relation between£,« and cos∣6”.", The velocity of the CM frame in the observer frame can be expressed as The total energy of say the electron $E_e$ in the observer frame can then be formulated using the Lorentz transform from the CM to the observer frames providing a relation between$E_e$ and $\cos\theta'_1$.
 A gamma-ray photon going through a soft photon gas of density da/dedQ 1s absorbed at a rate per unit of path length / The absorption rate gives the probability for a gamma-ray of energy ει to be absorbed but does not give the energy of the pair created in the interaction., A gamma-ray photon going through a soft photon gas of density $dn/d\epsilon d\Omega$ is absorbed at a rate per unit of path length $l$ The absorption rate gives the probability for a gamma-ray of energy $\epsilon_1$ to be absorbed but does not give the energy of the pair created in the interaction.
" Following ?.. the probability for à gamma-ray of energy ει to be absorbed between / and /+d/ yielding an electron of energy between E, and E,+dE, (with a positron of energy E,se— for ει>ε) 1s As with anisotropic inverse Compton scattering (2).. it is useful to consider the case of à monoenergetic beam of soft photons."," Following \citet{1971MNRAS.152...21B}, the probability for a gamma-ray of energy $\epsilon_1$ to be absorbed between $l$ and $l+dl$ yielding an electron of energy between $E_e$ and $E_e+dE_e$ (with a positron of energy $E_{e^+}\approx\epsilon_1-E_e$ for $\epsilon_1\gg\epsilon$ ) is As with anisotropic inverse Compton scattering \citep{2008A&A...477..691D}, it is useful to consider the case of a monoenergetic beam of soft photons."
 The normalised soft photon density in the observer frame Is where 0 is the Dirac distribution., The normalised soft photon density in the observer frame is where $\delta$ is the Dirac distribution.
 Injecting Eq. (A6)), Injecting Eq. \ref{dnph}) )
 into Eq. (A5)), into Eq. \ref{gkern}) )
 gives the anisotropic pair production kernel. a convenient tool for spectral computations.," gives the anisotropic pair production kernel, a convenient tool for spectral computations."
 The detailed calculation is presented in Appendix B and the complete expression given in Eq. (C5))., The detailed calculation is presented in Appendix B and the complete expression given in Eq. \ref{kernel}) ).
" The pair production kernel has a strong angular dependence and a symmetric structure. centered at E,=ej/2 and peaked at E,=E. (see Appendix B. Fig. Cl)."," The pair production kernel has a strong angular dependence and a symmetric structure, centered at $E_e=\epsilon_1/2$ and peaked at $E_e=E_{\pm}$ (see Appendix B, Fig. \ref{kern_gg}) )."
" The effect of the angle 4 is reduced close to the threshold where the particles share equally the energy of the primary gamma-ray photon E,= ej/2.Far from the threshold. one particlecarries away almost all the available energy E,s ej."," The effect of the angle $\theta_0$ is reduced close to the threshold where the particles share equally the energy of the primary gamma-ray photon $E_e\approx E_{e^+}\approx\epsilon_1/2$ .Far from the threshold, one particlecarries away almost all the available energy $E_e\approx\epsilon_1$ ."
 The anisotropic kernel integrated over all the pitch angles. in the case of an isotropic gas of photons. Is consistentwith the kernel found by ?.. ?..," The anisotropic kernel integrated over all the pitch angles, in the case of an isotropic gas of photons, is consistentwith the kernel found by \citet{1983Afz....19..323A}. \citet{1997A&A...325..866B}."
tota] sample of LAIC ceutra stars presented iu Fie.,total sample of LMC central stars presented in Fig.
 L EIQo objects) is slightly higher than the average mass of both white dwarfs ane ceitral stars of PNe in the Galaxy reported in the literature., 4 (37 objects) is slightly higher than the average mass of both white dwarfs and central stars of PNe in the Galaxy reported in the literature.
" The ceutral star mass ¢epends mainly on the stellar mass during the Maiu-Sequeuce phase (hereafter. the initial mass). auc on the mass-loss during the ACD νάνο,"," The central star mass depends mainly on the stellar mass during the Main-Sequence phase (hereafter, the initial mass), and on the mass-loss during the AGB phase."
 Mass-loss during the ACB phase las a strong depeudency on imoetallicityv as it is thought to be driven mainly by «ust (Wood1979:BowenLOSS).," Mass-loss during the AGB phase has a strong dependency on metallicity as it is thought to be driven mainly by dust \citep{Wod:79,Bow:88}."
. The dust formation process depends on the chemical composition of the e:w: the lower the metallicity the sanaller the amount of dust formed. aud the lower the efficieicy of the momentum trauster to the eas.," The dust formation process depends on the chemical composition of the gas: the lower the metallicity the smaller the amount of dust formed, and the lower the efficiency of the momentum transfer to the gas."
 Thus. low inetallicity stars with dust-driven winds are expected to loose simaller anounts of matter and therefore are expected to cud-up wih higher ceutral star masses.," Thus, low metallicity stars with dust-driven winds are expected to loose smaller amounts of matter \citep{Wetal:00} and therefore are expected to end-up with higher central star masses."
 It has been shown that mass-loss during the ACB phase can also occur in the absence of dust (Willson2000).. but iu this case the niass-loss efficiency is much lower.," It has been shown that mass-loss during the AGB phase can also occur in the absence of dust \citep{Wil:00}, but in this case the mass-loss efficiency is much lower."
 The metallicity of the LAIC is ou average half tvat of the solar mix 1990).," The metallicity of the LMC is on average half that of the solar mix \citep{Rb:89,Rd:90}."
. Therefore. it is well expected that tie efficiency. of mass-loss duris the ACD phase will be reduced in the LAIC.," Therefore, it is well expected that the efficiency of mass-loss during the AGB phase will be reduced in the LMC."
 As a result a higher central sar muss should be the outcome of the evolution for a given initia progenitor., As a result a higher central star mass should be the outcome of the evolution for a given initial progenitor.
 If we bolieve the higher average central star mass of PNe we find iu the LAIC we wieght have the first ooervational evidence from PNe progeuitors for reduced mass-loss rates in a lower metallicity euviroineunt., If we believe the higher average central star mass of PNe we find in the LMC we might have the first observational evidence from PNe progenitors for reduced mass-loss rates in a lower metallicity environment.
 The consequences are very iniportant iu terms of ealactic chemical enrichimen ες a higher fraction of main sequence stars should reach the Claudraseckhay mass luit in the LAIC ‘than in the Calaxy. (Uiea.Nomoto.Yamaoka.&Stramero1999:Cürardi.Bressan.Bertelli.&Chiosi 2000).," The consequences are very important in terms of galactic chemical enrichment, as a higher fraction of main sequence stars should reach the Chandrasekhar mass limit in the LMC than in the Galaxy \citep{Uetal:99,Detal:99,Getal:00}."
. Tt is portant to mention tat higher masses are otained from We-burning evolutionary tracks han from W-burning tracks., It is important to mention that higher masses are obtained from He-burning evolutionary tracks than from H-burning tracks.
 As mentioned i1 $112 the nature of the tracks in stellar evolution models depeuc5 Oll ε 10wtificially selectec point of departiue from the ACD. with differen authors using ditfereut criteria.," As mentioned in 4.2 the nature of the tracks in stellar evolution models depends on the artificially selected point of departure from the AGB, with different authors using different criteria."
" Since we ¢zunot coustrain the nature of the racς from observalons. we have tried to check the consisteucv oOur results with our best uass estimate""H"," Since we cannot constrain the nature of the track from observations, we have tried to check the consistency of our results with our best mass estimates."
8 We rave selected from the tota saple of objects those with ceitral y.ars well detected above the uellar eve1 and with IIe Zaustra teiuperatiures., We have selected from the total sample of objects those with central stars well detected above the nebular level and with He Zanstra temperatures.
 For the following aualvsis we have excluded 8 ceutral stars locat edi ithe IIR. diverano with II Zaustra temperature determinaloli (1 central stars frou lis paper aud frou Villaveret:id. 2PO03))., For the following analysis we have excluded 8 central stars located in the HR diagram with H Zanstra temperature determinations (4 central stars from this paper and 4 from \citealt{Vss:03}) ).
 We have excluded as well the 6 ceitral y.ars marked in Tab lthat have avrge errors in f16 magnitude meastroinent., We have excluded as well the 6 central stars marked in Table 1 that have large errors in the magnitude measurement.
 This leaves us with 23 ceitral SEAT lasses out o the EIQo original otal sauiple., This leaves us with 23 central star masses out of the 37 original total sample.
" Siuce [-burning tracks for the initial LAIC composition1 are not available im the ,aliterature for the Suler cenral star masses (λλες<< 2 MN.). we have estimate the central star masses 1slne the ealacic post-AGB II-burning tracks by Vassiliadis&Wood(1991)."," Since H-burning tracks for the initial LMC composition are not available in the literature for the smaller central star masses $_{MS}<$ 2 ), we have estimated the central star masses using the galactic post-AGB H-burning tracks by \cite{Vw:94}."
. The tracks ont1ο IIR. diagram or the W-buruing stars calculated for the Galactic aud LAIC initial abundances are very siniav. with a small x:ift towards ieher Παπος]ies for the LMC composition.," The tracks on the HR diagram for the H-burning stars calculated for the Galactic and LMC initial abundances are very similar, with a small shift towards higher luminosities for the LMC composition."
 We have estimated the shift based ou the tracμη hat we have 1 common for tf1e Galactic and LMC composition. then applied that shift whe1 estimating he II- nrnugnuasses of the low-mass cenral stars.," We have estimated the shift based on the tracks that we have in common for the Galactic and LMC composition, then applied that shift when estimating the H-burning masses of the low-mass central stars."
 T16 core niws-Inuinuositv relation for uwniug post-ACB stars (Vassiliadis&WoodJ991) has been used o determine the ΤΠηιο masses ] the cases where tie central star lies on the horizoutal part of the track., The core mass-luminosity relation for H-burning post-AGB stars \citep{Vw:94} has been used to determine the H-burning masses in all the cases where the central star lies on the horizontal part of the track.
 These mass determinatious are sed on fuel coustuuption principles aud have a neelieide dependency on metallicity., These mass determinations are based on fuel consumption principles and have a negligible dependency on metallicity.
 The re-calculated masses from II-burniug racks for the ceutral stars iu this pa)or are Lister in Table 5., The re-calculated masses from H-burning tracks for the central stars in this paper are listed in Table 5.
 For some objects we list two mass determinations. the first one listed is the best detcrimination available from the LAIC ITe-burniug tracss at hand aud the secoud one is the mass determinatio1i from the W-buruing tracks as explained above.," For some objects we list two mass determinations, the first one listed is the best determination available from the LMC He-burning tracks at hand and the second one is the mass determination from the H-burning tracks as explained above."
 The masses from U-burning tracks have also been derived for the central stars prescuted in 3)., The masses from H-burning tracks have also been derived for the central stars presented in \cite{Vss:03}.
. The hatched listoeramC» in Fie., The hatched histogram in Fig.
Oo E shows the mass distribution obtained for the reduced aud homoeencously, 4 shows the mass distribution obtained for the reduced and homogeneously
Oo E shows the mass distribution obtained for the reduced aud homoeencouslyO, 4 shows the mass distribution obtained for the reduced and homogeneously
Oo E shows the mass distribution obtained for the reduced aud homoeencouslyOo, 4 shows the mass distribution obtained for the reduced and homogeneously
the ppeak brightness temperature. with the positions of the sshell as measured by Meaburn. ancl the sshell #991 (this paper). is shown in Fig.14..,"the peak brightness temperature, with the positions of the shell as measured by Meaburn, and the shell 91 (this paper), is shown in \ref{fig:ha}."
 The ionising mechanism of this sshell is still unknown., The ionising mechanism of this shell is still unknown.
 Meaburn (1986) suggests a single O star is responsible for the illumination of the sshell., Meaburn (1986) suggests a single O star is responsible for the illumination of the shell.
 Parker has commented that UV. source FAUST 392 corresponds closely. to the centre of the shell. is probably a low surface brightness Planetary. nebula (PN) or even a supernova remnant. although the low energy derived in the presen μαucly does not suggest a typical supernova as the mechanism for this shell.," Parker has commented that UV source FAUST 392 corresponds closely to the centre of the shell, is probably a low surface brightness Planetary nebula (PN) or even a supernova remnant, although the low energy derived in the present study does not suggest a typical supernova as the mechanism for this shell."
 Graham et al. (, Graham et al. (
2001) have located a Woltfavel (WI) candidate within the shell rim. and suggest that this object may be responsible for causing the expansion of the shell.,"2001) have located a Wolf-Rayet (WR) candidate within the shell rim, and suggest that this object may be responsible for causing the expansion of the shell."
 A number of OB associations are cistributed around the high density rrim of this region (Dica Schmitt 1995). and at. present. this is the only sshell within the Magellanic Dridgo that can he unmistakably attributed to a stellar origin.," A number of OB associations are distributed around the high density rim of this region (Bica Schmitt 1995), and at present, this is the only shell within the Magellanic Bridge that can be unmistakably attributed to a stellar origin."
 ‘Table 6 shows that the age and radius determined here for 91 as derived from the data is in general agreement with these parameters determined from dedata by Aleaburn (1986). although there is considerable ciscrepaney of the expansion velocity. anc hence the kinematic age with findings of Graham et al. (," Table \ref{tab:hacomp} shows that the age and radius determined here for 91 as derived from the data is in general agreement with these parameters determined from data by Meaburn (1986), although there is considerable discrepancy of the expansion velocity, and hence the kinematic age with findings of Graham et al. ("
2001).,2001).
 Fie.15 ≱∖⇂↥∪∖∖⊽⋡∖↿⇂↥∢⋅∖⇁⋖⋅↓⋯∙↓↿∙∖⇁≱∖⇂⊔⇍∢⊾⋜∐∐∢⋅≼∙⇂↓⊔⋜∐↓∪⊔∿⋀≟≟≟∆⊰≟↦∐⊔⊾., \ref{fig:ha-spec} shows the velocity slice at Declination.
 . MN−∣∕⋅∕∕⊳∖ ↥∖∖⊽∪↓≻∢⋅⋜↧↓∡≱∖⋡⋜∐∐⋖⋅↓⊲↓∪≼⇍∢⊾⊔↿↓⋰⊔⇍∖⇁∢⊾↓∪≼⋰↓↿⊲⊓⊾⊳∖∪⇂⋅∿⊔↖∖⋅↱≻↳⊔↓⊳∖⊥ aare those corresponding to the approaching and. receding sides of the shell.," The two peaks, at Heliocentric velocities of are those corresponding to the approaching and receding sides of the shell."
 We do not find any eemission peaks corresponding to those in aas measured by Graham et al., We do not find any emission peaks corresponding to those in as measured by Graham et al.
 In addition. another rregion (region #21172) parameterisecl bv Meaburn (1986). is found to correlate well with a similarly shaped high density rregion. as shown in Fig.14..," In addition, another region (region 172) parameterised by Meaburn (1986), is found to correlate well with a similarly shaped high density region, as shown in \ref{fig:ha}."
 This survey has selected a sample of. shells that. compared with the sshell population of the SAIC. appears to be relatively deficient in laree-racii shells (See LObb).," This survey has selected a sample of shells that, compared with the shell population of the SMC, appears to be relatively deficient in large-radii shells (See \ref{fig:ra_smc-mb}b b)."
 This is almost certainly due to a different and tighter selection. function., This is almost certainly due to a different and tighter selection function.
 This survey demancs a regular and identifiable ring shape in all three projections before such à structure can be accepted as an expanding, This survey demands a regular and identifiable ring shape in all three projections before such a structure can be accepted as an expanding
formula (equation 8)) rellection amplitude gets. reduced to O.S for μα80.25.,formula (equation \ref{equ:refl}) ) reflection amplitude gets reduced to 0.8 for $\tauh \approx 0.25$.
 Quality of current data is. usually sullicient to distinguish /?=0.8 from /?= Lin typical NXrav spectra of AGN DDone et 22000)., Quality of current data is usually sufficient to distinguish $R=0.8$ from $R=1$ in typical X–ray spectra of AGN Done et 2000).
 The Thomson thickness of the LIL changes with radius. even for a constant PNο. since el is not constant with r.," The Thomson thickness of the HL changes with radius, even for a constant $\FX/\FD$, since $A$ is not constant with $r$ ."
" We computed. radial dependencies of 7, for jj=3 and three values of£=0.01.0.3 and 0.6."," We computed radial dependencies of $\tauh$ for $\eta=3$ and three values of $\xi = 0.01, 0.3$ and $0.6$."
 Values of other parameters were as before: AZ=105M.. mi— 0.05. a=0.1.," Values of other parameters were as before: $M = 10^7\,\MSun$, $\dot m = 0.05$ , $\alpha=0.1$."
 Results are plotted in Fig. 3.., Results are plotted in Fig. \ref{fig:taurad}.
" The thickness is largest at ro lür,."," The thickness is largest at $r\approx 10\,\Rg$."
 Ht thon drops slowly. roughly in accord with the formula of Navakshin (2000a).," It then drops slowly, roughly in accord with the formula of Nayakshin (2000a)."
 A consequence of that particular zytr) clistribution is a relative suppression of highly relativistically smearecl Component of the reprocessed. spectrum., A consequence of that particular $\tauh(r)$ distribution is a relative suppression of highly relativistically smeared component of the reprocessed spectrum.
 On the other hand. the reprocessecl photons that do manage to diffuse from. below the hot laver close to the central BILL suller Comptonization smearing. which in practice may be dillicult to distinguish. from relativistic smearing (see Sec. 5.3)).," On the other hand, the reprocessed photons that do manage to diffuse from below the hot layer close to the central BH, suffer Comptonization smearing, which in practice may be difficult to distinguish from relativistic smearing (see Sec. \ref{sec:rin_vs_r}) )."
 Obviously. in the magnetic Hare scenario there is no reason for changes of£ and i to be perfectly correlated on all radii.," Obviously, in the magnetic flare scenario there is no reason for changes of $\xi$ and $\eta$ to be perfectly correlated on all radii."
 One can thus imagine rather different values at cilferent. radii. leacling to μα(1) rather cillerent than those plotted in Fig. 3..," One can thus imagine rather different values at different radii, leading to $\tauh(r)$ rather different than those plotted in Fig. \ref{fig:taurad}."
" On timescales long compared to £444, one could perhaps obtain time average €(7) and (ec) employing a particular variability model. tthat of Poutanen Fabian (1999)."," On timescales long compared to $\tdyn$ one could perhaps obtain time average $\xi(r)$ and $\eta(r)$ employing a particular variability model, that of Poutanen Fabian (1999)."
 The qualitative relation between the thickness of the LLL and the illuminating NX.rav flux is obvious: the stronger the Xrav flux the thicker the HELL., The qualitative relation between the thickness of the HL and the illuminating X–ray flux is obvious: the stronger the X–ray flux the thicker the HL.
 In this Section we present the quantitative relation from our moclel., In this Section we present the quantitative relation from our model.
 In Figure 4 we again plot contours of amplitude of rellection. /? in the £ a plane. together wit1i contours of the observed X.rav flux. Aad. as well as the. projected dependence Ro μαleui," In Figure \ref{fig:reflfhard} we again plot contours of amplitude of reflection $R$ in the $\xi$ $\eta$ plane, together with contours of the observed X–ray flux, $\Fhard$, as well as the projected dependence $R$ $\Fhard$."
 For 42 close to 1. doubling5 PN. results in only modest decrease of ἰ. by 1020 »r cent.," For $R$ close to 1, doubling $\FX$ results in only modest decrease of $R$, by 10–20 per cent."
 Por smaller /? the process is more ellective., For smaller $R$ the process is more effective.
 Dutstill. to £o from R=O.sfoR=O04requiresaninceredsc ofla by a factor of zS (when the movement is along the £ axis. for ye 4).," Butstill, to go from $R=0.8$ to $R=0.4$ requires an increase of $\Fhard$ by a factor of $\ga 8$ (when the movement is along the $\xi$ axis, for $\eta \approx 4$ )."
 Going from 2=0.6 to &=0.3 requires that F4 increases at least 4 times. again approximately. alone the £ axis.," Going from $R=0.6$ to $R=0.3$ requires that $\Fhard$ increases at least 4 times, again approximately along the $\xi$ axis."
 In no case does it scems possible to obtain an inverse proportionality of μα and oso that RoPagaà:Const.Thus. these results seem to rule out the possibility that the absolute Hux of the Fe line may remain constant despite continuum variability. although certain reduction of the line variability amplitude (compared to that of the continuum) can be expected. (seenext Section)," In no case does it seems possible to obtain an inverse proportionality of $\Fhard$ and $R$, so that $R\times \Fhard \approx {\rm const}$.Thus, these results seem to rule out the possibility that the absolute flux of the Fe line may remain constant despite continuum variability, although certain reduction of the line variability amplitude (compared to that of the continuum) can be expected (seenext Section)."
" We note that achange of PZx is more ellective in changing nr. i FN increases or decreases due to changing fraction of energy. dissipated in the disc. £. rather than qj. ""The reason is that rremovinge the energyIp clissipation from"," We note that achange of $\FX$ is more effective in changing $\tauh$, if $\FX$ increases or decreases due to changing fraction of energy dissipated in the disc, $\xi$ , rather than $\eta$ The reason is that removing the energy dissipation from"
" We note that achange of PZx is more ellective in changing nr. i FN increases or decreases due to changing fraction of energy. dissipated in the disc. £. rather than qj. ""The reason is that rremovinge the energyIp clissipation from."," We note that achange of $\FX$ is more effective in changing $\tauh$, if $\FX$ increases or decreases due to changing fraction of energy dissipated in the disc, $\xi$ , rather than $\eta$ The reason is that removing the energy dissipation from"
Finally. a few other possible mechanisms have been suggested [ον gas-phase H» formation.,"Finally, a few other possible mechanisms have been suggested for gas-phase $\mHt$ formation."
 Latter&Black(1991) propose that IH» can form as a result of direct radiative association provided Chat one of the hydrogen atoms is in an excited electronic state., \citet{lb} propose that $\mHt$ can form as a result of direct radiative association provided that one of the hydrogen atoms is in an excited electronic state.
" show that a more efficient mechanism is formation of Il by associative ionization with the IL, thereafter forming IH» by reaction 4 above.", \citet{rdb} show that a more efficient mechanism is formation of $\mHtp$ by associative ionization with the $\mHtp$ thereafter forming $\mHt$ by reaction \ref{h2f4} above.
 This mechanism again requires one of the hydrogen atoms to be in an excited atomic state., This mechanism again requires one of the hydrogen atoms to be in an excited atomic state.
 However. (his requirement means that in general these reactions are not important. as the necessary population of excited atomic hvedrogen is only found in a few unusual circumstances. such as in the universe immeciatelv after recombination.," However, this requirement means that in general these reactions are not important, as the necessary population of excited atomic hydrogen is only found in a few unusual circumstances, such as in the universe immediately after recombination."
 Despite its importance in local interstellar chemistry. the rate of Ils formation on dust erains is still uncertain.," Despite its importance in local interstellar chemistry, the rate of $\mHt$ formation on dust grains is still uncertain."
 In local molecular clouds. observations suggest a lormation rate (Jura1975) Observations of Ha in the LAIC and SAIC with the satellite suggest a value thal is an order of magnitude smaller. but this is consistent with the underlving rate per unit dust mass being the same. since (he mean dust-to-gas ratio within these galaxies is significantly smaller than in the Milkv. Wavy (Issaefal.1990).," In local molecular clouds, observations suggest a formation rate \citep{jura}
 Observations of $\mHt$ in the LMC and SMC with the satellite \citep{tum} suggest a value that is an order of magnitude smaller, but this is consistent with the underlying rate per unit dust mass being the same, since the mean dust-to-gas ratio within these galaxies is significantly smaller than in the Milky Way \citep{issa}."
. Unfortunately. direct measurements of this kind can only give us information about II» formation in physical conditions that are easily accessible to observations. and provide little basis on which to predict the IH» formation rate in different regimes.," Unfortunately, direct measurements of this kind can only give us information about $\mHt$ formation in physical conditions that are easily accessible to observations, and provide little basis on which to predict the $\mHt$ formation rate in different regimes."
 For this. we must (tum to theory.," For this, we must turn to theory."
 A large body of theoretical work exists on the subject of H» formation on grains (see.for(herein).. stretching back almost lorty vears to the pioneering work of GouldandSalpeter (1963).," A large body of theoretical work exists on the subject of $\mHt$ formation on grains \citep[see, for example, the review of][and the many references 
therein]{pir}, stretching back almost forty years to the pioneering work of \citet{gs}. ."
. In a highly influential paper. Hollenbachefa£.(1971) parameterized (he IH» formation rate as," In a highly influential paper, \citet{hws} parameterized the $\mHt$ formation rate as"
foreground sample has a narrow redshift distribution centered at r=rg. then we can take Wy to bea Dirac-delta fiction aud evaluate the iutegral over +.,"foreground sample has a narrow redshift distribution centered at $r=r_{\rm f}$, then we can take $W_{\rm f}$ to be a Dirac-delta function and evaluate the integral over $r$."
 All terms except g(rg5j) ave then functions of re. the redshift of the lensing mass.," All terms except $g(r_{\rm f},r_{\rm b})$ are then functions of $r_{\rm f}$, the redshift of the lensing mass."
 The coupling of the foreground aud background distributions is contained solely in g(r¢.c).," The coupling of the foreground and background distributions is contained solely in $g(r_{\rm f},r_{\rm b})$."
" ence if we take the ratio of the cross-correlation fortwo background populations with mean redshifts 2, and το. we ect where πι denote the values of the functious for the background population with mean redslüft npoand the second approximation is in the Πιτ that the backeround galaxies also have a dolta-fuuction distribution."," Hence if we take the ratio of the cross-correlation fortwo background populations with mean redshifts $z_1$ and $z_2$, we get where $w_1, g_1$ denote the values of the functions for the background population with mean redshift $z_1$, and the second approximation is in the limit that the background galaxies also have a delta-function distribution."
 The above equations show that the change iu the cross-correlation with backeround redshitt does not depeud on the ealaxy-uass power spectrum. nor on 0.," The above equations show that the change in the cross-correlation with background redshift does not depend on the galaxy-mass power spectrum, nor on $\theta$."
 We can simply use measurements over a rauge of Ó to estimate the distance ratio of equation (26)) for cach pair of foregrouud-backerounud redshifts., We can simply use measurements over a range of $\theta$ to estimate the distance ratio of equation \ref{ratio}) ) for each pair of foreground-background redshifts.
" The distance ratio in turn depends ou the cosmological paramcters Oq o. and its evolution /a,"," The distance ratio in turn depends on the cosmological parameters $\Omega_{\rm de}$, $w$, and its evolution $w'$."
 A simple way to estimate the signal-to-noise for the cross-correlation approach is to regard the forceround ealaxies as providing a template for the shear fields of the background galaxies., A simple way to estimate the signal-to-noise for the cross-correlation approach is to regard the foreground galaxies as providing a template for the shear fields of the background galaxies.
 For a perfect template (i.c. for high density of foreground galaxies aud no biasing). the errors are solely due to the finite itiusic cllipticitics of backeround galaxies.," For a perfect template (i.e. for high density of foreground galaxies and no biasing), the errors are solely due to the finite intrinsic ellipticities of background galaxies."
 Thus the fractional error im our measurement of the background shears Is πρίν where the total umuber of background galaxies is Nai=1gekDaPlay. “bis the survey area. the lensing induced xus shear pian.&0.01. the intrinsic ellipticity dispersion σε=0.3.Pa aud where the uiuuber deusity vy has uuits per square arcuuuute.," Thus the fractional error in our measurement of the background shears is simply where the total number of background galaxies is $N_{\rm total} = n_g A = n_g 
f_{\rm sky} A_{\rm sky}$, $A$ is the survey area, the lensing induced rms shear $\langle\gamma\rangle_{\rm rms} \simeq 0.04$, the intrinsic ellipticity dispersion $\sigma_\epsilon=0.3$, and where the number density $n_g$ has units per square arcminute."
 Thus for the fiducial parameters faa=0.1 aud ng=LOO. one can expect to meastre the background shear to accuracy at about 5-7.," Thus for the fiducial parameters $\fsky=0.1$ and $n_g=100$, one can expect to measure the background shear to accuracy at about $\sigma$."
 We find that such a signal corresponds to chanecs in (7 of a few percent: hence this is the approximate scusitivity we expect in the absence of systematic errors., We find that such a signal corresponds to changes in $w$ of a few percent; hence this is the approximate sensitivity we expect in the absence of systematic errors.
 We perform a \? minimization over the mean shear amplitudes at the two backeround distributions for cachforeground slice to fit for the dark cucrey parameters., We perform a $\chi^2$ minimization over the mean shear amplitudes at the two background distributions for eachforeground slice to fit for the dark energy parameters.
 The time dependence of wis parameterized as anmang|wy(la) (Lander 2002)., The time dependence of $w$ is parameterized as $w=w_0+w_a (1-a)$ (Linder 2002).
" For comparison with other work we will compare iw, to « defined by a6maegdu!zs", For comparison with other work we will compare $w_a$ to $w'$ defined by $w=w_0+w'z$.
 Siuce the u parameterization is uusuitable for the large redshift rause we use. any conrparisou with it cau be made only for a choice of redshift.," Since the $w'$ parameterization is unsuitable for the large redshift range we use, any comparison with it can be made only for a choice of redshift."
" For example. at 2=1.which is well probed by our method aud is of interest in discriminating dark energy models (Linder 2002). uw,=2u’."," For example, at $z=1$,which is well probed by our method and is of interest in discriminating dark energy models (Linder 2002), $w_a = 2 w'$."
" For forceromud slices labeled by iudex / and two backerouud suuples by 1 and 2. the \? is eiven by where R is the distance ratio of equation (26)) for eivou values of Ομ«e aud v. aud R is the fiducial model with O,—0.7.«€Low,0."," For foreground slices labeled by index $l$ and two background samples by $1$ and $2$, the $\chi^2$ is given by where $R$ is the distance ratio of equation \ref{ratio}) ) for given values of $\ol, w$ and $w_a$, and $R^0$ is the fiducial model with $\ol=0.7, 
w=-1, w_a=0$."
 The weights C; are given by where fp is the fraction of the surveyarea A covered by halo apertures in the /-tl lens slice., The weights $U_{l}$ are given by where $f_l$ is the fraction of the surveyarea $A$ covered by halo apertures in the $l$ -th lens slice.
 The factor of 2 in the denominator arises because we are using oulv one componcut of the measured ellipticity whereas σὲ denotes the sini of the variances of both components., The factor of $2$ in the denominator arises because we are using only one component of the measured ellipticity whereas $\sigma_\epsilon^2$ denotes the sum of the variances of both components.
 The results are shown in Figures 6.., The results are shown in Figures \ref{fig:omegaw}. .
" Figure 6 (LIIS) shows the constraints im the Q,aw plane.", Figure \ref{fig:omegaw} (LHS) shows the constraints in the $\ol-w$ plane.
 The ellipses show the 68% coufidence region given by Ay?= 2.3., The ellipses show the $68\%$ confidence region given by $\Delta\chi^2=2.3$ .
 The elongated inner contour is for fixed tu= 0., The elongated inner contour is for fixed $w_a=0$ .
" The two outer contours margimalize over wy, assuming external coustraints on ος from the CMD and other probes. correspouding to σος)=0.01. 0.00."," The two outer contours marginalize over $w_a$ assuming external constraints on $\ol$ from the CMB and other probes, corresponding to $\sigma(\ol)=0.01, 0.03$ ."
"aaz accordingly, assuming that the residual viscosity in the dead-zone is αρ;=1.0x1077.","$\alpha_{AZ}$ accordingly, assuming that the residual viscosity in the dead-zone is $\alpha_{DZ}=1.0\times 10^{-7}$."
" For the different values of Hpz we considered, the corresponding value for waz can be found in Table 1 and Fig."," For the different values of $H_{DZ}$ we considered, the corresponding value for $\alpha_{AZ}$ can be found in Table 1 and Fig."
" | displays the corresponding a-parameter as a function of the distance from the disk equatorial plane The planet is initially placed on a circular orbit at a—1, and our main interest is to examine the orbital evolution of planets with masses my=3X107 and 10M,, corresponding to Saturn-mass (Ms) and Jupiter-mass (M) planets, respectively."," \ref{fig:alpha} displays the corresponding $\alpha$ -parameter as a function of the distance from the disk equatorial plane The planet is initially placed on a circular orbit at $a=1$, and our main interest is to examine the orbital evolution of planets with masses $m_p=3\times 10^{-4}$ and $10^{-3}\;M_*$, corresponding to Saturn-mass $M_S$ ) and Jupiter-mass $M_J$ ) planets, respectively."
" In order to conserve mass as the planet grows and opens a gap, we proceed in two 1) we consider a 30Mg protoplanet held at a=1 on a fixed circular orbit."," In order to conserve mass as the planet grows and opens a gap, we proceed in two i) we consider a $30\; M_\oplus$ protoplanet held at $a=1$ on a fixed circular orbit."
 This body is allowed to accrete gas from the disk on a timescale corresponding to ~1500 orbits., This body is allowed to accrete gas from the disk on a timescale corresponding to $\sim 1500$ orbits.
" Due to the very long run times required for the planet mass to reach 1Mj, we have performed, for this step, low-resolution simulations using N,=64, Ng=192 and Νο=64 grid cells."," Due to the very long run times required for the planet mass to reach $1\;M_J$, we have performed, for this step, low-resolution simulations using $N_r=64$, $N_\phi=192$ and $N_\theta=64$ grid cells."
" ii) once the planet mass has reached 1Ms or 1ΜΙ, we restart the calculations, but with the planet being allowed to migrate due to its interaction with the disk, and accretion being switched off."," ii) once the planet mass has reached $1\;M_S$ or $1\;M_J$, we restart the calculations, but with the planet being allowed to migrate due to its interaction with the disk, and accretion being switched off."
" For this second step, we have performed higher resolution simulations using N,=128, Ng=384 and Ng=64 grid cells."," For this second step, we have performed higher resolution simulations using $N_r=128$, $N_\phi=384$ and $N_\theta=64$ grid cells."
 The new values for the disk physical quantities were computed from the old ones using bi-linear interpolation., The new values for the disk physical quantities were computed from the old ones using bi-linear interpolation.
" At the inner edge of the computational domain, we model accretion onto the central star by using a ‘viscous’ boundary condition, for which we set the radial velocity in the innermost cells to v,=BVyisc(Tin), where Vyisc(Vin)=—3v/2ri, is the typical disk inward drift velocity due to viscous diffusion, and β is a free parameter which is set to B=5 in this work (Pierens Nelson 2008)."," At the inner edge of the computational domain, we model accretion onto the central star by using a `viscous' boundary condition, for which we set the radial velocity in the innermost cells to $v_r=\beta v_{visc}(r_{in})$, where $v_{visc}(r_{in}) =-3\nu/2r_{in}$ is the typical disk inward drift velocity due to viscous diffusion, and $\beta$ is a free parameter which is set to $\beta=5$ in this work (Pierens Nelson 2008)."
" At the outer edge of the computational domain, and at the lower meridional boundary as well, we prevent mass loss from the disk by employing reflecting boundary conditions."," At the outer edge of the computational domain, and at the lower meridional boundary as well, we prevent mass loss from the disk by employing reflecting boundary conditions."
" Assuming that the disk is symmetric with respect to its midplane, we also impose a symmetry boundary condition at the upper meridional boundary, which corresponds to the disk midplane."," Assuming that the disk is symmetric with respect to its midplane, we also impose a symmetry boundary condition at the upper meridional boundary, which corresponds to the disk midplane."
" Consequently, we consider only the upper half of the disk in the simulations described below."," Consequently, we consider only the upper half of the disk in the simulations described below."
" For each value of Hpz we consider, we have performed a simulation in which a 30Mg planet held ona circular orbit can accrete gas from the disk until its mass reaches |M;."," For each value of $\hdz$ we consider, we have performed a simulation in which a $30\;\mearth$ planet held on a circular orbit can accrete gas from the disk until its mass reaches $1\;M_J$."
 In the simulations presented here accretion is modelled by removing at each time-step a fraction of the gas located inside the Roche lobe of the planet and then adding the corresponding amount of matter to the mass of the planet (e.g. Kley 1999; Nelson et al., In the simulations presented here accretion is modelled by removing at each time-step a fraction of the gas located inside the Roche lobe of the planet and then adding the corresponding amount of matter to the mass of the planet (e.g. Kley 1999; Nelson et al.
 2000)., 2000).
" The e-folding time for gas accretion was chosen to be the orbital period of the planet, which corresponds to the maximum rate at which the planet can accrete gas (Kley 1999)."," The e-folding time for gas accretion was chosen to be the orbital period of the planet, which corresponds to the maximum rate at which the planet can accrete gas (Kley 1999)."
" 'The choice of a 30Me protoplanet to act as a seed onto which gas can accrete is broadly consistent with evolutionary models of gas giant planets forming in protoplanetary disks, which suggest that rapid gas accretion occurs once the planet mass reaches 30—40Mg (Papaloizou Nelson The time evolution of the planet mass for each model is displayed in Fig. 2.."," The choice of a $30 \; \mearth$ protoplanet to act as a seed onto which gas can accrete is broadly consistent with evolutionary models of gas giant planets forming in protoplanetary disks, which suggest that rapid gas accretion occurs once the planet mass reaches $30-40\;\mearth$ (Papaloizou Nelson The time evolution of the planet mass for each model is displayed in Fig. \ref{massvstime}."
 We see that the evolution of the planet mass depends only weakly on the size of the dead-zone and proceeds similarly in each case., We see that the evolution of the planet mass depends only weakly on the size of the dead-zone and proceeds similarly in each case.
 The early evolution involves rapid gas accretion with the planet growing to become a Saturn-mass planet in ~100 orbits., The early evolution involves rapid gas accretion with the planet growing to become a Saturn-mass planet in $\sim 100$ orbits.
" As the planet mass increases, non-linear effects can tidally truncate the disk, leading to a decrease in the accretion rate such that it takes 1500 orbits for a Saturn-mass planet to reach a Jovian mass."," As the planet mass increases, non-linear effects can tidally truncate the disk, leading to a decrease in the accretion rate such that it takes $\sim 1500$ orbits for a Saturn-mass planet to reach a Jovian mass."
" It is worth noting, however, that although at earlier times the accretion rate should not depend strongly on the size of the dead-zone, since the planet is able to accrete material which is on neighbouring orbits, we expect this to be not true from the time the gravitational torque is largely deposited in the disk in the near-vicinity of the planet."," It is worth noting, however, that although at earlier times the accretion rate should not depend strongly on the size of the dead-zone, since the planet is able to accrete material which is on neighbouring orbits, we expect this to be not true from the time the gravitational torque is largely deposited in the disk in the near-vicinity of the planet."
 This occurs when the thermal criterion for gap opening is satisfied (Lin Papaloizou 1986;, This occurs when the thermal criterion for gap opening is satisfied (Lin Papaloizou 1986;
0.5cm Alshordi. N. 2010. arXiv:1003.4811.,"0.5cm Afshordi, N. 2010, arXiv:1003.4811."
 Komatsu. E.. 2010. submitted to ApJS. arXiv:LOOLA538.," Komatsu, E., 2010, submitted to ApJS, arXiv:1001.4538."
ARF files egenerated usinge the andxissimarfgen.,ARF files generated using the and.
 Among the eleven observations we used. (he AXP can be resolved from the SNR Ives 73 onlv in the acid observations.," Among the eleven observations we used, the AXP can be resolved from the SNR Kes 73 only in the and observations."
 For these. it is possible to extract either the neutron stars spectrum or the combined spectrum of the neutron star and (he SNR.," For these, it is possible to extract either the neutron star's spectrum or the combined spectrum of the neutron star and the SNR."
 By contrast. only combined spectra can be extracted from the and observations.," By contrast, only combined spectra can be extracted from the and observations."
 The spectra of AXPs are often parametrized by à blackbody plus a power-law (although (his is known to be an approximation to a likely Comptonized blackbody spectrum — see Thompson et al., The spectra of AXPs are often parametrized by a blackbody plus a power-law (although this is known to be an approximation to a likely Comptonized blackbody spectrum – see Thompson et al.
 2002 ancl. for example. Rea et al.," 2002 and, for example, Rea et al."
 2008)., 2008).
 The spectra of SNRs are often fit with models like. for example. VSEDOV (a plane-parallel shock radiation model with separate ion and electron temperatures). VNEI (a non-equilibrium ionization collisional plasma model). or VPSIIOCH (a plane-parallel shocked plasma model).," \nocite{tlk02,rzt+08}
 The spectra of SNRs are often fit with models like, for example, VSEDOV (a plane-parallel shock radiation model with separate ion and electron temperatures), VNEI (a non-equilibrium ionization collisional plasma model), or VPSHOCK (a plane-parallel shocked plasma model)."
 5ee ?. for a review of these models., See \citealt{blr01} for a review of these models.
 In this paper. we modeled (he neutron star radiation with a blackbodx plus power-law (BB+POW). and the SNR radiation with a VSEDOV model. using12.," In this paper, we modeled the neutron star radiation with a blackbody plus power-law (BB+POW), and the SNR radiation with a VSEDOV model, using."
5.0°.. The focus of our investigation is on the AXP’s X-ray flux: in modelling the SNR we sought only a suitable parameterization to allow us to subtract off its thax reliably., The focus of our investigation is on the AXP's X-ray flux; in modelling the SNR we sought only a suitable parameterization to allow us to subtract off its flux reliably.
 As we show below. the VSEDOV mocdel is adequate for these purposes.," As we show below, the VSEDOV model is adequate for these purposes."
 We modeled the interstellar absorption bv multiplving a WADS (a photo-electrie absorption model. in which (he interstellar absorption is characterized by a single parameter μι the neutral hydyogen column density. along the line of sight) model to both the BB+POW and VSEDOV models.," We modeled the interstellar absorption by multiplying a WABS (a photo-electric absorption model, in which the interstellar absorption is characterized by a single parameter $N_H$, the neutral hydrogen column density along the line of sight) model to both the BB+POW and VSEDOV models."
 Figure 3. shows the combined spectra from and the components of the model., Figure \ref{fig:spec} shows the combined spectra from and the components of the best-fit model.
 The AXP power-law component clearly dominates (he spectra above 4 keV. Therefore. we chose to study the ANP flux in the 410 keV. band only. in order to minimize ONR contamination.," The AXP power-law component clearly dominates the spectra above $\sim$ 4 keV. Therefore, we chose to study the AXP flux in the 4–10 keV band only, in order to minimize SNR contamination."
 Nevertheless. we still attempted to remove (he remaining small contribution of SNR. in this band for the fluxes measured from and observations. so that we could compare them with the neutron-star-only [Inxes measured with andIXALAL.," Nevertheless, we still attempted to remove the remaining small contribution of SNR in this band for the fluxes measured from and observations, so that we could compare them with the neutron-star-only fluxes measured with and."
 It is reasonable to assume (hat both the interstellar absorption and SN. radiation do nol change over a lime scale of about. a decade., It is reasonable to assume that both the interstellar absorption and SNR radiation do not change over a time scale of about a decade.
" Consequently. in our attempt (o remove the SNR flux. we used the same Vy, and VSEDOV parameters for all the spectra of the different observations. and allowed only the BB+POW model to vary. [rom observation to"," Consequently, in our attempt to remove the SNR flux, we used the same $N_H$ and VSEDOV parameters for all the spectra of the different observations, and allowed only the BB+POW model to vary from observation to"
"Bürrgi 1986) were based on measurements and calculations of the charge exchange cross section c, for the reaction H-H-H-«H complemented at low energies with the polarization cross section computed with the Langevin formula eq. (A4)).","Bürrgi 1986) were based on measurements and calculations of the charge exchange cross section $\sigma_{\rm ce}$ for the reaction ${\rm H}+{\rm
H}^+\rightarrow {\rm H}^++{\rm H}$ complemented at low energies with the polarization cross section computed with the Langevin formula eq. \ref{lange}) )."
 Since the charge transfer process proceeds with little momentum transfer between the interacting particles. eq. (4) ," Since the charge transfer process proceeds with little momentum transfer between the interacting particles, eq. \ref{sigmadiff}) )"
"with O=z gives Oy=20, (Dalgamo 1958. Banks Holzer 1968)."," with $\Theta=\pi$ gives $\sigma_{\rm mt} \approx
2\sigma_{\rm ce}$ (Dalgarno 1958, Banks Holzer 1968)."
 As shown by Fig. 12..," As shown by Fig. \ref{hp_cs},"
 a combination of the polarization cross section and twice the value of the charge exchange cross section roughly reproduces the accurate results of GKS., a combination of the polarization cross section and twice the value of the charge exchange cross section roughly reproduces the accurate results of GKS.
 However. the momentum transfer rate estimated by Geiss Bürrgi (1986) with this approximation for temperatures between 10? K and 2x[0 K is about higher than the rate obtained by a numerical integration of the momentum transfer cross section of GKS. shown in Fig.," However, the momentum transfer rate estimated by Geiss Bürrgi (1986) with this approximation for temperatures between $10^3$ K and $2\times 10^4$ K is about higher than the rate obtained by a numerical integration of the momentum transfer cross section of GKS, shown in Fig."
 13 for different values of the drift velocity., \ref{hp} for different values of the drift velocity.
 The momentum transfer cross section for e-H collisions has been computed by Dalgarno. Yan. Liu (1999) with the quantal formula of Dalgarno Griffing (1958) and the phase shifts of Rudge (1975) and Das Rudge (1976) at Ex10 eV. and by van Wyngaarden Walters (1986) in the energy range 100—300 eV. Laboratory measurements of the e-H momentum transfer cross sections have been performed by Williams (1975a.b). Callaway Williams (1975). Shyn Cho (1989). and Shyn Grafe (1992) (for a detailed review of the experimental methods and results. see Bederson Kieffer 1971 and Trajmar Kanik 1995).," The momentum transfer cross section for $e$ –H collisions has been computed by Dalgarno, Yan, Liu (1999) with the quantal formula of Dalgarno Griffing (1958) and the phase shifts of Rudge (1975) and Das Rudge (1976) at $E \lesssim 10$ eV, and by van Wyngaarden Walters (1986) in the energy range 100–300 eV. Laboratory measurements of the $e$ –H momentum transfer cross sections have been performed by Williams (1975a,b), Callaway Williams (1975), Shyn Cho (1989), and Shyn Grafe (1992) (for a detailed review of the experimental methods and results, see Bederson Kieffer 1971 and Trajmar Kanik 1995)."
 Theoretical and experimental results are shown in Fig. 14.., Theoretical and experimental results are shown in Fig. \ref{eh_cs}.
 The dependence of the cross section on collision energy is clearly non-Langevin: at low energies the cross section is approximately constant. 7=4x107? em™. whereas at high energies. it decreases with energy as E/.," The dependence of the cross section on collision energy is clearly non-Langevin: at low energies the cross section is approximately constant, $\sigma\approx 4\times 10^{-15}$ $^{-2}$, whereas at high energies, it decreases with energy as $E_{\rm
cm}^{-1.8}$."
 As a result. the momentum transfer rate. shown in Fig. 15.. ," As a result, the momentum transfer rate, shown in Fig. \ref{eh}, ,"
1s lower by about one order of magnitude than the Langevin value at Tx10 K. and larger by ~40% at T=107 K. with a weak dependence on the relative drift velocity.," is lower by about one order of magnitude than the Langevin value at $T\approx 10$ K, and larger by $\sim 40\%$ at $T\approx 10^4$ K, with a weak dependence on the relative drift velocity."
 With the exception of collisions with H or electrons. to our knowledge. there are no experimental or theoretical data available for elastic collisions between He atoms and charged species.," With the exception of collisions with $^+$ or electrons, to our knowledge, there are no experimental or theoretical data available for elastic collisions between He atoms and charged species."
" An estimate based on the Langevin approximation (see Appendix). gives (OV TNC ry) where 5 =H or H». and p, is the polarizability of species n (see Appendix)."," An estimate based on the Langevin approximation (see Appendix), gives v }= v where $n=$ H or $_2$, and $p_n$ is the polarizability of species $n$ (see Appendix)."
 According to this equation. the momentum transfer rate for collision of tons with He is. in general. a factor 0.4-0.5 of the corresponding rate forcollisions with H» and a factor 0.3-0.4 of the corresponding rate for collisions with H.," According to this equation, the momentum transfer rate for collision of ions with He is, in general, a factor 0.4-0.5 of the corresponding rate forcollisions with $_2$ and a factor 0.3-0.4 of the corresponding rate for collisions with H."
10 GeV as Dio and the value at 1 GeV if one extrapolates the power-law behavior at high energy downward.,10 GeV as $D_{10}$ and the value at 1 GeV if one extrapolates the power-law behavior at high energy downward.
" The latter is for comparison with ?,, who uses a strict power-law relation."," The latter is for comparison with \citet{2008arXiv0812.4457P}, who uses a strict power-law relation."
 We adopt the analysis of ? to determine the expected spatial locations of magnetars and pulsars., We adopt the analysis of \citet{Gill07} to determine the expected spatial locations of magnetars and pulsars.
 This distribution has two components., This distribution has two components.
 One owes to the high mass stars throughout the Galaxy (??)..," One owes to the high mass stars throughout the Galaxy \citep{2000AJ....120..314R,2005AJ....130.1652R}."
 This distribution decays exponentially from the center of the Galaxy with a scale length of 2.8 kpc and vertically away from the galactic disk with a scale height of 45 pc., This distribution decays exponentially from the center of the Galaxy with a scale length of 2.8 kpc and vertically away from the galactic disk with a scale height of 45 pc.
 The second component is the overabundance of high mass stars known as the Gould belt., The second component is the overabundance of high mass stars known as the Gould belt.
 Many of the nearby middle-aged neutron stars are probably associated with this recent star formation (7).., Many of the nearby middle-aged neutron stars are probably associated with this recent star formation \citep{2003A&A...406..111P}.
 Including this population is critical because nearby young sources can dominate the observed spectrum of cosmic rays., Including this population is critical because nearby young sources can dominate the observed spectrum of cosmic rays.
" To determine the ages of the sources, we assume that the birthrate of pulsars and magnetars has been uniform in time throughout the Galaxy, so we simply choose 20,000 ages from a uniform distribution between zero and 10° years for pulsars and 10” years for magnetars."," To determine the ages of the sources, we assume that the birthrate of pulsars and magnetars has been uniform in time throughout the Galaxy, so we simply choose 20,000 ages from a uniform distribution between zero and $10^6$ years for pulsars and $10^7$ years for magnetars."
" Although we examine sources with ages up to 10” years, the bulk of the emission emerges within the first 10,000 years for magnetars or shorter for pulsars."," Although we examine sources with ages up to $10^7$ years, the bulk of the emission emerges within the first 10,000 years for magnetars or shorter for pulsars."
" Therefore, even with a kick of up to 2,000 km/s, the sources move at most twenty parsecs from their birthplaces during their active phases."," Therefore, even with a kick of up to 2,000 km/s, the sources move at most twenty parsecs from their birthplaces during their active phases."
 It is reasonable to neglect the motion of the sources through the Galaxy during their active period., It is reasonable to neglect the motion of the sources through the Galaxy during their active period.
" This contrasts with who used present day positions of pulsars, which leads to a more diffuse distribution (e.g. more extended perpendicular to the Galactic disk) than when the sources were active because of natal kicks given to neutron stars."," This contrasts with who used present day positions of pulsars, which leads to a more diffuse distribution (e.g. more extended perpendicular to the Galactic disk) than when the sources were active because of natal kicks given to neutron stars."
 'There are two important questions to address., There are two important questions to address.
 The first is whether the magnetic fields of the magnetars carry sufficient energy to account for the observed fluxes of cosmic rays., The first is whether the magnetic fields of the magnetars carry sufficient energy to account for the observed fluxes of cosmic rays.
" The second is whether or not magnetars can account for this observed spectrum of cosmic rays incident upon the Earth, given the assumed spectrum of cosmic ray production."," The second is whether or not magnetars can account for this observed spectrum of cosmic rays incident upon the Earth, given the assumed spectrum of cosmic ray production."
 We are interested in both the mean cosmic ray abundance over the realizations but also the range., We are interested in both the mean cosmic ray abundance over the realizations but also the range.
" Understanding the range is crucial because one or two nearby young sources can dominate the abundances, and we may simply be living in a somewhat special place at a somewhat special time."," Understanding the range is crucial because one or two nearby young sources can dominate the abundances, and we may simply be living in a somewhat special place at a somewhat special time."
 It is important to mention that our results even for pulsars do not agree with those of ? because of the aforementioned differences in modeling., It is important to mention that our results even for pulsars do not agree with those of \citet{2008arXiv0812.4457P} because of the aforementioned differences in modeling.
 Fig., Fig.
 2 shows the expected abundance of cosmic rays for pulsars and magnetars for the two different diffusion scenarios., \ref{fig:all} shows the expected abundance of cosmic rays for pulsars and magnetars for the two different diffusion scenarios.
" Although the total energy reservoir is the same for a particular pulsar or magnetar, the magnetars are ten-times less numerous, so they are assigned a ten times larger efficiency so that the total cosmic-ray production is the same"," Although the total energy reservoir is the same for a particular pulsar or magnetar, the magnetars are ten-times less numerous, so they are assigned a ten times larger efficiency so that the total cosmic-ray production is the same"
others).,others).
 uci -..- − where w. z. andor):j=1.2 are the positions of a source. an image. and the lens elements of fractional masses e;:j=1.2 in the two dimensional skv as a complex plane.," = z - -, where $\omega$ , $z$ and $x_j: j =1,2$ are the positions of a source, an image, and the lens elements of fractional masses $\epsilon_j: j =1,2$ in the two dimensional sky as a complex plane."
 We have chosen the lens axis to be along the real axis so (hat c4 and ure are real. and the unit distance scale is given by the Einstein ring radius £25.," We have chosen the lens axis to be along the real axis so that $x_1$ and $x_2$ are real, and the unit distance scale is given by the Einstein ring radius $R_E$."
" qns L=Rpe=VAGAMD::MIGATD:: dod=D, tnu where D is the reduced distance.", 1 = R_E =; = + where $D$ is the reduced distance.
 When there are 7 point lens elements where »>2. we only need to extend the range of the index to j=1.2.....n and replace the lens position vectors to 7; because we can nol line them up allon (he real axis.," When there are $n$ point lens elements where $n > 2$, we only need to extend the range of the index to $j = 1, 2, ... , n$ and replace the lens position vectors to $\bar x_j$ because we can not line them up allon the real axis."
 The form of the Jacobian matrix in equation (1.1)) applies lo anv quasi-analytic lens equation. and &=Oc is easily calenlated for each class of lens ecualions.," The form of the Jacobian matrix in equation \ref{eqJacobian}) ) applies to any quasi-analytic lens equation, and $\kappa \equiv \partial \bar\omega$ is easily calculated for each class of lens equations."
 The quasi-analylic lens equations the lens equation is not analytic. but the differentials ave have been discussed in RBCPLX and is reviewed here briefly.," The quasi-analytic lens equations – the lens equation is not analytic, but the differentials are – have been discussed in RBCPLX and is reviewed here briefly."
 The eigenvalues of the Jacobian matrix are easy tofind.and A vanishes on the critical curve (|&|=1<=J 0).," The eigenvalues of the Jacobian matrix are easy tofind,and $\lambda_-$ vanishes on the critical curve $|\kappa|=1 \Leftrightarrow J =0$ )."
 Αα (45," = 1 | ,"
 Αα (45)," = 1 | ,"
width for this star. according to our calculations. leads to the magnesium abundance logz(Mg)=7.37. whereas our HV. value gives log(Mg)=7.48 that is substantially closer to the solar abundance log2.(Mg)=7.55 (Lodders 2003).,"width for this star, according to our calculations, leads to the magnesium abundance $\log \varepsilon({\rm Mg})=7.37$, whereas our $W$ value gives $\log \varepsilon({\rm Mg})=7.48$ that is substantially closer to the solar abundance $\log
\varepsilon_{\sun}({\rm Mg})=7.55$ (Lodders 2003)."
 On the whole. Fig.3 confirms the stated accuracy of our V. values.," On the whole, Fig.3 confirms the stated accuracy of our $W$ values."
 More than 30 years ago Mihalas (1972) first showed that a non-LTE approach is necessary in the 4481.2 lline analysis for early B stars and especially O stars., More than 30 years ago Mihalas (1972) first showed that a non-LTE approach is necessary in the 4481.2 line analysis for early B stars and especially O stars.
 According to his calculations. the non-LTE equivalent widths IV. of the line are greater than the LTE ones. and the discrepancy increases with increasingJive.," According to his calculations, the non-LTE equivalent widths $W$ of the line are greater than the LTE ones, and the discrepancy increases with increasing."
 Our computations contirm this conclusion: moreover. the ΤΕ increment seems to be greater for B. giants than for B dwarfs.," Our computations confirm this conclusion; moreover, the $W$ increment seems to be greater for B giants than for B dwarfs."
 In particular. when == 3.5. a value corresponding approximately to giants. the difference in WW) between the non-LTE and LTE cases is about 5—6 per cent at == 20000-25000 K. i.e. comparable with errors in the measured W values. whereas it exceeds 50 per cent at == 30000 K. Since our sample includes both dwarfs and giants. we apply the non-LTE approach to all stars.," In particular, when = 3.5, a value corresponding approximately to giants, the difference in $W$ between the non-LTE and LTE cases is about 5–6 per cent at = 20000–25000 K, i.e. comparable with errors in the measured W values, whereas it exceeds 50 per cent at = 30000 K. Since our sample includes both dwarfs and giants, we apply the non-LTE approach to all stars."
 The AHS1.2 lline was treated in our compuations as a triplet. and for its three components the same oscilator strengths were adopted as in Daflon et al," The 4481.2 line was treated in our computations as a triplet, and for its three components the same oscillator strengths were adopted as in Daflon et al."
/s (2003). work.,'s (2003) work.
 In the non-LTE calculations of the line we used the codes (Giddings 1981: Butler 1994) and (Butler. 1984)., In the non-LTE calculations of the line we used the codes (Giddings 1981; Butler 1994) and (Butler 1984).
 Tye former code determines the atomic level populations by joinly solving the radiative transfer and statistical equilibrium equations., The former code determines the atomic level populations by jointly solving the radiative transfer and statistical equilibrium equations.
 The latter one computes the emergent flux and. therefore. the line protile.," The latter one computes the emergent flux and, therefore, the line profile."
 We employed Przybilla et al, We employed Przybilla et al.
/s (2001) magnesium model atom.,'s (2001) magnesium model atom.
 It includes all atomic levels with principal quantum numbers n << 9. all levels with n x 10 and the ground. state.," It includes all atomic levels with principal quantum numbers n $\leqslant$ 9, all levels with n $\leqslant$ 10 and the ground state."
 This model atom is likely the most complete one for magnesium today., This model atom is likely the most complete one for magnesium today.
 The computations were implemented on the basis of the LTE model atmospheres calculated in Paper III with the code of Kuruez (1993)., The computations were implemented on the basis of the LTE model atmospheres calculated in Paper III with the code of Kurucz (1993).
 In order to analyse the effect of the microturbulent parameter oon the A4481.2 lline equivalent width. we made trial calculations of the line for some model atmospheres from Kuruez's (1993) grid.," In order to analyse the effect of the microturbulent parameter on the 4481.2 line equivalent width, we made trial calculations of the line for some model atmospheres from Kurucz's (1993) grid."
 We confirmed that the line strengthens and its sensivity to iincreases as the effective temperature ddecreases from 30000 to 14000 K. Therefore. the effect of errors inl; oon the Mg abundance determination is largest for coolest B stars from our list.," We confirmed that the line strengthens and its sensivity to increases as the effective temperature decreases from 30000 to 14000 K. Therefore, the effect of errors in on the Mg abundance determination is largest for coolest B stars from our list."
 The derived magnesium abundances logz(Mg) are presented in Table I., The derived magnesium abundances $\log \varepsilon({\rm Mg})$ are presented in Table 1.
 When averaging these values for all 52 stars. we obtained the mean abundance logz(Mg)=7.6750.21.," When averaging these values for all 52 stars, we obtained the mean abundance $\log \varepsilon({\rm Mg})
= 7.67\pm0.21$."
 The difference with the solar value of 7.55 is 0.12 dex. re. substantially less than the uncertainty in the mean value.," The difference with the solar value of 7.55 is 0.12 dex, i.e., substantially less than the uncertainty in the mean value."
 We estimated typical errors in the abundances. which originate from uncertainties in the equivalent width VV. effective temperatureTo. surface gravity g.. and microturbulent velocityV;.," We estimated typical errors in the abundances, which originate from uncertainties in the equivalent width $W$, effective temperature, surface gravity , and microturbulent velocity."
. As mentioned above. the typical uncertainty in Wo is —5 per cent.," As mentioned above, the typical uncertainty in $W$ is $\pm5$ per cent."
 Contributions of three other parameters can depend onJip. so we divided the stars into four groups as follows: 15000 K. bbetween 15000 and 19000 K. bbetween 19000 and 24000 K. (24000 A. EneachgrouplhemeanerrorsinTa aand aare evaluated from the individual errors (see Paper ID.," Contributions of three other parameters can depend on, so we divided the stars into four groups as follows: $\leqslant$ 15000 K, between 15000 and 19000 K, between 19000 and 24000 K, $>$ 24000 K. In each group the mean errors in and are evaluated from the individual errors (see Paper II)."
 As far as uncertainties in aare concerned. we adopted the values 32.0 aand 2.5 ffor stars with UTE aand — lO+. respectively.," As far as uncertainties in are concerned, we adopted the values $\pm2.0$ and $\pm2.5$ for stars with $<$ 5 and $\sim$ 10, respectively."
 We found by this method that the full typical error in logz(Mg) is about 0.14 dex for stars with bbetween 19000 and 30000 K. about 0.20 dex for stars with bbetween 15000 and 19000 K and can attain 0.30 dex for coolest programme stars with aaround 14000 K. It is important to note that the uncertainty in the microturbulent parameter ggives the dominant contribution to the full error. namely from 40 to 65 per cent when ddecreases from 30000 to 19000 K and 70-80 per cent for cooler stars.," We found by this method that the full typical error in $\log
\varepsilon({\rm Mg})$ is about 0.14 dex for stars with between 19000 and 30000 K, about 0.20 dex for stars with between 15000 and 19000 K and can attain 0.30 dex for coolest programme stars with around 14000 K. It is important to note that the uncertainty in the microturbulent parameter gives the dominant contribution to the full error, namely from 40 to 65 per cent when decreases from 30000 to 19000 K and 70–80 per cent for cooler stars."
 The latter conclusion willplay an important role in further discussion., The latter conclusion willplay an important role in further discussion.
since the discovery of the genuine brown dwarl G12229D (Nakajimaetal.1995).. a large number of ullvacool dwarls have been discovered (e.g.Straussοἱal.1999:Ixirkpatricket2000:Durgasseretal. 2002a).,"Since the discovery of the genuine brown dwarf 229B \citep{nak95}, a large number of ultracool dwarfs have been discovered \citep[e.g.][]{str99, kir00, bur02a}."
. The newly discovered ultracool dwarls are now classified, The newly discovered ultracool dwarfs are now classified
orbital period.,orbital period.
 Tides ou the primary then raise the eccentricity., Tides on the primary then raise the eccentricity.
 Double-suchrouous svstenis. however. experience damping due to both the tides ou the secondary and those ou the primary.," Double-synchronous systems, however, experience damping due to both the tides on the secondary and those on the primary."
 Assuming a water-ice composition for Pluto Ge=dos1019dynescin 7). we calculate the eccentricity damping timescale due to tides raised by Charon. στ from equation 25 to 0 0.1 Alves.," Assuming a water-ice composition for Pluto $\mu=4~\times 10^{10}~{\rm dynes~cm^{-2}}$ ), we calculate the eccentricity damping timescale due to tides raised by Charon, $\tau_{d,1}$ from equation \ref{eqTidalDamping} to be 5.1 Myrs."
 The shortest damping timescale due to tides frou Pluto acting on Charon. Το is found by assumnidue Charon is also nade of water-ice: we find iu this case a timescale of 8.2 Myr.," The shortest damping timescale due to tides from Pluto acting on Charon, $\tau_{d,2}$ is found by assuming Charon is also made of water-ice; we find in this case a timescale of 8.2 Myr."
 The longest timescale assumes a rocky composition (ji—6.5-ςlottdyresClin. 7): we find this corresponds to 133 \vr., The longest timescale assumes a rocky composition $\mu=6.5~\times 10^{11}~{\rm dynes~cm^{-2}}$ ); we find this corresponds to 133 Myr.
 The overal damping of the svsteni is given w the suu of the damping rates., The overall damping of the system is given by the sum of the damping rates.
 The short damping timescale of tides ou Pluto prevents Charon from contributing sigificautly to the combined effect of both tides. reucing the importance of its composiion.," The short damping timescale of tides on Pluto prevents Charon from contributing significantly to the combined effect of both tides, reducing the importance of its composition."
 The longest eccentricity dampine tinescale that resits frou both tides is 1.9 Abvr., The longest eccentricity damping timescale that results from both tides is 4.9 Myr.
 The inclinatious of the outer satellites relative to he Phito-Charon plare are also dauped by tidal dissipation., The inclinations of the outer satellites relative to the Pluto-Charon plane are also damped by tidal dissipation.
" For a circular svcironous orbit he timescale for iuclination camonus is longer than the timescale for eccentricity calpine by a factor of ~72,", For a circular synchronous orbit the timescale for inclination damping is longer than the timescale for eccentricity damping by a factor of $\sim i^{-2}$.
 We ignore the damping of inclinations 1 ietation 15 for all three satellites., We ignore the damping of inclinations in equation \ref{eqDiffioft} for all three satellites.
 As discussed 1 i? and secti1 5.2.0.. secular interactions betweeithe satellites are visible iu the long erm calculations of their orbits.," As discussed in \citet{TBGE07} and section \ref{secInterpret}, secular interactions between the satellites are visible in the long term calculations of their orbits."
 For t1e best-fit values of he masses of Nix ancl Uvdra. their ecceutriciies are modulated on the order of 10:4 over timesc:des of vears: we neglect these fluctuations fx this work.," For the best-fit values of the masses of Nix and Hydra, their eccentricities are modulated on the order of $10 \%$ over timescales of years; we neglect these fluctuations for this work."
 It is more important iu this model to determine whetLOY sCCIlar evolution can cause the eccentricity oNis or IIvdra «Issipate via Clharon's orbit., It is more important in this model to determine whether secular evolution can cause the eccentricity of Nix or Hydra dissipate via Charon's orbit.
 We use linear sectlay theory to describe the coupled evolution of the eccentricity aud longitude of periapse of cach satellite (2).., We use linear secular theory to describe the coupled evolution of the eccentricity and longitude of periapse of each satellite \citep{MD99}.
 We fux that the nudamped secular evolution agrees qualitatively witi the uuuercal orbit determinations., We find that the undamped secular evolution agrees qualitatively with the numerical orbit determinations.
 We add a term to t1e differcutial equatious describing Charou's eccentricity that reduces it at a constant timescale (Charon=CCharon/ Ta)., We add a term to the differential equations describing Charon's eccentricity that reduces it at a constant timescale $\dot e_{\rm Charon} = - e_{\rm Charon}/\tau_d$ ).
 The frequencies of the oscillations of the eigeumodes of t10 solutiorare practically uuchauged by this term. however cach cigclummode gains a dissipative factor.," The frequencies of the oscillations of the eigenmodes of the solution are practically unchanged by this term, however each eigenmode gains a dissipative factor."
 Quautitativelv. only one eigennmode is damped ou timescales shorter tman than 1.5 Cr.," Quantitatively, only one eigenmode is damped on timescales shorter than than 4.5 Gyr."
 By integrating the dampce secular equatiois with differcut initial periapses. we determined that the secular iiteractious do not catse substautia damping of Nix aud Uvra.," By integrating the damped secular equations with different initial periapses, we determined that the secular interactions do not cause substantial damping of Nix and Hydra."
 Equation 22. civss the frequcacy of perturbatiois duc to colidons of perturers outo each moon relative to the frequeney of porturvations caused by eravitational scatteriues. οςnation 19..," Equation \ref{eqRatio} gives the frequency of perturbations due to collisions of perturbers onto each moon relative to the frequency of perturbations caused by gravitational scattering, equation \ref{eqPintermediate}."
 For Charon. t16 collisional perturbations Increase ple) bv ony 2 perceit.," For Charon, the collisional perturbations increase $p(e)$ by only 2 percent."
 Siuce. Nix aud [velra are snialky. perturbations by collisious have a exeater relative effect: however it is onlv a 2) percent contributio1i to the tota perturbation frequency or Nix aud 15 perceut for Ivdra.," Since Nix and Hydra are smaller, perturbations by collisions have a greater relative effect; however it is only a 20 percent contribution to the total perturbation frequency for Nix and 15 percent for Hydra."
" We solve eqilation 23 to find e,(£) aud /,.(¢) for cach of Plutos moos.", We solve equation \ref{eqDiffeoftgeneral} to find $e_c(t)$ and $i_c(t)$ for each of Pluto's moons.
" For Chiron we f ule.=2.6«105, and 4.=(.29""."," For Charon we find $e_c=2.6 \times 10^{-6}$, and $i_c=0.029^{\circ}$."
 This vaue of e. correspouds to the most likely perturbation durimg a damping tiluescae of 1.9 Myr. and is wich simaller than the observed value of 3.5«103 (?y.," This value of $e_c$ corresponds to the most likely perturbation during a damping timescale of 4.9 Myr, and is much smaller than the observed value of $3.5 \times 10^{-3}$ \citep{TBGE07}."
 Usiug equatiou 2[.. we calculate tiat eivei this value of ος. the proability of Cliaron's eccentricity being as liel as its observed value is 0.2 percent.," Using equation \ref{eqHighTail}, we calculate that given this value of $e_c$, the probability of Charon's eccentricity being as high as its observed value is 0.2 percent."
" For Nix we caCllate cB5O93)2L8&10 ""and (15Gyr)=0.17. and for Πάνα, 7.1«10.P and 0.15? respectively."," For Nix we calculate $e_c(4.5 ~{\rm Gyr})=4.8\times 10^{-3}$ and $i_c(4.5 ~{\rm Gyr})=0.1^{\circ}$, and for Hydra, $7.1 \times 10^{-3}$ and $0.15^{\circ}$ respectively."
 The distributioas specifier by these values are quite consistent with the free eccentricity we determine in table 1.., The distributions specified by these values are quite consistent with the free eccentricity we determine in table \ref{tabFitResults}.
 Two other Iuiper belt ojects have satellites ou low ecceutricity orbits:ELgj.. and Eris.," Two other Kuiper belt objects have satellites on low eccentricity orbits:, and Eris."
 Aong with Pluto these are τος of the four most massive IXDOs known. all with radii of about 1000 ki.," Along with Pluto these are three of the four most massive KBOs known, all with radii of about 1000 km."
 ELgjhas two known satellites., has two known satellites.
 The largest has a 50 day orbit and a measured orbital eccentricity of 0.0504d0.003 ο). , The largest has a 50 day orbit and a measured orbital eccentricity of $0.050 \pm 0.003$ \citep{BBR05}. .
An additional smaller satellite orbits with a period of about 35 davs (?).., An additional smaller satellite orbits with a period of about 35 days \citep{BVB06}.
 The orbital parieers of the immer satellie are uncoustrained. however the relative inclination between the two is about 107.," The orbital parameters of the inner satellite are unconstrained, however the relative inclination between the two is about $40^{\circ}$."
 The masses of the satellites are negheible compared to the mass ofΕν., The masses of the satellites are negligible compared to the mass of.
.. The helioceuvic Inclination of the svstem ds 287., The heliocentric inclination of the system is $28^{\circ}$.
 ? argue that if the tidal respouse of and its large satelite are flnid-like. tida interactions shoul damp their eccentricity on a timescale of about 300 Myr.," \citet{BBR05} argue that if the tidal response of and its large satellite are fluid-like, tidal interactions should damp their eccentricity on a timescale of about 300 Myr."
" With these paralueters We use equatio 123 to calculate an equilibrium e,=L3«101", With these parameters we use equation \ref{eqDiffeoftgeneral} to calculate an equilibrium $e_c=4.3 \times 10^{-4}$.
 The disributiou with this ecceutricity scale xediets an observed eccentricity of 0.05 at a probability of three perceut., The distribution with this eccentricity scale predicts an observed eccentricity of 0.05 at a probability of three percent.
" IIowever, for sinaller bodies. internal clastic forces dominate the tidal deformation of their shape: it is more reasoi asstuue that the tidal respouse of the satellite is characterized by its materia streneth."," However, for smaller bodies, internal elastic forces dominate the tidal deformation of their shape; it is more reasonable to assume that the tidal response of the satellite is characterized by its material strength."
 Then. the fides raise ie primary have the ereatest effect and the eccentricity of the svsteui erows on the same timescale as the erowt the seniüanajor axis.," Then, the tides raised on the primary have the greatest effect and the eccentricity of the system grows on the same timescale as the growth of the semi-major axis."
 Forced eccentricity growth and an evolving orbital perio can be incorporate iuto equation 25.., Forced eccentricity growth and an evolving orbital period can be incorporated into equation \ref{eqDiffeoftgeneral}.
 However. these corrections are only an order unity correction since the erowtli timescale. bv defuilon. Is conrabe to the age of the system.," However, these corrections are only an order unity correction since the growth timescale, by definition, is comparable to the age of the system."
" Assuming Ziyi, is fixed and ignoring the eccentricity erowtl. we calculate 6(L5vrjt.1052."," Assuming $T_{\rm orb}$ is fixed and ignoring the eccentricity growth, we calculate $e_c(4.5~{\rm
 Gyr})=0.0052$."
 The 95 percent coufideuce interval around this e. is 0.001-0.2: the observe eccentricity of LELgiis within this range., The 95 percent confidence interval around this $e_c$ is 0.001-0.2; the observed eccentricity of is within this range.
 The dwart plane Evis is orjted by the satellite Dysnomia., The dwarf planet Eris is orbited by the satellite Dysnomia.
 Observations have shown au upper liit to their eccentricity of 0.015 (?).., Observations have shown an upper limit to their eccentricity of 0.013 \citep{BVB06}.
 The system has a 15 dav orbital period. aud orbits the sun at a semianuajor axis of 67.7. AU with au eccentricity of 0.EL ane a heliocentric inclination of LL’.," The system has a 15 day orbital period, and orbits the sun at a semi-major axis of 67.7 AU with an eccentricity of 0.44 and a heliocentric inclination of $44^{\circ}$."
 In addition to the reduction im effective perturbing density caused by t1ο daclinatiou. the high ecceutricity reduces the effective perturber density by au additional factor of 0.09.," In addition to the reduction in effective perturbing density caused by the inclination, the high eccentricity reduces the effective perturber density by an additional factor of 0.09."
 The semiVor axis of he binary is consistent with [.5 Cove of tidal evolution away from an initially very close orbi τα the tidal response of the secondary that of a streneth-less fiuid. then its eccentricity is damped ou a timescale of 50 Myr.," The semi-major axis of the binary is consistent with 4.5 Gyr of tidal evolution away from an initially very close orbit; if the tidal response of the secondary that of a strength-less fluid, then its eccentricity is damped on a timescale of 50 Myr."
" These parameters vield an e,=2.2«10©.", These parameters yield an $e_c=2.2\times 10^{-6}$.
 However. if the material streueth of the secondary is stronger than its own self-eravity. then he tides raised on the primary cause the eccentricity of the satellite to erow.," However, if the material strength of the secondary is stronger than its own self-gravity, then the tides raised on the primary cause the eccentricity of the satellite to grow."
 Iu this case the relevant timescale is the age of the system. and we find that «(5Gyr)=10« |.Both values axebelow the ohserved upper limit.," In this case the relevant timescale is the age of the system, and we find that $e_c(4.5~{\rm
 Gyr})=1.0\times 10^{-4}$ .Both values arebelow the observed upper limit."
 Iu addition to the high mass ratio and low eccentricity I&uiper belt binaries. there are other known binaries of aliiost," In addition to the high mass ratio and low eccentricity Kuiper belt binaries, there are other known binaries of almost"
allow the GSMF to be computed (Salueci&Persic1999:Balogh 2003:: Baldry.Glazebrook.&Driver 2008.. hereafter. BGDO8).,"allow the GSMF to be computed \citealt{SP99,balogh01,bell03}; \citealt*{BGD08}, hereafter, BGD08)."
 Measurement of the GSMF has now become a standard tool to gain insights into galaxy evolution with considerable effort to extend analyses to 2~1 (Droryetal.2009:Pozzetti2010:Gilbanketal.2011:Vuleani2011) and higher (Elsner.Feul-ner.&Hopp 2008: Kayisawaetal.2009:MarchesiniCaputietal.201I:González2011:Mortlock 20113.," Measurement of the GSMF has now become a standard tool to gain insights into galaxy evolution with considerable effort to extend analyses to $z\sim1$ \citep{drory09,pozzetti10,gilbank11,vulcani11} and higher \citealt*{EFH08}; \citealt{kajisawa09,marchesini09,caputi11,gonzalez11,mortlock11}) )."
 Overall the cosmic stellar mass density is observed to grow by a factor of 10 between >— 2-3 and 2=0 (Dickinsonetal.2003:Elsneretal.2008) with significantly less relative growth in massive 7104MI. galaxies since >~ 1-2 (Wakeetal.2006:Pozzettietal.2010:Caputi 2011.," Overall the cosmic stellar mass density is observed to grow by a factor of 10 between $z\sim2$ –3 and $z=0$ \citep{dickinson03,EFH08} with significantly less relative growth in massive $>10^{11}\Msun$ galaxies since $z\sim1$ –2 \citep{wake06,pozzetti10,caputi11}."
 The evolution in the GSMF is uncertain. however. with some authors suggesting there could be evolution in the stellar initial mass function (IMF) (Davé2008:Wilkinsetal.vanDokkum2008). and considering the range of uncertainties associated with estimating stellar masses Marastonetal.2006:: Conroy.Gunn.&White 2009)).," The evolution in the GSMF is uncertain, however, with some authors suggesting there could be evolution in the stellar initial mass function (IMF) \citep{Dave08,wilkins08,vanDokkum08} and considering the range of uncertainties associated with estimating stellar masses \citealt{maraston06}; \citealt*{CGW09}) )."
 The observed GSMF. defined as the number density of galaxies per logarithmie mass bin. has a declining distribution with mass with a sharp cutoffor break at high masses often fitted with a Schechter(1976) function.," The observed GSMF, defined as the number density of galaxies per logarithmic mass bin, has a declining distribution with mass with a sharp cutoff or break at high masses often fitted with a \citet{Schechter76} function."
" At low redshift. the characteristic mass of the Schechter break has been determined to be between 101°"" and 104AI. (Panteretal.2007: BGDOS: Li&White 2009))."," At low redshift, the characteristic mass of the Schechter break has been determined to be between $10^{10.6}$ and $10^{11}\Msun$ \citealt{panter07}; BGD08; \citealt{LW09}) )."
 The GSMF shape. however. is not well represented by a single Schechter function with a steepening below 107M. giving rise to a double Schechter function shape overall BGDOS).," The GSMF shape, however, is not well represented by a single Schechter function with a steepening below $10^{10}\Msun$ giving rise to a double Schechter function shape overall (BGD08)."
 Peng(2010b) note that this shape arises naturally in a model with simple empirical laws for quenching of star formation in galaxies., \citet{peng10} note that this shape arises naturally in a model with simple empirical laws for quenching of star formation in galaxies.
 This is one example of the potential for insights that can be obtained by studying the inferred GSMF as opposed to comparing observations and theoretical predictions of the GLF: though we note that it is in some sense more natural for theory to predict the GLF because model galaxies have a known' star-formation history., This is one example of the potential for insights that can be obtained by studying the inferred GSMF as opposed to comparing observations and theoretical predictions of the GLF; though we note that it is in some sense more natural for theory to predict the GLF because model galaxies have a `known' star-formation history.
 Abundance matching between a theoretical galactic halo mass function and à GLF or GSMF demonstrates that. in order to explain the GSMF shape. the fraction of baryonic mass converted to stars increases with mass to a peak before decreasing (Marinoni&Hud-son2002:Shankaretal. 2006::BGDOS: Conroy&Wechsler2009:Guoetal.2010:Moster 20100).," Abundance matching between a theoretical galactic halo mass function and a GLF or GSMF demonstrates that, in order to explain the GSMF shape, the fraction of baryonic mass converted to stars increases with mass to a peak before decreasing \citealt{MH02,shankar06}; BGD08; \citealt{CW09,guo10,moster10}) )."
 Galaxy formation theory must explain the preferred mass for star formation efficiency. the shallow low-mass end slope compared to the halo mass function. and the exponential cutoff at high masses (Oppenheimeretal. 2010).," Galaxy formation theory must explain the preferred mass for star formation efficiency, the shallow low-mass end slope compared to the halo mass function, and the exponential cutoff at high masses \citep{oppenheimer10}."
.. At high masses. feedback from active galactic nuclei has been invoked to prevent cooling of gas leading to star formation (Bestetal.2005:KeresBower2006:Cro-etal. 2006).," At high masses, feedback from active galactic nuclei has been invoked to prevent cooling of gas leading to star formation \citep{best05,keres05,bower06,croton06}."
. The preferred mass scale may correspond to a halo mass of ~1077M. above which gas becomes more readily shock heated (Dekel&Birnboim2006)., The preferred mass scale may correspond to a halo mass of $\sim 10^{12}\Msun$ above which gas becomes more readily shock heated \citep{DB06}.
. Toward lower masses. supernovae feedback creating galactic winds is thought to play a major role in regulating star formation (Larson1974:1986:Lacey&Silk1991:Kayetal. 2002): while Oppenheimeretal. hhave argued that it is re-aecretion of these winds that is critical in shaping the GSMFE.," Toward lower masses, supernovae feedback creating galactic winds is thought to play a major role in regulating star formation \citep{larson74,DS86,LS91,kay02}; while \citeauthor{oppenheimer10} have argued that it is re-accretion of these winds that is critical in shaping the GSMF."
 Others have argued that star. formation in the lowest mass haloes is also suppressed by photoionization (Efstathiou1992:Thoul&Weinberg1996:Somerville2002). in particular. to explain the number ofsatellites in the Local Group (Bensonetal.2002).," Others have argued that star formation in the lowest mass haloes is also suppressed by photoionization \citep{Efstathiou92,TW96,Somerville02}, in particular, to explain the number ofsatellites in the Local Group \citep{benson02}."
". Recently. Guoetal.(2011) used a semi-analytical model applied to the Millenium Simulation (MS) and the higher resolution MS-II (Boylan-Kolchinetal.2009). to predict the cosmic-average ""field! GSMF down to LO°AL.."," Recently, \citet{guo11} used a semi-analytical model applied to the Millenium Simulation (MS) and the higher resolution MS-II \citep{boylan-kolchin09} to predict the cosmic-average `field' GSMF down to $10^{6}\Msun$."
" They tind that the GSMF continues to rise to low masses reaching ον0.1 galaxies per Mpc? for 10""—10' AL... however. they caution that their model produces a larger passive fraction than is observed amongst the low-mass population."," They find that the GSMF continues to rise to low masses reaching $>0.1$ galaxies per $^3$ for $10^{6}$ $10^{7}\Msun$, however, they caution that their model produces a larger passive fraction than is observed amongst the low-mass population."
 Mamonetal.(2011). apply a simple one-equation prescription. on top of a halo merger tree. that requires star formation to occur within a minimum mass set by the temperature of the inter-galactic medium.," \citet{mamon11} apply a simple one-equation prescription, on top of a halo merger tree, that requires star formation to occur within a minimum mass set by the temperature of the inter-galactic medium."
 Their results give a rising baryonic mass function down to 10AL.. with the peak of the mass function of the star-forming galaxy population at 10AL. .," Their results give a rising baryonic mass function down to $10^{5.5}\Msun$, with the peak of the mass function of the star-forming galaxy population at $\sim10^{7}\Msun$ ."
 We note that it is useful for theorists to predict the tield GSMF of the star-forming population because measuring this to low masses. while challenging. is significantly easier than for the passive population.," We note that it is useful for theorists to predict the field GSMF of the star-forming population because measuring this to low masses, while challenging, is significantly easier than for the passive population."
 Measurements of the GLF reaching low luminosities have been made for the Local Group (Koposovetal.2008).. selected groups (Trentham&Tully2002:Chiboucas.Karachentsev.2009).. clusters (Sabatinietal.2003:Rines&Geller2008) and superclusters (Mercurioetal.2006).," Measurements of the GLF reaching low luminosities have been made for the Local Group \citep{koposov08}, selected groups \citep*{TT02,CKT09}, clusters \citep{sabatini03,RG08} and superclusters \citep{mercurio06}."
. To accurately measure the cosmic-average GSMF. it is necessary to survey random volumes primarily beyond ~LOMMpc because: () at smaller distances. themeasurement is limited in accuracy by systematic uncertainties in distances to galaxies (Masters.Haynes.&Giovanelli2004): and Gi) a local volume survey is significantly biased. e.g.. the D-band luminosity density out to MMpe is about a factor of 5 times the cosmic average (using data from 2004 in comparison with Norbergetal.2002:Blanton2003bn.," To accurately measure the cosmic-average GSMF, it is necessary to survey random volumes primarily beyond $\sim10$ Mpc because: (i) at smaller distances, themeasurement is limited in accuracy by systematic uncertainties in distances to galaxies \citep*{MHG04}; and (ii) a local volume survey is significantly biased, e.g., the $B$ -band luminosity density out to Mpc is about a factor of 5 times the cosmic average (using data from \citealt{karachentsev04} in comparison with \citealt{norberg02,blanton03ld}) )."
 The Sloan Digital Sky Survey (SDSS) made a significant breakthrough with redshifts obtained to r«17.5 mmag and multi-colour photometry (Stoughtonetal.2002). in particular. with the low-redshift sample described by Blantonetal.(2005a).," The Sloan Digital Sky Survey (SDSS) made a significant breakthrough with redshifts obtained to $r<17.8$ mag and multi-colour photometry \citep{stoughton02}, in particular, with the low-redshift sample described by \citet{blanton05}."
. In order to extend and check the low-mass GSMF (BGDOS). it is necessary to go deeper over a still significant area of the sky.," In order to extend and check the low-mass GSMF (BGD08), it is necessary to go deeper over a still significant area of the sky."
 Here we report on the preliminary analysis to determine the 2«0.06 GSMF from the Galaxy And Mass Assembly (GAMA) survey. which has obtained redshifts to p.«19.5 mmag currently targeted using SDSS imaging but which ultimately will be updated with deeper imaging.," Here we report on the preliminary analysis to determine the $z<0.06$ GSMF from the Galaxy And Mass Assembly (GAMA) survey, which has obtained redshifts to $r<19.8$ mag currently targeted using SDSS imaging but which ultimately will be updated with deeper imaging."
 The plan of the paper is as follows., The plan of the paper is as follows.
 ης 2.. the data. sample selection and methods are described: in 3.. the GLF and GSMF results are presented and discussed.," In \ref{sec:data}, the data, sample selection and methods are described; in \ref{sec:results}, the GLF and GSMF results are presented and discussed."
 Summary and conclusions are given in 4+., Summary and conclusions are given in\ref{sec:summary}.
 Magnitudes are corrected for Galactic extinction using the dusts maps of Schlegel.Finkbeiner.&Davis(1998). and are À- corrected to compute rest-frame colours and absolute magnitudes using v4_2? (Blantonetal.2003a:Blanton&Roweis 2007)...," Magnitudes are corrected for Galactic extinction using the dusts maps of \citet*{SFD98}, and are $k$ -corrected to compute rest-frame colours and absolute magnitudes using 2 \citep{blanton03kcorr,BR07}. ."
" We assume a flat ACDM cosmology with df)= and Q,,.0= 0.3."," We assume a flat $\Lambda$ CDM cosmology with $H_0=70\hunits$ and $\Omega_{m,0}=0.3$ ."
 The Chabrier(2003) IMF (similar to the Kroupa2001 IMF) is assumed for stellar mass estimates., The \citet{Chabrier03} IMF (similar to the \citealt{Kroupa01} IMF) is assumed for stellar mass estimates.
 Solar absolute magnitudes are taken from table | of (2010)... and mass-to-light ratios are given in solar units.," Solar absolute magnitudes are taken from table 1 of \citet{hill10}, , and mass-to-light ratios are given in solar units."
The GAMA survey aims to provide redshifts and multi-wavelength images of c 2500000 galaxies over >250deg tor 19.5mmag (Driveretal.2009.2011:Baldry 2010).,"The GAMA survey aims to provide redshifts and multi-wavelength images of $>250$ 000 galaxies over $>250\,\sqdeg$ to $r<19.8$ mag \citep{driver09,driver11,baldry10}. ."
 A core component of this programme is a galaxy redshift survey using the upgraded 2dF instrument AAOmega, A core component of this programme is a galaxy redshift survey using the upgraded 2dF instrument AAOmega
forming galaxies: for the highest luminosity bin of the star forming galaxies and the lowest luminosity bin of the AGN. this systematic error is likely to be comparable to or larger than the Poissonian uncertainties.,"forming galaxies: for the highest luminosity bin of the star forming galaxies and the lowest luminosity bin of the AGN, this systematic error is likely to be comparable to or larger than the Poissonian uncertainties."
 The radio luminosity functions are displayed in Figure 1. along with the results of Sadler shorteitesadO2— for the 2dFGRS and Machalski Godlowski (2000) for the LCRS (both corrected to the cosmology adopted in this paper: note that these determinations are not corrected for incompleteness either).," The radio luminosity functions are displayed in Figure \ref{lumfuncplot}, along with the results of Sadler \\shortcite{sad02} for the 2dFGRS and Machalski Godlowski (2000) for the LCRS (both corrected to the cosmology adopted in this paper; note that these determinations are not corrected for incompleteness either)."
 The luminosity function of radio—loud AGN generally agrees well with these previous analyses. although with notably smaller errors.," The luminosity function of radio–loud AGN generally agrees well with these previous analyses, although with notably smaller errors."
 The apparent small mismatches between the Sadler rresults and those of this paper at 10757 and 10777 + are likely to be due to cosmic variance., The apparent small mismatches between the Sadler results and those of this paper at $10^{24.5}$ and $10^{25.5}$ $^{-1}$ are likely to be due to cosmic variance.
 The luminosity function of star forming galaxies has similar shape to previous measurements. but with slightly higher space densities at high luminosities CL1¢:Hy107 .," The luminosity function of star forming galaxies has similar shape to previous measurements, but with slightly higher space densities at high luminosities $L_{\rm 1.4GHz} > 10^{23}$ $^{-1}$ )."
 There are three possible differences between the analyses which could account for this., There are three possible differences between the analyses which could account for this.
 First. the different optical magnitude limits of the different surveys may influence the population of radio star—forming galaxies studied.," First, the different optical magnitude limits of the different surveys may influence the population of radio star--forming galaxies studied."
 Second. the combined FIRST-NVSS radio—optical cross—correlation method adopted here will lead to a more complete sample. particularly for low-redshift star forming galaxies with extended radio emission.," Second, the combined FIRST–NVSS radio–optical cross–correlation method adopted here will lead to a more complete sample, particularly for low-redshift star forming galaxies with extended radio emission."
 Third. the disparity might arise from the contrasting ways in which different analyses treat radio—quiet AGN with associated star formation activity. for which he radio emission is due to the star formation.," Third, the disparity might arise from the contrasting ways in which different analyses treat radio–quiet AGN with associated star formation activity, for which the radio emission is due to the star formation."
 The technique used in the current paper for separating the star forming and AGN yopulations would classify such objects as star forming galaxies. but in emission line ratio classifications (as used. for example. by Sadler al.) they might be classified as AGN.," The technique used in the current paper for separating the star forming and AGN populations would classify such objects as star forming galaxies, but in emission line ratio classifications (as used, for example, by Sadler ) they might be classified as AGN."
 This would lead to orevious studies estimating a lower space density of star forming galaxies. particularly at the highest radio luminosities.," This would lead to previous studies estimating a lower space density of star forming galaxies, particularly at the highest radio luminosities."
 Note that if star formation dominates the radio and far-infrared emission of hese radio-quiet AGN. then these objects would be expected to ie on the far-infrared radio correlation for star forming galaxies. despite being classitied (by emission line means) as AGN.," Note that if star formation dominates the radio and far–infrared emission of these radio–quiet AGN, then these objects would be expected to lie on the far–infrared radio correlation for star forming galaxies, despite being classified (by emission line means) as AGN."
 In this respect it is interesting to consider Figure 10 of Sadler Which shows the far-infrared radio relation for the objects in their sample: many of the objects which lie on the far-infrared radio relation for star forming galaxies. but which have radio luminosities Lacs107 +. are indeed classified as AGN.," In this respect it is interesting to consider Figure 10 of Sadler which shows the far–infrared radio relation for the objects in their sample; many of the objects which lie on the far-infrared radio relation for star forming galaxies, but which have radio luminosities $L_{\rm 1.4GHz} >
10^{23}$ $^{-1}$, are indeed classified as AGN."
 If just some of these objects are truly radio quiet AGN. with radio emission due to associated star formation activity. they could easily account for the small difference between the luminosity function determinations.," If just some of these objects are truly radio quiet AGN, with radio emission due to associated star formation activity, they could easily account for the small difference between the luminosity function determinations."
 It is instructive to compare the radio luminosity function for star forming galaxies with that derived at far-infrared (FIR) wavelengths., It is instructive to compare the radio luminosity function for star forming galaxies with that derived at far-infrared (FIR) wavelengths.
 Star-forming galaxies show a tight correlation between their radio and far-infrared luminosities. which Yun shorteiteyunOl showed for the range of luminosities probed in the current study to be indistinguishable from a linear relation: ο/Wllz51510H77LauL..," Star–forming galaxies show a tight correlation between their radio and far–infrared luminosities, which Yun \\shortcite{yun01}
 showed for the range of luminosities probed in the current study to be indistinguishable from a linear relation: $L_{\rm 1.4GHz} / {\rm W
Hz}^{-1} = 10^{11.95} L_{{\rm 60}\mu{\rm m}} / L_{\odot}$."
 The local FIR luminosity function need only be adjusted by this factor to estimate the local radio luminosity function., The local FIR luminosity function need only be adjusted by this factor to estimate the local radio luminosity function.
 Takeuchi derived the local FIR luminosity function using the IRAS Point Source Catalogue redshift survey (PSCz: Saunders 220001.., Takeuchi \\shortcite{tak03} derived the local FIR luminosity function using the IRAS Point Source Catalogue redshift survey (PSCz; Saunders \nocite{sau00}. .
" They fitted the data with an analytic function of the form suggested by Sandage shorteitesan79.. namely with a=1.23+0.04. 46,=(2.6000.30)1ο7h*Mpe . Ol] and a characteristic luminosity of £,=(4.344UST)107L. (where h is /4, in units of lo0kkmss!Mpe +)."," They fitted the data with an analytic function of the form suggested by Sandage \\shortcite{san79}, namely with $\alpha = 1.23 \pm 0.04$, $\phi_* = (2.60 \pm 0.30) \times
10^{-2} h^3$ $^{-3}$, $\sigma = 0.724 \pm 0.01$ and a characteristic luminosity of $L_* = (4.34 \pm 0.87) \times 10^8 h^{-2} L_{\odot}$ (where $h$ is $H_0$ in units of $^{-1}$ $^{-1}$ )."
 Converting the characteristic luminosity by he factor given above. the equivalent local radio luminosity unction is shown as the solid line in Figure 12..," Converting the characteristic luminosity by the factor given above, the equivalent local radio luminosity function is shown as the solid line in Figure \ref{sflumfunc}."
 This provides a good match to the data at high radio luminosities. supporting he division adopted between AGN and star forming galaxies.," This provides a good match to the data at high radio luminosities, supporting the division adopted between AGN and star forming galaxies."
 The match is less than perfect at lower luminosities. however.," The match is less than perfect at lower luminosities, however."
" The uminosity range covered by the radio observations is not sufficient constrain the parameters for a fit of the above form using the radio data. but the dotted and dashed lines show the effect of doubling the characteristic luminosity or setting the faint end slope à to unity (with corresponding changes in ©, }: these provide a much better tit o the data."," The luminosity range covered by the radio observations is not sufficient constrain the parameters for a fit of the above form using the radio data, but the dotted and dashed lines show the effect of doubling the characteristic luminosity or setting the faint end slope $\alpha$ to unity (with corresponding changes in $\phi_*$ ); these provide a much better fit to the data."
 However. these represent much larger changes than are allowed by the errors on the fitted FIR parameters or on the radio o FIR conversion.," However, these represent much larger changes than are allowed by the errors on the fitted FIR parameters or on the radio to FIR conversion."
 The difference between the radio and FIR luminosity unctions means that the observed radio to FIR correlation stops being a linear relation at low luminosities., The difference between the radio and FIR luminosity functions means that the observed radio to FIR correlation stops being a linear relation at low luminosities.
" This has been suggested before in terms of a steepening of the relation below 10""L. (cf.", This has been suggested before in terms of a steepening of the relation below $L_{{\rm 60}\mu{\rm m}} \sim 10^9 L_{\odot}$ (cf.
 Yun 22001 and references therein) but questions have been raised as to whether the previous studies may be affected by selection biases in the samples under study., Yun 2001 and references therein) but questions have been raised as to whether the previous studies may be affected by selection biases in the samples under study.
 Here it is shown that the difference is also present in the luminosity functions., Here it is shown that the difference is also present in the luminosity functions.
 The difference occurs for the lowest luminosity sources. which are generally at the lowest redshifts and therefore may have larger angular sizes. in which case it may be caused by photometric errors due to aperture effects.," The difference occurs for the lowest luminosity sources, which are generally at the lowest redshifts and therefore may have larger angular sizes, in which case it may be caused by photometric errors due to aperture effects."
 This is unlikely to be the case. however.," This is unlikely to be the case, however."
 The NVSS is sensitive to emission on angular scales out to several aremins. much larger than potential host galaxies.," The NVSS is sensitive to emission on angular scales out to several arcmins, much larger than potential host galaxies."
 The IRAS photometry is susceptible to missing extended emission. but for PSCz galaxies this has been corrected for (2).. and in any case any missing IRAS flux would lower the far-IR to radio ratio. which is in the opposite sense to the observed differences.," The IRAS photometry is susceptible to missing extended emission, but for PSCz galaxies this has been corrected for \cite{sau00}, and in any case any missing IRAS flux would lower the far-IR to radio ratio, which is in the opposite sense to the observed differences."
 More likely is that there is a genuine effect at work: either the radio luminosity or the FIR luminosity is not directly proportional to the star formation., More likely is that there is a genuine effect at work: either the radio luminosity or the FIR luminosity is not directly proportional to the star formation.
 One way in which this might occur is if there is an additional low-level contribution to the FIR luminosity of galaxies.for example from dust heated by low mass stars. whic ris usually swamped by the FIR emission associated with star formation. but becomes significant at low star," One way in which this might occur is if there is an additional low–level contribution to the FIR luminosity of galaxies,for example from dust heated by low mass stars, which is usually swamped by the FIR emission associated with star formation, but becomes significant at low star"
190210). with a pair of straight lanes that slightly curve invards in the inner ends.,", with a pair of straight lanes that slightly curve inwards in the inner ends."
 These findings are cousisteut with the predicted morphology from bar-driven ποσαχ inflow., These findings are consistent with the predicted morphology from bar-driven nuclear inflow.
 The physical properties of these clumps are discussed in the following subsection., The physical properties of these clumps are discussed in the following subsection.
 Tn Figure 1 and Table 2.. the peak brightuess teiiperatures of individual clumps are from 2 to ὃ Is. These values are lower than the typical tempcraturcs of molecular gas as expected in the euvironinent of a starburst (~LOO I). and as estimated by our ΤΑ results in Paper I and this work.," In Figure \ref{fig-mom0} and Table \ref{t.clumps}, the peak brightness temperatures of individual clumps are from 2 to 8 K. These values are lower than the typical temperatures of molecular gas as expected in the environment of a starburst $\sim 100$ K), and as estimated by our LVG results in Paper I and this work."
" This lower brightuecss teiiperature max be due to the simall beam filling factor: where fi, is the beam filling factor. 0, aud 0), are the source size and the beam size. respectively."," This lower brightness temperature may be due to the small beam filling factor: where $f_{\rm b}$ is the beam filling factor, $\theta_{\rm s}$ and $\theta_{\rm b}$ are the source size and the beam size, respectively."
 We assume 0.«Oy., We assume $\theta_{\rm s} \ll \theta_{\rm b}$.
" Tj, is the brightuess temperature and 7i is the actual temperature of the clouds.", $T_{\rm b}$ is the brightness temperature and $T_{\rm c}$ is the actual temperature of the clouds.
 We assume here that the source size is compact aud much smaller than the beam., We assume here that the source size is compact and much smaller than the beam.
" If we assune the ΤΑ predicted. Tj, —100 Is Sect.", If we assume the LVG predicted $T_{\rm b}\sim$ 100 K Sect.
" 3.L0. for narrow line ring clamps. aud an average observed Ti, —5 IK. then fi,~ 0.05."," \ref{sect-ratio} for narrow line ring clumps, and an average observed $T_{\rm b}\sim$ 5 K, then $f_{\rm b}\sim$ 0.05."
" This suggests 0, is 20 pe or association of much sinaller clumps for the narrow line ring clumps.", This suggests $\theta_{\rm s}$ is $\sim$ 20 pc or association of much smaller clumps for the narrow line ring clumps.
" In the case of the broad line ving clumps. with an average observed Ti, of ~5 Ik aud IVC predicted Ti, of ~20 Ik. then fi, is ~0.25 and 0.  |E pe."," In the case of the broad line ring clumps, with an average observed $T_{\rm b}$ of $\sim$ 5 K and LVG predicted $T_{\rm b}$ of $\sim$ 20 K, then $f_{\rm b}$ is $\sim$ 0.25 and $\theta_{\rm s}$ $\sim$ 44 pc."
 The size of the broad line ring cblunips is a factor of 2 higher than the narrow line ring clumps., The size of the broad line ring clumps is a factor of 2 higher than the narrow line ring clumps.
 Given the estimated low volue uuniber density of the broad line chumps in Sect. 2.1.0...," Given the estimated low volume number density of the broad line clumps in Sect. \ref{sect-ratio},"
 the inconsisteney between high Nip and low umuber density mentioned is possibly due to the large line-ofsight path. or larger scale height ofthe broad Le chips.," the inconsistency between high $\Sigma_{\rm H_2}$ and low number density mentioned is possibly due to the large line-of-sight path, or larger scale height of the broad line clumps."
 If the assumption of a splierical shape ofthe clumps hold. the larger size estimated above secs to be consistent with this scenario.," If the assumption of a spherical shape of the clumps hold, the larger size estimated above seems to be consistent with this scenario."
 However. considering the higher opacity ofthe broad Lue clumps as suggested by the high it is likely that we are tracing the diffuseρα and cold gas at Sy.the surface of CALA rather than the deuse and wari gas.," However, considering the higher opacity of the broad line clumps as suggested by the high $\Sigma_{\rm H_2}$, it is likely that we are tracing the diffuse and cold gas at the surface of GMA rather than the dense and warm gas."
 Ou the other haud. the narrow line clumps show the opposite trends to trace the relatively wari and dense gas.," On the other hand, the narrow line clumps show the opposite trends to trace the relatively warm and dense gas."
 Iu Figure &.. we found the observed (and intrinsic) line widths. and “yp. show variations aloug the azimuthal direction iu the ring.," In Figure \ref{fig-clump-peak}, we found the observed (and intrinsic) line widths, and $\Sigma_{\rm H_{2}}$, show variations along the azimuthal direction in the ring."
" There are local maxima of line widths and at the position of the twin-peak at the orbit “Ny,crowding regions.", There are local maxima of line widths and $\Sigma_{\rm H_{2}}$ at the position of the twin-peak at the orbit crowding regions.
 Since the brightucss temperature docs uot varv dramatically between the cluission peaks along the rine. the deduced. peaks in Il» cohuuu deusitv can be directly attributed to the increased line widths.," Since the brightness temperature does not vary dramatically between the emission peaks along the ring, the deduced peaks in $_{2}$ column density can be directly attributed to the increased line widths."
 Beam ΠΠ is possibly Huportant as imnultiple streams may converge within a svuthesized beam., Beam smearing is possibly important as multiple streams may converge within a synthesized beam.
 However. as shown iu Fig 5b Chhanced line widths occur even over extended regions.," However, as shown in Fig \ref{fig-mom1}b b, enhanced line widths occur even over extended regions."
 The intrinsic velocity dispersion of both the narrow aud the broad line chuups cannot be thermal as the inmplied cluperature would be 200010000 Ik. Iu the Calactic GAICs. non-thermal line broadening has been attributed o turbulence from πακοση mechanisms.," The intrinsic velocity dispersion of both the narrow and the broad line clumps cannot be thermal, as the implied temperature would be 2000–10000 K. In the Galactic GMCs, non-thermal line broadening has been attributed to turbulence from unknown mechanisms."
 Iu the case of NGC 1097. turbulence could have been generated woshocks of the orbit crowding region.," In the case of NGC 1097, turbulence could have been generated by shocks of the orbit crowding region."
 Shocked eas as indicated bv Πο S(1-0) cussion has been reported oward the twin-peak of NGC 1097 (sotilainenctal., Shocked gas as indicated by $_{2}$ S(1-0) emission has been reported toward the twin-peak of NGC 1097 \citep{kot00}.
 The narrow line chuups further aloug the ring nay be due to subsequent dissipation of the kinetic enerev from the shock wave., The narrow line clumps further along the ring may be due to subsequent dissipation of the kinetic energy from the shock wave.
 This iud of large velocity widths up to ~100 kin s+ were also observed in NGC 6916., This kind of large velocity widths up to $\sim$ 100 km $^{-1}$ were also observed in NGC 6946.
 With resolutions down to CAC-scale of 10. pc. multiple components m the spectra were seeu at the unclear twin-peak by Schinnereretal.(2007).," With resolutions down to GMC-scale of 10 pc, multiple components in the spectra were seen at the nuclear twin-peak by \citet{schinnerer07}."
. However. the mechanisin to cause the broadened line widths is not clear at this scale.," However, the mechanism to cause the broadened line widths is not clear at this scale."
 As noted earlier. the “intrinsic” line widths we derived contain not onlv the raudon dispersion but also the velocity eradicuts due to nou-circular motions ecucratec by shock frouts.," As noted earlier, the “intrinsic” line widths we derived contain not only the random dispersion but also the velocity gradients due to non-circular motions generated by shock fronts."
 Towever. our observations do not have suffüiiient angular resolution to resolve the locations and magnitudes of the discrete velocity jumps to be expected across the shock frout (Draine&\IcIvee1993).," However, our observations do not have sufficient angular resolution to resolve the locations and magnitudes of the discrete velocity jumps to be expected across the shock front \citep{draine93}."
. A detailed livcdrvodvuamical model is also needed to quantitatively predict the magnitude of the non-circular velocity eradient in the rine., A detailed hydrodynamical model is also needed to quantitatively predict the magnitude of the non-circular velocity gradient in the ring.
 Tow do the CALAs form in the starburst rine?, How do the GMAs form in the starburst ring?
 In the ring of NGC 1097. we consider gravitational collapse due to Toomre instability (Toomre1961).," In the ring of NGC 1097, we consider gravitational collapse due to Toomre instability \citep{too64}."
. We estimate the Toomme OQ parameter (Meir Nau) to see if the rotation of the ring is able to stabilize against the fragmentation into clumps., We estimate the Toomre Q parameter $\Sigma_{\rm crit}$ $\Sigma_{\rm gas}$ ) to see if the rotation of the ring is able to stabilize against the fragmentation into clumps.
 Tere the Toomre critical density can be expressed as: where the constant à is unity. CG is the eravitational constant. & is the epicvele frequency. V. ds rotational velocity. and F is the radius of the ring.," Here the Toomre critical density can be expressed as: where the constant $\alpha$ is unity, G is the gravitational constant, $\kappa$ is the epicycle frequency, $V$ is rotational velocity, and $R$ is the radius of the ring."
 If Xj exeeeds Mog then the eas will be eravitationally uustable aud collapse.," If $\Sigma_{\rm H_{2}}$ exceeds $\Sigma_{\rm crit}$, then the gas will be gravitationally unstable and collapse."
 We approximate the velocity gradient dV /dR as close to zero in Figure 15.., We approximate the velocity gradient $V$ $R$ as close to zero in Figure \ref{fig-gal}.
 because of the fat rotation curve of the galaxy at the position of the starburst ring., because of the flat rotation curve of the galaxy at the position of the starburst ring.
 Therefore &— LILI S/R., Therefore $\kappa \sim$ $V$ $R$.
" V is ~ 338 kan | in the ealactic plane assuniug au inclination of ~ον,", $V$ is $\sim$ 338 km $^{-1}$ in the galactic plane assuming an inclination of $\sim$.
 We fined the ratio of Xj: Mu is less than τπτ in the ring (~0.6)., We find the ratio of $\Sigma_{\rm crit}$ $\Sigma_{\rm H_{2}}$ is less than unity in the ring $\sim$ 0.6).
 Since Moa. consists of Πο. IIT. ancl metals. this ratio of 0.6 is an upper lait.," Since $\Sigma_{\rm gas}$ consists of $_{2}$, HI, and metals, this ratio of 0.6 is an upper limit."
 However. he III is often absent iu ceuters of ealaxics. and NGC 1)97 also shows a III hole in the ceutral (που&Wallin2003).," However, the HI is often absent in centers of galaxies, and NGC 1097 also shows a HI hole in the central \citep{hi03}."
. Hence the III eas does not have an important contribution iu the nuclear region., Hence the HI gas does not have an important contribution in the nuclear region.
 A ratio less tha1 unitv sugeests that the ring is unstable and will fraeuxc3f into clumps., A ratio less than unity suggests that the ring is unstable and will fragment into clumps.
 As for whether the CALA itc ‘fis exavitational bouud or not. iu Sect.," As for whether the GMA itself is gravitational bound or not, in Sect."
 3.2.0) we found at Ao Mau Is around unity in the uarrow line chu5 aud larger than unity bv a factor of more than 2 in the broad line clumps., \ref{sect-mass} we found that $M_{\rm vir}$ $M_{\rm gas}$ is around unity in the narrow line clumps and larger than unity by a factor of more than 2 in the broad line clumps.
moves inward (in mass) following the motion of the RW and allows photons to escape sooner than they would if the photosphere were fixed in the outmost layer of the envelope.,moves inward (in mass) following the motion of the RW and allows photons to escape sooner than they would if the photosphere were fixed in the outmost layer of the envelope.
" As a consequence, advective cooling induced by the WR motion becomes dominant."," As a consequence, advective cooling induced by the WR motion becomes dominant."
 The energy radiated away at this stage is the sum of the residual internal energy left over after expansion and that liberated during recombination., The energy radiated away at this stage is the sum of the residual internal energy left over after expansion and that liberated during recombination.
" The energy deposited by gamma-rays becomes significant only when the RW reaches the innermost zones, full of (seealsoYoung2004;Berstenetal."," The energy deposited by gamma-rays becomes significant only when the RW reaches the innermost zones, full of \citep[see also][]{Y04,bersten11}."
" The bolometric luminosity, initially almost constant, 2011)..plummets when the RW reaches the center (see the top panel in Figure 9))."," The bolometric luminosity, initially almost constant, plummets when the RW reaches the center (see the top panel in Figure \ref{fig:mod13vsY}) )."
 The bulk of the envelope (~ in mass) is recombined after ~ 110 days from the breakout of the shock wave at the stellar surface (see Figure 16))., The bulk of the envelope $\sim$ in mass) is recombined after $\sim$ 110 days from the breakout of the shock wave at the stellar surface (see Figure \ref{fig:modB_TvsM}) ).
" The photopheric velocity decreases because the photosphere moves inward with the RW, reaching inner and slower layers as time elapses the middle panel in Figure (se"," The photopheric velocity decreases because the photosphere moves inward with the RW, reaching inner and slower layers as time elapses (see the middle panel in Figure \ref{fig:mod13vsY}) )."
"eThe velocity of propagation of 9)).the RW is determined by the physical conditions in the envelope, in particular the temperature, density, amount of9?6Ni and their distributions."," The velocity of propagation of the RW is determined by the physical conditions in the envelope, in particular the temperature, density, amount of and their distributions."
 The motion of the photospheric radius for a distant observer is the result of the interplay between the inward motion of the RW in mass and the expansion of the ejecta., The motion of the photospheric radius for a distant observer is the result of the interplay between the inward motion of the RW in mass and the expansion of the ejecta.
" Consequently, as shown in Figure 18,, from ~ 35 up to ~ 65 days, the photospheric radius increases, while later on it stays at an almost constant (eulerian) radial coordinate for about ~ 20 days."," Consequently, as shown in Figure \ref{fig:modB_radius}, from $\sim$ 35 up to $\sim$ 65 days, the photospheric radius increases, while later on it stays at an almost constant (eulerian) radial coordinate for about $\sim$ 20 days."
" 'Then, the photosphere starts to recede in radius and the luminosity plummets."," Then, the photosphere starts to recede in radius and the luminosity plummets."
 The duration and steepness of the transition from the plateau to the radioactive tail depend on the mass (see sect. 4.3)), The duration and steepness of the transition from the plateau to the radioactive tail depend on the mass (see sect. \ref{subsec:survey}) )
 and its distribution in the ejecta., and its distribution in the ejecta.
" During this last phase, the evolution is completely governed by the deposition and reprocessing of the energy released from the radioactive decay of°°Co into5"," During this last phase, the evolution is completely governed by the deposition and reprocessing of the energy released from the radioactive decay of into."
"6Fe, The envelope is sufficiently opaque to the gamma- emitted in the radioactive decays that a large fraction of them are effectively absorbed and their energy deposited in the ejecta.", The envelope is sufficiently opaque to the gamma-rays emitted in the radioactive decays that a large fraction of them are effectively absorbed and their energy deposited in the ejecta.
 This energy is easily radiated away by lower energy photons on a timescale much shorter than the expansion timescale., This energy is easily radiated away by lower energy photons on a timescale much shorter than the expansion timescale.
" Also the heating time, which is essentially the decay time, is smaller than the expansion time and, hence, the loss of internal energy due to expansion is negligible."," Also the heating time, which is essentially the decay time, is smaller than the expansion time and, hence, the loss of internal energy due to expansion is negligible."
" Therefore, the bolometric luminosity is the total heating rate from the radioactive decays, proportional to the mass of synthesized in the explosion (see also sect. 4.3))."," Therefore, the bolometric luminosity is the total heating rate from the radioactive decays, proportional to the mass of synthesized in the explosion (see also sect. \ref{subsec:survey}) )."
" The sample of models in Table 2)) enabled us to study the effects of the(reported variation of each parameter (namely, envelope mass Λήοπυ, initial outer radius Ro, total ejecta energy E, and amount of My;) on the main observables, while holding the others fixed."," The sample of models (reported in Table \ref{tab_models}) ) enabled us to study the effects of the variation of each parameter (namely, envelope mass $M_{env}$, initial outer radius $R_0$ , total ejecta energy $E$, and amount of $M_{Ni}$ ) on the main observables, while holding the others fixed."
 Figures 19 through 22 summarize the results of this analysis., Figures \ref{fig:mass_env} through \ref{fig:ni} summarize the results of this analysis.
" We note, however, that this investigation is not meant to be realistic model survey for a detailed quantitative comparisona with observations, because it does not include models computed starting from realistic initial conditions."," We note, however, that this investigation is not meant to be a realistic model survey for a detailed quantitative comparison with observations, because it does not include models computed starting from realistic initial conditions."
 This is postponed to a follow-up investigation., This is postponed to a follow-up investigation.
" As can be seen from Figure 19,, more massive envelopes lead to a fainter bolometric light curve during the diffusive phase, a longer plateau phase, a hotter photospheric temperature during the first ~ 20-30 days, a lower photospheric velocity up to ~ 50 days and a slower decline at longer times."," As can be seen from Figure \ref{fig:mass_env}, more massive envelopes lead to a fainter bolometric light curve during the diffusive phase, a longer plateau phase, a hotter photospheric temperature during the first $\sim$ 20-30 days, a lower photospheric velocity up to $\sim$ 50 days and a slower decline at longer times."
" As known, this behavior is a consequence of the increase in the diffusion timescale with increasing envelope mass, that causes a slower leakage of photons and hence a lower luminosity, longer plateau and higher temperature."," As known, this behavior is a consequence of the increase in the diffusion timescale with increasing envelope mass, that causes a slower leakage of photons and hence a lower luminosity, longer plateau and higher temperature."
" At the same time, increasing the mass and keeping the initial kinetic energy constant (which is half of the total energy; see Sect. 3.2))"," At the same time, increasing the mass and keeping the initial kinetic energy constant (which is half of the total energy; see Sect. \ref{sec:simul:models}) )"
" results in a smaller photospheric velocity during the first weeks and a slower decline later on, caused by the slower motion of the RW in a higher density envelope."," results in a smaller photospheric velocity during the first weeks and a slower decline later on, caused by the slower motion of the RW in a higher density envelope."
 The effects of varying the initial radius are shown in Figure 20.., The effects of varying the initial radius are shown in Figure \ref{fig:radius}. .
" Larger values of Ro cause a higher luminosity during the diffusive and recombination phases, a longer plateau, and a smaller photospheric velocity up to ~ 25days."," Larger values of $R_0$ cause a higher luminosity during the diffusive and recombination phases, a longer plateau, and a smaller photospheric velocity up to $\sim$ 25days."
 The higher luminosity L during the diffusivephaseis caused by the fact that L is proportional to, The higher luminosity $L$ during the diffusivephaseis caused by the fact that $L$ is proportional to
This flaring episode marks a record among ACUNs auk. iudeecl. all non-GBB sources lor its rate of change in apyarent luminosity. La/.M.,"This flaring episode marks a record among AGNs and, indeed, all non-GRB sources for its rate of change in apparent luminosity, $L_\gamma/\Delta t$."
" Using a 6-hoir variability time scale. then erg 1 lps) 10/9Ls/1pergis?. noting that 6 hr/(14-2)~10! s. By comparison. the eiaut flares of PINS2: 155-301 CAliaronianetal.2007) reachec ouly <10eres 1/3005 zz3x10!ere  og.Gin the TeVT regi""ue)."," Using a 6-hour variability time scale, then $L_\gamma/\Delta t\simeq10^{50}L_{50}$ erg $^{-1}/(10^4\:t_4$ s) $\simeq10^{46}L_{50}/t_4\:\rm{erg}\:\rm{s}^{-2}$, noting that $6$ $/(1+z)\simeq10^4$ s. By comparison, the giant flares of $\:$ $-$ 304 \citep{Aha07} reached only $\lesssim10^{47}\:\rm{erg}$ $^{-1}/300\:$ s $\approx3\times10^{44}\:\rm{erg}$ $^{-2}$ (in the TeV regime)."
 This value now greatly exceeds Lj;αςο)=1.3x10Peres 7D? given by the ratio of the Edcdiugton luminosity aud the light crossing ime across the Schwarzschild radius of a black hole. and stongly violates optically thin. Eclkdiugto1-lunited accretion scenarios Shapiro197 1).. showing that such a condition is unlikely to apply to the highly asymanetric disk/jet system of a blazar.," This value now greatly exceeds $L_{\rm Edd}/(R_{\rm S}/c)\approx1.3\times10^{43}\:\rm{erg}$ $^{-2}$ given by the ratio of the Eddington luminosity and the light crossing time across the Schwarzschild radius of a black hole, and strongly violates optically thin, Eddington-limited accretion scenarios \citep{Ell74}, showing that such a condition is unlikely to apply to the highly asymmetric disk/jet system of a blazar."
 The Fermi--LAT Collaboration acknowledges support from a number of agencies aud institutes for both development aud the operation of the LAT as well as scientific data analysis., The -LAT Collaboration acknowledges support from a number of agencies and institutes for both development and the operation of the LAT as well as scientific data analysis.
 These include NASA aud DOE in the United States. CEA/Irfu aud IN2P3/CNRS in France. ASI and INFN in Italy. MENT. WEI. and JANA in Japan. aud the kW. A. Wallenbere Foundation. the Sweclish Research Council aud the National Space Board in Sweden.," These include NASA and DOE in the United States, CEA/Irfu and IN2P3/CNRS in France, ASI and INFN in Italy, MEXT, KEK, and JAXA in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the National Space Board in Sweden."
 Additional support from INAF in Italy aud CNES in France for science aualysis during tlie operations pliase is also gratefully acknowledge., Additional support from INAF in Italy and CNES in France for science analysis during the operations phase is also gratefully acknowledged.
- galaxies near the cluster core. should. experience. more stripping: that the high Sx values in the literature are generally being revised downwards (see c.g. Forte et al.,- galaxies near the cluster core should experience more stripping; that the high $_N$ values in the literature are generally being revised downwards (see e.g. Forte et al.
 2002) - this makes the high Sy systems less extreme and hence less accretion is recquired., 2002) - this makes the high $_N$ systems less extreme and hence less accretion is required.
 Although there have been developments on. the observational front. there has been little modelling. work carried out since the initial simulations by J. €. Muzzio and colleagues in the 1980s (Forte et al.," Although there have been developments on the observational front, there has been little modelling work carried out since the initial simulations by J. C. Muzzio and colleagues in the 1980s (Forte et al."
 1982: Muzzio et al., 1982; Muzzio et al.
 1984: Muzzio 1986a.b: Muzzio ct al.," 1984; Muzzio 1986a,b; Muzzio et al."
 LOST: Muzzio LOST)., 1987; Muzzio 1987).
 Thev found that the GC's accreted by the most cluster galaxies do not come from cwarf galaxies but rather galaxies of similar mass., They found that the GCs accreted by the most cluster galaxies do not come from dwarf galaxies but rather galaxies of similar mass.
 All cluster galaxies eain and lose GCs due to tida stripping. and for many galaxies the net outcome was a loss of GCs to the ICM.," All cluster galaxies gain and lose GCs due to tidal stripping, and for many galaxies the net outcome was a loss of GCs to the ICM."
 When the galaxies represented a smal fraction of the total cluster mass. both the GC gains ane losses were smaller.," When the galaxies represented a small fraction of the total cluster mass, both the GC gains and losses were smaller."
 1n the twenty vears since the initial models of Muzzio. computing power has advanced significantly.," In the twenty years since the initial models of Muzzio, computing power has advanced significantly."
 “Phis combines with further observational evidence means that the time is ripe to revisit this issue of GC acerction with a N-body simulation., This combined with further observational evidence means that the time is ripe to revisit this issue of GC accretion with a N-body simulation.
 It is however still a formidable task to perform a fully self-consistent simulation encompassing the dvnanical evolution of galaxies with vastly cdillerent masses (from small dwarfs to central massive cDs) and that of GC systems., It is however still a formidable task to perform a fully self-consistent simulation encompassing the dynamical evolution of galaxies with vastly different masses (from small dwarfs to central massive cDs) and that of GC systems.
 Llere we focus exclusively on perhaps the best case for tidal stripping and accretion. Lc. the GC svstems of NCC 1399 and NGC 1404 in the Fornax cluster.," Here we focus exclusively on perhaps the best case for tidal stripping and accretion, i.e. the GC systems of NGC 1399 and NGC 1404 in the Fornax cluster."
 Several lines of evidence suggest that NGC 1399 is currently in a non-equilibrium state. and possibly undergoing a dynamical interaction with its nearby partner NOC 1404.," Several lines of evidence suggest that NGC 1399 is currently in a non-equilibrium state, and possibly undergoing a dynamical interaction with its nearby partner NGC 1404."
 ROSAT TRL and. Chandra. data analysed. by Paolillo et al. (, ROSAT HRI and Chandra data analysed by Paolillo et al. (
2001) indicates that the hot gas centroid of NGC 1399 is olfset by ~ 5 kpe to the SW of its optical counterpart.,2001) indicates that the hot gas centroid of NGC 1399 is offset by $\sim$ 5 kpc to the SW of its optical counterpart.
 These authors also find that NGC 1399 has an extended and asymmetric gas distribution on cluster scales (r > 90kpc). which exhibits prominent structures. (holes and filamentary features) expected from N-bocky numerical simulations ος. Barnes 2000).," These authors also find that NGC 1399 has an extended and asymmetric gas distribution on cluster scales (r $>$ 90kpc), which exhibits prominent structures ('holes' and filamentary features) expected from N-body numerical simulations (e.g. Barnes 2000)."
 Independent evidence comes from. discrete. cynanical tracers such as GCs (CGrllmair etal., Independent evidence comes from discrete dynamical tracers such as GCs (Grillmair etal.
 1994: Minniti etal., 1994; Minniti etal.
 1998: Iissler-Patig etal., 1998; Kissler-Patig etal.
 1999) ancl planetary nebulae (PNe. Arnaboldi etal.," 1999) and planetary nebulae (PNe, Arnaboldi etal."
 1994: Napolitano et al., 1994; Napolitano et al.
 2002)., 2002).
 In particular. Napolitani et al. (," In particular, Napolitani et al. ("
2002) find evidence for a disturbed velocity structure after re-analvsing the PNe data of Xrnaboldi etal.,2002) find evidence for a disturbed velocity structure after re-analysing the PNe data of Arnaboldi etal.
 Their non-equilibrium dynamical. analysis shows a peak rotation of 250 km [or the PNe at ~ 12.6 kpe from the optical centre of NGC 1399. coincident with a velocity dispersion minimum at this point. which subsequently. rises at larger radii.," Their non-equilibrium dynamical analysis shows a peak rotation of 250 km $^{-1}$ for the PNe at $\sim$ 12.6 kpc from the optical centre of NGC 1399, coincident with a velocity dispersion minimum at this point, which subsequently rises at larger radii."
 X viable analytical explanation for this kinematical behavior is that NGC) 1404. has. undergone a Ivbv of NGC 1399. whose stellar halo is currently attempting to return to equilibrium (Napolitani et al.," A viable analytical explanation for this kinematical behavior is that NGC 1404 has undergone a ""flyby"" of NGC 1399, whose stellar halo is currently attempting to return to equilibrium (Napolitani et al."
 2002)., 2002).
 Thus the purpose of this paper ids to investigate numerically whether tidal stripping of the NGC 1404 GC system by the global gravitational field of the Fornax cluster (and thus NGC 1399) can explain physical properties of its GC system., Thus the purpose of this paper is to investigate numerically whether tidal stripping of the NGC 1404 GC system by the global gravitational field of the Fornax cluster (and thus NGC 1399) can explain physical properties of its GC system.
 In. particular. we investigate (1) whether the observed. relatively low ον value of 2 in NGC 1404 can be explained by the tical stripping of GC's ancl (2) how the density profile of the GC system can change alter GC stripping.," In particular, we investigate (1) whether the observed relatively low $_N$ value of 2 in NGC 1404 can be explained by the tidal stripping of GCs and (2) how the density profile of the GC system can change after GC stripping."
 We also try to identify observational signatures of the GC stripping ancl accretion process., We also try to identify observational signatures of the GC stripping and accretion process.
 White (1987) suggested. that intracluster GCs can be formed. owing to tidal stripping of GC's from cluster member galaxies. and Dassino et al. (, White (1987) suggested that intracluster GCs can be formed owing to tidal stripping of GCs from cluster member galaxies and Bassino et al. (
2002) have recently found GC candidates in the Fornax cluster.,2002) have recently found GC candidates in the Fornax cluster.
 ln light of these results. we discuss the origin of intracluster GCs in the Fornax cluster in the context of GC stripping from NCC 1404.," In light of these results, we discuss the origin of intracluster GCs in the Fornax cluster in the context of GC stripping from NGC 1404."
 This paper is the first in à series of papers in which we seek a self-consistent understanding of dvnamücal evolution of GC systems in cluster environments., This paper is the first in a series of papers in which we seek a self-consistent understanding of dynamical evolution of GC systems in cluster environments.
 Here we focus on the limited case of the interaction between NGC 1399 anc NGC 1404. and its cllect on their GC systems.," Here we focus on the limited case of the interaction between NGC 1399 and NGC 1404, and its effect on their GC systems."
 The distance of the Fornax cluster is assumed to be 18.6 Alpe throughout this paper., The distance of the Fornax cluster is assumed to be 18.6 Mpc throughout this paper.
 We consider a collisionless stellar system. of an elliptical ealaxy with a mass and size similar to those of NGC 1404. orbiting the centre of Fornax cluster of galaxies (ie. NGC 1399).," We consider a collisionless stellar system of an elliptical galaxy with a mass and size similar to those of NGC 1404, orbiting the centre of Fornax cluster of galaxies (i.e., NGC 1399)."
 Since the gravitational Ποιά around NGC 1399 at distances greater than 40 kpe is observed to be dominated by the global cluster rather than by luminous components of NGC 1899 itself (c.g. Wissler-Patig et al.," Since the gravitational field around NGC 1399 at distances greater than 40 kpc is observed to be dominated by the global cluster rather than by luminous components of NGC 1399 itself (e.g., Kissler-Patig et al."
 1999: Napolitano et al., 1999; Napolitano et al.
 2002). we consider that the gravitational field of the dark matter halo of the cluster has the strongest influence on the dynamical evolution of the globular cluster svsteni in NGC 1404.," 2002), we consider that the gravitational field of the dark matter halo of the cluster has the strongest influence on the dynamical evolution of the globular cluster system in NGC 1404."
 Accordingly. we model only the cluster tidal fielcl ancl clo not include any tidal elects of other cluster member galaxies in the present simulations.," Accordingly, we model only the cluster tidal field and do not include any tidal effects of other cluster member galaxies in the present simulations."
 Although these simulations are idealized in some aspects. we believe that our mocdel still contains the essential ingredients for the cdvnanmical evolution of NGC 1404s eglobular cluster svstem in Fornax cluster.," Although these simulations are idealized in some aspects, we believe that our model still contains the essential ingredients for the dynamical evolution of NGC 1404's globular cluster system in Fornax cluster."
 ‘To give our model a realistic racial density profile for the dark matter halo. we base it on both the X-ray observational results of Jones et al. (," To give our model a realistic radial density profile for the dark matter halo, we base it on both the X-ray observational results of Jones et al. ("
1997) and the predictions from the standard: cold. dark matter cosmogony (Navarro. Frenk. White 1996. hereafter NEW).,"1997) and the predictions from the standard cold dark matter cosmogony (Navarro, Frenk, White 1996, hereafter NFW)."
 The NEW profile is described as. where po and rj are the central density and the scale length of a dark halo. respectively.," The NFW profile is described as, where $\rho_{0}$ and $r_{\rm s}$ are the central density and the scale length of a dark halo, respectively."
 po is chosen such that the total mass of Fornax cluster within 125 kpe is the same as the observed. one (8.11072AL. ) estimated from. X-ray observations (Jones et al., $\rho_{0}$ is chosen such that the total mass of Fornax cluster within 125 kpc is the same as the observed one $8.1 \times 10^{12} \rm M_{\odot}$ ) estimated from X-ray observations (Jones et al.
 LOOT)., 1997).
 We adopt 55 kpe for i. which is reasonable value for a CDM halo with the mass similar to that of Fornax cluster., We adopt 55 kpc for $r_{\rm s}$ which is reasonable value for a CDM halo with the mass similar to that of Fornax cluster.
 NGC 1404 is modeled as a fully scll-eravitating svsteni anc assumed. to consist of dark matter halo. stellar component. and GCs.," NGC 1404 is modeled as a fully self-gravitating system and assumed to consist of dark matter halo, stellar component, and GCs."
 Phe density profile of the dark matter, The density profile of the dark matter
distance and Vj; is the line-of-sight velocity difference.,distance and $V_{ij}$ is the line-of-sight velocity difference.
 The scaling factor Z2(z) is introduced in order to take into account the decrement of (he galaxy number density due to the apparent nagnitude limit cutoll (see eq., The scaling factor $R(z)$ is introduced in order to take into account the decrement of the galaxy number density due to the apparent magnitude limit cutoff (see eq.
 5 in Huchra&Geller1982))., 5 in \citealt{hg82}) ).
 We have adopted a(transversal inking length Dy corresponding to an overdensitv of 0p/p=80. a line-of-sight linking length of Vy=200kmsJ| and a fiducial distance of LO5.!Mpe.," We have adopted atransversal linking length $D_0$ corresponding to an overdensity of $\delta \rho/\rho=80$, a line-of-sight linking length of $V_0=200~\kms$ and a fiducial distance of $10~\mpc$."
 As in (2005).. we have also carried oul an improvement of the rich group identification.," As in \citet{mz05}, we have also carried out an improvement of the rich group identification."
 This improvement consists in performing a second identification on galaxv groups will at least ten members in order (o split merged svstems or (o eliminate spurious member detections., This improvement consists in performing a second identification on galaxy groups with at least ten members in order to split merged systems or to eliminate spurious member detections.
 This second identification uses a higher densitv contrast. 0p/p~315. which produces a more reliable eroup identilication (see Diazetal. 2005)).," This second identification uses a higher density contrast, $\delta \rho/\rho \sim 315$, which produces a more reliable group identification (see \citealt{diaz05}) )."
 Group center locations for these eroups have been improved using an iterative procedure developed by Diazetal.(2005)., Group center locations for these groups have been improved using an iterative procedure developed by \citet{diaz05}.
. The procedure defines a new group center estimation by using the projected local number density of each member galaxy for weighting their group center distances. aud (hen iterates {his estimation by removing galaxies bevond a given distance.," The procedure defines a new group center estimation by using the projected local number density of each member galaxy for weighting their group center distances, and then iterates this estimation by removing galaxies beyond a given distance."
 The iteration follows until the center location remains unchanged., The iteration follows until the center location remains unchanged.
 Since (he method needs to compute the projected local nunmber density with five galaxies. this procedure can only be applied to group will al least ien members.," Since the method needs to compute the projected local number density with five galaxies, this procedure can only be applied to group with at least ten members."
 Finally. the group sample comprises 14004 groups wilh at least 4 members. adding up (o 85728 galaxies.," Finally, the group sample comprises 14004 groups with at least 4 members, adding up to 85728 galaxies."
 Mean properties of groups in (his sample are similar to those of the DIA3 eroup catalog as quoted by Alerchan&Zanclivarez (2005).., Mean properties of groups in this sample are similar to those of the DR3 group catalog as quoted by \citet{mz05}. .
 We obtain a median velocity dispersion. virial mass and radius of 232kms|. 3.9xLOMhtM.. and 111hIMpe respectively.," We obtain a median velocity dispersion, virial mass and radius of $232 \ \kms$, $3.9\times10^{13} \ h^{-1} \ {\cal M}_{\odot}$, and $1.11 \ \mpc$ respectively."
 The magnitudes we use in this work are the Petrosian ones. and have been corrected for Galactic extinction following Schlegeletal.(1998).," The magnitudes we use in this work are the Petrosian ones, and have been corrected for Galactic extinction following \citet{sch98}."
".. Absolute magnitudes have been computed assuming Q=0.3. Q4—0.7 and a Hubble constant Z4,=100kms+Mpe|. and. A —corrected using the method of Blantonetal.(20034)4."," Absolute magnitudes have been computed assuming $\Omega_0=0.3$, $\Omega_{\Lambda}=0.7$ and a Hubble constant $H_0=100~ h~ {\rm km~s^{-1}~Mpc^{-1}}$, and $K-$ corrected using the method of \citet{blantonk}."
1.. We have adopted a band shilt to a redshift 0.1. ie. to approximately (he mean redshift of the MainGalaxy Sample of SDSS. as suggested by Blantonοἱal.(2003a).," We have adopted a band shift to a redshift $0.1$, i.e. to approximately the mean redshift of the MainGalaxy Sample of SDSS, as suggested by \citet{blantonk}."
. We have also included evolution corrections to this redshift for each for u. q. r. ἐν z bands respectively (Blantonetal. 2003b).," We have also included evolution corrections to this redshift for each galaxy of the form $({\rm z}-0.1)Q$ where $Q$ varies with the band: 4.22, 2.04, 1.62, 1.61 and 0.76 for $u$, $g$, $r$, $i$, $z$ bands respectively \citep{blantonlf}. ."
". Throughout this work we will relerto these shifted bands as ""tuMtg1j1; 17 ", Throughout this work we will referto these shifted bands as $^{0.1}u \ ^{0.1}g \ ^{0.1}r \ ^{0.1}i \ ^{0.1}z$ .
All magnitudes are in tbe AB system., All magnitudes are in the AB system.
 Following the comparative study of different luminosity function estimators by, Following the comparative study of different luminosity function estimators by
Tot coronae are the enignmiatic Link between co1. convective stars aud their euviroument.,"Hot coronae are the enigmatic link between cool, convective stars and their environment."
 While most oftnr hot plasma (>109 IK) is coutained by magnetic fields. sonie nay escape due to overpressure as a hot stellar wind along open field lines.," While most of this hot plasma $>10^{6}$ K) is contained by magnetic fields, some may escape due to overpressure as a hot stellar wind along open field lines."
 The exteut of iteuse coronal Cluissions iu N-ravs or radio waves thus vields a lower lait to the size of closed magnetic loops. ic. the size of tl1ο stellar 1nagnuetosphiere.," The extent of intense coronal emissions in X-rays or radio waves thus yields a lower limit to the size of closed magnetic loops, i.e. the size of the stellar magnetosphere."
 Raclio chussion frouseler active reeious at cni waveloneth originates from altitudes above tl1ο pliotospliere between 5 to 10«LOS cu. or 0.006 - 0.015 R... (oe. Asclavancenetal. 1995).," Radio emission from active regions at 3 cm wavelength originates from altitudes above the photosphere between 5 to $10\times 10^8$ cm, or 0.006 - 0.015 $R_\odot$, (e.g. \cite{Aschw} 1995)."
 It is generally attributed to thermal evroresonaLCC CLUISSIOLL., It is generally attributed to thermal gyroresonance emission.
 The size of the radio nuage of the Sun inereases af loreer wavelengths., The size of the radio image of the Sun increases at longer wavelengths.
 Iu soft N-ravs aud EUV Ine Cluissions. coronal loops reach 3100 (0.5 FP.) 4e.g. Sturrockeal.19963).," In soft X-rays and EUV line emissions, coronal loops reach $3\times 10^{10}$ cm (0.5 $R_\odot$ ) (e.g. \cite{Sturr}) )."
 Magnetic loops iu excess of 1.1«10Hon (2 R.) have becu observed im metric U ο (Labuu&Stewart1970))., Magnetic loops in excess of $1.4\times 10^{11}$ cm (2 $R_\odot$ ) have been observed in metric U bursts \cite{Labrum}) ).
 Corouograph observations in white ight. however. do not regularly see loops of hat size. sugeesting that they are shortlived.," Coronograph observations in white light, however, do not regularly see loops of that size, suggesting that they are shortlived."
 In genera. large magneic loops are coufined o low latitudes aud. consequentLy he radio image of the Sun is more extende in the equatorial direction.," In general, large magnetic loops are confined to low latitudes and, consequently, the radio image of the Sun is more extended in the equatorial direction."
 Very Long Basclue Tuterferoiietry (VLBI) has maeedt xossible to study the size aud shape ofc, Very Long Baseline Interferometry (VLBI) has made it possible to study the size and shape of.
"oronac, At! )cu. Bengctal. (1998) have resolved he dMe star UV Cet D at an higher aud variable flux evel iuto two coniponeuts separated by. L4«01e (L1 Ri)."," At 3.6 cm, \cite{B4} (1998) have resolved the dMe star UV Cet B at an higher and variable flux level into two components separated by $4.4\times 10^{10}$ cm (4.4 $R_\star$ )."
 One of he components was spatially resolved with he size of about the stellar photosphere., One of the components was spatially resolved with the size of about the stellar photosphere.
 The orieutalon of the two sotrees was found to lie aloug the probable axis of rotation. srougly sugecstive of coronal eulancemoents extending at cast 2.1« 10270 (2.1 Ry.) above the poles.," The orientation of the two sources was found to lie along the probable axis of rotation, strongly suggestive of coronal enhancements extending at least $2.1\times 10^{10}$ cm (2.1 $R_\star$ ) above the poles."
 Thus. UV Ce D differs considerably from the Suu in size and shape of the raclo corona.," Thus, UV Cet B differs considerably from the Sun in size and shape of the radio corona."
 More VLBI observations of dMe stars have been reported at LS cin wavelength., More VLBI observations of dMe stars have been reported at 18 cm wavelength.
" For YZ CAL. Benz&Alcf (1991) found au upver liuüt of 8.7« dUGu. sugeestingOO an extent of a circuar corona above the piotosphiere. of less than Ls« Loteu (0.71 R,)."," For YZ CMi, \cite{B1} (1991) found an upper limit of $8.7\times 10^{10}$ cm, suggesting an extent of a circular corona above the photosphere of less than $1.8\times 10^{10}$ cm (0.74 $R_\star$ )."
" Two size measurements of AD Leo by Beuzοtal. (1995) suggest a coronal extent of less than 2« 1019cn (1.0 Ry) aud 5.Es Lote (2.6 R,) above the pjiotosphere. assuming a circular. concentric shape."," Two size measurements of AD Leo by \cite{B2} (1995) suggest a coronal extent of less than $2\times 10^{10}$ cm (1.0 $R_\star$ ) and $5.4\times 10^{10}$ cm (2.6 $R_\star$ ) above the photosphere, assuming a circular, concentric shape."
" A small total s«zeo ‘less than 1.9«1HU on for EO Pee (Benzctal. 1995) refers to au observation durus a totally poarized flare. and an extremely large size of 2,2«10M en was rey)ortec for thedMe close binary YY Cem CAlefeal. 1997))."," A small total size of less than $4.9\times 10^{10}$ cm for EQ Peg \cite{B2} 1995) refers to an observation during a totally polarized flare, and an extremely large size of $2.2\times 10^{11}$ cm was reported for thedMe close binary YY Gem \cite{Alef1}) )."
 The radi) coronae of acive. rapidly rotating dMo stars have been modeled to deeriuue the enmüssiou process.," The radio coronae of active, rapidly rotating dMe stars have been modeled to determine the emission process."
 It is generally agreed (Cuidel1991: : Whiteetal. 1989)), It is generally agreed \cite{Manuel}; ; \cite{White}) )
xobe of the cosmic reionization epoch that. complements measurements of QSO Gunn-Peterson. troughs or CMD »olarization anisotropies. which probe the neutral and ionized. Components of the IGM. respectively.,"probe of the cosmic reionization epoch that complements measurements of QSO Gunn-Peterson troughs or CMB polarization anisotropies, which probe the neutral and ionized components of the IGM, respectively."
 On the one 1and. observationally deducing the global UV emissivity and rence the cosmic star formation rate from the latter two is »oblematie due to uncertainties in the inhomogencity of the LGAL (clumping factor) and the escape fraction of ionizing οποίος from the host galaxies (Alacdau et al.," On the one hand, observationally deducing the global UV emissivity and hence the cosmic star formation rate from the latter two is problematic due to uncertainties in the inhomogeneity of the IGM (clumping factor) and the escape fraction of ionizing photons from the host galaxies (Madau et al."
 1999. Αλνο et al.," 1999, Wyithe et al."
 2009)., 2009).
 On the other. the direct. census of the > UV luminosity density. from. deep. ποσα surveys are wlected by the uncertain integrated contribution of faint galaxies below the telescope detection limit (c.g. Bouwens et al.," On the other, the direct census of the $z$ UV luminosity density from deep, near-IR surveys are affected by the uncertain integrated contribution of faint galaxies below the telescope detection limit (e.g. Bouwens et al."
 2007)., 2007).
 Observing 55 absorption in high-z sources may allow more robust measurements of the evolution of the cosmic WV emissivity. and in combination with other data. possibly the determination of the escape fraction and/or the IGM clumping factor as well.," Observing $\gamma\gamma$ absorption in $z$ sources may allow more robust measurements of the evolution of the cosmic UV emissivity, and in combination with other data, possibly the determination of the escape fraction and/or the IGM clumping factor as well."
 These inferences are general ancl independent of any particular model for reionization. but will be investigated in more quantitative detail in the near future.," These inferences are general and independent of any particular model for reionization, but will be investigated in more quantitative detail in the near future."
 Likewise. the implications for constraining Lya or llo-dissociating radiation [rom 5*5 absorption will be discussed in future work.," Likewise, the implications for constraining $\alpha$ or $\rm H_2$ -dissociating radiation from $\gamma\gamma$ absorption will be discussed in future work."
 We now briclly address whether the cllects cliscussecl above are observable in real sources with current or future ganima-ray instruments., We now briefly address whether the effects discussed above are observable in real sources with current or future gamma-ray instruments.
 bor blazars. the most. prominent and numerous extragalactie sources of GeV eamma-ravs. the üghest redshift confirmed. so far is z~3 (Hartman ct al.," For blazars, the most prominent and numerous extragalactic sources of GeV gamma-rays, the highest redshift confirmed so far is $z \sim 3$ (Hartman et al."
 1999: Abdo et al., 1999; Abdo et al.
 2009b)., 2009b).
 However. objects similar to the most powerful known blazars such as 3€454.3 with apparent uminosities L10ergs. should be detectable byFermi out to 2N.10 i£ they exist at such redshilts (e.g. Romani et al.," However, objects similar to the most powerful known blazars such as 3C454.3 with apparent luminosities $L \sim 10^{49} {\rm erg\ s^{-1}}$ should be detectable by out to $z \sim 8-10$ if they exist at such redshifts (e.g. Romani et al."
 2004)., 2004).
" Xcecording to the latest blazar evolution models (Inoue ""Totani 2009). it may be plausible for. to detect some blazars above z6 during its survey period. or which deep. pointed observations may indeed reveal the IHE absorption features described above."," According to the latest blazar evolution models (Inoue Totani 2009), it may be plausible for to detect some blazars above $z \sim 6$ during its survey period, for which deep, pointed observations may indeed reveal the IRF absorption features described above."
 CRBs are also promising as they are known to occur al zoc6 (Ixawal et al., GRBs are also promising as they are known to occur at $z>6$ (Kawai et al.
 2005: Greiner et al., 2005; Greiner et al.
 2009). at leas up to.~8S2 (Tanvir et al.," 2009), at least up to $z \sim 8.2$ (Tanvir et al."
 2009: Salvaterra ct al., 2009; Salvaterra et al.
 2009). and perhaps out to the very first epochs of star formation in the universe (e.g. Bromm Loch 2006: Salvaterra e al.," 2009), and perhaps out to the very first epochs of star formation in the universe (e.g. Bromm Loeb 2006; Salvaterra et al."
 2008)., 2008).
 Although the spectral properties of GIUDs in the GeV domain are still rather uncertain. previous detections by COGRO/EGRIET (lHlurlev. et al.," Although the spectral properties of GRBs in the GeV domain are still rather uncertain, previous detections by CGRO/EGRET (Hurley et al."
 1994). and. the recen detection. of GRB 080916C. at =4.35 byFermi (Abdo et al., 1994) and the recent detection of GRB 080916C at $z = 4.35$ by (Abdo et al.
 2009a) demonstrate that at least some GRBs have luminous emission extending to 210 GeV. which can also be expected theoretically (e.g. Zhang Aleszaros 2001: Asano et al.," 2009a) demonstrate that at least some GRBs have luminous emission extending to $>$ 10 GeV, which can also be expected theoretically (e.g. Zhang Meszaros 2001; Asano et al."
 2000)., 2009).
 A burst similar to GRB 080916€ may still. be detectable at several Ce by Ferini/LANT at ος<T. and even out to higher z if the V.spectrum was somewhat harder.," A burst similar to GRB 080916C may still be detectable at several GeV by /LAT at $z \lesssim 7$, and even out to higher $z$ if the spectrum was somewhat harder."
 Even better for this purpose would be proposed: ground-based. telescopes with much larger elective area ancl multi-GeV energy. threshold. such as the Cherenkov Telescope Array57. Advanced Gamma-ray Imaging System or the 5«5 array (Aharonian ct al.," Even better for this purpose would be proposed ground-based telescopes with much larger effective area and multi-GeV energy threshold, such as the Cherenkov Telescope Array, Advanced Gamma-ray Imaging System or the 55 array (Aharonian et al."
 2001)., 2001).
 Together with measurements of Lvo damping wines (MeGQuinn ct al., Together with measurements of $\alpha$ damping wings (McQuinn et al.
 2009) ancl possibly radio dispersion (loka 2003: Inoue 2004).," 2009) and possibly radio dispersion (Ioka 2003; Inoue 2004),"
spectrum. linking lines together which are correlated in the input sky spectra. and weights all bins equally.,"spectrum, linking lines together which are correlated in the input sky spectra, and weights all bins equally."
 However. if an emission or absorption feature occurs exactly at the location of an OH line. some combination of principal components can sometimes be found to reconstruct the feature. without increasing the rms in the rest of the spectrum signiticantly.," However, if an emission or absorption feature occurs exactly at the location of an OH line, some combination of principal components can sometimes be found to reconstruct the feature, without increasing the rms in the rest of the spectrum significantly."
 Such behaviour is particularly likely ifthe line feature lies in a noisy part of the spectrum., Such behaviour is particularly likely if the line feature lies in a noisy part of the spectrum.
 For most applications in which the sky-residual subtraction scheme might be employed. it is possible to mask known emission and absorption features. thereby circumventing the problem.," For most applications in which the sky-residual subtraction scheme might be employed, it is possible to mask known emission and absorption features, thereby circumventing the problem."
 In Section ??. we show how such masked features are unaffected by the sky-residual subtraction procedure., In Section \ref{sec_cat} we show how such masked features are unaffected by the sky-residual subtraction procedure.
 The disadvantage is that real sky features which happen to fall in the masked regions do not contribute to the projection onto the principal components and the sky-residual subtraction may not be fully effective in these regions., The disadvantage is that real sky features which happen to fall in the masked regions do not contribute to the projection onto the principal components and the sky-residual subtraction may not be fully effective in these regions.
 In some potential applications. it is not known in advance where absorption and emission features may occur and we present such an example in Section ??..," In some potential applications, it is not known in advance where absorption and emission features may occur and we present such an example in Section \ref{sec_dla}."
 Features are masked by removing the relevant pixels during projection onto the principal components., Features are masked by removing the relevant pixels during projection onto the principal components.
 Alternatively. replacing the pixels with the local mean results in almost identical reconstruction.," Alternatively, replacing the pixels with the local mean results in almost identical reconstruction."
 We similarly mask bad pixels (where the SDSS noise array is set fo Zero)., We similarly mask bad pixels (where the SDSS noise array is set to zero).
 Once the object spectrum has been continuum subtracted. we divide by the SDSS noise spectrum of the relevant plate and project onto the sky principal components (Eq. A3)).," Once the object spectrum has been continuum subtracted, we divide by the SDSS noise spectrum of the relevant plate and project onto the sky principal components (Eq. \ref{eq_pcs}) ),"
 leaving out those pixels identified as possibly containing emission and absorption features., leaving out those pixels identified as possibly containing emission and absorption features.
 The resulting principal component amplitudes are used to reconstruct the residual sky-subtraction signal (Eq. A49) , The resulting principal component amplitudes are used to reconstruct the residual sky-subtraction signal (Eq. \ref{eq_recon}) )
and the reconstruction is subtracted from the object spectrum. including masked pixels.," and the reconstruction is subtracted from the object spectrum, including masked pixels."
" Re-multiplication by the noise spectrum. followed by the addition of the object continuum, returns the object spectrum cleaned of OH sky emission line residuals."," Re-multiplication by the noise spectrum, followed by the addition of the object continuum, returns the object spectrum cleaned of OH sky emission line residuals."
 Fig., Fig.
" 9— illustrates the process of sky-residual subtraction on a typical SDSS galaxy spectrum,", \ref{fig_gal1} illustrates the process of sky-residual subtraction on a typical SDSS galaxy spectrum.
 Each class of spectroscopic science targets has different spectral characteristics., Each class of spectroscopic science targets has different spectral characteristics.
 The effective application of the sky residual subtraction scheme requires the removal of the large scale “continuum” signal from the target object and the identification of wavelength intervals where narrow emission or absorption features may be present., The effective application of the sky residual subtraction scheme requires the removal of the large scale “continuum” signal from the target object and the identification of wavelength intervals where narrow emission or absorption features may be present.
 The extremely high identification success rate achieved in the SDSS means that the wavelengths of strong absorption and emission features in the spectra of stars and galaxies are known: there are only 3.002 spectra without secure identifications among the 329.382 object spectra included in DR2.," The extremely high identification success rate achieved in the SDSS means that the wavelengths of strong absorption and emission features in the spectra of stars and galaxies are known; there are only 3,002 spectra without secure identifications among the 329,382 object spectra included in DR2."
 Potential systematic biases in the sky residual subtraction can be prevented by masking the wavelength intervals that include such features., Potential systematic biases in the sky residual subtraction can be prevented by masking the wavelength intervals that include such features.
 The exact nature of the pre-processing applied to spectra prior to the implementation of the sky residual subtraction depends on the scientitic goal., The exact nature of the pre-processing applied to spectra prior to the implementation of the sky residual subtraction depends on the scientific goal.
 However. in subsequent sections we describe schemes that are likely to have wide application in the analysis of the 3 main classes of SDSS science targets: galaxies. quasars and stars.," However, in subsequent sections we describe schemes that are likely to have wide application in the analysis of the 3 main classes of SDSS science targets: galaxies, quasars and stars."
 The DR2 catalogue contains 249.678 unique objects spectroscopically classified as galaxies.," The DR2 catalogue contains 249,678 unique objects spectroscopically classified as galaxies."
 The strong systematic trends in the absorption- and emission-line properties of the galaxies as one moves from early through to late type objects necessitates a sub-classification of the population prior to the application of the sky-residual subtraction., The strong systematic trends in the absorption- and emission-line properties of the galaxies as one moves from early through to late type objects necessitates a sub-classification of the population prior to the application of the sky-residual subtraction.
 Therefore. we classify each galaxy as either an absorption line. emission line or extreme emission line object.," Therefore, we classify each galaxy as either an absorption line, emission line or extreme emission line object."
 The spectral type parameter (“ECLASS™) in the SDSS catalogue. provides the basis for the absorption line (ECLASS 0.05) and emission line = ).05) classification., The spectral type parameter ”) in the SDSS catalogue provides the basis for the absorption line $<-0.05$ ) and emission line $\ge -0.05$ ) classification.
" The extreme emission line galaxies are identitied through the presence of emission lines with very largeequivalent widths (EW) (EW,27200A. 2«O04: or EWeour2200A. 2o« 0.84)."," The extreme emission line galaxies are identified through the presence of emission lines with very largeequivalent widths (EW) ${\rm EW_{H\alpha}}>200$, $z<0.4$; or ${\rm EW_{[OIII]}}>
200$, $z<0.84$ )."
 An appropriate feature mask is then applied depending on the galaxy type (e.g. see Fig. 9))., An appropriate feature mask is then applied depending on the galaxy type (e.g. see Fig. \ref{fig_gal1}) ).
 A total of aare masked in absorption/emission/extreme emission line objects respectively. over the entire rest-frame wavelength range of ANA0—9100 Α.. Le. in the observed-frame wavelength range of," A total of are masked in absorption/emission/extreme emission line objects respectively, over the entire rest-frame wavelength range of $3830-9100\,$ , i.e. in the observed-frame wavelength range of"
Col.,Col.
 9: the B-band cllective radius rege and its error: Col., 9: the B-band effective radius $r_{e B}$ and its error; Col.
 19: he classification ac'cording to the B-banel profile decomposition (see Col., 10: the classification according to the B-band profile decomposition (see Col.
 5): Col., 5); Col.
 11: the B-bancl bulge-to-total luminosity ratio Bite (see Col., 11: the B-band bulge-to-total luminosity ratio $B/T_B$ (see Col.
 6): Col., 6); Col.
 12: ie observed. total LE-band magnitude LI and its error: CoL., 12: the observed total H-band magnitude H and its error; Col.
 13: the observed total B-band magnitude 2 and its οτοῦ., 13: the observed total B-band magnitude B and its error.
 We note that 5 objects (io: VCC'T1745.. 1122... 1308. 1386 and 1499) change classification [rom a de Vaucouleurs- to à | disk svstem. ancl 1: οἱject 7786) changes its classification [rom an exponential-disk to a | disk svstem. from the near-LB to the optical case.," We note that 5 objects (i.e.: 745, 1122, 1308, 1386 and 1499) change classification from a de Vaucouleurs- to a $+$ disk system, and 1 object 786) changes its classification from an exponential-disk to a $+$ disk system, from the near-IR to the optical case."
 The B-band surface brightness profile of 7786 ts decomposed into relatively extended: and. equally. faint bulge- and. clisk-components (cf., The B-band surface brightness profile of 786 is decomposed into relatively extended and equally faint bulge- and disk-components (cf.
 GOL). so that. its prolile fitting may. be questionable but not its values of D and rg.," G01), so that its profile fitting may be questionable but not its values of B and $r_{e B}$."
 In the case of 11499. he L-bancl surface brightness profile extends up to of the radial extension of its B-bancl photometry. so that the w»hotometric parameters of this object are reliable.," In the case of 1499, the H-band surface brightness profile extends up to of the radial extension of its B-band photometry, so that the photometric parameters of this object are reliable."
 ὃν contrast. for 7745. 1122. 1808 ancl 1386. the H-band surface brightness profiles extend «nly up to of the racial extension of the B-bancl ones.," By contrast, for 745, 1122, 1308 and 1386, the H-band surface brightness profiles extend only up to of the radial extension of the B-band ones."
 For these 4+ galaxies. ib may. be questioned that a faint. extended: exponential-disk might not have been deteced against the near-LR background (tvpically of 20.5 L-mi(o aresec72 in the images of these galaxies).," For these 4 galaxies, it may be questioned that a faint, extended exponential-disk might not have been detected against the near-IR background (typically of 20.5 H-mag $\rm arcsec^{-2}$ in the images of these galaxies)."
 Loan exponenial-disk component was indeed: missed/misidentified by the! near-Hi. observations. a best-lit ce Vaucouleurs-Iww would iinclerestimate the surface intensity in the outer regions of tjose systems.," If an exponential-disk component was indeed missed/misidentified by the near-IR observations, a best-fit de Vaucouleurs-law would underestimate the surface intensity in the outer regions of these systems."
 “Phe visual inspection of the radial photometric profiles of 7745. 1122. 1308 and 1386 displaved in GOL suggests that. the previous systematic effect. if any. is not strong.," The visual inspection of the radial photometric profiles of 745, 1122, 1308 and 1386 displayed in G01 suggests that the previous systematic effect, if any, is not strong."
 We estimate that the L-band total magnitudes of these 4 galaxies. listed in Col.," We estimate that the H-band total magnitudes of these 4 galaxies, listed in Col."
 11 of Tab., 11 of Tab.
 2. may be under-Iuminous by ~0.2mag. while their values of rg may be underestimated w c..," 2, may be under-luminous by $\rm \sim 0.2~mag$, while their values of $r_{e H}$ may be underestimated by $\sim$."
 We anticipate that these potential systematic uncertainties do not bias our results (cf., We anticipate that these potential systematic uncertainties do not bias our results (cf.
 Sect., Sect.
 3)., 3).
 In addition to these IS VCC early-tvpe dwarfs.. we Consider. as a comparison. a sample of 29 giant elliptical anc lenticular galaxies of the Coma cluster. optically selected from the Catalogue of Galaxies and. Clusters of Galaxies (COCG) of Zwicky ct al. (," In addition to these 18 VCC early-type dwarfs, we consider, as a comparison, a sample of 29 giant elliptical and lenticular galaxies of the Coma cluster, optically selected from the Catalogue of Galaxies and Clusters of Galaxies (CGCG) of Zwicky et al. ("
L961LOGS) and observed in the L-band by Scodeggio e al. (,1961–1968) and observed in the H-band by Scodeggio et al. (
1908 hereafter referred to as SOS).,1998 – hereafter referred to as S98).
 We adop a distance from the Coma cluster to us of 96.0 \Ipe from SOs., We adopt a distance from the Coma cluster to us of 96.0 Mpc from S98.
 The L-band data reduction and analysis of SOS is the same of GOL. except that all the radial surface brightness profiles of the SOS salaxies were fitted: with a de Vaucouleurs-Iaw.," The H-band data reduction and analysis of S98 is the same of G01, except that all the radial surface brightness profiles of the S98 galaxies were fitted with a de Vaucouleurs-law."
" ""These 20 COC carly-type giants were observed in the B-banc ον cilferent authors. listed in S98. adopting either photoelectric aperture photometry or CCD surface photometry. but their B-band photomoetric parameters were derivec by Saglia. Bender Dressler (1993) by fitting a de Vaucouleurs-law o the radial photomoetric profile derived. from 2D. data."," These 29 CGCG early-type giants were observed in the B-band by different authors, listed in S98, adopting either photoelectric aperture photometry or CCD surface photometry, but their B-band photometric parameters were derived by Saglia, Bender Dressler (1993) by fitting a de Vaucouleurs-law to the radial photometric profile derived from 2D data."
 TPherefore. for these. giants. only fitted effective radii are available.," Therefore, for these giants, only fitted effective radii are available."
 Both observed total 1I- ancl B-band magnitudes of these 29 galaxies come from C. Gavazzi (2001. private communication).," Both observed total H- and B-band magnitudes of these 29 galaxies come from G. Gavazzi (2001, private communication)."
 These H-band total magnitudes were derived. by SOUS hy adopting the same procedure of GOL, These H-band total magnitudes were derived by S98 by adopting the same procedure of G01.
" By contrast. these B-bancl total magnitudes were either taken from the literature. if derived from surface photometry. or derived by Gavazzi Boselli (1996) by applying the ""growth curves” technique to the available photoclectric aperture measurements."," By contrast, these B-band total magnitudes were either taken from the literature, if derived from surface photometry, or derived by Gavazzi Boselli (1996) by applying the “growth curves” technique to the available photoelectric aperture measurements."
 Both LI- and B-band total observed: magnitudes. have a typical uncertainty of 0.1 magnitucle., Both H- and B-band total observed magnitudes have a typical uncertainty of 0.1 magnitude.
 In Tab., In Tab.
 3. we list the properties of the 29 eiant I2 and," 3, we list the properties of the 29 giant E and"
time at which we estimate a SN explosion will destroy the GMC.,time at which we estimate a SN explosion will destroy the GMC.
 From figure we see that these are expanding as a group away from one another (in fact this is true of the GMC structure in general)., From figure we see that these are expanding as a group away from one another (in fact this is true of the GMC structure in general).
 Furthermore. the distance between is roughly [Ope after about 13Myr.," Furthermore, the distance between is roughly 10pc after about 13Myr."
 Thus the group of clusters have the appearance of an OB association. with the individual being OB subgroups that are expanding about some common point.," Thus the group of clusters have the appearance of an OB association, with the individual being OB subgroups that are expanding about some common point."
 In this section we examine the properties of the and compare them to the observations of OB associations., In this section we examine the properties of the and compare them to the observations of OB associations.
 In figure4. the left hand panel shows the positions of the that are large enough to contain stars greater than at t=9Myr. assuming a star formation efficiency of505€ and the IMF presented in section4+.," In figure, the left hand panel shows the positions of the that are large enough to contain stars greater than at t = 9Myr, assuming a star formation efficiency of and the IMF presented in section."
 Their positions are plotted at the time we estimate the SN event to start expelling gas from the cloud., Their positions are plotted at the time we estimate the SN event to start expelling gas from the cloud.
 We now assume that the SN event removes the gas from the GMC quickly enough such that the motions of objects have no time to adjust to the change in potential., We now assume that the SN event removes the gas from the GMC quickly enough such that the motions of objects have no time to adjust to the change in potential.
 We assume that this is true both at the scale of the motions and at the smaller scale of the stellar motions inside theSFCs., We assume that this is true both at the scale of the motions and at the smaller scale of the stellar motions inside the.
. The right hand panel shows the positions of the after a further 4 Myr. i.e. at t= 13 Myr. assuming that they continue on the path they had before the gas expulsion.," The right hand panel shows the positions of the after a further 4 Myr, i.e. at t = 13 Myr, assuming that they continue on the path they had before the gas expulsion."
 The circles denote the size of the at t= 13 Myr. which have been evaluated from r2ray|AVY4 Myr. where AW is the region's internal velocity dispersion and rsx is the radius of the at the point when the SN event occurs (i.e. at 9 Myr).," The circles denote the size of the at t = 13 Myr, which have been evaluated from $\rm{r = r_{SN} +
\Delta V \times 4}$ Myr, where $\rm{\Delta V}$ is the region's internal velocity dispersion and $\rm{r_{SN}}$ is the radius of the at the point when the SN event occurs (i.e. at 9 Myr)."
 This assumes that the star forming regions will disperse at roughly their internal velocity dispersion once the gas has been expelled., This assumes that the star forming regions will disperse at roughly their internal velocity dispersion once the gas has been expelled.
 Figure clearly shows that the are expanding away from one another., Figure clearly shows that the are expanding away from one another.
 By determining the average radius of the from their common centre of mass. both at t = 9 Myr and at t = 13 Myr. we can get an estimate of their expansion velocity from their dynamical centre.," By determining the average radius of the from their common centre of mass, both at t = 9 Myr and at t = 13 Myr, we can get an estimate of their expansion velocity from their dynamical centre."
 At t = 9 Myr the average distance of the from their centre of mass is 18.4pc. while after 13 Myr it is Ὄδρο.," At t = 9 Myr the average distance of the from their centre of mass is 18.4pc, while after 13 Myr it is 25pc."
 This corresponds to an expansion velocity (that is a 3- velocity) for the of +., This corresponds to an expansion velocity (that is a 3-dimensional velocity) for the of $^{-1}$.
 We compare this. for example. to the observed expansion of the OB subgroups in Per OB which is roughly 1 (?2)..," We compare this, for example, to the observed expansion of the OB subgroups in Per OB which is roughly $^{-1}$ \citep{Fredrick1956, Blaauw1964}."
 We also see that if the themselves are able to expand after the gas expulsion. they become an extended distribution of stars after only 13 Mys. as is shown by the circles in the figure.," We also see that if the themselves are able to expand after the gas expulsion, they become an extended distribution of stars after only 13 Mys, as is shown by the circles in the figure."
 The stellar mass density is another important feature of OB associations., The stellar mass density is another important feature of OB associations.
 Generally. OB associations have a density of OB stars of roughly  (see the introduction for references).," Generally, OB associations have a density of OB stars of roughly $^{-3}$ (see the introduction for references)."
 In this simulation at t — 9 Myr. the density of OB type stars is . and the mass density of stars Z2 is pe.7.," In this simulation at t = 9 Myr, the density of OB type stars is $^{-3}$, and the mass density of stars $\ge$ is $^{-3}$."
 This is calculated by taking the total mass in the of stars of greater than the required mass type and dividing by the volume of region containing all the with these types of stars., This is calculated by taking the total mass in the of stars of greater than the required mass type and dividing by the volume of region containing all the with these types of stars.
 After the system has had ime to evolve for 4 Myr. the densities are 0.06 and  or the OB type stars and those with masses = respectively.," After the system has had time to evolve for 4 Myr, the densities are 0.06 and $^{-3}$ for the OB type stars and those with masses $\ge$ respectively."
 ote these figures are based on the having a star formation efficiency of50% and containing the IMF of stellar objects that was resented in section4., Note these figures are based on the having a star formation efficiency of and containing the IMF of stellar objects that was presented in section.
 We can compare this to the density of high mass stars in the at the point of the SN explosion., We can compare this to the density of high mass stars in the at the point of the SN explosion.
 If we take the largest.. with mass and radius of 0.7pe. and assume again that of this is contained in stars.," If we take the largest, with mass and radius of 0.7pc, and assume again that of this is contained in stars."
 Then the total mass in stars of mass greater than is 1763.0.15/2=132M...," Then the total mass in stars of mass greater than is $1763 \times 0.15 / 2
=$."
 The density of massive stars is then 132/0.7=384M. ., The density of massive stars is then $132/0.7^{3} = 384$ $^{-3}$.
 The turbulent flows are thus able to create a series of star forming regions that have roughly the same properties as those found in OB associations., The turbulent flows are thus able to create a series of star forming regions that have roughly the same properties as those found in OB associations.
 Since the regions (the SFCs)) are formed within large flows. the stars that form will have roughly the same motion as the gas stream that formed them. potentially explaining why ? finds that the gas surrounding OB subgroups is generally moving with the group.," Since the regions (the ) are formed within large flows, the stars that form will have roughly the same motion as the gas stream that formed them, potentially explaining why \citet{Blaauw1991} finds that the gas surrounding OB subgroups is generally moving with the group."
 Observations of some OB associations also indicate distinct age spreads between their subgroups., Observations of some OB associations also indicate distinct age spreads between their subgroups.
 This generally takes the form of an age progression from one side of the association to the next., This generally takes the form of an age progression from one side of the association to the next.
 The ages are generally derived from where the very high mass stars Π off the main sequence. which is a much more reliable method than using pre-main-sequence (PMS) tracks of low mass objects.," The ages are generally derived from where the very high mass stars turn off the main sequence, which is a much more reliable method than using pre-main-sequence (PMS) tracks of low mass objects."
 Also the high mass end is normally the only part of the mass spectrum that is well established in OB associations., Also the high mass end is normally the only part of the mass spectrum that is well established in OB associations.
 This age spread has been the motivation behind the triggered sequential star formation model developed by ?.. which is in turn motivated by the observations of ?..," This age spread has been the motivation behind the triggered sequential star formation model developed by \citet{ElmegreenLada1977}, which is in turn motivated by the observations of \citet{Blaauw1964}."
 However. we note here that the Orion OB association exhibits no discernible age progression in the subgroups (2)..," However, we note here that the Orion OB association exhibits no discernible age progression in the subgroups \citep{Brownetal1999}."
 Does our simulation show a convincing age spread between hesubgroups/SFCs?, Does our simulation show a convincing age spread between the?
? In figure we plot the age of the ootoclusters (the sink particles that group together to form the SFCs)) and their position from their common centre of mass., In figure we plot the age of the protoclusters (the sink particles that group together to form the ) and their position from their common centre of mass.
 All he points are plotted at t = 13 Myr. with the positions being he y-direction in the simulation. since the are more spaced out in this direction.," All the points are plotted at t = 13 Myr, with the positions being the y-direction in the simulation, since the are more spaced out in this direction."
 The ages are determined in two ways., The ages are determined in two ways.
 The crosses denote the ages determined by when the protocluster first orms., The crosses denote the ages determined by when the protocluster first forms.
 The filled hexagons are determined by the time when he protoclusters reach a mass of134M... the point at which a star can form.," The filled hexagons are determined by the time when the protoclusters reach a mass of, the point at which a star can form."
 Note that in the previous sections we determined when stars could form based on the mass contained in an.. rather than its constituent protoclusters and gas.," Note that in the previous sections we determined when stars could form based on the mass contained in an, rather than its constituent protoclusters and gas."
 We are forced to use the individual protoclusters here since the are not coherent objects throughout the entire evolution of the simulation., We are forced to use the individual protoclusters here since the are not coherent objects throughout the entire evolution of the simulation.
 We see clearly from figure that while a large range of ages exist at any particular distance from the centre of mass. no trend is resent in the ages with distance.," We see clearly from figure that while a large range of ages exist at any particular distance from the centre of mass, no trend is present in the ages with distance."
 Thus our simulation predicts that he OB association would be essentially coeval., Thus our simulation predicts that the OB association would be essentially coeval.
 However this is just a symptom of our idealised initial conditions., However this is just a symptom of our idealised initial conditions.
 The initial uniform density sphere. with multiple Jeans masses. allows the entire cloud © proceed directly to star formation. via the dissipation of kinetic energy.," The initial uniform density sphere, with multiple Jeans masses, allows the entire cloud to proceed directly to star formation, via the dissipation of kinetic energy."
 Since the turbulence is the same throughout the cloud. star ormation occurs simultaneously in quite separate locations.," Since the turbulence is the same throughout the cloud, star formation occurs simultaneously in quite separate locations."
 If on he other hand our GMC needs to accumulated in a large scale shock. as suggested by ?.. then there would naturally be an age spread as the laver in which the GMC forms starts to grow.," If on the other hand our GMC needs to accumulated in a large scale shock, as suggested by \citet{Pringleetal2001}, then there would naturally be an age spread as the layer in which the GMC forms starts to grow."
 The most important point in this picture is that the whole region would not be at the same density. but instead would have to evolve to star forming densities as the GMC accumulates.," The most important point in this picture is that the whole region would not be at the same density, but instead would have to evolve to star forming densities as the GMC accumulates."
 The simulation presented in this paper highlights that GMCs need not be regarded as objects in virial equilibrium. or even bound. for them to be sites of star formation.," The simulation presented in this paper highlights that GMCs need not be regarded as objects in virial equilibrium, or even bound, for them to be sites of star formation."
 Globally unbound GMCs can form stellar clusters very quickly. on roughly their crossing time.," Globally unbound GMCs can form stellar clusters very quickly, on roughly their crossing time."
 Furthermore. the unbound state of the cloud ensures that whole region is also dispersing while it is forming stars.," Furthermore, the unbound state of the cloud ensures that whole region is also dispersing while it is forming stars."
 They are thus naturally transient features., They are thus naturally transient features.
 This evolutionary picture of a cloud forming. producing a stellar population. and then dispersing has," This evolutionary picture of a cloud forming, producing a stellar population, and then dispersing has"
aand more rotation curves becoming available. the sampling in morphology should. become less biased. (ο late-type galaxies.,"and more rotation curves becoming available, the sampling in morphology should become less biased to late-type galaxies."
 We obtained oobservations of the earlv-tvpe galaxy NGC 2974 and found that the neutral gas resides in a ring., We obtained observations of the early-type galaxy NGC 2974 and found that the neutral gas resides in a ring.
" Phe ring starts around 50"". and extends to 120"". which corresponds to 12 kpe or 5 ellective radii."," The ring starts around $^{\prime \prime}$, and extends to $^{\prime \prime}$, which corresponds to 12 kpc or 5 effective radii."
 The total mass of the neutral gas is 10341..., The total mass of the neutral gas is $5.5 \times 10^8 M_\odot$ .
 We compared the velocity field of the rring with the kinematies of the ionised gas., We compared the velocity field of the ring with the kinematics of the ionised gas.
 We found that both velocity. fieles. are very regular ancl nicely aligned. indicating that they could form a single disc.," We found that both velocity fields are very regular and nicely aligned, indicating that they could form a single disc."
 A harmonic decomposition of the velocity field showed. that at large radii the gravitational potential is consistent with an axisvmmetrie shape., A harmonic decomposition of the velocity field showed that at large radii the gravitational potential is consistent with an axisymmetric shape.
 We introduced a new wav to correct the rotation curve of the ionisecl gas for asvnimetric drift., We introduced a new way to correct the rotation curve of the ionised gas for asymmetric drift.
 We found that the correction approaches a constant value ancl this enabled. us to remove the ellect of turbulence on the rotation curve. assuming a constant asymmetric drift correction throughout the galaxy.," We found that the correction approaches a constant value and this enabled us to remove the effect of turbulence on the rotation curve, assuming a constant asymmetric drift correction throughout the galaxy."
 We confirmed that this assumption is valid in NGC 2974. by comparing with the asvnimetric drift corrected rotation curve of the stars Gvhich was not allected bv turbulence).," We confirmed that this assumption is valid in NGC 2974, by comparing with the asymmetric drift corrected rotation curve of the stars (which was not affected by turbulence)."
 An interesting question is whether other galaxies show the same behaviour., An interesting question is whether other galaxies show the same behaviour.
 LW this is the case. then with our method we would be able to investigate rotation curves of ionisec eas and the cllects of turbulence in more detail in other galaxies. and search for connections with e.g. spiral structure and bars.," If this is the case, then with our method we would be able to investigate rotation curves of ionised gas and the effects of turbulence in more detail in other galaxies, and search for connections with e.g. spiral structure and bars."
 Although in principle we could for NGC 2974 also have used the stellar rotation curve together with the tto constrain the mass models. this will not be the case for all galaxies.," Although in principle we could for NGC 2974 also have used the stellar rotation curve together with the to constrain the mass models, this will not be the case for all galaxies."
 For instance. in low surface brightness galaxies stellar kinematics are not easy to obtain. and even in hieh surface brightness galaxies. the absorption line kinematics need to be binned to higher signal-to-noise than the emission line kinematics. provided that ionised gas is present.," For instance, in low surface brightness galaxies stellar kinematics are not easy to obtain, and even in high surface brightness galaxies, the absorption line kinematics need to be binned to higher signal-to-noise than the emission line kinematics, provided that ionised gas is present."
 ]t is clear from the rotation curve of NGC 2974 that dark matter is required to explain the observed velocities., It is clear from the rotation curve of NGC 2974 that dark matter is required to explain the observed velocities.
We found that the total mass-to-light ratio increases from 4.3 Αιεν αι 1 B 108.5 AL.fh. 5 BR...,"We found that the total mass-to-light ratio increases from 4.3 $M_\odot/L_{\odot,I}$ at 1 $R_e$ to 8.5 $M_\odot/L_{\odot,I}$ at 5 $R_e$ ."
 This last value would correspond to 14 AL.ἐνο in D-band.," This last value would correspond to 14 $M_\odot/L_{\odot,B}$ in $B$ -band."
 Even in the maximal disc model. 55 per cent of the total mass is dark. and an accditional dark halo needs to be included.," Even in the maximal disc model, 55 per cent of the total mass is dark, and an additional dark halo needs to be included."
 We constructed mass models of NGC 2974. where we modeled both the stellar and &aseous contribution to the gravitational potential.," We constructed mass models of NGC 2974, where we modeled both the stellar and gaseous contribution to the gravitational potential."
" The latter is negligible compared to the stars Clauc0.00137,). but. still included in. our models."," The latter is negligible compared to the stars $M_{\mathrm{gas}} \sim
0.001 M_*$ ), but still included in our models."
 For the dark halo. we tested two cilferent. profiles: the core-clominatecl pseudo-isothermal sphere and the cuspy NEW. profile.," For the dark halo, we tested two different profiles: the core-dominated pseudo-isothermal sphere and the cuspy NFW profile."
 We experimented with dillerent values for the stellar mass-to-light ratio. but found that wecannot constrain this value with just the rotation curve: for most AL£L smaller than the maximal dise value. we could obtain a decent fit for both the pseudo-isothermal sphere and the NEW profile.," We experimented with different values for the stellar mass-to-light ratio, but found that wecannot constrain this value with just the rotation curve: for most $M_*/L$ smaller than the maximal disc value, we could obtain a decent fit for both the pseudo-isothermal sphere and the NFW profile."
" I£ we compare models with M;/L; from single stellar population models (2.34 M./L.j) with maximal disc model (AL,/L;= 3.8 AL.fL.1). then the first provide better fits to the data."," If we compare models with $M_*/L_I$ from single stellar population models (2.34 $M_\odot/L_{\odot,I}$ ) with maximal disc model $M_*/L_I = $ 3.8 $M_\odot/L_{\odot,I}$ ), then the first provide better fits to the data."
" Especially the inner datapolnts are better reproduced. with AM/L;= 2.34 M.fL.εν but we note that the ddata points are better fitted in the models with the larger Adl.£L,; value."," Especially the inner datapoints are better reproduced with $M_*/L_I =$ 2.34 $M_\odot/L_{\odot,I}$, but we note that the data points are better fitted in the models with the larger $M_*/L_I$ value."
 The pseudo-isothermal sphere fits our data miareinally better than the NEW profile. but the dillerence is not significant.," The pseudo-isothermal sphere fits our data marginally better than the NFW profile, but the difference is not significant."
 With MOND we can also reproduce the observed rotation curve. but not as well as with models that include a dark matter halo.," With MOND we can also reproduce the observed rotation curve, but not as well as with models that include a dark matter halo."
 The largest uncertainty in our analysis is the stellar mass-to-light ratio., The largest uncertainty in our analysis is the stellar mass-to-light ratio.
 We can only derive an upper limit on this ratio from the maximal disc model or c.g. from Schwarzschild modeling. since. Al./L should always be equal to or smaller than the dynamical ML.," We can only derive an upper limit on this ratio from the maximal disc model or e.g. from Schwarzschild modeling, since $M_*/L$ should always be equal to or smaller than the dynamical $M/L$."
" Values for ALL from stellar. population svnthesis models. depend significantly on the model assumptions: we mentioned already that goine from a WKroupa to a Salpeter IME can increase Al,/L by as much as 40 per cent.", Values for $M_*/L$ from stellar population synthesis models depend significantly on the model assumptions: we mentioned already that going from a Kroupa to a Salpeter IMF can increase $M_*/L$ by as much as 40 per cent.
 Also. even low- secondary star formation can allect Al./L severely.," Also, even low-level secondary star formation can affect $M_*/L$ severely."
 Furthermore. there is no reason why the Al./L should remain constant over 5 elfective radii. which we assumed when modeling the stellar mass.," Furthermore, there is no reason why the $M_*/L$ should remain constant over 5 effective radii, which we assumed when modeling the stellar mass."
 Lf the stellar mass-to-light ratio were known. we would be able to determine the dark matter [fraction in the galaxy with more accuracy. and either rule out or confirm the maximal cise hypothesis.," If the stellar mass-to-light ratio were known, we would be able to determine the dark matter fraction in the galaxy with more accuracy, and either rule out or confirm the maximal disc hypothesis."
 Also. since ALL is the onlv free parameter when fitting a rotation curve in MOND. knowing this value would provide us with a rotation curve that can be compared to the data directly. providing a clear test for MOND.," Also, since $M_*/L$ is the only free parameter when fitting a rotation curve in MOND, knowing this value would provide us with a rotation curve that can be compared to the data directly, providing a clear test for MOND."
 We have shown in this paper that it) djs. possible to combine rotation curves of neutral and ionised gas. correcting the latter one for asymmetric drift using the Jeans equations and the higher order velocity. moments of the collisionless Boltzmann equations.," We have shown in this paper that it is possible to combine rotation curves of neutral and ionised gas, correcting the latter one for asymmetric drift using the Jeans equations and the higher order velocity moments of the collisionless Boltzmann equations."
 Our method. to correct for the asvmametrie drift therefore does not. require a cold disc assumption (e Vi., Our method to correct for the asymmetric drift therefore does not require a cold disc assumption $\sigma \ll V_c$ ).
 With more earls-tvpe galaxies eettingdetected. in ILL. and more high quality rotation curves becoming available. we can now study the shape of their dark matter halocs.," With more early-type galaxies gettingdetected in , and more high quality rotation curves becoming available, we can now study the shape of their dark matter haloes."
"For the modeling of the 1998 SED of W Comae we have fixed the effective size scale of the emission region to 2,=iol,D where f,210h is the measured soft X-ray. variability lime scale.",For the modeling of the 1998 SED of W Comae we have fixed the effective size scale of the emission region to $R_b=\frac{1}{2} c t_{\rm{var}} D$ where $t_{\rm{var}}\approx 10$ h is the measured soft X-ray variability time scale.
 We consider bulk Doppler [actors in the range D—5. 20 for the fittàng procedure. which is consistent with the moderate superluminal motion detected by Massaro.(2001).," We consider bulk Doppler factors in the range $D = 5$ – 20 for the fitting procedure, which is consistent with the moderate superluminal motion detected by \cite{massaro01}."
. The primary relativistic electrons emit svnchrotron photons. which serve as the Larget photon field for photon-proton interactions aud cascading.," The primary relativistic electrons emit synchrotron photons, which serve as the target photon field for photon-proton interactions and cascading."
" The svuchrotron spectrum [rom these electrons shows a break at around 1057 Hz where the svnchrotron cooling time scale liu228x10(D/1G)?5 Lec equals the adiabatic loss time scale {μι22€12),/¢ [or a relativistic jet with £<1. taking into account a possible non-spherical geometry. effects of a possible accelerating (i.e. non-constant speed) jet. ete."," The synchrotron spectrum from these electrons shows a break at around $10^{13}$ Hz where the synchrotron cooling time scale $t_{\rm{e,syn}} \approx 8 \times 
10^8 \, (B/1 \, {\rm G})^{-2} \, \gamma^{-1}$ sec equals the adiabatic loss time scale $t_{\rm{ad}} \approx \xi R_b/c$ for a relativistic jet with $\xi\leq 1$, taking into account a possible non-spherical geometry, effects of a possible accelerating (i.e. non-constant speed) jet, etc."
 In the soft X-ray regime. the spectrum (urns over steeplv when the cooling time scale becomes shorter than the acceleration time scale face=rp/(Qje) (rj; = Larmor radius. ηx1 = acceleration efficiency).," In the soft X-ray regime, the spectrum turns over steeply when the cooling time scale becomes shorter than the acceleration time scale $t_{\rm{acc}} = r_L / (\eta c)$ $r_L$ = Larmor radius, $\eta \leq 1$ = acceleration efficiency)."
 Note that the theory of plasma turbulence predicts significantly lower 7 values for electrons than for protons., Note that the theory of plasma turbulence predicts significantly lower $\eta$ values for electrons than for protons.
 Fie., Fig.
 8 shows a stummary of SPB-moclels best representing the March/Alav 1998 data., \ref{SPBfits} shows a summary of SPB-models best representing the March/May 1998 data.
 similar to the leptonic SSC model. the SPD-model seems to be not compatible with the March 1998 EGRET data if the May 1998 LECS + MECS + PDS data from BeppoSAX are modeled (see models 3 5).," Similar to the leptonic SSC model, the SPB-model seems to be not compatible with the March 1998 EGRET data if the May 1998 LECS + MECS + PDS data from BeppoSAX are modeled (see models 3 – 5)."
 On the other hand. the BeppoSAX LECS + MECS data together wilh the EGRET spectrum can be explained by hadronic models (see models 1 + 2). which however underestimate the flix in the PDS energy band by about a [actor of 3.," On the other hand, the BeppoSAX LECS + MECS data together with the EGRET spectrum can be explained by hadronic models (see models 1 + 2), which however underestimate the flux in the PDS energy band by about a factor of 3."
 The of the EGRET- with the BeppoSAX-data in the modeling procedure might be caused by (heir non-simultaneity and (he poor significance of the EGBRIZI-detection., The non-compatibility of the EGRET- with the BeppoSAX-data in the modeling procedure might be caused by their non-simultaneity and the poor significance of the EGRET-detection.
 Note also that during the May 1998 BeppoSAX observing run some technical problems occured whieh might have affected the PDS data (Taglialerrietal.2000)., Note also that during the May 1998 BeppoSAX observing run some technical problems occured which might have affected the PDS data \citep{tagliaferri00}.
. In the framework of the hadronic SPD-model (he hard. X-ray. spectrum can naturally be explained bv strong svuchrotron emission [rom (he relativistic protons provided strong magnetic fields 77 of several tens of Gauss exist in the emission region., In the framework of the hadronic SPB-model the hard X-ray spectrum can naturally be explained by strong synchrotron emission from the relativistic protons provided strong magnetic fields $B$ of several tens of Gauss exist in the emission region.
" For the modeling (models 3°05) we use B=30. 40 Goa, μυ.=5 LOX105. a number density ratio of primary. relativistic electrons to protons. e/p20.1. and a proton energy density up,260 150 eres 7 somewhat above the equipartition value. which is not surprising during aclivitv in the source."," For the modeling (models 3 – 5) we use $B = 30$ – 40 G, $\alpha_p = 1.5$, $\gamma_{\rm{p,max}} = 5$ – $10 \times 10^8$, a number density ratio of primary, relativistic electrons to protons, $e/p\approx 0.1$, and a proton energy density $u_p\approx 60$ – 150 ergs $^{-3}$, somewhat above the equipartition value, which is not surprising during activity in the source."
 With Doppler factors D=12. 15 the target photon energy density in the jet frame is ~10HOC 1011 eV 7., With Doppler factors $D = 12$ – 15 the target photon energy density in the jet frame is $\sim 10^{10}$ – $10^{11}$ eV $^{-3}$.
 Because proton svnchrotron losses dominate in the hieh enerev region over pion production losses (see Fig. 11)).," Because proton synchrotron losses dominate in the high energy region over pion production losses (see Fig. \ref{loss_timescales}) ),"
 the model predicts the main power oulpul al several LOQ MeV. due to proton svnchrotron radiation. wilh a strong steepening bv about 2 orders of magnitude in (he GeV range. ancl y-ray emission [rom the z-cascades extending up to about 100. TeV with a break at about 10. TeV at the source.," the model predicts the main power output at several 100 MeV due to proton synchrotron radiation, with a strong steepening by about 2 orders of magnitude in the GeV range, and $\gamma$ -ray emission from the $\pi$ -cascades extending up to about 100 TeV with a break at about 10 TeV at the source."
 Photons above ~100 GeV Gn the co-moving frame) will be subject to 55 absorption within, Photons above $\sim 100$ GeV (in the co-moving frame) will be subject to $\gamma\gamma$ absorption within
"The width of the resonance function depends on the perturbation strength of the turbulence Aj,=Avj/v,cV/9B/B= /Ma).","The width of the resonance function depends on the perturbation strength of the turbulence $\Delta \mu=\Delta v_\|/v_\bot\simeq
\sqrt{\delta B/B}=\sqrt{M_A}$ )."
" For gyroresonance (n=+1,2,...) the result depends on whether µ is strongly or weakly perturbed by regular field."," For gyroresonance $n=\pm
1,2,...$ ) the result depends on whether $\mu$ is strongly or weakly perturbed by regular field."
" If ~>>Aq, the result is similar to QLT, because the exponents in Eq.(9)) become close to ó-functions."," If $\mu\gg \Delta \mu$, the result is similar to QLT, because the exponents in \ref{resfunc}) ) become close to $\delta$ -functions."
" For ji<Aq, however, the result is different."," For $\mu<\Delta \mu$, however, the result is different."
 To demonstrate this we can consider the case of 90? scattering., To demonstrate this we can consider the case of $90^\circ$ scattering.
" Indeed, if 4— 0, the resonance happens mostly at kypes~ while in QUT kypes~Ω/υι> oo."," Indeed, if $\mu\rightarrow 0$ , the resonance happens mostly at $k_{\|,res}\sim \Omega/\Delta v$, while in QLT $k_{\|,res}\sim\Omega/v_\|\rightarrow \infty$ ."
" Compared to TTD, Ω/Δυ,however, for gyroresonance is still smaller in incompressible case D,,,,(see Fig. 4))"," Compared to TTD, however, $D_{\mu\mu}$ for gyroresonance is still smaller in incompressible case (see Fig. \ref{strongturb}) )"
 due to anisotropy., due to anisotropy.
 Assuming the tensor of magnetic perturbations introduced in Cho et al. (, Assuming the tensor of magnetic perturbations introduced in Cho et al. (
"2002), which is consistent with the GS95 model, we can calculate scattering from TTD and gyroresonance.","2002), which is consistent with the GS95 model, we can calculate scattering from TTD and gyroresonance."
" Assuming small energies corresponding to Larmor radii much smaller than the outer scale one gets for TTD (YL08): xy where €=kL, E,(£)=fjdtexp(—€t)/t and q=(€1mas 2/3, "," Assuming small energies corresponding to Larmor radii much smaller than the outer scale one gets for TTD (YL08): ], where $\xi=kL$, $E_1(\xi)=\int_1^\infty dt \exp(-\xi t)/t$ and $q=(\xi_{\bot,max}M_A^2)^{-2/3}$ ."
Fig., Fig.
 4 MA)displays the pitch angle diffusion coefficients resulting from TTD scattering and gyroresonance (YLOS)., \ref{strongturb} displays the pitch angle diffusion coefficients resulting from TTD scattering and gyroresonance (YL08).
" We see that gyroresonance is mostly subdominant, however at small pitch angles TTD is inefficient and gyroresonance dominates."," We see that gyroresonance is mostly subdominant, however at small pitch angles TTD is inefficient and gyroresonance dominates."
" scattering property was measured in the tracing experimentsDy, where an ensemble of particles with the same ry (energy) and a particular µο were traced by a certain time.", $D_{\mu \mu}$ scattering property was measured in the tracing experiments where an ensemble of particles with the same $r_L$ (energy) and a particular $\mu_0$ were traced by a certain time.
 This time was determined by the condition that the rms of deviations of w is small (i.e. 0.1-0.01)., This time was determined by the condition that the rms of deviations of $\mu$ is small (i.e. 0.1-0.01).
" Then the curves of the ensemble-averaged —µο)) were fitted with a linear curve, and so D,,,, was((u obtained."," Then the curves of the ensemble-averaged $\langle(\mu-\mu_0)^2\rangle$ were fitted with a linear curve, and so $D_{\mu \mu}$ was obtained."
 The for trans-Alfvenic case is presented on Fig. 5.., The $D_{\mu \mu}$ for trans-Alfvenic case is presented on Fig. \ref{dmumu}.
" For sub-AlfvenicDy, case we noticed that there were very few 90? scattering events.", For sub-Alfvenic case we noticed that there were very few $90^\circ$ scattering events.
 This will be explained in the next section., This will be explained in the next section.
 As we see from Fig., As we see from Fig.
 5 the measurement of scattering frequency isincompatible with QLT., \ref{dmumu} the measurement of scattering frequency is with QLT.
 The scattering frequency normalized to the gyration frequency is proportional to the Larmor radius i.e. it is constant with energy (as Orr=v& ο).," The scattering frequency normalized to the gyration frequency is proportional to the Larmor radius i.e. it is constant with energy (as $\Omega
r_L=v \approx c$ )."
" It would be reasonable to assume then that particles of all energies scatter on the same objects, magnetic bottles, formed by large scale slow-mode perturbations."," It would be reasonable to assume then that particles of all energies scatter on the same objects, magnetic bottles, formed by large scale slow-mode perturbations."
" The same result could be obtained from NLT, taking into account Ay~yu in strong turbulence."," The same result could be obtained from NLT, taking into account $\Delta
\mu \sim \mu$ in strong turbulence."
 At larger energies scattering becomes less efficient i.e. high energy particles “feel” less mirrors., At larger energies scattering becomes less efficient i.e. high energy particles “feel” less mirrors.
" This transition happen at around rr,/Le0.1.", This transition happen at around $r_L/L\approx 0.1$.
" Due to the lack of outer scale, the D,,,, for sub-Alfvenic case is supposed to be QLT-like and very small."," Due to the lack of outer scale, the $D_{\mu \mu}$ for sub-Alfvenic case is supposed to be QLT-like and very small."
" As such it was severely contaminated by numerical error, in particular, fields interpolation error andwas not obtained"," As such it was severely contaminated by numerical error, in particular, fields interpolation error andwas not obtained"
atmospheres.,atmospheres.
" In this parameter space, these coefficients also almost bracket the corresponding photommetric LDCs which suggests a simple, if rough-and-ready, means of comparing observational and model-atmosphere parametrizations."," In this parameter space, these coefficients also almost bracket the corresponding metric LDCs which suggests a simple, if rough-and-ready, means of comparing observational and model-atmosphere parametrizations."
" Furthermore, if one had to choose a linear limb-darkening coefficient to compare with photommetric results, then the FC1 value is probably the least poor option; for randomly inclined orbits, smaller impact parameters are more probable than larger ones (and observational selection effects also favour higher orbital inclinations), and photommetrically determined limb darkening coefficients are generally closest to the FC1 LDC in this The variations in linear limb-darkening coefficient are present for the quadratic coefficients, although here the interpretation is less straightforward because of the well-known strong correlation between wu; and u», evident in the left-hand panels of Fig."," Furthermore, if one had to choose a linear limb-darkening coefficient to compare with metric results, then the FC1 value is probably the least poor option; for randomly inclined orbits, smaller impact parameters are more probable than larger ones (and observational selection effects also favour higher orbital inclinations), and metrically determined limb darkening coefficients are generally closest to the FC1 LDC in this The variations in linear limb-darkening coefficient are present for the quadratic coefficients, although here the interpretation is less straightforward because of the well-known strong correlation between $u_1$ and $u_2$, evident in the left-hand panels of Fig."
 4 (see also Fig., \ref{fig:qPlot} (see also Fig.
 2 in Southworth 2008))., 2 in \citealt{Southworth08}) ).
" Pal(2008) and Kipping&Bakos(2011a) point out that this correlation is largely removed through a rotation onto new principal axes, with $~40°."," \citet{Pal08} and \citet{Kipping11a}
 point out that this correlation is largely removed through a rotation onto new principal axes, with $\phi \simeq 40^\circ$."
" Results rotated to these co-ordinates are shown in the right-hand panel of Fig. 4,,"," Results rotated to these co-ordinates are shown in the right-hand panel of Fig. \ref{fig:qPlot},"
" and confirm that, while the w; values continue to show a large variation with impact parameter, 02 is more nearly constant."," and confirm that, while the $w_1$ values continue to show a large variation with impact parameter, $w_2$ is more nearly constant."
 The correspondence between the photommetric and model-atmosphere results is less straightforward than with the linear law; the model-atmosphere representations of limb darkening show no simple relationship to the mmetrically-determined equivalents (notwithstanding rough quantitative similarities)., The correspondence between the metric and model-atmosphere results is less straightforward than with the linear law; the model-atmosphere representations of limb darkening show no simple relationship to the metrically-determined equivalents (notwithstanding rough quantitative similarities).
" Nevertheless, the small dispersion found for the we coefficient in observational and model-atmosphere characterizations of limb darkening indicates that this should be the parameter of choice when making comparisons."," Nevertheless, the small dispersion found for the $w_2$ coefficient in observational and model-atmosphere characterizations of limb darkening indicates that this should be the parameter of choice when making comparisons."
Freedinan. R.C. Ienuicutt. & JR. Our story begius in the ruidl-1980s with community-wide discussions on Ixey. Projects for the NASA/ESA Hubble Space Telescope.,"Freedman, R.C. Kennicutt, & J.R. Mould}\tikzmark{mainBodyEnd6} %% header left hand page %%
%{}



\tikzmark{mainBodyStart7}\begin{document} Our story begins in the mid-1980s with community-wide discussions on Key Projects for the NASA/ESA Hubble Space Telescope."
 The extragalactic cistauce scale was the perfect example of a project that would be awarded a generous allocation of time in order that vital scientific goals would be accomplished even if the lifetime of the telescope proved to be short., The extragalactic distance scale was the perfect example of a project that would be awarded a generous allocation of time in order that vital scientific goals would be accomplished even if the lifetime of the telescope proved to be short.
" As Mare Aaronson (Figure 1). the original principal investigator of the project. said in lis Pierce Prize Lecture in 1952. ~The distauce scale path las been a long aud torturous oue. but with the tuuninent απο of HST there is good reason to believe that the end is finally iu sight."""," As Marc Aaronson (Figure 1), the original principal investigator of the project, said in his Pierce Prize Lecture in 1985, “The distance scale path has been a long and torturous one, but with the imminent launch of HST there is good reason to believe that the end is finally in sight."""
 Marc Aaronson died tragicallye in an accident in 1987. haviugOm written a successful proposal for the key Project. a project cesigued to shrink the scatter shown in Figure 2 to and put an eucl to 60 years of debate. commencing with Hubble's estimates in. 1929.," Marc Aaronson died tragically in an accident in 1987, having written a successful proposal for the Key Project, a project designed to shrink the scatter shown in Figure 2 to and put an end to 60 years of debate, commencing with Hubble's estimates in 1929."
 The principal reason for the uncertainty in Πρ is evideut in Figure 3., The principal reason for the uncertainty in $_0$ is evident in Figure 3.
 Large scale structure is seen out to distauces of LOO Mpc., Large scale structure is seen out to distances of 100 Mpc.
 Ground-based Cepheid distances. however. extended to ouly |," Ground-based Cepheid distances, however, extended to only 4"
Gamma-ray burst (RB) alterglows are. produced. by jetted outllows slowing down from ultrarelativistic velocities to non-relativistic velocities.,Gamma-ray burst (GRB) afterglows are produced by jetted outflows slowing down from ultrarelativistic velocities to non-relativistic velocities.
 Svachrotron emission. results when the blast wave interacts with the cireeumburst medium and electrons get shock-aceclerated and are accelerated in magnetic fields that are also usually presumed to. he eencrated at the shock., Synchrotron emission results when the blast wave interacts with the circumburst medium and electrons get shock-accelerated and are accelerated in magnetic fields that are also usually presumed to be generated at the shock.
 The jet nature of afterglows is not observed. directly (there are no spatially resolved. jet images)), The jet nature of afterglows is not observed directly (there are no spatially resolved jet images).
 Theoretically. he energetics of the fireball model require that the outllow »v concentrateck towards the observer. since a spherical outflow would imply unphysically high explosion energy on he order of the Solar rest mass (.107! erg) instead. of a more reasonable ~~1017 erg.," Theoretically, the energetics of the fireball model require that the outflow be concentrated towards the observer, since a spherical outflow would imply unphysically high explosion energy on the order of the Solar rest mass $\backsim 10^{54}$ erg) instead of a more reasonable $\backsim 10^{52}$ erg."
 Observationallv. afterglow ight curves at various frequencies show a break. followed. » a steepening of the curve.," Observationally, afterglow light curves at various frequencies show a break followed by a steepening of the curve."
 This can be explained. as abreak. bevond which relativistic beaming effects have decreased in strength to an extent where it becomes possible o distinguish between a jet and spherical outflow.," This can be explained as a, beyond which relativistic beaming effects have decreased in strength to an extent where it becomes possible to distinguish between a jet and spherical outflow."
 A lack of emission [rom bevond the jet opening angle is now seen., A lack of emission from beyond the jet opening angle is now seen.
 A second elfect that is theorized to occur at roughly the same ime is a diminishing of svnchrotron emission due to the onset of significant lateral expansion of the jet., A second effect that is theorized to occur at roughly the same time is a diminishing of synchrotron emission due to the onset of significant lateral expansion of the jet.
" The conventional theoretical argument for the appearance of a jet break compares the 0, of the jet to the ιά Lorentz factor . directly. behind the shock front.", The conventional theoretical argument for the appearance of a jet break compares the $\theta_\mathrm{h}$ of the jet to the fluid Lorentz factor $\gamma$ directly behind the shock front.
 Once the latter has decreased to 5νο1/64. beaming has sullicientlv decreased. ancl the absence οἱ emission [rom angles beyond. &j becomes noticable.," Once the latter has decreased to $\gamma \backsim 1 / \theta_\mathrm{h}$, beaming has sufficiently decreased and the absence of emission from angles beyond $\theta_\mathrm{h}$ becomes noticable."
 Since us ignores the basic shape of the svnehrotron spectrum. is well as electron cooling and the increase. in. optical epth due to synchrotron self-absorption. this suggests an break in the lisht curve.," Since this ignores the basic shape of the synchrotron spectrum as well as electron cooling and the increase in optical depth due to synchrotron self-absorption, this suggests an break in the light curve."
 Llowever. achromatic jet breaks are relatively rare in 1e literature.," However, achromatic jet breaks are relatively rare in the literature."
 Observations in the era often clo not garow a clear jet break in the X-ray when the optical light curve does show a break (c.g. GIUD990510.. CRBO30829. CRBOGO20G6).," Observations in the era often do not show a clear jet break in the X-ray when the optical light curve does show a break (e.g. GRB990510, GRB030329, GRB060206)."
 Also. the jet opening angle inferred [rom racio observations is often much larger than that [rom (earlier) X-rav or optical observations. which is again at odds with the expected. achromaticity of the break.," Also, the jet opening angle inferred from radio observations is often much larger than that from (earlier) X-ray or optical observations, which is again at odds with the expected achromaticity of the break."
 Dilferent explanations for the lack of truly achromatic breaks have been put forth in the literature., Different explanations for the lack of truly achromatic breaks have been put forth in the literature.
 Staving close to the data. first of all ? show that current observations clo not actually rule out an achromatic break between X-ray and optical and that both single and broken power law fits are often consistent with the X-ray data.," Staying close to the data, first of all \cite{Curran2008} show that current observations do not actually rule out an achromatic break between X-ray and optical and that both single and broken power law fits are often consistent with the X-ray data."
 On the theoretical side. the afterglow jet has been expanded: into a structured jet (e.g. 2)) or a superposition of multiple harcl-ccged jets with dilferent opening angle.," On the theoretical side, the afterglow jet has been expanded into a structured jet (e.g. \citealt{Rossi2002}) ) or a superposition of multiple hard-edged jets with different opening angle."
 By now superpositions of up to three jets have been used to fit the data of GIXDO30329. with the opening angle explaining the radio light curve significantly lareer than the others (2)..," By now superpositions of up to three jets have been used to fit the data of GRB030329, with the opening angle explaining the radio light curve significantly larger than the others \citep{vanderHorst2005}."
 An overview of afterglow jet structure and dynamics can be found in ?.., An overview of afterglow jet structure and dynamics can be found in \cite{Granot2007}.
 Oddly enough. the analytical argument. leading to an achromatic break has never been challenged.," Oddly enough, the analytical argument leading to an achromatic break has never been challenged."
 ba this paper we present results from. high resolution numerical jet, In this paper we present results from high resolution numerical jet
is always uonzero.,is always nonzero.
 This case is simular to that of Solution 1., This case is similar to that of Solution 1.
 Thus. this solution. as iu Solution 1. may be interpreted as representing a cosmological model.," Thus, this solution, as in Solution 1, may be interpreted as representing a cosmological model."
 We can see that this solution is equal to Solution 9. which is a solution studied by Iirschiiuim. Wang Wu 23...," We can see that this solution is equal to Solution 9, which is a solution studied by Hirschmann, Wang Wu \cite{HWW04}."
 Now. we consider the solutious of equatious (31))-(31)) for az0.," Now, we consider the solutions of equations \ref{I}) \ref{IV}) ) for $w\neq0$."
 From equation (31)) we see that for 0<w<1 the space-time is the same as that obtained by Miguolote et al. [3L)..," From equation \ref{I}) ) we see that for $0\leq\omega\leq1$ the space-time is the same as that obtained by Miguelote et al. \cite{Yasuda},"
 but for a constant scalar field which. without loss of geucralitv. can be oy=0.," but for a constant scalar field which, without loss of generality, can be $\phi_0=0$."
 From equation (021). we find that the corresponding metric can be written iu the form. Wy?," From equation \ref{II}) ), we find that the corresponding metric can be written in the form dr^2."
 The eeoumetrical radius is giveu by, The geometrical radius is given by.
 We assume that Sy>0. since AR.20.," We assume that $S_0>0$, since ${\cal R} > 0$."
 Let us now investigate the behavior of the igoiueg aud outgoiug expansious of the null gcodesics., Let us now investigate the behavior of the ingoing and outgoing expansions of the null geodesics.
 From equations (32)). (7O)) aud (713) we fiud that aud where," From equations \ref{II}) ), \ref{B2}) ) and \ref{B3}) ) we find that and where (-t)"
this suggestion (Chapman et al..,"this suggestion (Chapman et al.,"
 2003: Taylor et al in prep)., 2003; Taylor et al in prep).
" ""λογο is currently little known about cool cust in normal galaxies in the 0.5«z«1 range because it is quite dilliculy to find à clean sample of such objects.", There is currently little known about cool dust in normal galaxies in the $<$ $<$ 1 range because it is quite difficuly to find a clean sample of such objects.
 Phe SNla host galaxies (sce eg., The SN1a host galaxies (see eg.
 Sullivan ct al. (, Sullivan et al. (
2003): Fonry. et al. (,2003); Tonry et al. (
20033). though. provide an ideal selection for such studies.,"2003)), though, provide an ideal selection for such studies."
 The cliscovery of the CLB also raises the overall question of the evolution of the dust content of galaxies and its role in obscuring starlight in these objects and reprocessing i into thermal cust emission., The discovery of the CIB also raises the overall question of the evolution of the dust content of galaxies and its role in obscuring starlight in these objects and reprocessing it into thermal dust emission.
 Dust obscuration is known to have a significant ellect locally (Lresse Alackdox. 1998). but the evolution of dust. content and. obscuration is no well constrained.," Dust obscuration is known to have a significant effect locally (Tresse Maddox, 1998), but the evolution of dust content and obscuration is not well constrained."
 Chemical evolution models. (Calzetti lleckman. 1999: Pei Pall Hauser. 1999) predict tha dust. obscuration should. peak at 2-3 times the curren value at 1<2<2 before gradually declining to higher redshifts.," Chemical evolution models (Calzetti Heckman, 1999; Pei, Fall Hauser, 1999) predict that dust obscuration should peak at 2-3 times the current value at $1<z<2$ before gradually declining to higher redshifts."
 However. we currently: know little about the dus content of quiescent svstems which make up the bulk of the galaxy population at any epoch.," However, we currently know little about the dust content of quiescent systems which make up the bulk of the galaxy population at any epoch."
 The host galaxies of high z supernovae. however. have not been selected on the basis of active star formation. but have spectroscopic redshifts anc abundant ancillary data. including. for many. HST images and multicolour optical and near infrared colours.," The host galaxies of high z supernovae, however, have not been selected on the basis of active star formation, but have spectroscopic redshifts and abundant ancillary data, including, for many, HST images and multicolour optical and near infrared colours."
 They are thus an ideal sample with which to study the role of dust in quicscent galaxies at cosmological recshilts., They are thus an ideal sample with which to study the role of dust in quiescent galaxies at cosmological redshifts.
 This paper is the second to result. [rom our ongoing search for dust emission in high z SN host galaxies., This paper is the second to result from our ongoing search for dust emission in high z SN host galaxies.
 Our first paper (Farrah et al.," Our first paper (Farrah et al.,"
 2004. hereinafter Paper 1) presented the results of SCUBA submim photometry of a sample of 17 z-0.5 SNla host galaxies.," 2004, hereinafter Paper 1) presented the results of SCUBA submm photometry of a sample of 17 z=0.5 SN1a host galaxies."
 We here present additional observations of a further 14 galaxies. extending the sample size to 31. and increasing the number of directly. detected objects to three.," We here present additional observations of a further 14 galaxies, extending the sample size to 31, and increasing the number of directly detected objects to three."
 The paper is structured. as follows., The paper is structured as follows.
 1n section 2 we discuss the observations and present our results., In section 2 we discuss the observations and present our results.
 In section 32 we discuss the sample as a whole and. discuss the overall dust content of the quiescent galaxy. population at z=0.5., In section 3 we discuss the sample as a whole and discuss the overall dust content of the quiescent galaxy population at z=0.5.
 In section 4 we examine the properties of the three ealaxies individually detected in our observations. while in section 5 we discuss the implications of our results for the overall submillimetre luminosity distribution of galaxies at z=0.5.," In section 4 we examine the properties of the three galaxies individually detected in our observations, while in section 5 we discuss the implications of our results for the overall submillimetre luminosity distribution of galaxies at z=0.5."
 We draw our conclusions in section 6., We draw our conclusions in section 6.
" We assume 0,=10,03.0,0.7 and Ly=τιIAMpe1 throughout this paper."," We assume $\Omega_0 =1, \Omega_m = 0.3, \Omega_{\Lambda}=0.7$ and $H_0 = 70 kms^{-1}
Mpc^{-1}$ throughout this paper."
 The observations described here extend the earlier work of Paper Lon the host galaxies of z~0.5 type la supernova host galaxies., The observations described here extend the earlier work of Paper 1 on the host galaxies of $\sim$ 0.5 type 1a supernova host galaxies.
 As with our Paper 1 observations. our targets were selected from the HZ and the SCP supernova lists to be the rost galaxies of type la supernovae ancl to lie in a narrow (+ 0.1) range of redshilts centred on z20.5.," As with our Paper 1 observations, our targets were selected from the HZT and the SCP supernova lists to be the host galaxies of type 1a supernovae and to lie in a narrow $\pm$ 0.1) range of redshifts centred on z=0.5."
 This is to allow easy combination of submum Iluxes from the targets with no need for &-corrections to shift the fluxes to correspond to he same rest-[rame wavelength., This is to allow easy combination of submm fluxes from the targets with no need for $k$ -corrections to shift the fluxes to correspond to the same rest-frame wavelength.
 Observations were made of 14 high redshift supernova la host galaxies at z~ 0.5 between July. 2003 and January 2004 (see table 1)., Observations were made of 14 high redshift supernova 1a host galaxies at $\sim$ 0.5 between July 2003 and January 2004 (see table 1).
" Observing conditions where generally &ood. with του ranging [from 0.2 to 0.15 and τι, ranging [rom 1.3 to 0.85."," Observing conditions where generally good, with $\tau_{850}$ ranging from 0.2 to 0.15 and $\tau_{450}$ ranging from 1.3 to 0.85."
 These optical depth values were determined by standard skvclip observations at azimuths relevant to the targets and are classified as grade 1 or 2 conditions by the ΑΟΝΤ., These optical depth values were determined by standard skydip observations at azimuths relevant to the targets and are classified as grade 1 or 2 conditions by the JCMT.
 The sources were observed with SCUBA (Lollane οἱ al..," The sources were observed with SCUBA (Holland et al.,"
 1999) in photometer mocle using two bolometer chopping., 1999) in photometer mode using two bolometer chopping.
 This means that for cach channel. 850 or 450 jun. as well as being observed by the central bolometer on the array. a second bolometer observes the souree in the reference position.," This means that for each channel, 850 or 450 $\mu$ m, as well as being observed by the central bolometer on the array, a second bolometer observes the source in the reference position."
 Xn observed Lux can be extracted from both these bolometers which are then combined. using appropriate noise weighting. to increase the sensitivity over that of a normal single bolometer chopping observation by ~v2.," An observed flux can be extracted from both these bolometers which are then combined, using appropriate noise weighting, to increase the sensitivity over that of a normal single bolometer chopping observation by $\sim \sqrt 2$."
 This combination takes place at the enc of the data reduction process. once Hat fielding. background subtraction and calibration have been completecd.," This combination takes place at the end of the data reduction process, once flat fielding, background subtraction and calibration have been completed."
 The cata from SCUBA was reduced. in a standard wav using the SURE data reduction package (Jenness Lightfoot. 2000).," The data from SCUBA was reduced in a standard way using the SURF data reduction package (Jenness Lightfoot, 2000)."
 Regular pointing observations were made to ensure pointing accuracy. and skydips were also taken regularlv.," Regular pointing observations were made to ensure pointing accuracy, and skydips were also taken regularly."
 Flux calibration factors. (ECTS) for the two bolometers used to detect the sources were caleulate separatelv., Flux calibration factors (FCFs) for the two bolometers used to detect the sources were calculated separately.
 Calibration sources used. were CRLGLS anc Uranus., Calibration sources used were CRL618 and Uranus.
 The individual observations of a source with a eiven bolometer are combined using a Ixolmogorov-Smirnoll technique which masks out any discordant points tha remain after the data processing., The individual observations of a source with a given bolometer are combined using a Kolmogorov-Smirnoff technique which masks out any discordant points that remain after the data processing.
 No unusual numbers of points were excluded in this analysis., No unusual numbers of points were excluded in this analysis.
 When an object was observed on more than one dav. the Duxes measured in each separate observation are combined using à variance weiehtec scheme.," When an object was observed on more than one day, the fluxes measured in each separate observation are combined using a variance weighted scheme."
 Our results are presented in table 1., Our results are presented in table 1.
 Onlv one source. the host galaxy of SN1996cÉ. à z20.57 σα. was detected. with a Dux of 1110 mJy at 8505/42. This source was only detected? with 1.60 significance at 450742. with a Dux of 254315 m.," Only one source, the host galaxy of SN1996cf, a z=0.57 SN1a, was detected, with a flux of $\pm$ 1.6 mJy at $\mu$ m. This source was only 'detected' with $\sigma$ significance at $\mu$ m, with a flux of $\pm$ 15 mJy."
 For the host galaxy o£ SNI996cL. we obtained. Llubble Space Telescope (LIST) imaging from the LIST data archive.," For the host galaxy of SN1996cf, we obtained Hubble Space Telescope (HST) imaging from the HST data archive."
 Observations were taken using the Space Telescope Imaging Spectrograph (STIS) in imaging mode using a clear filter., Observations were taken using the Space Telescope Imaging Spectrograph (STIS) in imaging mode using a clear filter.
 The data consisted of three exposures. cach of 300 seconds. taken with a 10 pixel ollset between successive exposures to facilitate the subtraction of cosmic rav events.," The data consisted of three exposures, each of 300 seconds, taken with a 10 pixel offset between successive exposures to facilitate the subtraction of cosmic ray events."
 The data were reduced. ancl combined into a single image. using the LAL reduction. packagecastis.," The data were reduced, and combined into a single image, using the IRAF reduction package."
 Phe image of the host. galaxy. presented in Fig.," The image of the host galaxy, presented in Fig."
 1. has had the low surface brightness host enhanced by the application of a 2x2 pixel boxear filter.," 1, has had the low surface brightness host enhanced by the application of a 2x2 pixel boxcar filter."
 The evolution of dust. content. and. dust. obseuration. in normal galaxies can be examined by looking at the average properties of the sample we have observed., The evolution of dust content and dust obscuration in normal galaxies can be examined by looking at the average properties of the sample we have observed.
 We follow the approach discussed in Paper 1. but apply it to the full sample of 31 galaxies 17 from Paper 1 and 14 from the current paper.," We follow the approach discussed in Paper 1, but apply it to the full sample of 31 galaxies — 17 from Paper 1 and 14 from the current paper."
 We exclude 2 objects from this combination. the two objects whose Iluxes are strongly detected SN1996cf (this paper) anc SNI1997ev (Paper 1).," We exclude 2 objects from this combination, the two objects whose fluxes are strongly detected — SN1996cf (this paper) and SN1997ey (Paper 1)."
 The fluxes are combined using an inverse variance weighting scheme., The fluxes are combined using an inverse variance weighting scheme.
 The average observed. frame δρα Hux from tvpe la supernova host ealaxies calculated in this way is O44 + 0.22 mw., The average observed frame $\mu$ m flux from type 1a supernova host galaxies calculated in this way is 0.44 $\pm$ 0.22 mJy.
 This is less than the mean flux of 1.01250.33. mJy obtained. in, This is less than the mean flux of $\pm$ 0.33 mJy obtained in
 abbsorbed., bsorbed.
the identified. systems. (particularly the Llickson Compact Groups) and the effect. of interlopers (e.g... Alamon1986:etal.1995:Ponmanct 1996)).,"the identified systems (particularly the Hickson Compact Groups) and the effect of interlopers (e.g., \citealt{mamon1986,hickson1988b,walke1989,hernquist1995,ponman1996}) )."
 In this series of papers. we are conducting a homogeneous and systematic study of compact groups using a combination of theoretical and observational galaxy catalogues to provide a statistically-powerlul platform from which to probe the οσα of galaxy interactions on al aspects of galaxy evolution.," In this series of papers, we are conducting a homogeneous and systematic study of compact groups using a combination of theoretical and observational galaxy catalogues to provide a statistically-powerful platform from which to probe the effect of galaxy interactions on all aspects of galaxy evolution."
 In the first paper of this series MeConnachieetal.2008.. hereafter Paper D). we identifie compact groups in a mock catalogue constructed [rom the Millennium Simulation (Springelctal.2005:DeLucia&Blaizot 2007)) and developed: a robust understanding. of their spatial ancl dynamical properties.," In the first paper of this series \citealt{mcconnachie2008a}, hereafter Paper I), we identified compact groups in a mock catalogue constructed from the Millennium Simulation \citealt{springel2005,delucia2007}) ) and developed a robust understanding of their spatial and dynamical properties."
 “Phis allowed us to refine the compact group selection criteria to more efficiently identify these svstems and understand. the sources of contamination in any observed sample., This allowed us to refine the compact group selection criteria to more efficiently identify these systems and understand the sources of contamination in any observed sample.
 In the second. paper of this series (Brasseurctal.2008.. hereafter Paper LL). we compared the physical propertics of compact group galaxics in our mock catalogue to previous observational studies.," In the second paper of this series \citealt{brasseur2008}, hereafter Paper II), we compared the physical properties of compact group galaxies in our mock catalogue to previous observational studies."
 We demonstrated consistency with these earlier studies. and we concluded that interloping galaxies misidentified as compact eroup members have potentially alfected our understanding of the influence of interactions on galaxy evolution and morphology.," We demonstrated consistency with these earlier studies, and we concluded that interloping galaxies misidentified as compact group members have potentially affected our understanding of the influence of interactions on galaxy evolution and morphology."
 In this paper. the third in the series. we create the largest observational catalogue of compact group galaxies to date by. identifving all such eroups in. the Sloan Digital Sky Survey Data Release 6. consisting of more than mmillion galaxies to a limiting magnitude of r= 2].," In this paper, the third in the series, we create the largest observational catalogue of compact group galaxies to date by identifying all such groups in the Sloan Digital Sky Survey Data Release 6, consisting of more than million galaxies to a limiting magnitude of $r = 21$ ."
 We make the resulting catalogue of compact groups publicly available through online tables associated with this paper., We make the resulting catalogue of compact groups publicly available through online tables associated with this paper.
 This catalogue is ideal for Large statistical studies of compact groups. the role of environment. on ealaxy cvolution. and the ellect of galaxy interactions in determining galaxy morphology.," This catalogue is ideal for large statistical studies of compact groups, the role of environment on galaxy evolution, and the effect of galaxy interactions in determining galaxy morphology."
 Section 2 details our procedure for the identification of compact groups. Section 3 presents some of the basic observable propertics of these systems. and Section 4 summarises our results.," Section 2 details our procedure for the identification of compact groups, Section 3 presents some of the basic observable properties of these systems, and Section 4 summarises our results."
 llickson(1982) define a CG as a group of galaxies with projected. properties such that AN(GNm-—-3) is. the number of galaxies within 3mmaegnitudes of the brightest. galaxy ancl ya is. the ellective surface brightness of these galaxies. where the total Hux of the galaxies is averaged over the smallest. circle which contains their gcometric centres and has an angular diameter θα.," \cite{hickson1982} define a CG as a group of galaxies with projected properties such that $N\left(\Delta\,m = 3\right)$ is the number of galaxies within magnitudes of the brightest galaxy and $\mu_e$ is the effective surface brightness of these galaxies, where the total flux of the galaxies is averaged over the smallest circle which contains their geometric centres and has an angular diameter $\theta_G$."
 ον is the angular diameter. of the largest concentric circle. which contains no additional galaxies in this magnitude range or brighter., $\theta_N$ is the angular diameter of the largest concentric circle which contains no additional galaxies in this magnitude range or brighter.
 All magnitudes and surface brightnesses are measured in the rr band., All magnitudes and surface brightnesses are measured in the $r-$ band.
" We hereafter refer to these criteria collectively as the ""Hickson criteria’.", We hereafter refer to these criteria collectively as the `Hickson criteria'.
 Since the Lickson criteria were first introduced. there has been considerable debate regarding the physical nature of the galaxy associations identified (ο... Alamon1986:Lickson&ltood1988:WalkeAlamon1989)).. and determining the three climensional reality of systems identified as compact groups has remained a focus of theoretical ancl observational studs (e.g... Liernquistctal.1995:Ponmanctal.19963).," Since the Hickson criteria were first introduced, there has been considerable debate regarding the physical nature of the galaxy associations identified (e.g., \citealt{mamon1986,hickson1988b,walke1989}) ), and determining the three dimensional reality of systems identified as compact groups has remained a focus of theoretical and observational study (e.g., \citealt{hernquist1995,ponman1996}) )."
 To aclelress this issue. in Paper I of this series. we applied the Lickson criteria to an all-skv mock galaxy catalogue. with a limiting magnitude of r=lS. to determine the physical reality. of the systems that these criteria identify.," To address this issue, in Paper I of this series, we applied the Hickson criteria to an all-sky mock galaxy catalogue, with a limiting magnitude of $r = 18$, to determine the physical reality of the systems that these criteria identify."
" We found that the identified galaxy associations prelerentially ας a threc-dimensional linking length. /.x200htkkpe (comoving. where 100 ""Mpc 1 7)."," We found that the identified galaxy associations preferentially had a three-dimensional linking length, $l \le 200 h^{-1}$ kpc (comoving, where $H_o = 100\,h\,$ $^{-1}$ $^{-1}$ )."
" Defined⋅ in. this. way. 30. ""genuine"" compact groups. while the remaining svstenis were found to contain one or more interloping ealaxies and were treated as contamination."," Defined in this way, $\sim 30$ “genuine” compact groups, while the remaining systems were found to contain one or more interloping galaxies and were treated as contamination."
 We found that this physically well-defined sample. of genuine compact. groups. could. be identified. with greatlv reduced. levels. of contamination bv modifving the original Hickson criteria to select more isolated eroups ancl higher surface. brightness groups: by changing the latter from yn.<26.0 to yy<25.0.24.0 and 23.0 aarcsec.27. the contamination. rates decrease from TI'A toστ... and33%... respectively.," We found that this physically well-defined sample of genuine compact groups could be identified with greatly reduced levels of contamination by modifying the original Hickson criteria to select more isolated groups and higher surface brightness groups: by changing the latter from $\mu_e \leq 26.0$ to $\mu_e \leq 25.0, 24.0$ and $23.0$ $^{-2}$, the contamination rates decrease from $\sim 71$ to, and, respectively."
 This is in eeneral agreement with the search strategies adopted by some earlier surveys for compact. groups (e.g.. Ilovinoetal.2003:Leeetal. 2004)) which modified these criteria to try ο reduce contamination.," This is in general agreement with the search strategies adopted by some earlier surveys for compact groups (e.g., \citealt{iovino2003,lee2004}) ) which modified these criteria to try to reduce contamination."
 In what follows. we apply the Liekson criteria in heir original form to create our main compact group catalogues.," In what follows, we apply the Hickson criteria in their original form to create our main compact group catalogues."
 Sub-catalogues can be created. [from this xibliely-available resource. with different cuts applied in. for example. surface brightness. isolation or brightest members. depending upon the requirements of the specific project xung undertaken (e.g. statistical size of dataset: versus expected: contamination rates)," Sub-catalogues can be created from this publicly-available resource, with different cuts applied in, for example, surface brightness, isolation or brightest members, depending upon the requirements of the specific project being undertaken (e.g., statistical size of dataset versus expected contamination rates)."
 The SDSS DRG (Xdelman-MeC'arthyetal. 2008)) catalogue contains photometric parameters for unique objects (stellar and. galactic) over (7234 of the sky). of which approximately 1.27 million objects have associated: spectra.," The SDSS DR6 \citealt{adelmanmccarthy2008}) ) catalogue contains photometric parameters for unique objects (stellar and galactic) over $\sim
23$ of the sky), of which approximately 1.27 million objects have associated spectra."
 As such. SDSS DRG is presenthy the largest publically available photometric and. spectroscopic clataset of galaxies.," As such, SDSS DR6 is presently the largest publically available photometric and spectroscopic dataset of galaxies."
 Some previous searches for compact groups of galaxies have identified compact groups in spectroscopic galaxy catalogues through linking-length analyses in projection aud redshift space (following Lluchra&Geller1982: e.g. the CTA®2 redshift survey. Bartonetal.1996: the Las Campanas redshift) survey. Allan&Tucker2000: the UZC galaxy catalogue. Focardi&Ixelm2002: the SDSS DR45 and DRG. Dengetal.2007. 2008)).," Some previous searches for compact groups of galaxies have identified compact groups in spectroscopic galaxy catalogues through linking-length analyses in projection and redshift space (following \citealt{huchra1982}; e.g., the CfA2 redshift survey, \citealt{barton1996}; the Las Campanas redshift survey, \citealt{allam2000}; the UZC galaxy catalogue, \citealt{focardi2002}; the SDSS DR5 and DR6, \citealt{deng2007,deng2008}) )."
 Llowever. spectroscopic galaxy catalogues are necessarily much smaller than corresponding photometric catalogues. and one of the main motivations for this work is to obtain a statistically large sample. of compact groups for subsequent study.," However, spectroscopic galaxy catalogues are necessarily much smaller than corresponding photometric catalogues, and one of the main motivations for this work is to obtain a statistically large sample of compact groups for subsequent study."
 Further. compact eroups generally have small angular extent. (5 laarcmün)). and the SDSS sullers from fiber collisions for objects which are very close together (Straussetal. 2002)). meaning," Further, compact groups generally have small angular extent $\lesssim 1$ arcmin), and the SDSS suffers from fiber collisions for objects which are very close together \citealt{strauss2002}) ), meaning"
massive (πι> 10°~1°h~'!Mo).,massive $m \geqslant 10^{9\sim10} h^{-1}M_{\odot} $ ).
" When truncated NFW profiles are assumed, lower mass haloes would also cause a significant amount of violations."," When truncated NFW profiles are assumed, lower mass haloes would also cause a significant amount of violations."
" As can be seen from Table 4,, when the lower mass limit of line-of-sight haloes decreases from 1055! to 1095! (10h! Ms), the corresponding violation Maprobabilities, Ρως.Mc, increase by ~2% (1%)), ~6% (4%)) and (7%)) when assuming truncated singular isothermal spheres and truncated NFW profiles with the M08 and the BO1-M05 concentration-mass relations, respectively."," As can be seen from Table \ref{tab:MCPRcusp}, when the lower mass limit of line-of-sight haloes decreases from $10^8 h^{-1}M_{\odot}$ to $10^6 h^{-1}M_{\odot}$ $10^7 h^{-1}M_{\odot}$ ), the corresponding violation probabilities, $P^{90}(\Rcusp^{0.187})$, increase by $\sim$ ), $\sim$ ) and ) when assuming truncated singular isothermal spheres and truncated NFW profiles with the M08 and the B01-M05 concentration-mass relations, respectively."
" Comparing Table 4 with Table 2,, it can be seen that our Monte-Carlo results are similar to those obtained using the Millennium-II lensing cones in the mass range above 108p,—1""Mo."," Comparing Table \ref{tab:MCPRcusp} with Table \ref{tab:MSIIlosRcusp}, it can be seen that our Monte-Carlo results are similar to those obtained using the Millennium-II lensing cones in the mass range above $10^8 h^{-1}M_{\odot}$."
 This: suggests that the clustering. of haloes is. not a dominant effect in the production of flux-ratio anomalies for galactic-scale lenses., This suggests that the clustering of haloes is not a dominant effect in the production of flux-ratio anomalies for galactic-scale lenses.
breaksup intowoconstituents. as shownin Fig.l: (a) breaking into (gq) andqiwil,"probability $(1-c_1^2)(1-P_{PM})$, (b) emission of gluons converting into a quark-antiquark"
breaksup intowoconstituents. as shownin Fig.l: (a) breaking into (gq) andqiwilh,"probability $(1-c_1^2)(1-P_{PM})$, (b) emission of gluons converting into a quark-antiquark"
Déppartement Terre-Univers-Environnement. the Presidential Fellowship from the Graduate School of the Ohio State University. a Hubble Fellowship from the Space Telescope Science Institute (STScD. which is operated by the Association of Universities for Research in Astronomy (AURA). Inc.. under NASA contract NAS5-26555. the Jet Propulsion Laboratory (JPL) contract 1226901. grants AST 97-27520 and AST 95-30619 from the National Science Foundation (NSF). and grants NAGS-7589 and from the National Aeronautics and Space Administration (NASA).,"Déppartement Terre-Univers-Environnement, the Presidential Fellowship from the Graduate School of the Ohio State University, a Hubble Fellowship from the Space Telescope Science Institute (STScI), which is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under NASA contract NAS5-26555, the Jet Propulsion Laboratory (JPL) contract 1226901, grants AST 97-27520 and AST 95-30619 from the National Science Foundation (NSF), and grants NAG5-7589 and NAG5-10678 from the National Aeronautics and Space Administration (NASA)."
 This paper utilizes publie domain data obtained by the MACHO Project. Jointly funded by the US Department of Energy through the University of California. Lawrence Livermore National Laboratory under contract WW-7405-Eng-48. by the NSF through the Center for Particle Astrophysics of the University of California under cooperative agreement AST-8809616. and by the Mount Stromlo and Siding Spring Observatory. part of the Australian National University.," This paper utilizes public domain data obtained by the MACHO Project, jointly funded by the US Department of Energy through the University of California, Lawrence Livermore National Laboratory under contract W-7405-Eng-48, by the NSF through the Center for Particle Astrophysics of the University of California under cooperative agreement AST-8809616, and by the Mount Stromlo and Siding Spring Observatory, part of the Australian National University."
 noticed that the lens well approximates the binary lens system in the vicinity of each individual lens component of extreme wide-separation (¢>>1) binaries and in the vicinity of the secondary of extreme close-separation (7.«1) binaries while the quadrupole lens (QL) approximation works nicely near the center of mass of extreme close-separation binaries., noticed that the lens well approximates the binary lens system in the vicinity of each individual lens component of extreme wide-separation $d\gg 1$ ) binaries and in the vicinity of the secondary of extreme close-separation $d\ll 1$ ) binaries while the quadrupole lens (QL) approximation works nicely near the center of mass of extreme close-separation binaries.
" He further showed that the size and shape of the caustics and the behavior of the magnification field associated with them are very similar among the true binary lenses. the CRL approximation. and the QL approximation if the shear. 7. of the CRL and the absolute eigenvalue of the quadrupole moment tensor. Q (for simplicity. hereafter Q will be just referred to ""the quadrupole moment""). of the QL are both very small and their numerical values are close to each other (—Q« 1)."," He further showed that the size and shape of the caustics and the behavior of the magnification field associated with them are very similar among the true binary lenses, the CRL approximation, and the QL approximation if the shear, $\gamma$, of the CRL and the absolute eigenvalue of the quadrupole moment tensor, $\hat Q$ (for simplicity, hereafter $\hat Q$ will be just referred to “the quadrupole moment”), of the QL are both very small and their numerical values are close to each other $\gamma\simeq\hat Q\ll 1$ )."
 These findings also imply the existence of a correspondence between a wide binary with >=dquil|dy) Landa close binary with Q=d2y4.(1|4.)7. sometimes referred to as ad€»d.+correspondence. (," These findings also imply the existence of a correspondence between a wide binary with $\gamma=d_w^{-2} q_w (1+q_w)^{-1}$ and a close binary with $\hat Q=d_c^2 q_c (1+q_c)^{-2}$, sometimes referred to as a $d\leftrightarrow d^{-1}$correspondence. ("
"Here and throughout this appendix. we use the subscript ,. and ,, to distinguish the parameters associated with the close and wide binaries.)","Here and throughout this appendix, we use the subscript $_c$ and $_w$ to distinguish the parameters associated with the close and wide binaries.)"
 Here we rederive the basic result for this correspondence. and explore it more thoroughly.," Here we rederive the basic result for this correspondence, and explore it more thoroughly."
 The general form of the binary lens mapping equation can be expressed in notation utilizing complex numbers1990).. and themagnification associated with a single image can be found by. where ¢. +. 4. and :» are the positions of the source. the image. and the two lens components normalized by the Einstein radius of some mass. and ει and e» are the masses of lens components in units of the same mass.," The general form of the binary lens mapping equation can be expressed in notation utilizing complex numbers, and themagnification associated with a single image can be found by, where $\zeta$, $z$, $z_1$, and $z_2$ are the positions of the source, the image, and the two lens components normalized by the Einstein radius of some mass, and $\epsilon_1$ and $\epsilon_2$ are the masses of lens components in units of the same mass."
 For the extreme close-binary case. If one chooses the center of mass as the origin and the binary axis as the real axis and sets the combined mass to be unity. then +)—9d.e). τοdoeg 64=(11gq.) landes—q(1|4.) land the lens equation (AD)) becomes Here the monopole term (+ +) is the same as for a PSPL and the first non-PSPL term is the quadrupole (2. 7). which acts as the main perturbation to the PSPL if the quadrupole moment is small: Q=d2eqe;d2q(1|q.)?«1.," For the extreme close-binary case, if one chooses the center of mass as the origin and the binary axis as the real axis and sets the combined mass to be unity, then $z_1=d_c\epsilon_2$, $z_2=-d_c\epsilon_1$, $\epsilon_1=(1+q_c)^{-1}$, and $\epsilon_2=q_c(1+q_c)^{-1}$, and the lens equation \ref{eqn:lenseq}) ) becomes Here the monopole term $\bar z^{-1}$ ) is the same as for a PSPL and the first non-PSPL term is the quadrupole $\bar z^{-3}$ ), which acts as the main perturbation to the PSPL if the quadrupole moment is small; $\hat Q=d_c^2\epsilon_1\epsilon_2=d_c^2q_c(1+q_c)^{-2}\ll 1$."
 For a given source position c. let the image position for the PSPL be τμ.," For a given source position $\zeta$, let the image position for the PSPL be $z_0$."
" Then. under the perturbative approach. the image for the QL approximation is found at >=cy| à. where |ó;,«[|~ 1."," Then, under the perturbative approach, the image for the QL approximation is found at $z=z_0+\delta z_c$ , where $|\delta z_c|\ll|z_0|\sim 1$ ."
 Using the fact that z is the image position corresponding to ¢ for the PSPL (Le. C=iy5 1. one obtains," Using the fact that $z_0$ is the image position corresponding to $\zeta$ for the PSPL (i.e., $\zeta=z_0-\bar z_0^{-1}$ ), one obtains"
"years after the impact exposing the ice-rich The dust flux with respect to time for an impact at the equator on a period of 60 years, starting 10 years after the impact, is shown in figure 2..","years after the impact exposing the ice-rich The dust flux with respect to time for an impact at the equator on a period of 60 years, starting 10 years after the impact, is shown in figure \ref{fig2}."
 The reduction of the dust flux from orbit to orbit can be clearly seen., The reduction of the dust flux from orbit to orbit can be clearly seen.
" For impacts at higher latitudes, the dust flux is correspondingly reduced, similarly to what happens to the gas flux, and is almost null when the impact crater is supposed to be located close to the pole."," For impacts at higher latitudes, the dust flux is correspondingly reduced, similarly to what happens to the gas flux, and is almost null when the impact crater is supposed to be located close to the pole."
" The erosion level of the surface of the crater varies with the latitude of the impact and is proportional to the intensity of dust and gas emissions, as can be seen in figure 3,, showing the stratigraphy (surface radius, in meters, with respect to time in years) for a period of 50 years after the impact: it is almost null close to the poles (lower panel), where the solar input is minimum, while at the sub-solar point the available ice is consumed in less than one thousand years (almost two meters of surface lost per orbit, upper panel)."," The erosion level of the surface of the crater varies with the latitude of the impact and is proportional to the intensity of dust and gas emissions, as can be seen in figure \ref{fig3}, showing the stratigraphy (surface radius, in meters, with respect to time in years) for a period of 50 years after the impact: it is almost null close to the poles (lower panel), where the solar input is minimum, while at the sub-solar point the available ice is consumed in less than one thousand years (almost two meters of surface lost per orbit, upper panel)."
" The temperature profiles shown in figure 4 are photographing the situation at the aphelion, after almost 9 hundreds years of revolutions around the Sun."," The temperature profiles shown in figure \ref{fig4} are photographing the situation at the aphelion, after almost 9 hundreds years of revolutions around the Sun."
" At the equator only 30 meters of active material remain (panel a), while at 85 deg of latitude (panel b) not even 1 centimeter of surface has been lost."," At the equator only 30 meters of active material remain (panel a), while at 85 $\deg$ of latitude (panel b) not even 1 centimeter of surface has been lost."
" Surface and interior temperatures give an explanation for this difference: at temperatures equal or less than 145 K, as is the case at latitudes close to the pole, water ice can be considered stable against sublimation."," Surface and interior temperatures give an explanation for this difference: at temperatures equal or less than 145 K, as is the case at latitudes close to the pole, water ice can be considered stable against sublimation."
" At equator, in the 30 meters of icy material remaining after 900 years of activity, interior temperatures are much higher, always well above the sublimation limit."," At equator, in the 30 meters of icy material remaining after 900 years of activity, interior temperatures are much higher, always well above the sublimation limit."
 The first 5 meters under the surface are under the influence of the orbital heat wave., The first 5 meters under the surface are under the influence of the orbital heat wave.
" In the deeper layers the temperature slowly decreases until it reaches 155 K, 25 K higher than the temperature at the time of the impact (130 K)."," In the deeper layers the temperature slowly decreases until it reaches 155 K, 25 K higher than the temperature at the time of the impact (130 K)."
" In order to trigger some activity, it is not necessary that the impact exposes directly icy-rich layers to the action of the Sun."," In order to trigger some activity, it is not necessary that the impact exposes directly icy-rich layers to the action of the Sun."
" The result of a shallow impact in a devolatilized mantle could be excavate a crater, without directly exposing ice-rich layers, but leaving only a thinner dust layer covering regions that had remained safely buried for millions of years."," The result of a shallow impact in a devolatilized mantle could be excavate a crater, without directly exposing ice-rich layers, but leaving only a thinner dust layer covering regions that had remained safely buried for millions of years."
" In this case it could be possible not only activate the body (as a consequence of the impact itself) but also generate a stable or periodic activity, although fainter than in the situation described in the preceding section."," In this case it could be possible not only activate the body (as a consequence of the impact itself) but also generate a stable or periodic activity, although fainter than in the situation described in the preceding section."
" It is well known that ice sublimation can be possible from under a mantled surface (see, for example, Capria et al. 2001)),"," It is well known that ice sublimation can be possible from under a mantled surface (see, for example, Capria et al. \cite{capria2}) ),"
 providing that ice-rich, providing that ice-rich
"The problem becomes one of fincling the zero energy solutions of the frequency dependent ""effective potential V(ro) (Alahajan&Krishnan2006)..","The problem becomes one of finding the zero energy solutions of the frequency dependent “effective potential” $V(r,\omega)$ \citep{IFSR-1133}."
 IL the potential is positive everywhere. (he solutions are monotonic. ancl itis impossible to construct a global solution satisfvine both boundary conditions.," If the potential is positive everywhere, the solutions are monotonic, and it is impossible to construct a global solution satisfying both boundary conditions."
 It is therefore necessary that V(ro)«Qin some region in r for a global mode to be possible.," It is therefore necessary that $V(r,\omega) <0$ in some region in r for a global mode to be possible."
 There are (svo distinct wavs for (his to occur: If the equilibrium magnetic field is purely toroidal. the effective potential becomes: Vina) o (o BO? ee mento) e Qum)," There are two distinct ways for this to occur: If the equilibrium magnetic field is purely toroidal, the effective potential becomes: ) = (1 - ^2+2 r -N^2 - 2 r ) ) + Q(r)."
 Since. the equilibriumE. magnetic. field. isH perpendicularB to k. the term F—>pur. and (he only coupling to the magnetic field is through the equilibrium magnetic shear οο.," Since the equilibrium magnetic field is perpendicular to $\kk$, the term $F\to\rho \omega^2$, and the only coupling to the magnetic field is through the equilibrium magnetic shear $2 r \WB \WB'$."
 If the modified Rayleigh criterion is salis[ied. the potential is always positive for purely growing modes. and the svstem is stable (om—0 perturbations (i.e. there are no global axisvimetric MIRI modes).," If the modified Rayleigh criterion is satisfied, the potential is always positive for purely growing modes, and the system is stable to $m=0$ perturbations (i.e. there are no global axisymmetric MRI modes)."
 In the absence of rotation. (his is the Tavler “pinch” stability criterion (Tavler1973)..," In the absence of rotation, this is the Tayler “pinch” stability criterion \citep[][]{1973MNRAS.161..365T}."
 The configuration Qy=3r7 is always stabilizing., The current-free configuration $\WB = \beta r^{-2}$ is always stabilizing.
 In what follows. we examine only purely axial magnetic fields. ancl defer consideration of toroidal fields to a later paper examining non-axisvnnnetric disturbances.," In what follows, we examine only purely axial magnetic fields, and defer consideration of toroidal fields to a later paper examining non-axisymmetric disturbances."
In all the cases studied. the output. values. which we use to classify the SNe. Pec and Dj4. ave also indicative of the quality of the fit. aud the reliability of the result.,"In all the cases studied, the output values, which we use to classify the SNe, $P_{CC}$ and $P_{Ia}$, are also indicative of the quality of the fit, and the reliability of the result."
" The mean values of Pee and Pj, (rack the success rates of the SN-ABC. and can be used both to deline subsamples with lower uncertainties. aud (o estimate confidence intervals."," The mean values of $P_{CC}$ and $P_{Ia}$ track the success rates of the SN-ABC, and can be used both to define subsamples with lower uncertainties, and to estimate confidence intervals."
 Methocds such as these. ancl their [uture refinements. are a prerequisite lor pushing (hie exploration ol the SN population to fainter magnitudes and higher redshifts.," Methods such as these, and their future refinements, are a prerequisite for pushing the exploration of the SN population to fainter magnitudes and higher redshifts."
 A public release version of ihe SN-ABC is in preparation., A public release version of the SN-ABC is in preparation.
 We (hank the SNLS (eam. specifically BR. Pain and P. Nugent. for access to SNLS data and valuable comments. and 8S. Leach. E. O. Olek. and Ix. Sharon. for useful discussions.," We thank the SNLS team, specifically R. Pain and P. Nugent, for access to SNLS data and valuable comments, and S. Leach, E. O. Ofek, and K. Sharon, for useful discussions."
 A.C. acknowledges support by NASA through Hubble Fellowship grant. Z£ILLIST-HHE-01158.01-A awarded by STSel. which is operated by AURA. Inc.. for NASA. under contract NAS," A.G. acknowledges support by NASA through Hubble Fellowship grant HST-HF-01158.01-A awarded by STScI, which is operated by AURA, Inc., for NASA, under contract NAS 5-26555."
detector ou the(SIRTF).,detector on the.
 To estimate the sky backeround. we use the ΙΤ observed sky brightucss tabulated frou: DIRBE data in the range L.25jan-L2jau (Hauser et al.," To estimate the sky background, we use the minimum observed sky brightness tabulated from DIRBE data in the range $1.25\mu$ $12\mu$ m (Hauser et al."
 1995. Table 2).," 1998, Table 2)."
 We fined that this backerouud coutributes ~20050% of the noise iu the 1-5.5 yan range. while it is less important x51054) compared to the increased detector noise at A25.541. The sky background is dominated by the zodiacal liebt. and might be substantially reduced for NOST compared to DIRBE. depending on ANGST s orbit.," We find that this background contributes $\sim 20-50\%$ of the noise in the 1-5.5 $\mu$ m range, while it is less important $\lsim 10\%$ ) compared to the increased detector noise at $\lambda>5.5\mu$ m. The sky background is dominated by the zodiacal light, and might be substantially reduced for ${\it NGST}$ compared to DIRBE, depending on ${\it NGST}$ 's orbit."
 The increase of the detector noise bevoud A>5.51u affects he relative detectability of the ΠΤΙ aud Πα lunes., The increase of the detector noise beyond $\lambda>5.5\mu$ m affects the relative detectability of the HeII and $\alpha$ lines.
 For a source at redshift 7;<32.16.11. the Te A16LO. À3203. A1686 lines lic iu the favorable 1-5.5 pau rauge: by contrast. the Ta line redshifts to A>5.5 au for z>r.," For a source at redshift $z_{\rm s,i} < 32, 16, 11$ , the He $\lambda 1640$, $\lambda 3203$, $\lambda 4686$ lines lie in the favorable 1-5.5 $\mu$ m range; by contrast, the $\alpha$ line redshifts to $\lambda > 5.5 \, \mu$ m for $z_{\rm s} > 7$."
" Thus. in the redshift range 7<22.4 the relative signal to noise is (S/N)g/{ςμι,& 0.(09/0.05)(65/1.2)."," Thus, in the redshift range $7 < z < z_{\rm s,i}$ the relative signal to noise is ${\rm (S/N)_{He,i}/(S/N)_{H\alpha}} \approx 0.5 (Q/0.05) (q_{\rm i}/1.2)$ ."
 As an cxaple. for aietalfree stellar population with a Salpeter IAIF. the deection of the brightest line. [ell ALG LO. would require a ninteeration time z 1 times longer than that required for Ta: a quasar with a=1 would an iuteeratiou thue ~6 iues shorter for ΠΟ A1610 than for Πα.," As an example, for ametal–free stellar population with a Salpeter IMF, the detection of the brightest line, HeII $\lambda 1640$ would require an integration time $\approx$ 4 times longer than that required for $\alpha$; a quasar with $\alpha=1$ would an integration time $\sim 6$ times shorter for HeII $\lambda 1640$ than for $\alpha$."
 More generally. for redshifts below το. a day's integration for a Tell ine vields where the left fleure sin square brackets are to be used for metalfree stars and the right figures are to be used for niniquasars.," More generally, for redshifts below $z_{\rm s,i}$, a day's integration for a HeII line yields where the left figures in square brackets are to be used for metal–free stars and the right figures are to be used for mini–quasars."
" Απο hat faa;LOW of the eas is processed into stars ud fon~0.3% collapses to the central DII (see the models for lieh+vedshift starbursts and miniquasars by Uaiman Loch 1997. 1998). the requirement of S/N=10 corresponds to dark halos with total mass Mya,~109AM. a >=9(note that Fa.fou should be regarded as adjustable parameters uncertain to within an order of magnitude}."," Assuming that $f_{{\rm
star}} \sim 10\%$ of the gas is processed into stars, and $f_{{\rm BH}} \sim
0.3\%$ collapses to the central BH (see the models for high-redshift starbursts and mini–quasars by Haiman Loeb 1997, 1998), the requirement of S/N=10 corresponds to dark halos with total mass $M_{\rm halo} \sim 10^{9} \, {\rm
M_{\odot}}$ at $z=9$(note that $f_{{\rm star}},f_{{\rm BH}}$ should be regarded as adjustable parameters uncertain to within an order of magnitude)."
 We assuue that eas in sources cools aud «κlapses to form discs with aneular scale rane9 Arg. wheπο A~0.05 is the spin parameter: thus. most photons ar'6 converted to recombination line photons iu the dense cores of halos.," We assume that gas in sources cools and collapses to form discs with angular scale $r_{\rm disc} \sim \lambda r_{\rm vir}$ , where $\lambda \sim
0.05$ is the spin parameter; thus, most photons are converted to recombination line photons in the dense cores of halos."
 Du this case most sources real spatially uuresolved. aud subteud a solid auele Ozzmax|1.(A3.50? LOL arcsec?.," In this case most sources remain spatially unresolved, and subtend a solid angle $\Omega \approx {\rm max}[1,
(\lambda/3.5 \mu{\rm m})^{2}]$ 0.01 ${\rm arcsec}^{2}$."
 From the observed recombination line fluxes. one cau deteriuue the relative uuuber of IIT and ΠΟ ionizing plotous: Quis=(l/yΠΕia).," From the observed recombination line fluxes, one can determine the relative number of HI and HeII ionizing photons: $Q_{\rm obs} = (1/q_{\rm i}) (J_{\rm
HeII,i}/J_{\rm H\alpha})$."
" There is. however, an upper liit o the observable ratio of Well and Πα line streneths."," There is, however, an upper limit to the observable ratio of HeII and $\alpha$ line strengths."
 Ioniziug photon ratios iu excess of NIElon/ETNTLs1 do not further iucrease the observed line. ratios. because zzhow ofthe opacity at E=51. leV is contributed by III rather than Well. iuhiliting the erowth of a Well reeiou further than the exteut of the WIT region.," Ionizing photon ratios in excess of $\dot{N}_{\rm ion}^{\rm HeII}/\dot{N}_{\rm ion}^{\rm HI} \sim 1$ do not further increase the observed line ratios, because $\approx 50\%$ of the opacity at $E=54.4$ eV is contributed by HI rather than HeII, inhibiting the growth of a HeIII region further than the extent of the HII region."
" In practice. this limit can be approached only by uuusuallv hid. sources with a spectral iudex such that £,z const (azz 0)."," In practice, this limit can be approached only by unusually hard sources with a spectral index such that $F_\nu\approx$ const $\alpha\approx 0$ )."
 The relative iuteusities are also proportional to the relative escape fractions: Qui.κπωήνx{4FEYALCC PED: (bus. unequal escape fractious would lead to incorrect interred (Q.," The relative intensities are also proportional to the relative escape fractions: $Q_{\rm obs} \propto J_{\rm HeII, i}/J_{\rm H\alpha} \propto (1-
f_{\rm esc}^{\rm HeII})/(1-f_{\rm esc}^{\rm HI})$ ; thus, unequal escape fractions would lead to incorrect inferred $Q$."
 However. as lone as the escape fraction for both III and Well ionizing photous is small. οςA05. this is a small effect.," However, as long as the escape fraction for both HI and HeII ionizing photons is small, $f_{\rm esc} < 10 \%$, this is a small effect."
" Furthermore. while the inferred values of XUNi.ΑΤΠΟΗNios from Jip,πω are subject to uncertainties about the clectrou teniperature aud dust scattering. their ratio is much LOLC robust."," Furthermore, while the inferred values of $\dot{N}^{HI}_{\rm ion}, \dot{N}_{\rm ion}^{\rm HeII}$ from $J_{\rm H\alpha},
J_{\rm HeII, i}$ are subject to uncertainties about the electron temperature and dust scattering, their ratio is much more robust."
" Iu particular. the inferred value of Q has only a T""35 dependence ou the electron temperature and is lareclyOo msenusitive to ↕∐↑↸∖↥⋅↴∖↴↑↸∖∐⋜∐⋅↥⋅↸∖≺∐∐∖∐↕∐∶↴∙⊾⋖≼∶⋜∐⋅∐↸∖↑↑↸"," In particular, the inferred value of Q has only a $T^{-0.15}$ dependence on the electron temperature and is largely insensitive to interstellar reddening (Garnett et al 1991)."
∖↑⋜↕↕↕∩∩⊔∙ It is interesting to ask how many sources are expected to e bright cnough for detection in Mell ciissiou byVG‘ST., It is interesting to ask how many sources are expected to be bright enough for detection in HeII emission by.
 Based on equation 3.. the máiuinaiun halo mass associated with a detectable source is at least ~109AD...," Based on equation \ref{eq:SN}, the minimum halo mass associated with a detectable source is at least $\sim
10^9~{\rm M_\odot}$."
" The eas in jose lados have virial temperatures Zu,>LOK. allowing ficient atomic line cooling aud subsequent star or BIT orlmation."," The gas in these halos have virial temperatures $T_{\rm
vir} > 10^{4}$ K, allowing efficient atomic line cooling and subsequent star or BH formation."
 We now imake further simple assunuptious about the efficiency of star aud. DIT formation to compute 1c expected number counts based on the abundance of dark halos.," We now make further simple assumptions about the efficiency of star and BH formation to compute the expected number counts, based on the abundance of dark halos."
 The mass function of halos has receutlv jen determined accurately (to within ~20%) in large weedimensional simulations (Jeukius et al., The mass function of halos has recently been determined accurately (to within $\sim20\%$ ) in large three–dimensional simulations (Jenkins et al.
 2000). aud we adopt their fitting formula (them eq.," 2000), and we adopt their fitting formula (their eq."
 9)., 9).
 The halo uasses relevant here are factor of a few above the “kuec™ of the mass function. where the abundance of halos is slightly larger than in the standard Press-Schechter (197L) hneorv.," The halo masses relevant here are factor of a few above the “knee” of the mass function, where the abundance of halos is slightly larger than in the standard Press-Schechter (1974) theory."
 We also adopt a fat cold dark matter (CDA cosinoloey with a cosmological coustaut. ic. ACDM with (QuOn.Onimain)=(LT0:3:000007.1).," We also adopt a flat cold dark matter (CDM) cosmology with a cosmological constant, i.e. $\Lambda$ CDM with $(\Omega_\Lambda,\Omega_{\rm m}, \Omega_{\rm b},h,\sigma_{\rm
8h^{-1}},n)=(0.7,0.3,0.04,0.7,1,1)$."
 The estimate of the number of detectable1. metalfree starbursts is difficult. since the leugth of the epoch of completely iuetalfree star formation is not sown.," The estimate of the number of detectable metal–free starbursts is difficult, since the length of the epoch of completely metal–free star formation is not known."
 Even trace curichinent of star forming regions to low jietallicities Z~10? results in stars with significantly softer spectra ClPuiulinson Shull 2000). with a production rate of ΠΟ ioniziug photons lowerby 5 orders of maguitude. from which Tel recombination radiatiou would be mnobscrvable.," Even trace enrichment of star forming regions to low metallicities $Z
\sim 10^{-3}$ results in stars with significantly softer spectra (Tumlinson Shull 2000), with a production rate of HeII ionizing photons lowerby 5 orders of magnitude, from which HeII recombination radiation would be unobservable."
 It is possible hat such trace enrichment could take place very quickly. on timescales of order the lifetime of the first generation of stars.," It is possible that such trace enrichment could take place very quickly, on timescales of order the lifetime of the first generation of stars."
 To circiunvent this uncertainty. we sinplv asstuue that some fixed fraction f. of the barvouic mass of every halowith Των> 1011 undergoes a metalfree starburst.," To circumvent this uncertainty, we simply assume that some fixed fraction $f_{*}$ of the baryonic mass of every halowith $T_{\rm vir} > 10^{4}$ K undergoes a metal--free starburst."
 Of course. in reality f.(Ayal.2) is likely a function of both halo mass aud redshift. aud iu particular declines with redshift as stars pollute the ICAL with metals.," Of course, in reality $f_{*}(M_{\rm halo},z)$ is likely a function of both halo mass and redshift, and in particular declines with redshift as stars pollute the IGM with metals."
 Our ansatz is therefore valid ouly at Ligh redshift :tpollure before metal pollution becomes widespread: at lower redshifts the counts are overestimates., Our ansatz is therefore valid only at high redshift $z > z_{\rm pollute}$ before metal pollution becomes widespread; at lower redshifts the counts are overestimates.
 For detection with NOST. to be feasible zi; must be low. either because metal mining is ineficient or widespread star formation only takes place at low redshift.," For detection with NGST to be feasible $z_{\rm pollute}$ must be low, either because metal mixing is inefficient or widespread star formation only takes place at low redshift."
 We define the efficiency parameter e=(f./0.10)(Q/0.05). and in Figure lL we show the uuuber of detectable objects in the three Hell Hines. as a fuuctiou of redshift. for twodifferent values of €=1 and 0.1.," We define the efficiency parameter $\epsilon=(f_{*}/0.10) (Q/0.05)$, and in Figure \ref{fig:stars} we show the number of detectable objects in the three HeII lines, as a function of redshift, for twodifferent values of $\epsilon=1$ and $0.1$."
 We requie S/N=10.aud adopt the field of view of Ls of NCST.," We require S/N=10,and adopt the field of view of $4^\prime \times 4^\prime$ of ."
 Thecurves are obtained by computing the toal abundance of halos brighter than the S/N threshold. aud uniltiplvine by the duty.cvele f. /fg6z). where μετ) as the age of the universe at redshift 2. aud f.=10° or f=10° vears is the," Thecurves are obtained by computing the total abundance of halos brighter than the S/N threshold, and multiplying by the duty–cycle $t_{*}/t_H(z)$ , where $t_H(z)$ is the age of the universe at redshift $z$ , and $t_*=10^{7}$ or $t_*=10^{6}$ years is the"
Some stars in our sample were not visible in the epochs of our observing runs.,Some stars in our sample were not visible in the epochs of our observing runs.
" For these stars, and for the ones with no Balmer lines in their spectrum, we used the available IR photometry to obtain their photometric Τεῃ."," For these stars, and for the ones with no Balmer lines in their spectrum, we used the available IR photometry to obtain their photometric $T_{\rm eff}$."
" The V magnitudes were obtained from the catalogues used to build the sample and from the SIMBAD database, photometry was collected from the 2MASS All Sky Catalog whenavailable."," The $V$ magnitudes were obtained from the catalogues used to build the sample and from the SIMBAD database, photometry was collected from the 2MASS All Sky Catalog whenavailable."
 For V magnitude we assumed an uncertainty of 0.02 mag as errors are seldom available., For $V$ magnitude we assumed an uncertainty of 0.02 mag as errors are seldom available.
 The Τεῃ for each object was obtained by adapting the method of to WDs., The $T_{\rm eff}$ for each object was obtained by adapting the method of to WDs.
 This procedure consists in calculating synthetic photometry using the WD atmospheres of?., This procedure consists in calculating synthetic photometry using the WD atmospheres of.
" Subsequently, we developed a fitting algorithm to compare the observational and theorical values and minimise the y? using the Levenberg-Marquardt method, and x? was defined from the differences between the observed and synthetic V/HK magnitudes."," Subsequently, we developed a fitting algorithm to compare the observational and theorical values and minimise the $\chi^{2}$ using the Levenberg-Marquardt method, and $\chi^{2}$ was defined from the differences between the observed and synthetic $VJHK$ magnitudes."
 The uncertainties in the calculated photometric temperatures were derived from the covariance matrix., The uncertainties in the calculated photometric temperatures were derived from the covariance matrix.
 The VJHK magnitudes and photometric Τεῃ for the sample stars are provided in Table 5.., The $VJHK$ magnitudes and photometric $T_{\rm eff}$ for the sample stars are provided in Table \ref{VJHK_Teff}.
" In the cases where bothspectroscopic data and V and 2MASS photometry were available, the photometric Τεῃ was used to evaluate the reliability of the resulting Τεῃ obtained by the line profile analysis."," In the cases where bothspectroscopic data and $V$ and 2MASS photometry were available, the photometric $T_{\rm eff}$ was used to evaluate the reliability of the resulting $T_{\rm eff}$ obtained by the line profile analysis."
" In most of the cases, both Τομ were in good agreement, as shown in Fig. 5.."," In most of the cases, both $T_{\rm eff}$ were in good agreement, as shown in Fig. \ref{tsptph}."
 NLTT26379 is the object showing the largest deviation., NLTT26379 is the object showing the largest deviation.
" For our subsequent analysis, we consider the Teg value obtained from spectroscopy, since it should be more reliable."," For our subsequent analysis, we consider the $T_{\rm eff}$ value obtained from spectroscopy, since it should be more reliable."
" It is worth noting that the spectroscopic analysis of WDs with Teg « 12000K should be done with special care, since their atmospheres could be enriched in helium while retaining their DA spectral type(?)."," It is worth noting that the spectroscopic analysis of WDs with $T_{\rm eff}$ $<$ 12000K should be done with special care, since their atmospheres could be enriched in helium while retaining their DA spectral type."
". In this case, photometric Teg provide the needed cross-check to ensure that the overall atmospheric parameters are consistent and accurate."," In this case, photometric $T_{\rm eff}$ provide the needed cross-check to ensure that the overall atmospheric parameters are consistent and accurate."
 It is reassuring to confirm that our photometric and spectroscopic Teg values are in good concordance for the cooler targets of our sample., It is reassuring to confirm that our photometric and spectroscopic $T_{\rm eff}$ values are in good concordance for the cooler targets of our sample.
" Together with Τομ, our procedure requires a value for log g."," Together with $T_{\rm eff}$ , our procedure requires a value for $\log g$ ."
 Given the absence of any other possibility for the objects with, Given the absence of any other possibility for the objects with
The evolution of massive galaxies around z 2. when the cosmic star-formation rate density was at its peak. is currently the subject of intense study.,"The evolution of massive galaxies around $\sim$ 2, when the cosmic star-formation rate density was at its peak, is currently the subject of intense study."
 A key parameter 1n constraining their nature and stellar-mass buildup is the instantaneous star-formation rate (SFR)., A key parameter in constraining their nature and stellar-mass buildup is the instantaneous star-formation rate (SFR).
 While there are various methods for estimating SERs (see?.forareview).. itis notoriously difficult to constrain SERs of z-2 galaxiesfew.," While there are various methods for estimating SFRs \citep[see ][ for a review]{Kennicutt98}, it is notoriously difficult to constrain SFRs of $\sim$ 2 galaxies."
 One of the reasons is that calibrations between observed luminosities (rest-frame UV. mid-IR. and submm being the most accessible and widely used) and bolometric SFRs are based on local galaxies and their validity at high z has not yet been firmly established.," One of the reasons is that calibrations between observed luminosities (rest-frame UV, mid-IR, and submm being the most accessible and widely used) and bolometric SFRs are based on local galaxies and their validity at high z has not yet been firmly established."
 Both UV (BX/BM) and optical/near-IR. (BzK) selected samples of star-forming galaxies at z-2 have been successful in producing large samples for galaxy evolution studies (2222) ," Both UV (BX/BM) and optical/near-IR (BzK) selected samples of star-forming galaxies at $\sim$ 2 have been successful in producing large samples for galaxy evolution studies \citep{Reddy05, Perez-Gonzalez05, Daddi07a, Santini09}."
However. UV-based SFRs are very sensitive to dust obscuration and there are uncertainties about the applicable reddening laws and dust/source geometry at high z (e.g...2)..," However, UV-based SFRs are very sensitive to dust obscuration and there are uncertainties about the applicable reddening laws and dust/source geometry at high z \citep[e.g., ][]{Reddy10}."
 Estimates from the 24 gam luminosities rely on template-based extrapolations to the total IR luminosity that are poorly constrained at high z and may be affected by an AGN., Estimates from the 24 $\mu$ m luminosities rely on template-based extrapolations to the total IR luminosity that are poorly constrained at high z and may be affected by an AGN.
 Likewise. submm luminosities rely on assumptions about IR SEDs. which depend on poorly known dust temperatures. composition. and spatial distribution.," Likewise, submm luminosities rely on assumptions about IR SEDs, which depend on poorly known dust temperatures, composition, and spatial distribution."
 Cosmological simulations predict a tight correlation between stellar mass and SFR with a slope similar to that observed (e.g..?).. but with SPRsthat are a factor ~4 lower than those inferred for z-2 massive galaxies from a combination of UV and 24 pm luminosities (22?)..," Cosmological simulations predict a tight correlation between stellar mass and SFR with a slope similar to that observed \citep[e.g.,][]{Finlator06}, but with SFRsthat are a factor $\sim$ 4 lower than those inferred for $\sim$ 2 massive galaxies from a combination of UV and 24 $\mu$ m luminosities \citep{Daddi07a, Wilkins08, Damen09}."
 Suggestions on how to resolve this discrepancy iclude changes to the adopted initial mass functions and star formation efficiency (?).. but these cannot be properly tested given the uncertainties associated with the common SER ndicators themselves.," Suggestions on how to resolve this discrepancy include changes to the adopted initial mass functions \citep[IMF, ][]{Dave08} and star formation efficiency \citep{Khochfar09}, but these cannot be properly tested given the uncertainties associated with the common SFR indicators themselves."
 The photo-detector arraycamera and spectrometer (PACS.?) onboard the space observatory (?) offers a new opportunity to infer the SER of z~2 galaxies from their far infrared (FIR) emission.," The photo-detector arraycamera and spectrometer \citep[PACS, ][]{Poglitsch10} onboard the space observatory \citep{Pilbratt10} offers a new opportunity to infer the SFR of $\sim$ 2 galaxies from their far infrared (FIR) emission."
 PACS observes at 160 jim (45-65 jim rest frame for the sample used here). close to the peak of the emission from dust heated by young stars. away from AGN-heated dust emission and with unprecedented spatial resolution that reduces confusion noise.," PACS observes at 160 $\mu$ m (45–65 $\mu$ m rest frame for the sample used here), close to the peak of the emission from dust heated by young stars, away from AGN-heated dust emission and with unprecedented spatial resolution that reduces confusion noise."
 It allows the most reliable and least biased SFR measurements to date. which avoid large SED extrapolation errors and avoid the uncertainties of attenuation corrections.," It allows the most reliable and least biased SFR measurements to date, which avoid large SED extrapolation errors and avoid the uncertainties of attenuation corrections."
 In this letter. we report on the first measurements of FIR-based calorimetric SERs of optically selected galaxies at 1.5<z<2.5 and compare them to results from previous UV and 24 um measurements.," In this letter, we report on the first measurements of FIR-based calorimetric SFRs of optically selected galaxies at $<$ $<$ 2.5 and compare them to results from previous UV and 24 $\mu$ m measurements."
" We adopt a Q,,= 0.3. O4= 0.7. and Hp=70 km s! Mpc! cosmology throughout this letter."," We adopt a $\Omega_m = 0.3$ , $\Omega_\Lambda = 0.7$ , and $H_0 = 70$ km $^{-1}$ $^{-1}$ cosmology throughout this letter."
 The PACS data consists entirely of PACS evolutionary probe (PEP) guaranteed-time observations in the GOODS-N field.," The PACS data consists entirely of PACS evolutionary probe (PEP) guaranteed-time observations in the GOODS-N field,"
"intensity S.,,, and that the cloud distribution obeys Poisson statistics.","intensity $S_{\rm c,\lambda}$, and that the cloud distribution obeys Poisson statistics."
" In this case, the escape probability of the emitted radiation can be approximated as Pa.c e""T, with Np the total number of clouds along the line of sight, and the intensity at a given location becomes: where Nc is the radial cloud density (i.e., the number of clouds per unit length)."," In this case, the escape probability of the emitted radiation can be approximated as $P_{\rm esc} \simeq e^{-N_{\rm T}}$ , with $N_{\rm T}$ the total number of clouds along the line of sight, and the intensity at a given location becomes: where $N_{\rm C}$ is the radial cloud density (i.e., the number of clouds per unit length)."
 With this formalism the only difference between the clumpy and continuous cases is that optical depth ty is replaced by its effective equivalent NqT(1l—e7v)~Nr (for tv>>1) and the absorption coefficient is replaced by Nc.," With this formalism the only difference between the clumpy and continuous cases is that optical depth $\tau_{\rm V}$ is replaced by its effective equivalent $N_{\rm
 T}(1-e^{-\tau_{\rm V}}) \simeq N_{\rm T}$ (for $\tau_{\rm V}$$\gg$ 1) and the absorption coefficient is replaced by $N_{\rm C}$."
" The main challenge lies with the calculation of the clump source function, S.3, that needs to properly take into account the illumination profile of the individual clouds and the effects of cloud shadowing."," The main challenge lies with the calculation of the clump source function, $S_{\rm c,\lambda}$, that needs to properly take into account the illumination profile of the individual clouds and the effects of cloud shadowing."
" In this section we wish to test the CLUMPY models, in particular how well they approximate the entire infrared SED, how unique a fitting set of parameters is and what physics can be extracted."," In this section we wish to test the CLUMPY models, in particular how well they approximate the entire infrared SED, how unique a fitting set of parameters is and what physics can be extracted."
" For simplicity, we will limit ourselves to models invoking a torus geometry with a Gaussian angular cloud distribution, ie., we will not consider a spherical distribution or the sharp-edge geometry."," For simplicity, we will limit ourselves to models invoking a torus geometry with a Gaussian angular cloud distribution, i.e., we will not consider a spherical distribution or the sharp-edge geometry."
" The CLUMPY torus models are available for two different dust compositions and have six parameters that can be adjusted: the optical depth of the cloud, rv, the average number of clouds along an equatorial line of sight, No, the power-law index of the radial cloud distribution, q, the angular width of the Gaussian cloud distribution, σ, the ratio between the outer and inner torus radius, Y, and the viewing angle, 0."," The CLUMPY torus models are available for two different dust compositions and have six parameters that can be adjusted: the optical depth of the cloud, $\tau_{\rm V}$, the average number of clouds along an equatorial line of sight, $N_0$, the power-law index of the radial cloud distribution, $q$, the angular width of the Gaussian cloud distribution, $\sigma$, the ratio between the outer and inner torus radius, $Y$, and the viewing angle, $\theta$."
" The dust composition is assumed to be a mix of silicates and graphite with silicates either as in the standard interstellar medium (?,codeISM-D) or with various materials added (?,codeOHM)..", The dust composition is assumed to be a mix of silicates and graphite with silicates either as in the standard interstellar medium \citep[][code ISM-D]{Draine03} or with various materials added \citep[][code OHM]{OHM92}.
" In general, the problem that one faces when choosing a CLUMPY model that best-fits the data is that its parameters are highly degenerate, with several permutations yielding very similar results (???).."," In general, the problem that one faces when choosing a CLUMPY model that best-fits the data is that its parameters are highly degenerate, with several permutations yielding very similar results \citep{BayesClumpy09a, BayesClumpy09b, Nik09}."
" In the following, we introduce an effective method to select a suitable model (by eye) and find that the high degeneracy is due to the fact that, with the exception of the dust composition, all parameters constrain only the radial mass density profile (and so the radial temperature profile)."," In the following, we introduce an effective method to select a suitable model (by eye) and find that the high degeneracy is due to the fact that, with the exception of the dust composition, all parameters constrain only the radial mass density profile (and so the radial temperature profile)."
" This then means that, although CLUMPY cannot uniquely determine the AGN torus structure, it is a versatile tool with possible application to other astrophysical objects."," This then means that, although CLUMPY cannot uniquely determine the AGN torus structure, it is a versatile tool with possible application to other astrophysical objects."
" As a first step, we find that our observations can constrain the dust composition."," As a first step, we find that our observations can constrain the dust composition."
 As Fig., As Fig.
" 8 shows, ISM-D models approximate well both the shape of the 10 um silicate emission feature and the spectral slope blueward of it, however, only if a redshift is applied (top panels)."," \ref{clumpydust} shows, ISM-D models approximate well both the shape of the 10 $\mu$ m silicate emission feature and the spectral slope blueward of it, however, only if a redshift is applied (top panels)."
" On the other hand, OHM models predict a narrower silicate feature than is observed and do not match well the blueward spectral flux, independent of whether we apply a redshift or not (bottom panels)."," On the other hand, OHM models predict a narrower silicate feature than is observed and do not match well the blueward spectral flux, independent of whether we apply a redshift or not (bottom panels)."
 We have then used in the following only ISM-D models., We have then used in the following only ISM-D models.
" In this respect, we note that our result differs from, but does not contradict, that of ?.."," In this respect, we note that our result differs from, but does not contradict, that of \citet{Sir08}."
 These authors constrain the dust composition of ultraluminous infrared galaxies based on the strengths of both the 10 zm and 18 jum silicate features to be that of the OHM models., These authors constrain the dust composition of ultraluminous infrared galaxies based on the strengths of both the 10 $\mu$ m and 18 $\mu$ m silicate features to be that of the OHM models.
" However, a careful inspection of their Figs."," However, a careful inspection of their Figs."
" 7-9 shows that their method cannot constrain the dust composition in type-1 AGN, such as our sources."," 7-9 shows that their method cannot constrain the dust composition in type-1 AGN, such as our sources."
" Next, we find that the most convenient and reliable way to constrain the five geometrical CLUMPY parameters is to use the height of the 10 um silicate emission peak relative to the ’dip’ blueward of it."," Next, we find that the most convenient and reliable way to constrain the five geometrical CLUMPY parameters is to use the height of the 10 $\mu$ m silicate emission peak relative to the 'dip' blueward of it."
" Then, this flux ratio is larger, the smaller No, q, σ and 0, and the larger Y are."," Then, this flux ratio is larger, the smaller $N_0$, $q$, $\sigma$ and $\theta$, and the larger $Y$ are."
" The most pronounced differences are produced by changing No, q, and o (Fig. 9)),"," The most pronounced differences are produced by changing $N_0$, $q$, and $\sigma$ (Fig. \ref{clumpydens}) ),"
" and the strongest degeneracy seems to be present between No and ϐ (i.e., we obtain a similar result, if we either increase No and decrease 0 or vice versa)."," and the strongest degeneracy seems to be present between $N_0$ and $\theta$ (i.e., we obtain a similar result, if we either increase $N_0$ and decrease $\theta$ or vice versa)."
 Since all these parameters effectively determine the cloud number density (see eq. (, Since all these parameters effectively determine the cloud number density (see eq. (
"2) of ?)), and the aforementioned degeneracy serves to keep it constant, this then means that our flux ratio is larger, the smaller Nc.","2) of \citet{Nen08b}) ), and the aforementioned degeneracy serves to keep it constant, this then means that our flux ratio is larger, the smaller $N_{\rm C}$."
" Once Nc is fixed, the selection of ry is straightforward, since models with small values predict much stronger 10 wm silicate emission and much less radiation at far-IR wavelengths than models with large values (seeFig.5of?).."," Once $N_{\rm C}$ is fixed, the selection of $\tau_{\rm V}$ is straightforward, since models with small values predict much stronger 10 $\mu$ m silicate emission and much less radiation at far-IR wavelengths than models with large values \citep[see Fig. 5 of][]{Nen08b}."
" Applying the CLUMPY models to the infrared SEDs of our sources, we find in allcases that they can approximate well the mid-IR part, but significantly underpredict the flux at both near-IR and far-IR wavelengths."," Applying the CLUMPY models to the infrared SEDs of our sources, we find in allcases that they can approximate well the mid-IR part, but significantly underpredict the flux at both near-IR and far-IR wavelengths."
" Furthermore, it is always necessary to apply a redshift to the models."," Furthermore, it is always necessary to apply a redshift to the models."
 We show the models (including the predicted AGN contribution) in, We show the models (including the predicted AGN contribution) in
have been scaled by a factor of 100/220 compared to the velocities contoured in the synthetic data plots.,have been scaled by a factor of 100/220 compared to the velocities contoured in the synthetic data plots.
 For both the synthetic data and the observed data the contour interval is 16 per cent of the rotation velocity., For both the synthetic data and the observed data the contour interval is 16 per cent of the rotation velocity.
" We again get a good qualitative comparison between the synthetic and real observations, taking into account that we do not model the inner 5 kpc of the galaxy."," We again get a good qualitative comparison between the synthetic and real observations, taking into account that we do not model the inner 5 kpc of the galaxy."
 The general behaviour of the contours is as expected i.e. the main disc of the galaxy is traced out as velocity increases and there are perturbations in the velocity contours due to non-circular velocities., The general behaviour of the contours is as expected i.e. the main disc of the galaxy is traced out as velocity increases and there are perturbations in the velocity contours due to non-circular velocities.
 Figure 7(b) clearly shows perturbations in the contours associated with the spiral arms whereas lower resolution data (Fig. 7(c))), Figure \ref{fig:synth_blur1_M33} clearly shows perturbations in the contours associated with the spiral arms whereas lower resolution data (Fig. \ref{fig:synth_blur6_M33}) )
 show much less detail but exhibit a broadening of the contours in the region of the spiral arms., show much less detail but exhibit a broadening of the contours in the region of the spiral arms.
 Our simulated galaxy is a grand design spiral which shows non-circular motions due to the presence of spiral shocks., Our simulated galaxy is a grand design spiral which shows non-circular motions due to the presence of spiral shocks.
heavy scattering due to interstellar plasma turbulence in the direction of the Cygnus OBI association.,heavy scattering due to interstellar plasma turbulence in the direction of the Cygnus OB1 association.
 This mechanism would produce extrinsic variability in the radio band but not in gamma-rays., This mechanism would produce extrinsic variability in the radio band but not in gamma-rays.
" Disentangling intrinsic and extrinsic variability in the radio light curves is a difficult problem, but a particular feature on the light curve of B2023+336 around MJD 54930 strongly suggests the possibility of an extreme scattering event "," Disentangling intrinsic and extrinsic variability in the radio light curves is a difficult problem, but a particular feature on the light curve of B2023+336 around MJD 54930 strongly suggests the possibility of an extreme scattering event ."
"Although extreme scattering events have (Fiedleronly been 1987)..detected at lower radio frequencies, the location of the source at low Galactic latitude and the characteristic symmetric flux decrease expected when an interstellar plasma lens moves through the line of sight, with the small flux increases at both ends of the event being caused by focusing of radio waves at the edges of the plasma cloud, strongly support this hypothesis 1998)."," Although extreme scattering events have only been detected at lower radio frequencies, the location of the source at low Galactic latitude and the characteristic symmetric flux decrease expected when an interstellar plasma lens moves through the line of sight, with the small flux increases at both ends of the event being caused by focusing of radio waves at the edges of the plasma cloud, strongly support this hypothesis ."
". To explore the effect of excluding the candidate extreme scattering event from the radio light curve of B20234-336, we use the same parameters as for the original analysis but exclude the radio data from MJD 54900 through MJD 54975."," To explore the effect of excluding the candidate extreme scattering event from the radio light curve of B2023+336, we use the same parameters as for the original analysis but exclude the radio data from MJD 54900 through MJD 54975."
 We find a slightly higher significance for the cross-correlation of at the same time lag., We find a slightly higher significance for the cross-correlation of at the same time lag.
 This supports the suggestion that radio-specific extrinsic effects reduce the observable cross-correlation., This supports the suggestion that radio-specific extrinsic effects reduce the observable cross-correlation.
" The SED for B2013+370 6,, data points in Table 5)) shows a two component (Figurestructure characteristic of blazars."," The SED for B2013+370 (Figure \ref{2015-sed}, data points in Table \ref{tab:2015-sed}) ) shows a two component structure characteristic of blazars."
 The relatively hard X-ray spectral index (ax=1.2— 1.8) and the dominance of the gamma-ray power output are typically observed in low-frequency-peaked BL Lacs (LBLs) or in flat spectrum radio quasars 1998)., The relatively hard X-ray spectral index $\alpha_X=1.2-1.8$ ) and the dominance of the gamma-ray power output are typically observed in low-frequency-peaked BL Lacs (LBLs) or in flat spectrum radio quasars .
where MINT daa. DL;qq and rk ds the distance from a source to a detector.,"where , , and $r$ is the distance from a source to a detector."
 Ph and hi. are the waveforms observed along the z axis., $h_+$ and $h_{\times}$ are the waveforms observed along the $z$ axis.
 1n the carly phase before the growth of the nonaxisvmmetrie perturbation saturates. the amplitude of eravitational waves increases gradually together. with the magnitude of η.," In the early phase before the growth of the nonaxisymmetric perturbation saturates, the amplitude of gravitational waves increases gradually together with the magnitude of $\eta$."
 Then. the growth of the amplitude saturates and subsequently. quasi-periodic gravitational waves are emitted for a much longer time than the rotational period.," Then, the growth of the amplitude saturates and subsequently, quasi-periodic gravitational waves are emitted for a much longer time than the rotational period."
 The amplitude of quasi-periodic gravitational waves depends on E and ct. as in the case of the saturated value of 4.," The amplitude of quasi-periodic gravitational waves depends on $\Gamma$ and $\hat A$, as in the case of the saturated value of $\eta$ ."
" For a given set of Jd and €, (or 3). it is smaller for smaller values of E."," For a given set of $\hat A$ and $C_a$ (or $\beta$ ), it is smaller for smaller values of $\Gamma$."
 This is because the star with smaller values of Eis more centrally condensed and. hence. the magnitudes of the quadrupole moments are smaller for the identical mass and radius.," This is because the star with smaller values of $\Gamma$ is more centrally condensed and, hence, the magnitudes of the quadrupole moments are smaller for the identical mass and radius."
 We found that for the parameters we studied (3zx;0.1. AX0.6 and angular velocity profiles (1) and (2)). the typical values of the amplitude and luminosity of gravitational waves for P=2 are rh~0. O.2CALFRo) and E0.005 0.01CAZHay.," We found that for the parameters we studied $\beta \alt 0.1$, $\hat A \leq 0.6$ and angular velocity profiles (1) and (2)), the typical values of the amplitude and luminosity of gravitational waves for $\Gamma=2$ are $r h_{+,\times} \sim 0.1$ $0.2(M^2/R_{\rm eq})$ and $\dot E \sim 0.005$ $0.01 (M/R_{\rm eq})^5$."
 For P=5/3. the magnitudes of then are only slightly. smaller than those for P—2.," For $\Gamma=5/3$, the magnitudes of them are only slightly smaller than those for $\Gamma=2$."
 However. for Ll—7/5. they are smaller by a factor of several as rho~O.OS(ALTRa) and FcO.00LAL/IY.," However, for $\Gamma=7/5$, they are smaller by a factor of several as $rh_{+,\times} \sim 0.05(M^2/R_{\rm eq})$ and $\dot E \sim 0.001 (M/R_{\rm eq})^5$."
 Using the results shown in Figures 12- 14... we can estimate the expected. effective amplitude of gravitational waves [rom the nonaxisvmmetric outcomes formed. after the dynamical instability saturates.," Using the results shown in Figures \ref{FIG12}- \ref{FIG14}, we can estimate the expected effective amplitude of gravitational waves from the nonaxisymmetric outcomes formed after the dynamical instability saturates."
 Llere. we pay particular attention to proto-neutron stars whichare Likely formed soon after the supernovae of mass 14M. ancl radius several 10. km.," Here, we pay particular attention to proto-neutron stars whichare likely formed soon after the supernovae of mass $\sim 1.4M_{\odot}$ and radius several 10 km."
 For the luminosity E-0.0014Hay , For the luminosity $\dot E = 0.001\epsilon(M/R_{\rm eq})^5$ 
338 iuillion objects.,338 million objects.
 These 2MÁASS stars are selected directly from the 2\TASS point source catalog without eoiug throueh NOMAD., These 2MASS stars are selected directly from the 2MASS point source catalog without going through NOMAD.
 The R magnitude was estimated based on the 2\LASS near-infrared JIN color aud stars with Ro € 17.0 or J x 15.5 are selected., The R magnitude was estimated based on the 2MASS near-infrared $-$ K color and stars with R $\le$ 17.0 or J $\le$ 15.5 are selected.
 The unique identifier for stars matched across catalogs is the MPOS star umber., The unique identifier for stars matched across catalogs is the MPOS star number.
 Individual carly epoch positious are output together with MPOS cutries (CCD epoch observations) aud sorted by MPOS umuher., Individual early epoch positions are output together with MPOS entries (CCD epoch observations) and sorted by MPOS number.
 Weighted proper motious and mean positions are heu calculated to obtain the UCACS release catalog data (Zachariasetal.2010)., Weighted proper motions and mean positions are then calculated to obtain the UCAC3 release catalog data \citep{u3r}.
.. Objects which did rot have either a reasonable proper notion determined or could not be matched with 2MÁASS iue dropped a this point., Objects which did not have either a reasonable proper motion determined or could not be matched with 2MASS are dropped at this point.
 Oulv hese compiled catalog mcan positious aud proper notious are published in UCACS. not the MPOS or FPOS data. which likely will be made available ‘or the final UCACE release after further updates.," Only these compiled catalog mean positions and proper motions are published in UCAC3, not the MPOS or FPOS data, which likely will be made available for the final UCAC4 release after further updates."
 A total of 1510 Ilipparcos stars in the & to 12 imaenitude range are randomly selected (about 300 all sky per magnitude interval) and flageccd in the UCAC data., A total of 1510 Hipparcos stars in the 8 to 12 magnitude range are randomly selected (about 300 all sky per magnitude interval) and flagged in the UCAC data.
 These stars are not used as reference stars in test reductions using Tvcho-2 reference stars., These stars are not used as reference stars in test reductions using Tycho-2 reference stars.
 Thus the obtained positions are field star positions from UCAC observations independent of the Hipparcos aud Tycho catalog positions., Thus the obtained positions are field star positions from UCAC observations independent of the Hipparcos and Tycho catalog positions.
 Individual UCAC observed positions are then compared o the original (ESA1997). and new Ilipparcos reductions (vanLeeuwen2007). at the epoch of UCAC observations. using Hipparcos ican positions. proper motions and parallaxes.," Individual UCAC observed positions are then compared to the original \citep{hiporig} and new Hipparcos reductions \citep{2007ASSL..350.....V} at the epoch of UCAC observations, using Hipparcos mean positions, proper motions and parallaxes."
 After excluding outliers (2 200 mas position difference in either coordinate). RMS values over observations dn each biu are calculated (Table 7)).," After excluding outliers $\ge$ 200 mas position difference in either coordinate), RMS values over observations in each bin are calculated (Table \ref{TYCt1}) )."
 Siuilulv sorting all observations by magnitude or color. respectively and binning over LOO observations lead to the plots shown in Figure 7 and &..," Similarly sorting all observations by magnitude or color, respectively and binning over 100 observations lead to the plots shown in Figure \ref{UHipmag} and \ref{UHipcol}."
 The expected position errors. from UCACS and IHipparcos data at the epoch of our UCAC observations are also presented in Table 7 together with the expected RAIS of the combined error aud the ratio of expected το observed scatter. separately for cach coordinate.," The expected position errors from UCAC3 and Hipparcos data at the epoch of our UCAC observations are also presented in Table \ref{TYCt1}
 together with the expected RMS of the combined error and the ratio of expected to observed scatter, separately for each coordinate."
 Iu all cases the observed errors (from the scatter of the Ilpparcos position differences) ds slightly smaller than the expected errors as calculated from the combined formal errors for the sale observations. thus at least some of these are overestimated (see also discussion section below).," In all cases the observed errors (from the scatter of the $-$ Hipparcos position differences) is slightly smaller than the expected errors as calculated from the combined formal errors for the same observations, thus at least some of these are overestimated (see also discussion section below)."
 UCAC position differcuces of those sampled Ilipparcos stars do not slow svsteatic errors as a function of maenitude or color exceeding about 10 mas over the range sampled., UCAC position differences of those sampled Hipparcos stars do not show systematic errors as a function of magnitude or color exceeding about 10 mas over the range sampled.
 Plots with respect to the original or new Iipparcos catalog are almost ideutical., Plots with respect to the original or new Hipparcos catalog are almost identical.
 However. 23 Ilipparcos stars of this salple} show very large differeuces (between 300 H1d GOO mas in either coordinate) when comparing the new reduction Iipparcos positious with the UCACS3 positions at UCAC epoch.," However, 23 Hipparcos stars of this sample) show very large differences (between 300 and 600 mas in either coordinate) when comparing the new reduction Hipparcos positions with the UCAC3 positions at UCAC epoch."
 Ao similar uuniber of stars is found when comparing with the original Wipparcos Catalogue: however. for not exactly the same stars.," A similar number of stars is found when comparing with the original Hipparcos Catalogue; however, for not exactly the same stars."
 All possible combinations of inconsistencies between the two [Lipparcos solutions aud UCAC data are found. with two of the three positious or all three separated by several standard errors of their internal errors.," All possible combinations of inconsistencies between the two Hipparcos solutions and UCAC data are found, with two of the three positions or all three separated by several standard errors of their internal errors."
 The use of an image profile model better matching the actual PSF than a Gaussian model is essential for the astrometric reductions of blendec images., The use of an image profile model better matching the actual PSF than a Gaussian model is essential for the astrometric reductions of blended images.
 A better matching model also does reduce the amplituce of the sub-pixel phase error ac is advisable to be used when no such corrections are being applied to the data., A better matching model also does reduce the amplitude of the sub-pixel phase error and is advisable to be used when no such corrections are being applied to the data.
 In particular. a conrparison of Figure 6 with a simular figure of the UCAC2 paper show that with a Ciaussian model iux 2.0 pixel/FWHAL sampling the pixe phase error has an amplitude of 11 mas. while with the image profile model 5 as used iu UCACS this amplitude is ouly about 6 mas.," In particular, a comparison of Figure \ref{AMPf1} with a similar figure of the UCAC2 paper show that with a Gaussian model and 2.0 pixel/FWHM sampling the pixel phase error has an amplitude of 11 mas, while with the image profile model 5 as used in UCAC3 this amplitude is only about 6 mas."
 The use of such a PSF profile model (still with the same ΠΙΟ of fit parameters per star as the traditional Caussian model) allows to neelect positional errors as functiou of sub-pixel phase completely for a sampling of about 2.5 pixel/EWIIM or larger without the need to investigate possible other depeudeucies of this systematic error as a function of other things., The use of such a PSF profile model (still with the same number of fit parameters per star as the traditional Gaussian model) allows to neglect positional errors as function of sub-pixel phase completely for a sampling of about 2.5 pixel/FWHM or larger without the need to investigate possible other dependencies of this systematic error as a function of other things.
 However. for single stars and with calibration data in haud to correct for the position offsets caused by a sub-pixel phase dependency. tle use," However, for single stars and with calibration data in hand to correct for the position offsets caused by a sub-pixel phase dependency, the use"
We have observed the superluuinal X-ray transicut (Mirabel Rodriguez 1991. hereafter MR91) with the MERLIN array in 1997 October = November following a major radio outburst.,"We have observed the superluminal X-ray transient (Mirabel Rodriguez 1994, hereafter MR94) with the MERLIN array in 1997 October – November following a major radio outburst."
 The MERLIN observations were made with an augular resolution of LO mas. five times better than previous VLA mapping. at a frequency of 5 GITz. on ten occasions over a period of 12 davs.," The MERLIN observations were made with an angular resolution of 40 mas, five times better than previous VLA mapping, at a frequency of 5 GHz, on ten occasions over a period of 12 days."
 The radio flux from CRS 1915|105 was also sinmltaueouslv mouitored at 2 8 GIIz with the Green Bank Interferometer (CB and at 15 GIIz with the Ryle Telescope (RT)., The radio flux from GRS 1915+105 was also simultaneously monitored at 2 8 GHz with the Green Bank Interferometer (GBI) and at 15 GHz with the Ryle Telescope (RT).
 Over the same period the system was monitored iu soft N-ravs with the Rossi NTE satellite., Over the same period the system was monitored in soft X-rays with the Rossi XTE satellite.
 Prior to our MERLIN observations CRS 1915105 had clearly beeu ii an unusual state iu both N-ravs and radio. summarised in Fig.," Prior to our MERLIN observations GRS 1915+105 had clearly been in an unusual state in both X-rays and radio, summarised in Fig."
 l., 1.
" Approximately 25 davs prior to our first epoch of mapping. the source had undergone a significant radio flare. and then eutered a ""plateau state."," Approximately 25 days prior to our first epoch of mapping, the source had undergone a significant radio flare, and then entered a `plateau' state."
 This state is characterised by relatively bright aud stable radio ciunission with a flat / inverted spectrum. aud low but persistent N-ray chussion with a hard spectrum.," This state is characterised by relatively bright and stable radio emission with a flat / inverted spectrum, and low but persistent X-ray emission with a hard spectrum."
 Previous iionitoriug reported at 15 (11 with the RT iu Pooley Feuder (1997) aud at lower frequencies in Bandyopadhyay ct al. (, Previous monitoring reported at 15 GHz with the RT in Pooley Fender (1997) and at lower frequencies in Bandyopadhyay et al. (
1998) confirm the association between the plateau state and relatively bright radio. aud perhaps infrared. cussion.,"1998) confirm the association between the plateau state and relatively bright radio, and perhaps infrared, emission."
 As indicated in Fie., As indicated in Fig.
 l. a sequence of ten MERLIN high-resolution radio maps were made of CRS," 1, a sequence of ten MERLIN high-resolution radio maps were made of GRS"
"Papers IVI) aud other survevs (σοι,Winnetal.2000.2008:Faureetal. 2008).. which have begun to deliver statistically significant samples of strong Ίος galaxies by using svetematic search techuiques.","Papers I–VI) and other surveys \citep[e.g.,][]{winn_pmn_i, winn_pmn_ii, winn_pmn_iii, winn_pmn_iv,
myers_class, browne_class, maoz_snap, morgan_ctq327, he_lens_i, he_lens_ii,
he_lens_iii, he_lens_iv, he_lens_v, he_lens_vi, he_lens_vii, ols1, ols2,
sdssqls1, sdssqls2, sdssqls3, mds_lens, lam_legs,
cabanac_sl2s, belokurov_lens, kubo_lens, faure_cosmos}, which have begun to deliver statistically significant samples of strong lens galaxies by using systematic search techniques."
 Previous studies have taken diverse approaches to the use of strone-lensing information for the measurement of carly-type galaxy iiass-deusitv structure., Previous studies have taken diverse approaches to the use of strong-lensing information for the measurement of early-type galaxy mass-density structure.
" Stroue-leusine aperture mnasses have been used by Busiu.Ἱνουμαποῖς,&Isectou(2003) and Rusin&Kochauck(2005) to provide eusenible coustraiuts upon the mass-deusitv structure of carly-type galaxies.", Strong-lensing aperture masses have been used by \citet*{rkk_03} and \citet{rusin_kochanek_05} to provide ensemble constraints upon the mass-density structure of early-type galaxies.
 Leusiug mass constraiuts have Όσσα combined in sclfcousistent fashion with stellar cdhvuamics to constrain the mass structure of leuses on a svsteni-byv-svsteni basis by the Leuses Structure and Dynamics survey (LSD: Isoopmaus&Treu2002.2003:Tren 2001)) aud the SLACS Survey (Paper TIT).," Lensing mass constraints have been combined in self-consistent fashion with stellar dynamics to constrain the mass structure of lenses on a system-by-system basis by the Lenses Structure and Dynamics Survey (LSD: \citealt{kt02, kt03, tk02, tk03, tk04}) ) and the SLACS Survey (Paper III)."
 IKochanek(2002) aud Itochaucketal.(2006) have used the time delays between iuultiple leused quasar iniages. together with a eiven value for the ITubble paralucter f7y to measure the local mass slope of the lensing galaxies.," \citet{kochanek_what} and \citet{kochanek_morgan_06}
 have used the time delays between multiple lensed quasar images, together with a given value for the Hubble parameter $H_0$ to measure the local mass slope of the lensing galaxies."
 Constraints on the mass profile of lenses based upon resolved lensed features have been published by Colinetal.(2001).. Munozetal. (2001).. Waythetal. (2005).. Dve&Warren (2005).. Brewer&Lewis (2006).. aud Dyeetal.(2007).," Constraints on the mass profile of lenses based upon resolved lensed features have been published by \citet{cohn_2001}, \citet{munoz_2001}, \citet{wayth_0047}, \citet{dye_warren_05}, \citet{brewer_06}, and \citet{dye_lbg}."
". Boltonetal.(2007.hereafterBOT) have used lensing aperture masses in combination with central stellar velocity dispersions aud measured effective radii to demonstrate on an enmipirical scaling basis that he iass-density structure of massive elliptical leuses roni the SLACS Survey is on average independent of πάσα, a result which we establish aud explore iu more detail in the current work."," \citet[][hereafter B07]{bolton_mfp}
 have used lensing aperture masses in combination with central stellar velocity dispersions and measured effective radii to demonstrate on an empirical scaling basis that the mass-density structure of massive elliptical lenses from the SLACS Survey is on average independent of mass, a result which we establish and explore in more detail in the current work."
 Iu this work. we employ the mass. light. aud. velocity neasureents of the full (HST)) Advanced Camera for Surveys (ACS) eravitational leus sample from the SLACS Survey. published iu Paper V. Oo derive nunerous enpiical scaling relations.," In this work, we employ the mass, light, and velocity measurements of the full ) Advanced Camera for Surveys (ACS) gravitational lens sample from the SLACS Survey, published in Paper V, to derive numerous empirical scaling relations."
 The analvsis of the initial SLACS sample in Paper ITE allowed us fo measure an oneaveraee isothermal mass-ceusity structure: the current leus sample is laree enough to investigate iu structure with mass aud velocity dispersion., The analysis of the initial SLACS sample in Paper III allowed us to measure an on-average isothermal mass-density structure; the current lens sample is large enough to investigate in structure with mass and velocity dispersion.
" We frame mich of our analysis aud discussion in terms of the Fundamental Plane scaling relation (FP: e.g.. Djorgovski&Davis1987:Dressleretal.Deuetal.2001:vanderWel 2005: Paper IE: Dü7) and the relationships between huuimnositv. ""dvuuuical lass”. and stroue-leusiug aperture mass that illuninate the structural explanation for the ""tilt of theFP."," We frame much of our analysis and discussion in terms of the Fundamental Plane scaling relation (FP; e.g., \citealt{dd_fp, dr_fp, bbf_92, renzini_ciotti_93,
guzman_93, pahre_95, pahre_iii, pahre_iv, jorgensen_fp,
vd_franx_96, clr_fp_96, kelson_97, graham_colless_97,
scodeggio_98, kochanek_lens_fp, treu_2001_iii, treu_2002, bcdp_02,
vd_stanford, bernardi_fp, vandeven_fp, tbb_fp, vanderwel_05}; Paper II; B07) and the relationships between luminosity, “dynamical mass”, and strong-lensing aperture mass that illuminate the structural explanation for the “tilt” of the."
. Iu the SLACS sample. we have a laree nuuber of carly-type galaxies distributed across the hieherauass cud of the FP. with uniform aud high-quality 116asuemieuts of the observables of redshift. surface brightness. velocity dispersion. and effective radius.," In the SLACS sample, we have a large number of early-type galaxies distributed across the higher-mass end of the FP, with uniform and high-quality measurements of the observables of redshift, surface brightness, velocity dispersion, and effective radius."
" These additional ass measurements add another dimension of plivsical coustraint to the SLACS siuuple that is not available for other FP galaxy sauuples. thus offerius the opportunitv to break some of the degeneracy inherent iu the plivsical interpretation of FP analyses,"," These additional mass measurements add another dimension of physical constraint to the SLACS sample that is not available for other FP galaxy samples, thus offering the opportunity to break some of the degeneracy inherent in the physical interpretation of FP analyses."
 This paper is arranged as follows., This paper is arranged as follows.
 Section 2. gives au overview of our measurements and analysis techniques., Section \ref{overview} gives an overview of our measurements and analysis techniques.
" Sections 3- 6 present the various scaling relations defined bv the SLACS sample. including the relative aliguinent aud flattenine of projected mass aud dieht distributions the relation between stellar aud lensing volocitv-dispersiou nieasurenments refe) the PPaudvinassplanc""relations(s reffpinpsce)). andvariousperspecticesonthercelationshipbetwecnd, refinml))"," Sections \ref{angular}- \ref{mml} present the various scaling relations defined by the SLACS sample, including the relative alignment and flattening of projected mass and light distributions \\ref{angular}) ), the relation between stellar and lensing velocity-dispersion measurements \\ref{v_v}) ), the FP and “mass plane” relations \\ref{fpmpsec}) ), and various perspectives on the relationship between dynamical mass, lensing mass, and luminosity \\ref{mml}) )."
 Ius vwcinakearobustdeteriminationoftheenscimbleaverageradi initssprofilcofthe SLACSsample., In \\ref{mofr} we make a robust determination of the ensemble average radial enclosed-mass profile of the SLACS sample.
Scection sprocidesanitemizedsun fdiscussprocidesaconeludingdiscussion.," Section \ref{summary} provides an itemized summary of our results, and \\ref{discuss} provides a concluding discussion."
" All computations in this work assume a general relativistic Friediuaumu-Bobertsou-Walker cosmology with iuatter-density parameter Qy,=0.3. vacuuni cherey-deusity parameter 94=07. and Hubble paramcter Hy=το tMAIpe |."," All computations in this work assume a general relativistic Friedmann-Robertson-Walker cosmology with matter-density parameter $\Omega_{\mathrm{M}} = 0.3$, vacuum energy-density parameter $\Omega_{\Lambda} = 0.7$, and Hubble parameter $H_0 = 70$ $^{-1}$ $^{-1}$."
" We consider the sample of 63 ""erade-À"" strong eravitational lenses presented iu PaperV.", We consider the sample of 63 “grade-A” strong gravitational lenses presented in Paper.
. For analyses cluploving stellar velocity dispersions. we restrict the suuple to the 53 early-type leus svstems with a median SDSS spectral signal-to-noise ratio of 10 or greater por + pixel over the rest-frame range of [100 toα," For analyses employing stellar velocity dispersions, we restrict the sample to the 53 early-type lens systems with a median SDSS spectral signal-to-noise ratio of 10 or greater per $^{-1}$ pixel over the rest-frame range of 4100 to."
νν The measurements upon which the current work is based are all preseuted im Paper V. and are described ouly briefly here.," The measurements upon which the current work is based are all presented in Paper V, and are described only briefly here."
 We use stellar velocity dispersious measured from Sloan Digital Sky Survey (SDSS: Yorketal.2000: Adechnan-MeCarthyetal. 2007)) spectroscopy. which sauples a 3”-cdiameter circular fiber aperture ceutered ou the target galaxy.," We use stellar velocity dispersions measured from Sloan Digital Sky Survey (SDSS: \citealt{york_sdss}; \citealt{dr6}) ) spectroscopy, which samples a $\arcsec$ -diameter circular fiber aperture centered on the target galaxy."
" We correct these measured velocity dispersions (which we denote bv dgapss} using the clupizical power-law relation of Jorecusenctal.(1995) o Uniform plysical apertures of either ιδ (to eive a “central” velocity dispersion os) or [6/2 (0,5. for a spatial aperture more closelv matched to that of the spectroscopy and of the stroue-leusine features)."," We correct these measured velocity dispersions (which we denote by $\sigma_{\mathrm{SDSS}}$ ) using the empirical power-law relation of \citet{jorgensen_vdisp}
 to uniform physical apertures of either $R_e / 8$ (to give a “central” velocity dispersion $\sigma_{e8}$ ) or $R_e / 2$ $\sigma_{e2}$, for a spatial aperture more closely matched to that of the spectroscopy and of the strong-lensing features)."
 We rote that these corrections are quite simallRAIS. of for R./2. and that the coefficients of logarithiuic scaling relations we derive are uot sensitive to the articular choice of velocitv-normalization aperture., We note that these corrections are quite small—RMS of for $R_e / 2$ —and that the coefficients of logarithmic scaling relations we derive are not sensitive to the particular choice of velocity-normalization aperture.
 We use maenuitudes. effective radii. projected axis ratios. aud xositiou angles for the leus galaxies ucasured from fitting de Vaucouleurs models to ΑΟΝΕΟ ΕΑΝ imagine.," We use magnitudes, effective radii, projected axis ratios, and position angles for the lens galaxies measured from fitting de Vaucouleurs models to ACS-WFC F814W imaging."
 To convert from observed iuaguitudes to rest-frame uuinosities. we first correct for Galactic dust extinction using the maps of Schlegel.Fiukbeimer.&Davis (199," To convert from observed magnitudes to rest-frame luminosities, we first correct for Galactic dust extinction using the maps of \citet*{sfd_dust}, ,"
 To convert from observed iuaguitudes to rest-frame uuinosities. we first correct for Galactic dust extinction using the maps of Schlegel.Fiukbeimer.&Davis (1998," To convert from observed magnitudes to rest-frame luminosities, we first correct for Galactic dust extinction using the maps of \citet*{sfd_dust}, ,"
 To convert from observed iuaguitudes to rest-frame uuinosities. we first correct for Galactic dust extinction using the maps of Schlegel.Fiukbeimer.&Davis (1998)," To convert from observed magnitudes to rest-frame luminosities, we first correct for Galactic dust extinction using the maps of \citet*{sfd_dust}, ,"
 To convert from observed iuaguitudes to rest-frame uuinosities. we first correct for Galactic dust extinction using the maps of Schlegel.Fiukbeimer.&Davis (1998).," To convert from observed magnitudes to rest-frame luminosities, we first correct for Galactic dust extinction using the maps of \citet*{sfd_dust}, ,"
 To convert from observed iuaguitudes to rest-frame uuinosities. we first correct for Galactic dust extinction using the maps of Schlegel.Fiukbeimer.&Davis (1998)..," To convert from observed magnitudes to rest-frame luminosities, we first correct for Galactic dust extinction using the maps of \citet*{sfd_dust}, ,"
The results (rom the detailed studies of Local Group dwarls cau be (incompletely) stummarizect as follows.,The results from the detailed studies of Local Group dwarfs can be (incompletely) summarized as follows.
 Local Group cwarls were found to vary widely in their star formation histories. uiean metallicity aud eurichiment histories. times of thelr major star formation episodes. fractional distribution of ages and subpopulatious.," Local Group dwarfs were found to vary widely in their star formation histories, mean metallicity and enrichment histories, times of their major star formation episodes, fractional distribution of ages and subpopulations."
 Indeed no two dwarf galaxies are alike. uot even if they are of the same morphological type or have similar luminosities (Cirebel 1997).," Indeed no two dwarf galaxies are alike, not even if they are of the same morphological type or have similar luminosities (Grebel 1997)."
 La part their properties appear to be correlated with galaxy mass aud with euviroument (proximity (ο massive galaxies)., In part their properties appear to be correlated with galaxy mass and with environment (proximity to massive galaxies).
 Iu —iuiv Local Croup dwarls spatial variatious in star formation history were detected., In many Local Group dwarfs spatial variations in star formation history were detected.
 Lu eeneral. there is a tendency for the vouuger populatious to be more centrally conceutrated (ancl possibly more enriclied). whereas older populatious are more extended.," In general, there is a tendency for the younger populations to be more centrally concentrated (and possibly more enriched), whereas older populations are more extended."
 This may in part be au effect of dynamical evolution. but may also iudicate that star formation was able to coutinue over all exteuce period of time in the central regious since these may have been able to retain gas louger for may have beeu rejuvenated by eas inflow in accretion events).," This may in part be an effect of dynamical evolution, but may also indicate that star formation was able to continue over an extended period of time in the central regions since these may have been able to retain gas longer (or may have been rejuvenated by gas inflow in accretion events)."
 For a stummary of population eracients in a unuumber of Local Group dSplis. see Harbeck et ((tlese proceedings).," For a summary of population gradients in a number of Local Group dSphs, see Harbeck et (these proceedings)."
 Harbeck et cconclude that presence or absence of these gradients does not show a clear correlation will environment., Harbeck et conclude that presence or absence of these gradients does not show a clear correlation with environment.
 A common property to all dwarf galaxies studied in sullicieut detail so far is the presence of at old population., A common property to all dwarf galaxies studied in sufficient detail so far is the presence of an old population.
 All claims of discoveries of purely young galaxies have subsequently been refutec once cleeper images or data with better coverage of the outskirts of these galaxies became available., All claims of discoveries of purely young galaxies have subsequently been refuted once deeper images or data with better coverage of the outskirts of these galaxies became available.
 Deep ground-based imaging of the “halos” of dIrrs led to the detection of old red giant. branches fee. Minniti Zijlstra 1996) All dSphs aud dEs for which deep photometry was obtained revealec horizontal brauches. a clear indicator of old populations.," Deep ground-based imaging of the “halos” of dIrrs led to the detection of old red giant branches (e.g., Minniti Zijlstra 1996) All dSphs and dEs for which deep photometry was obtained revealed horizontal branches, a clear indicator of old populations."
 The nearest candidate for a dwarf spiral. 33109. shows a presumably old red giant. branch iu its outer regious (Minniti. Zijlstra. Alonso 1999).," The nearest candidate for a dwarf spiral, 3109, shows a presumably old red giant branch in its outer regions (Minniti, Zijlstra, Alonso 1999)."
 Deep imaging of BCDs has revealed the presence of intermecdiate-age ancl possibly old populations (e.g.. Lyuds et 11993). as already inferred [rom integrated[n] colors.," Deep imaging of BCDs has revealed the presence of intermediate-age and possibly old populations (e.g., Lynds et 1998), as already inferred from integrated colors."
 The oldest populatious in the majority of nearby cllrrs aud dSplis are iucdistinguishable in age [rom the oldest globular clusters in the Galactic Lalo auc bulee (for a full list aud references. see CGrebel 2000).," The oldest populations in the majority of nearby dIrrs and dSphs are indistinguishable in age from the oldest globular clusters in the Galactic halo and bulge (for a full list and references, see Grebel 2000)."
 This itlicates a common epoch of the olclest measurable star formation episode., This indicates a common epoch of the oldest measurable star formation episode.
 Relative ages were derived from deep photometry extendiugD> below the main-sequence turu-oll., Relative ages were derived from deep photometry extending below the main-sequence turn-off.
 Du at least one dlir (he Small Magellanic Cloud). however. significant star lormation appears to have started with a delay of 2-3 Cyr.," In at least one dIrr (the Small Magellanic Cloud), however, significant star formation appears to have started with a delay of 2–3 Gyr."
 Data of sullicient depth aud quality to carry out differential of the oldest. populatious are so [ar only available for Milky Way companions. ie.. warl ealaxies withiu ~300 kpe.," Data of sufficient depth and quality to carry out differential age-dating of the oldest populations are so far only available for Milky Way companions, i.e., dwarf galaxies within $\sim 300$ kpc."
 Nearby dwarf galaxies typically show oue of two modes of star formation: Continuous or episocic., Nearby dwarf galaxies typically show one of two modes of star formation: Continuous or episodic.
 Hieh-mass dwarf galaxies tend to lorm stars fairly continuously with amplitude variatious of up to a [actor of three., High-mass dwarf galaxies tend to form stars fairly continuously with amplitude variations of up to a factor of three.
 They can continue to form stars over another Hubble time without exhausting their eas supply., They can continue to form stars over another Hubble time without exhausting their gas supply.
 They exhibit gradual eurichinent. since many of the metals produced in star formation episodes are recycled later ou.," They exhibit gradual enrichment, since many of the metals produced in star formation episodes are recycled later on."
 This mocle of star formation is observed tn high-mass ας aud dwarf spirals., This mode of star formation is observed in high-mass dIrrs and dwarf spirals.
 Lower-mass dlrrs. dEs. aud dSphs show coutinuous star formation with decreasing star formation rates.," Lower-mass dIrrs, dEs, and dSphs show continuous star formation with decreasing star formation rates."
 In dEs aud dSphs. ouly little gas or uo gas at all is observed. aud star formation has ceased at the present. time.," In dEs and dSphs, only little gas or no gas at all is observed, and star formation has ceased at the present time."
 One d5ph in the Local Group. Carina. shows episodic or repetitive star formation: This galaxy uucderweut star formation episodes separated by 2 Gyr long episodes of quiescence.," One dSph in the Local Group, Carina, shows episodic or repetitive star formation: This galaxy underwent star formation episodes separated by 2 Gyr long episodes of quiescence."
 Yet no sigulficant eurichinent appears to have occurred if one interprets the narrowness oL the red giant brauch as au indication of a narrow metallicity range., Yet no significant enrichment appears to have occurred if one interprets the narrowness of the red giant branch as an indication of a narrow metallicity range.
 This may suggest that the later episodes took place with accreted eas., This may suggest that the later episodes took place with accreted gas.
 Alternatively. age ancl metallicity may conspire to form one narrow red giant brauch.," Alternatively, age and metallicity may conspire to form one narrow red giant branch."
 The resolution of this question requires spectroscopy., The resolution of this question requires spectroscopy.
 It is uot vet uucerstood what caused the periods of quiescence and the renewed ouset of star formation lateron., It is not yet understood what caused the periods of quiescence and the renewed onset of star formation lateron.
 D5plis around the Milky Way tend to have increasing fractions of intermediate-age populations with iucreasiug distance [rom the Milky Way. suggestiveMOD of the impact of enviroumental effects:," DSphs around the Milky Way tend to have increasing fractions of intermediate-age populations with increasing distance from the Milky Way, suggestive of the impact of environmental effects:"
reduce the power drawn from commercial camera batteries by discarding the requirement for codec chips to be able to perform compression.,reduce the power drawn from commercial camera batteries by discarding the requirement for codec chips to be able to perform compression.
 Another application is to trade off the compression rate against number of measurements (??)..," Another application is to trade off the compression rate against number of measurements \citep{Shapiro:1993p2541, Said1996}."
" To describe CS concisely, we describe a general linear imaging system with where J is the target signal in vector form of length n, the vector V is the observations with length πι, and y is a matrix of size m by n."," To describe CS concisely, we describe a general linear imaging system with where $I$ is the target signal in vector form of length $n$ , the vector $V$ is the observations with length $m$, and $\psi $ is a matrix of size $m$ by $n$."
" If there are fewer observations than unknowns in the target signal 7, i.e., there are more columns than rows in y and m<n, we must try to recover the unknowns in the target signal with fewer observations."," If there are fewer observations than unknowns in the target signal $I$ , $i.e.$, there are more columns than rows in $\psi$ and $m\ll n$, we must try to recover the unknowns in the target signal with fewer observations."
" Although this equation may admit multiple solutions, if vector signal J is sufficiently sparse with respect to a known dictionary of basis functions, we can fully reconstruct the target signal J by using this extra information."," Although this equation may admit multiple solutions, if vector signal $I$ is sufficiently sparse with respect to a known dictionary of basis functions, we can fully reconstruct the target signal $I$ by using this extra information."
 That this is possible is known from the success of non-linear imaging algorithms such as the Hóggbom CLEAN., That this is possible is known from the success of non-linear imaging algorithms such as the Höggbom CLEAN.
 The advance in CS is a rigorous theory constraining under what circumstances this is possible., The advance in CS is a rigorous theory constraining under what circumstances this is possible.
" Compressive sensing theory has a number of important ingredients: sparsity, incoherence, the restricted isometry property, and reconstruction."," Compressive sensing theory has a number of important ingredients: sparsity, incoherence, the restricted isometry property, and reconstruction."
 We introduce these in the next subsections., We introduce these in the next subsections.
 A signal is sparse if there is is a given dictionary of basis functions in which the signal can be represented by most elements being zero., A signal is sparse if there is is a given dictionary of basis functions in which the signal can be represented by most elements being zero.
" Examples of dictionaries of basis functions include the Fourier transform, the wavelet transform, and the gradient representation for a piecewise constant signal."," Examples of dictionaries of basis functions include the Fourier transform, the wavelet transform, and the gradient representation for a piecewise constant signal."
" With a sparse basis function, Eq. (TJ) "," With a sparse basis function, Eq. \ref{equ_Isparse}) )"
"can be rewritten as where ©=y of size mxn and I=ga, a is a sparse representation when the transform matrix ¢ is adopted."," can be rewritten as where $\Theta= \psi\phi$ of size $m\times n$ and $I=\phi\alpha$, $\alpha$ is a sparse representation when the transform matrix $\phi$ is adopted."
" In general, ¢ is nx{ with / greater or equal to n."," In general, $\phi$ is $n\times l$ with $l$ greater or equal to $n$."
" This allows compressive sensing to have a wide application, because many signals often have a sparse representation in a certain basis dictionary."," This allows compressive sensing to have a wide application, because many signals often have a sparse representation in a certain basis dictionary."
" This can, of course, also be applied to the circumstances where the signal itself can be sparse, in which case ¢ is the identity matrix."," This can, of course, also be applied to the circumstances where the signal itself can be sparse, in which case $\phi$ is the identity matrix."
 Nyquist-Shannon sampling theory covers the requirements when sampling the signal directly., Nyquist-Shannon sampling theory covers the requirements when sampling the signal directly.
" In contrast, CS theory covers sensing or sampling of the target signal indirectly by means of a sensing matrix (for example, the partial Fourier matrix in ?)) y in Eq. (IJ) "," In contrast, CS theory covers sensing or sampling of the target signal indirectly by means of a sensing matrix (for example, the partial Fourier matrix in \citet{Candes:2007p2815}) ) $\psi$ in Eq. \ref
{equ_Isparse}) )"
or © in Eq. (2)., or $\Theta$ in Eq. \ref{equ_basissparse})).
" As proven in ?,, given a random selected measurements or observations V, the target signal I can be recovered exactly with overwhelmingly probability, when the number of measurements m satisfies wwhere s is the number of non-zero entries in a, u(F,$) is the mutual coherence, and F is the sensing system."," As proven in \citet{Candes:2007p2815}, given a random selected measurements or observations $V$, the target signal $I$ can be recovered exactly with overwhelmingly probability, when the number of measurements $m$ satisfies where $s$ is the number of non-zero entries in $\alpha$, $\mu(F, \phi)$ is the mutual coherence, and $F$ is the sensing system."
" Note that, y is a subset of F."," Note that, $\psi$ is a subset of $F$."
" For example, if the sensing system is in the Fourier domain, then the partial Fourier matrix y is assembled from the randomly selected rows of the Fourier transform matrix F."," For example, if the sensing system is in the Fourier domain, then the partial Fourier matrix $\psi$ is assembled from the randomly selected rows of the Fourier transform matrix $F$."
" The unit-normalised basis vectors of F are organized in rows, and the unit-normalised basis vectors of $ are organized in columns."," The unit-normalised basis vectors of $F$ are organized in rows, and the unit-normalised basis vectors of $\phi$ are organized in columns."
 CS requires that the correlation or coherence between F and ¢ is low., CS requires that the correlation or coherence between $F$ and $\phi$ is low.
" This is measured by the mutual u(F,$) where |«F;,9;> is the inner product between two vectors: the k row of F and the j column of ¢."," This is measured by the mutual $\mu(F, \phi)$ where $|<F_k, \phi_j>|$ is the inner product between two vectors: the $k^{th}$ row of $F$ and the $j^{th}$ column of $\phi$."
 The coherence measures the largest correlation between any two rows of F and 9., The coherence measures the largest correlation between any two rows of $F$ and $\phi$.
" If F and ¢ contain highly correlated elements, the coherence is large, and vice-versa."," If $F$ and $\phi$ contain highly correlated elements, the coherence is large, and vice-versa."
" Equation (3)) shows that as the coherence decreases, fewer samples are needed."," Equation \ref{equ_incoherent}) ) shows that as the coherence decreases, fewer samples are needed."
" Thus if there is a sparse representation in ¢, it must be spread out in the domain F in which it is acquired."," Thus if there is a sparse representation in $\phi$, it must be spread out in the domain $F$ in which it is acquired."
" For example, a spike signal in the time domain can be spread out in the frequency domain."," For example, a spike signal in the time domain can be spread out in the frequency domain."
" Therefore, the best way is to sense this signal in the frequency domain, because in this case u(F,$)=1."," Therefore, the best way is to sense this signal in the frequency domain, because in this case $\mu(F, \phi)=1$."
" This makes perfect sense because to measure the strength of a single pulse, all that is needed is a single measurement in Fourier space, as opposed to an exhaustive search in the time domain."," This makes perfect sense because to measure the strength of a single pulse, all that is needed is a single measurement in Fourier space, as opposed to an exhaustive search in the time domain."
 The discussion above focused only on the situation that the signal has a sparse representation with respect to a certain dictionary of basis functions., The discussion above focused only on the situation that the signal has a sparse representation with respect to a certain dictionary of basis functions.
 We note that “sparse” here means there are few non-zero entries.," We note that “sparse"" here means there are few non-zero entries."
" However, this is rarely the case, and more often most of the entries will be approximately zero."," However, this is rarely the case, and more often most of the entries will be approximately zero."
" CS theory is also applicable to this case but to explore it we need to introduce another concept, the restricted isometry property."," CS theory is also applicable to this case but to explore it we need to introduce another concept, the restricted isometry property."
" In Eq. (2)),"," In Eq. \ref{equ_basissparse}) ),"
 © is now the sensing matrix and a is a near sparse vector signal with s of the largest entries., $\Theta$ is now the sensing matrix and $\alpha$ is a near sparse vector signal with $s$ of the largest entries.
" For each integer s=1,2,---, we define the isometry constant ὅς in the matrices O as the smallest number such that which holds for all s sparse vectors α. If Z; is not too close to 1, then an equivalent description of RIP is to say that all subsets of s columns taken from the matrix © areapproximately orthogonal."," For each integer $s=1,2,\cdots$, we define the isometry constant $\zeta_s$ in the matrices $\Theta$ as the smallest number such that which holds for all $s$ sparse vectors $\alpha$ If $\zeta_s$ is not too close to 1, then an equivalent description of RIP is to say that all subsets of $s$ columns taken from the matrix $\Theta
$ are orthogonal."
" It cannot, of course, be exactly orthogonal, becauseit has more columns than rows."," It cannot, of course, be exactly orthogonal, becauseit has more columns than rows."
" ?shows that if the matrix © satisfies the RIP of order 2s and the isometry constant Zo,< 0.414, then the L1 norm minimization solution a* to Eq. (2))"," \citet{Candes:2004p2832} shows that if the matrix $\Theta$ satisfies the RIP of order $2s
$ and the isometry constant $\zeta_{2s}<\sqrt{2}-1=0.414$ , then the L1 norm minimization solution $\alpha^*$ to Eq. \ref{equ_basissparse}) )"
" obeys: wwhere a, is the vector o with all but the largest s entries set to zero.", obeys: where $\alpha_s$ is the vector $\alpha$ with all but the largest $s$ entries set to zero.
" In practical applications, the measured data will be corrupted by noise."," In practical applications, the measured data will be corrupted by noise."
"To investigate the effects of noise on CS, Eq. (2))","To investigate the effects of noise on CS, Eq. \ref{equ_basissparse}) )"
 can be rewritten as, can be rewritten as
(heir associations with supernova remmants.,their associations with supernova remnants.
 Dased on spin-down properties alone. the (rue pulsar age is impossible (o determine.," Based on spin-down properties alone, the true pulsar age is impossible to determine."
" However. we can estimate the age based on the standard spin-down model (2x—v"") given our measurement of »."," However, we can estimate the age based on the standard spin-down model $\dot{\nu} \propto -
\nu^n$ ) given our measurement of $n$."
 Integrating this model vields. Assuming that the initial spin frequeney was much lareer than the eurrent value. 7)2v. the age estimate for bbecomes. since (he initial spin Irequency is unknown. the above estimate provides an upper limit on the pulsar age.," Integrating this model yields, Assuming that the initial spin frequency was much larger than the current value, $\nu_0 \gg \nu$, the age estimate for becomes, Since the initial spin frequency is unknown, the above estimate provides an upper limit on the pulsar age."
 Therefore. assuming that η and A have remained constant over (he lifetime of the pulsar. the upper limit on the age of lis 884 vvr.," Therefore, assuming that $n$ and $K$ have remained constant over the lifetime of the pulsar, the upper limit on the age of is $\sim$ yr."
 This value is larger than the characterise age of vvr. but still smaller than the unambienously known age of the next voungest pulsar. (hat in the Crab Nebula.," This value is larger than the characteristic age of yr, but still smaller than the unambiguously known age of the next youngest pulsar, that in the Crab Nebula."
 Alereghettietal.(2002). cid an analysis of Irequency measurements of the aad data. as well as a small subset of the ddata reported here.," \citet{mbb+02} did an analysis of frequency measurements of the and data, as well as a small subset of the data reported here."
 Although data gaps prevented them [rom a firm conclusion regarding n because of the possibility of glitelies. their tentative estimate (made assuming no glitches nor substantial timing noise) was n=1.862:0.08. inconsistent with our result.," Although data gaps prevented them from a firm conclusion regarding $n$ because of the possibility of glitches, their tentative estimate (made assuming no glitches nor substantial timing noise) was $n=1.86 \pm 0.08$, inconsistent with our result."
 There are two plausible explanations for this discrepancy., There are two plausible explanations for this discrepancy.
 The first is that significant. timing noise and/or elitches cannot be definitely excluded in the 6-vr gap between the successive oobservations., The first is that significant timing noise and/or glitches cannot be definitely excluded in the 6-yr gap between the successive observations.
" The second is that the coordinate used to barveenter these data was ultimately [ound to be off bv ~7"".", The second is that the coordinate used to barycenter these data was ultimately found to be off by $\sim 7''$.
" The earlier study used coordinates derived from ddata with a 20"" position uncertainty. prior to the availabilitv of the new measurement provided by the used herein."," The earlier study used coordinates derived from data with a $20''$ position uncertainty, prior to the availability of the new measurement provided by the used herein."
 Our measured 7=2.6540.01 is significantly less (han 3. as is the case for all established values of n. which are shown in Table 2..," Our measured $n=2.65\pm0.01$ is significantly less than 3, as is the case for all established values of $n$, which are shown in Table \ref{table:indices}."
 There are several ideas for the nature of the deviation from the prediction of simple magnetic dipole braking., There are several ideas for the nature of the deviation from the prediction of simple magnetic dipole braking.
 A time-varving magnetic monent could produce an observed η less than the true ni=3 (Blancllord 1994)..., A time-varying magnetic moment could produce an observed $n$ less than the true $n_0=3$ \citep{bla94}. .
" A varving B-field can in principle be verified with a measurement of the third Ireeuency. derivative. 5, which may or may not ultimately be possible lor this source. depending on the number and strength of the elitches it experiences. as well as on the strength of ils Gimine noise."," A varying -field can in principle be verified with a measurement of the third frequency derivative, $\nudotdotdot$, which may or may not ultimately be possible for this source, depending on the number and strength of the glitches it experiences, as well as on the strength of its timing noise."
 Presently. 7 has been measured [for only (wo pulsars. both of whichare consistent with a," Presently, $\nudotdotdot$ has been measured for only two pulsars, both of whichare consistent with a"
the FRW inetzic. the distance modulus relates to cosmology according to ⊺∪⋯⋜∐↘↽↸∖∐⋖∶⋝⋜↧↴∖↴∶↴∙⊾↸∖∐↸∖↥⋅⋜↕↕⋜↧↴∖↴↻∪↴∖∷∖↴∏⋝↕↸∖⋅↖↖↽↸∖↖∏⋅↕↑↸∖↕↑⋜↧↴∖↴⋜↧↴∖↴⋯⊔∪↕⋟↴∖↴↑↸∖↻↕≯∏∐↸⊳,"the FRW metric, the distance modulus relates to cosmology according to where $\mu_{0}$ is called , $d_L(z)$ is the luminosity distance, and $H(z)$ is the parameter."
↑↕∪∐↴∖↴ Neve Ii, We use $H_0=72$ $\rm km~ s^{-1} Mpc^{-1}$ as the current value of the parameter \citep{komatsu09}.
") if j are constauts, is the vector formed by all 3). N4;, is the nuuber of redshift bius aud Az is the width of each biu."," To make $H(z)$ as general as possible, we write it as a sum of step functions where $\beta_{i}$ are constants, $\pmb{\beta}$ is the vector formed by all $\beta_i$, $N_{bin}$ is the number of redshift bins and $\Delta z$ is the width of each bin."
 This approach was proposed by ? in the coutext of deceleration paraucter analysis., This approach was proposed by \citet{shapiro06} in the context of deceleration parameter analysis.
 Although. when it is used for the parameter. the Fisher matrix calculations are simplified aud we still eet pretty general results.," Although, when it is used for the parameter, the Fisher matrix calculations are simplified and we still get pretty general results."
 Caven the definition above. 3; are now the parameters of our theory.," Given the definition above, $\beta_i$ are now the parameters of our theory."
 Plivsically. they represeut the value of the parameter in each redshift bin.," Physically, they represent the value of the parameter in each redshift bin."
 We can obviously express any functional form using this prescription. with higher resolution for a larger uunuber of bins.," We can obviously express any functional form using this prescription, with higher resolution for a larger number of bins."
 Iu this context. we are able to obtain analytical expressions for the luminosity distance aucl its derivatives. where L(i) corresponds to the integer part of £/47:.," In this context, we are able to obtain analytical expressions for the luminosity distance and its derivatives, where $L(z)$ corresponds to the integer part of $z/\Delta z$."
 Frou equatious (19). CD). aud (5)). we can calculate the Fisher matrix compoucuts as The paraucter may now be recoustructed as the suia of Las.and a lhuear combination of the new uncorrelated variables represeuted by the eigeuvectors of the Fisher matrix.," From equations \ref{eq:FMdefinicao}) ), \ref{eq:dist_mod_ap}) ), and \ref{eq:dist_lum_ap}) ), we can calculate the Fisher matrix components as The parameter may now be reconstructed as the sum of $H_{base}$and a linear combination of the new uncorrelated variables represented by the eigenvectors of the Fisher matrix."
 Mathematically.," Mathematically,"
circumstances we think that the effect of magnetic feedback is much more solidly assessed and should be considered as the ehief mechanism for reducing the compression in cosmic rav mocdified shock waves will evidences for amplified magnetic fields.,circumstances we think that the effect of magnetic feedback is much more solidly assessed and should be considered as the chief mechanism for reducing the compression in cosmic ray modified shock waves with evidences for amplified magnetic fields.
 On the other hand. the role of turbulent heating may become much more important for older remnants. when the shock velocity drops below ~2000km/s.," On the other hand, the role of turbulent heating may become much more important for older remnants, when the shock velocity drops below $\sim 2000
\rmn{km/s}$."
 At these times. the amplification of (he magnetic field max have become less important Irom the dvnamical point of view. so that (he magnetic feedback is also less important.," At these times, the amplification of the magnetic field may have become less important from the dynamical point of view, so that the magnetic feedback is also less important."
 These stages. as discussed bv Pluskin&Zirakashvili(2005) play an important role in determining (he spectrum of cosmic ravs observed at the Earth. at least at energies much lower than the knee energy.," These stages, as discussed by \cite{pz05}
 play an important role in determining the spectrum of cosmic rays observed at the Earth, at least at energies much lower than the knee energy."
 The authors are grateful to the anonvinous referee for a careful reading of the paper and for providing detailed comments that helped improving the manuscript., The authors are grateful to the anonymous referee for a careful reading of the paper and for providing detailed comments that helped improving the manuscript.
 This work was partially supported by PRIN-2006. by ASI through contract ASLINAF 1/088/06/0 and (for PB) by ihe US DOE and by NASA grant NAG5-10842.," This work was partially supported by PRIN-2006, by ASI through contract ASI-INAF I/088/06/0 and (for PB) by the US DOE and by NASA grant NAG5-10842."
 Fermilab is operated by Fermi Research Alliance. LLC under Contract No.," Fermilab is operated by Fermi Research Alliance, LLC under Contract No."
DE-ACO2-07C1111359 with the United States DOE.,DE-AC02-07CH11359 with the United States DOE.
to be Inminosity-depencent. since the twpical AGN contribution rises from 10 to ~60 per cent across (he ULIBG Iuninosity range.,"to be luminosity-dependent, since the typical AGN contribution rises from $\sim$ 10 to $\sim$ 60 per cent across the ULIRG luminosity range."
 Consequently. the most intriguing outcome of our mid-IR. analvsis is 3) the identification in several sources of elusive AGN components missed bv (the standard optical diagnostic tools.," Consequently, the most intriguing outcome of our mid-IR analysis is 3) the identification in several sources of elusive AGN components missed by the standard optical diagnostic tools."
 la particular. we find that the sources cliaracterized bv a steep continuum (which in our model is interpreted. as an effect of reddening). with deep absorption features and/or suppression of the polvevelic aromatic hydrocarbon (PAIL) tracers of star formation. do not usually show the optical line ratios of active galaxies. and occasionally are classified as pure IL regions.," In particular, we find that the sources characterized by a steep continuum (which in our model is interpreted as an effect of reddening), with deep absorption features and/or suppression of the polycyclic aromatic hydrocarbon (PAH) tracers of star formation, do not usually show the optical line ratios of active galaxies, and occasionally are classified as pure H regions."
 This subclass encompasses 10.15 per cent of (he local ULIRG population., This subclass encompasses $\sim$ 10–15 per cent of the local ULIRG population.
 Once corrected for extinction. some of these elusive AGN components account for most of the galaxy IR Iuminositv. falling in the quasar rather than in the Sevlert range.," Once corrected for extinction, some of these elusive AGN components account for most of the galaxy IR luminosity, falling in the quasar – rather than in the Seyfert – range."
 As a consequence. they represent the ideal targets for follow-up observations in the hard X-ray. baud. which are relevant to the quest for the most Inminous. obscured AGN (i.e. type 2 quasars) in the local Universe. and can also give deeper insight into the physical properties and geometrical structure of the obscuring material in à ULIBG-like enviroment.," As a consequence, they represent the ideal targets for follow-up observations in the hard X-ray band, which are relevant to the quest for the most luminous, obscured AGN (i.e. type 2 quasars) in the local Universe, and can also give deeper insight into the physical properties and geometrical structure of the obscuring material in a ULIRG-like enviroment."
 In this work we present (he X-rav analvsis of a sample of (en opticallv-elusive and IR-obseured. AGN with quasar-like luminosity. which span a large range with respect to the relative AGN/SB contribution. the degree of AGN obscuration and the overall UR luminosity. and are (herelore broadly representative of their parent class.," In this work we present the X-ray analysis of a sample of ten optically-elusive and IR-obscured AGN with quasar-like luminosity, which span a large range with respect to the relative AGN/SB contribution, the degree of AGN obscuration and the overall IR luminosity, and are therefore broadly representative of their parent class."
 New and observations have been obtainecl for four of these objects. i.e.IRAS 00397— 1312. IRAS 01003-2238. IRAS 01298—0744 and IRAS 12127-1412. while archival X-ray spectra are available for the other six buried AGN completing our sample.," New and observations have been obtained for four of these objects, i.e.IRAS $-$ 1312, IRAS $-$ 2238, IRAS $-$ 0744 and IRAS $-$ 1412, while archival X-ray spectra are available for the other six buried AGN completing our sample."
 All the sources at issue are introduced in Section 2. with the log of the X-ray observations ancl a brief description ol the data reduction.," All the sources at issue are introduced in Section 2, with the log of the X-ray observations and a brief description of the data reduction."
 In Section 3 we diseuss both the existing constraints and our new results on the sources of our X-ray sample. combining all (hese indications wilh our previous nucLIRo analvsis and interpreting them in (he wider context of the connection between cireumnuclear star formation anc BIL growth in Section 4.," In Section 3 we discuss both the existing constraints and our new results on the sources of our X-ray sample, combining all these indications with our previous mid-IR analysis and interpreting them in the wider context of the connection between circumnuclear star formation and BH growth in Section 4."
 The conclusions are drawn in Section 5., The conclusions are drawn in Section 5.
" Throughout this paper distances and luminosities have been computed assuming a ACDALcosmology based on the latest measures of the (Hy=70.5 km ! |. O4,=0.27 and O4= 0.73: Hinshaw οἱ al."," Throughout this paper distances and luminosities have been computed assuming a $\Lambda$ CDMcosmology based on the latest measures of the $H_0=70.5$ km $^{-1}$ $^{-1}$ , $\Omega_\rmn{m}=0.27$ and $\Omega_\Lambda=0.73$ ; Hinshaw et al."
 2009)., 2009).
A wav of investigating the large scale clustering properties of extragalactic objects. is to analyse their cosmological dipole moment.,"A way of investigating the large scale clustering properties of extragalactic objects, is to analyse their cosmological dipole moment."
 The anisotropy of the Cosmic Microwave Background (CAL) radiation and the solar motion relative to the Local Group of galaxies (LO) implies that. the LG has a peculiar velocity of ~000 kmi/see towards (Lb) = (277°.30°) (ef.," The anisotropy of the Cosmic Microwave Background $(CMB)$ radiation and the solar motion relative to the Local Group of galaxies $(LG)$ implies that the LG has a peculiar velocity of $\sim600$ km/sec towards (l,b) = $^{o}$ $^{o}$ ) (cf."
 Rowan-Robinson. Lvnden-Dell. 1988).," Rowan-Robinson, Lynden-Bell, 1988)."
 According to the linear perturbation theory (Peebles. 1980). the peculiar motion of the LG is in the same direction as the gravitational acceleration arising from the distribution of mass outside of the LG.," According to the linear perturbation theory (Peebles, 1980), the peculiar motion of the LG is in the same direction as the gravitational acceleration arising from the distribution of mass outside of the LG."
 Attempts to trace this mass distribution responsible for the gravitational. acceleration associated with the peculiar velocity of the LG have been mace using the LAS galaxies (Yahil. Walker," Attempts to trace this mass distribution responsible for the gravitational acceleration associated with the peculiar velocity of the LG have been made using the IRAS galaxies (Yahil, Walker"
absorption features and two narrow emission features: all hese have values that are inappropriate for real lines.,absorption features and two narrow emission features; all these have values that are inappropriate for real lines.
 Although very. clear in this figure. the line at cannot »e seen directly in the original spectrum. but is manifested as a lowering of the maximunm. that usually arises between he eroups of CN lines at and (see Fig. 1)).," Although very clear in this figure, the line at cannot be seen directly in the original spectrum, but is manifested as a lowering of the maximum that usually arises between the groups of CN lines at and (see Fig. \ref{spec}) )."
 Changing the ‘continuum’ fit from. quadratic to cubic or incar changes the set of selected Lines slightly and generally reduces (cubic) or increases (linear) the equivalent. widths., Changing the `continuum' fit from quadratic to cubic or linear changes the set of selected lines slightly and generally reduces (cubic) or increases (linear) the equivalent widths.
 However. most lines selected as lithium are recovered in each Case.," However, most lines selected as lithium are recovered in each case."
 At this point it is important to examine other possible sources of the features identified here., At this point it is important to examine other possible sources of the features identified here.
 Phe CN bancs coincident with AGTOT are: Q1 Q2(29) of the (12.77) band. Qs (44) of the (6.22) band and (22) Pye(18) of the (7.33) band (Davis&Phillips1963).," The CN bands coincident with $\lambda$ 6707 are: $_1$ $_2$ (29) of the 7) band, $_2$ (44) of the 2) band and $_1$ $_{12}$ (13) of the 3) band \cite{davis63}."
. Within each of these CN sub-bancds there are neighbouring bands which fall within the wavelength range and should. be present at similar strengths., Within each of these CN sub-bands there are neighbouring bands which fall within the wavelength range and should be present at similar strengths.
 These are not seen in the residual spectra. so it is unlikely that the line detected at is due to CN.," These are not seen in the residual spectra, so it is unlikely that the line detected at is due to CN."
 A similar argument applies to the R4(17) 2(16) I515) trio of lines belonging to the (1.44) Swan band of €» (Phillips&Davis 1965).. which appears atΑι. because the neighbouring trios at and are not seen.," A similar argument applies to the $_1$ $_2$ $_3$ (15) trio of lines belonging to the 4) Swan band of $_2$ \cite{phillips68}, which appears at, because the neighbouring trios at and are not seen."
 Other metal lines are unlikely to produce. significant absorption near (Barnbaum1994)., Other metal lines are unlikely to produce significant absorption near \cite{barnbaum94}.
. Another possible cause of spurious spectral features is spectral mismatch due to a temperature ciffercnee between the star and. the mean spectrum., Another possible cause of spurious spectral features is spectral mismatch due to a temperature difference between the star and the mean spectrum.
 A temperature dilference of sav KIN could produce a small apparent. absorption at due mainly to altering the contribution from the 77) band. but it would also &ererae larger features at anc6728A.," A temperature difference of say K could produce a small apparent absorption at due mainly to altering the contribution from the 7) band, but it would also gererate larger features at and."
. Since these are no seen. it is reasonable to assume that the feature is not due to a temperature mismatch.," Since these are not seen, it is reasonable to assume that the feature is not due to a temperature mismatch."
 The erouping of the stars in spectral subclasses helped: to minimize anv such problem., The grouping of the stars in spectral subclasses helped to minimize any such problem.
 Finally. it is possible that. in some cases the presence of a circumstellar component. in he absorption line can contaminate the photospheric eature.," Finally, it is possible that in some cases the presence of a circumstellar component in the absorption line can contaminate the photospheric feature."
 Although this possibility cannot be ruled out. it was not found to be a significant elect in Galactic carbon stars (Abia&Isern.2000).," Although this possibility cannot be ruled out, it was not found to be a significant effect in Galactic carbon stars \cite{abia00}."
.. Pherefore. the observed: absorption ines al seem to be correctly attributed: to. lithium.," Therefore, the observed absorption lines at seem to be correctly attributed to lithium."
 Ideally. rowever. high «dispersion. spectra of. these and. some comparison stars would be needed to confirm the weakest identifications.," Ideally, however, high dispersion spectra of these and some comparison stars would be needed to confirm the weakest identifications."
 Table la gives the final sample of carbon stars with absorption features within of AGTOT.S. with Wüozuz ο lend eit 2S x55.X0AX..," Table 1a gives the final sample of carbon stars with absorption features within of $\lambda$ 6707.8, with $_{6707}$ $>$ and with $\leq$ $\leq$."
 As seen in the previous section. features with Woso7 £004 larelibelglobeductoLi AGTOT at the 90 per cent confidence level. while those with 0.3; στον LarelibelylobeduetoLi AGTOT at the 5070 per cent. confidence level.," As seen in the previous section, features with $_{6707}$ $>$ are likely to be due to $\lambda$ 6707 at the 90 per cent confidence level, while those with $<$ $_{6707}$ $<$ are likely to be due to $\lambda$ 6707 at the 50–70 per cent confidence level."
 Column 1 gives the identification number of the star in the Ixontizas et al., Column 1 gives the identification number of the star in the Kontizas et al.
 (2001). catalogue. column 2 gives the spectral group assigned to each star (see Section 3.1). columns 3 to 6 give various photometric measurements which will be explained in Section 4. columns 7 and 8 give the Wosu7 (equivalent width) and measurements of the line atA.. column 9 gives the j-index taken from Morgan et al.," \shortcite{kontizas01} catalogue, column 2 gives the spectral group assigned to each star (see Section 3.1), columns 3 to 6 give various photometric measurements which will be explained in Section 4, columns 7 and 8 give the $_{6707}$ (equivalent width) and measurements of the line at, column 9 gives the j-index taken from Morgan et al."
 (2003) and column 10 provides cross references to Blanco. AleCarthy Blanco (1980): DMD. Dlanco AleCarthy (19000):: DM. Llughes (1989): SLEW. anc Westerlund ot al. (1078):," \shortcite{morgan03} and column 10 provides cross references to Blanco, McCarthy Blanco \shortcite{blanco80}: BMB, Blanco McCarthy \shortcite{blanco90}: BM, Hughes \shortcite{hughes89}: SHV, and Westerlund et al. \shortcite{westerlund78}:"
 λος, WORC.
 ‘Table 1b provides a list of LMC anc SAIC carbon stars with identification of .AGTOT recorded in the literature anc makes a noteworthy comparison with Table 1a., Table 1b provides a list of LMC and SMC carbon stars with identification of $\lambda$ 6707 recorded in the literature and makes a noteworthy comparison with Table 1a.
 SPLL95 reported. four Li-rich LAIC carbon. stars and a further 31 carbon. stars. for which lithium could. not. be detected., SPLL95 reported four Li-rich LMC carbon stars and a further 31 carbon stars for which lithium could not be detected.
 Richer. Olander Westerlund (1979). and Richer (1981). detected the lithium ino in two out of 52 stars and two out. of 25. stars respectively.," Richer, Olander Westerlund \shortcite{richer79}
 and Richer \shortcite{richer81} detected the lithium line in two out of 52 stars and two out of 25 stars respectively."
 With one in cach of the two pairs common o SPLL95. the total number of stars is six.," With one in each of the two pairs common to SPLL95, the total number of stars is six."
 SPLL95 also note two Li-rich SMC stars., SPLL95 also note two Li-rich SMC stars.
 These are both members of the tebeirot. Azzopardi Westerlund. catalogue (Itebeirot.al.1993). and both are J stars as seen in other 241 data (Cannon et al..," These are both members of the Rebeirot, Azzopardi Westerlund catalogue \cite{rebeirot93}
 and both are J stars as seen in other 2dF data (Cannon et al.,"
 in preparation)., in preparation).
 They. are also included. in ‘Table 1b., They are also included in Table 1b.
 First there is the question of commonality between the 2dl- ancl previously known Li-rich. stars., First there is the question of commonality between the 2dF-selected and previously known Li-rich stars.
 Ht turns out that not one of the six known Li-rich stars were included in the 2dE sample., It turns out that not one of the six known Li-rich stars were included in the 2dF sample.
 Nor were any of the stars. reported, Nor were any of the stars reported
We consider six He I lines. five lines for orthohelium A3890 (3s—2p). A4026 (5d—2p). A44T1 (4d— 2p). ABSTS (3d—2p). AT065 (3s—2p). and one line [ον parahelium. AGGTS (3d— 2p).,"We consider six He I lines, five lines for orthohelium $\lambda$ 3890 $3s\rightarrow 2p$ ), $\lambda$ 4026 $5d\rightarrow 2p$ ), $\lambda$ 4471 $4d\rightarrow 2p$ ), $\lambda$ 5875 $3d\rightarrow 2p$ ), $\lambda$ 7065 $3s\rightarrow 2p$ ), and one line for parahelium $\lambda$ 6678 $3d\rightarrow 2p$ )."
 The A3890 ancl ATOG5S are sensitive (o a [Iuorescent correction and thus to the raciative transfer., The $\lambda$ 3890 and $\lambda$ 7065 are sensitive to a fluorescent correction and thus to the radiative transfer.
 A4026 is generally weak. susceptible largely (o stellar absorption.," $\lambda$ 4026 is generally weak, susceptible largely to stellar absorption."
 We use the effective recombination coefficients of Benjamin et al. (, We use the effective recombination coefficients of Benjamin et al. (
1999). which include collisional excitation. and the radiative (ransler caleulation of Benjamin et al. (,"1999), which include collisional excitation, and the radiative transfer calculation of Benjamin et al. ("
2002) for fInorescent corrections. fi. which is controlled by the optical depth 7(3890).,"2002) for fluorescent corrections, $f_\lambda$, which is controlled by the optical depth $\tau(3890)$."
 We caleulate the abundance of sinely ionised helium as This is the same as that. adopted by OSO4 and that by ITO4 up to the inclusion. of αμα., We calculate the abundance of singly ionised helium as This is the same as that adopted by OS04 and that by IT04 up to the inclusion of $a_{\rm HeI}$.
 We do not know what ratios are to be taken for aja lor different lines., We do not know what ratios are to be taken for $a_{\rm HeI}$ for different lines.
 We assume here (hat all absorption strengths are identical in equivalent strenetls. as was done in O504.," We assume here that all absorption strengths are identical in equivalent strengths, as was done in OS04."
 This is probably not too bad an approximation in view of the observation for absorption in D stars (Lennon et al., This is probably not too bad an approximation in view of the observation for absorption in B stars (Lennon et al.
 1993: Lvubimkov οἱ al., 1993; Lyubimkov et al.
 2000) and the size of the resulting errors in our calculation that amount to 250% of the central values: more detailed line ratios are ihe matter al a higher order level., 2000) and the size of the resulting errors in our calculation that amount to $\approx$ of the central values: more detailed line ratios are the matter at a higher order level.
 We refer to Olive Skillman (2001) for more detailed discussion for this issue., We refer to Olive Skillman (2001) for more detailed discussion for this issue.
 Our method of analvsis differs from the usual one to find the parameters., Our method of analysis differs from the usual one to find the parameters.
" We fid the best likelihood solution in [ull four parameter space y. à, (electron density). αι ancl 7 Lor six lines. rather (han minimising the sum of 4? for each line. which has been adopted in the literature. for (he purpose to take the correlation among the lines into account."," We find the best likelihood solution in full four parameter space $y^+$, $n_e$ (electron density), $a_{\rm HeI}$ and $\tau$ for six lines, rather than minimising the sum of $\chi^2$ for each line, which has been adopted in the literature, for the purpose to take the correlation among the lines into account."
 The electron density is poorly constrained. but its indeterminacy affects the resulting Y. little due to its very weak dependence in (he recombination coefficient.," The electron density is poorly constrained, but its indeterminacy affects the resulting $Y$ little due to its very weak dependence in the recombination coefficient."
 We add the abundance of doubly ionised helium y to calculate Y when He II A4686 is detected., We add the abundance of doubly ionised helium $y^{++}$ to calculate $Y$ when He II $\lambda$ 4686 is detected.
 We take (he oxveen abundance from ITO4., We take the oxygen abundance from IT04.
" The final results are displaved [or the mass fraction of helium Y as a function of the oxvgen abundance relative to hvdrogen Ο/Η. and linear extrapolation is emploved to obtain the primordial helium abundance Y, in the zero oxvgen abundance limit (Peimbert Torres-Peimbert 1974). We adopt dY/d(O/1l)=18.2dY/dZ from ITO:"," The final results are displayed for the mass fraction of helium $Y$ as a function of the oxygen abundance relative to hydrogen O/H, and linear extrapolation is employed to obtain the primordial helium abundance $Y_p$ in the zero oxygen abundance limit (Peimbert Torres-Peimbert 1974), We adopt $dY/d({\rm O/H})=18.2 dY/dZ$ from IT04."
"where X=0.76 is the hydrogen mass fraction. OnM.+p. is the baryon density at z and p,=I0h (Mpe/1)?","where $X=0.76$ is the hydrogen mass fraction, $\rho_{\rm b}(z)=\Omega_{\rm b}
(1+z)^3\rho_{\rm c}$ is the baryon density at z and $\rho_{\rm c}= 2.7752 \times 10^{11}\ {\rm M_{\odot}}/h$ $({\rm Mpc}/h)^{-3}$."
 We assume that the total hydrogen mass in à given pixel of the experiment only depends on the halo mass so that the hydrogen mass density py is given. by pu-dMpuMgM)., We assume that the total hydrogen mass in a given pixel of the experiment only depends on the halo mass so that the hydrogen mass density $\rho_{\rm H}$ is given by $\rho_{\rm H} = \int_{M_{\rm min}}^{\infty} dM \frac{dn}{dM}M_{\rm HI}(M)$.
 To obtain Myj(M) we used the same Inaprocedure as before. querying the simulation. from Obreschkow et al. (," To obtain $M_{\rm HI}(M)$ we used the same procedure as before, querying the simulation from Obreschkow et al. ("
2009d) and adding the My) from the galaxies in each halo.,2009d) and adding the $M_{\rm HI}$ from the galaxies in each halo.
 The resulting scatter plot is shown in the right panel of Figure 1. together with the average in each mass bin (blue dots)., The resulting scatter plot is shown in the right panel of Figure \ref{fig:L_CO_M_HI} together with the average in each mass bin (blue dots).
" The red line shows a fitting function to the average values using My,=103:EET P975, where M is the halo mass. A=0.75. 0.74 and 0.75. and B=0.17. 0.23 and 0.07 for z26. 7 and 8 respectively."," The red line shows a fitting function to the average values using $M_{\rm HI}=10^{A\times\log_{10}(M)+B}$ , where $M$ is the halo mass, $A=0.75$, $0.74$ and $0.75$, and $B=0.17$, $0.23$ and $0.07$ for $z=6$, $7$ and $8$ respectively."
 Following the description related to the CO line intensity. the mean 2l-em temperature is taken to have spatial variations Z8brightness(x)ΤΕΙ+byó(x)). where by is the bias of galaxies containing neutral hydrogen Theηί bu) dusterins poweri of the 21-cm emission from galaxies is then P.Ko)spectrum=(TEbjPss.K).," Following the description related to the CO line intensity, the mean 21-cm brightness temperature is taken to have spatial variations $T^{\rm G}_{\rm b}({\bf x}) = \bar{T}^{\rm G}_{\rm b}(1+b_{\rm H}\delta({\bf x}))$, where $b_{\rm H}$ is the bias of galaxies containing neutral hydrogen (z) = The clustering power spectrum of the 21-cm emission from galaxies is then $P^{\rm G}_{\rm H}(z,k) = (\bar{T}^{\rm G}_{\rm b})^2 b^2_{\rm H}P_{\delta \delta}(z,k)$."
 Again. the shot noise power spectrum for 21-cm emission Is ΡΟ [dM JR," Again, the shot noise power spectrum for 21-cm emission is (z) = dM )^2."
 The total power spectrum of 21-em emission follows from a sum of shot-noise and clustering terms (see middle panel in figure 3))., The total power spectrum of 21-cm emission follows from a sum of shot-noise and clustering terms (see middle panel in figure \ref{fig:Pco}) ).
" The cross powerspectrum between 21-cm and CO line intensities is P5,=PROM+PE,EPIS where we again separate the contribution from neutral hydrogen in the IGM and neutral hydrogen remaining in individual galaxies."," The cross power spectrum between 21-cm and CO line intensities is $P^{\rm tot}_{\rm CO,H}\ =\ P^{\rm IGM}_{\rm CO,H} + P^{\rm G}_{\rm CO,H} + P^{\rm shot}_{\rm CO,H}$, where we again separate the contribution from neutral hydrogen in the IGM and neutral hydrogen remaining in individual galaxies."
 Based on the discussion related to 21-em fluctuations. the cross power spectrum of the CO line and 21-em emission in the IGM is HES0 = ο Pss] where P55(z.4) ts the cross power spectrum for the ionized fraction and the dark matter.," Based on the discussion related to 21-cm fluctuations, the cross power spectrum of the CO line and 21-cm emission in the IGM is (z,k) = c(z) ], where $P_{\delta_{x}\delta}(z,k)$ is the cross power spectrum for the ionized fraction and the dark matter."
 The IGM gas ts correlated with CO lines as they both trace the same underlying dark matter density field., The IGM gas is correlated with CO lines as they both trace the same underlying dark matter density field.
 The cross power spectrum of the CO line and 21-cm emission in individual galaxies is Wed = GobcobgPss(. while the shot noise power spectrum of the CO line and 2]-em emission in the galaxies is ης)poy —~ dM yD4? eG) In Figure left panel. we show the brightness temperature power spectrum3. for the CO line at z27. whilein the middle panel we show the 21-cm brightness temperature fluctuations at the same redshift and in the right panel. we show the cross-correlation between the two.," The cross power spectrum of the CO line and 21-cm emission in individual galaxies is (z,k) = (z,k), while the shot noise power spectrum of the CO line and 21-cm emission in the galaxies is (z) = dM ^2 c(z) In Figure 3, left panel, we show the brightness temperature power spectrum for the CO line at $z=7$, while in the middle panel we show the 21-cm brightness temperature fluctuations at the same redshift and in the right panel, we show the cross-correlation between the two."
 In the case of 21-cm fluctuations. the solid lines show the prediction based on the models of Mao et al. (," In the case of 21-cm fluctuations, the solid lines show the prediction based on the models of Mao et al. ("
2008). while in dashed lines we show the prediction from the semi-numerical simulation of Santos et al. (,"2008), while in dashed lines we show the prediction from the semi-numerical simulation of Santos et al. ("
2010).,2010).
 To discuss the possibility of measuring the CO signal and the CO-21 em cross-correlation we make use of a calculation similar to the one used in 21-em interferometers., To discuss the possibility of measuring the CO signal and the CO-21 cm cross-correlation we make use of a calculation similar to the one used in 21-cm interferometers.
 Following Santos et al. (, Following Santos et al. (
"2010). the noise power spectrum. Py for a given experimental ""pixel"" in. Fourier space is given by Py(k.0)(Daksin()/2z)] where A, the collecting=DOC areaTZ/[Azton of one element of the interferometer (which could be a station). fo is the total observation time and the function 160) captures the baseline density distribution on the plane perpendicular to the line of sight. assuming already it is rotationally invariant (& is the moduli of the wave mode k and 0 is the angle between k and the line of sight).","2010), the noise power spectrum, $P_N$ for a given experimental “pixel” in Fourier space is given by $P_N(k,\theta)=D_A^2 y (\lambda^4 T_{sys}^2)/[A_e^2 t_0 n\left(D_A k \sin(\theta)/2\pi\right)]$ where $A_e$ is the collecting area of one element of the interferometer (which could be a station), $t_0$ is the total observation time and the function $n()$ captures the baseline density distribution on the plane perpendicular to the line of sight, assuming already it is rotationally invariant $k$ is the moduli of the wave mode $\mathbf{k}$ and $\theta$ is the angle between $\mathbf{k}$ and the line of sight)."
" Typically this baseline distribution will be more concentrated around the core but for interferometers with high filling factors we can make the simplification that the distribution ts constant so that the required function for above is n)2A7N7/7Dz,,, with N, as the number of elements of the interferometer and D,,, the maximum baseline of the distribution.", Typically this baseline distribution will be more concentrated around the core but for interferometers with high filling factors we can make the simplification that the distribution is constant so that the required function for above is $n()=\lambda^2 N_a^2/\pi D_{max}^2$ with $N_a$ as the number of elements of the interferometer and $D_{max}$ the maximum baseline of the distribution.
" Note that the error in the measured power spectrum at a given k is just (Ps+Py)//CN,,). where Ps is the signal power spectrum and N,, 1s the number of modes contributing to a given binned measurement."," Note that the error in the measured power spectrum at a given $\mathbf{k}$ is just $\left(P_S+P_N\right)/\sqrt{(N_m)}$, where $P_S$ is the signal power spectrum and $N_m$ is the number of modes contributing to a given binned measurement."
 In order to count these number of modes. we consider a grid in & space with a resolution given experimentby (2x)/(yr FoVB). which is set by the volume of the (B is the bandwidth used in the analysis and FoV is the field of view).," In order to count these number of modes, we consider a grid in $k$ space with a resolution given by $(2\pi)^3/({\rm y r^2\cdot {\rm FoV}\cdot B})$, which is set by the volume of the experiment $B$ is the bandwidth used in the analysis and FoV is the field of view)."
 Typically we will be interested on linear scales (k<1.0 h/Mpe) corresponding to a few areminutes., Typically we will be interested on linear scales $k<1.0$ h/Mpc) corresponding to a few arcminutes.
 Given the frequencies involved. the need for large ΕΟΝ. and high sensitivity to 77K brightness temperature fluctuations. leads to an experimental setup that involves a total collecting area Aq=385 mr. bandwidth B=| GHz with spectral resolution àr=30 MHz and interferometer spacings between 0.7 and 25 m. The number of elements is 1000 with each having a receiver. with system temperature of 20K. In the left panel of Figure 3. we assume a total integration time of 3000 hours when caleulating the noise power spectrum.," Given the frequencies involved, the need for large FoV, and high sensitivity to $\mu$ K brightness temperature fluctuations leads to an experimental setup that involves a total collecting area $A_{\rm tot} = 385$ $^2$, bandwidth $B=1$ GHz with spectral resolution $\delta \nu=30$ MHz and interferometer spacings between 0.7 and 25 m. The number of elements is 1000 with each having a receiver with system temperature of 20K. In the left panel of Figure 3, we assume a total integration time of 3000 hours when calculating the noise power spectrum."
 For 21-cm noise calculations we make use of a setup similar to LOFAR. though we note that our calculations are not too different for an experiment like MWA.," For 21-cm noise calculations we make use of a setup similar to LOFAR, though we note that our calculations are not too different for an experiment like MWA."
 For experimental parameters related to LOFAR. we refer the reader to Harker et al. (," For experimental parameters related to LOFAR, we refer the reader to Harker et al. ("
2010).,2010).
" The values (at 150 MHz) are A,25«107 n. Ty,2 490K (instrument noise temperature). FOV=25 deg. bandwidth of 8 MHz with ὃν20.5 MHz and D,4,=2000 m. We take Ti,=1000 hours."," The values (at 150 MHz) are $A_{\rm tot}=5\times10^4$ $^2$, $T_{\rm sys}=490$ K (instrument noise temperature), FOV=25 $^2$, bandwidth of 8 MHz with $\delta \nu=0.5$ MHz and $D_{\rm max}=2000$ m. We take $T_{\rm int}=1000$ hours."
 For the proposed experimental setup the brightness temperature fluctuations can be detected with a cumulative signal-to-noise ratio that leads to more than 406 confidence., For the proposed experimental setup the brightness temperature fluctuations can be detected with a cumulative signal-to-noise ratio that leads to more than $\sigma$ confidence.
 However. CO(1-0) mapping could be impacted by foregrounds. including spectral lines associated with other molecules: In the case of other transitions of the CO lines. the contamination for CO(1-0). measurements at z 6 to 8 Is likely to be minimal: the CO(2-1)line for example must originate from z— 13 to 17.," However, CO(1-0) mapping could be impacted by foregrounds, including spectral lines associated with other molecules; In the case of other transitions of the CO lines, the contamination for CO(1-0) measurements at $z\sim$ 6 to 8 is likely to be minimal; the CO(2-1)line for example must originate from $z \sim$ 13 to 17."
 The most significant contaminations will likely come from molecular transitions that have rest wavelengths longward of the CO(1-0) line and thus coming from lower redshifts., The most significant contaminations will likely come from molecular transitions that have rest wavelengths longward of the CO(1-0) line and thus coming from lower redshifts.
 To avoid such contaminations and to improve the overall study of reionization we suggest a cross-correlation between 21-cm, To avoid such contaminations and to improve the overall study of reionization we suggest a cross-correlation between 21-cm
or 2ο Lwv-a enters the spectral range ane the issues again disappear.),for $z>2$ $\alpha$ enters the spectral range and the issues again disappear.)
 The overlap of LRG and EL populations with very different biases in the same redshift range 2=KT1.0 also olfers the possibility of erosscorrelation and reduction of sample variance (McDonaldetal.2008)., The overlap of LRG and EL populations with very different biases in the same redshift range $z=0.7-1.0$ also offers the possibility of crosscorrelation and reduction of sample variance \citep{urossamp}.
. Thus. hese results motivate shifting the EL redshift range to DTLT. achieving o(5)=0.040 (and 0.030 with Stage LIL information)," Thus, these results motivate shifting the EL redshift range to $z=0.7-1.7$, achieving $\sigma(\gamma)=0.040$ (and 0.030 with Stage III information)."
 The values of the galaxy number densities anc biases listed in Table 1 come from the references given., The values of the galaxy number densities and biases listed in Table \ref{spec} come from the references given.
 While it is bevond the scope of this paper to do detailed survey design. we can explore whether some variations in the adopted: values matter.," While it is beyond the scope of this paper to do detailed survey design, we can explore whether some variations in the adopted values matter."
 As we have seen in the previous subsection. a change in the constant bias of the ELC population from 0.8 to 1.2 has a οσοι on determining .," As we have seen in the previous subsection, a change in the constant bias of the ELG population from 0.8 to 1.2 has a effect on determining $\gamma$."
 We now consider an evolving moclel for bias., We now consider an evolving model for bias.
" Motivated by Padmanabhanetal.(2006) we take bppe;=b,|O42 with fiducial b,=1.6. and motivated by Sumivoshietal.(2009) we take be,=bo|(20.7)/2.6 with fiducial b»=I."," Motivated by \citet{padma06} we take $b_{LRG}=b_1+0.4z$ with fiducial $b_1=1.6$, and motivated by \citet{sumiyoshi} we take $b_{EL}=b_2+(z-0.7)/2.6$ with fiducial $b_2=1$."
 The constraints on the dark energy. parameters 5. uw. is improve byιν24... for BigBOSS and degrade by5'A..WM... for JDESM-PS.," The constraints on the dark energy parameters $\gamma$, $w_0$, $w_a$ improve by, for BigBOSS and degrade by, for JDEM-PS."
 These changes are due to altered: covariances between the bias parameters and the dark energy. parameters. involving an interplay between the nP factor in the ellective volume and the Fisher sensitivity OlInP/Ob;.," These changes are due to altered covariances between the bias parameters and the dark energy parameters, involving an interplay between the $nP$ factor in the effective volume and the Fisher sensitivity $\partial\ln P/\partial b_i$."
 Note that the latter quantity goes as 2/(b;|fy). so an increased. bias decreases the Fisher element.," Note that the latter quantity goes as $2/(b_i+f\mu)$, so an increased bias decreases the Fisher element."
 However. increasing the bias increases the ellective volume through raising n£.," However, increasing the bias increases the effective volume through raising $nP$."
 In the BieBOSS case. this second factor is more than sullicient to compensate for the reduced: sensitivity.," In the BigBOSS case, this second factor is more than sufficient to compensate for the reduced sensitivity."
 However. JDIM-PS has such a high galaxy number density that the change in nl? has little effect on the elfective volume. leaving only the reduced. sensitivity.," However, JDEM-PS has such a high galaxy number density that the change in $nP$ has little effect on the effective volume, leaving only the reduced sensitivity."
 Updating ‘Table 8. for the evolving bias case. Table 12) shows further eains in the figures of merit for BieBOSS relative to JDIEM-Ps.," Updating Table \ref{tab:fom} for the evolving bias case, Table \ref{tab:fombz} shows further gains in the figures of merit for BigBOSS relative to JDEM-PS."
 Regarding the number densities used. for the galaxy. populations. these come from selection functions. of the survey with respect to the intrinsic populations within the detection limits.," Regarding the number densities used for the galaxy populations, these come from selection functions of the survey with respect to the intrinsic populations within the detection limits."
 In general. target selection is a complicated procedure and these numbers represent a sculpted target sample not a Ilux- or volume-limited distribution.," In general, target selection is a complicated procedure and these numbers represent a sculpted target sample not a flux- or volume-limited distribution."
 We consider one simple variation in the BieBOSS LLG distribution. motivated by the previous subsection where the redshift range was shifted from 2—1 2to2=0.7 L7.," We consider one simple variation in the BigBOSS ELG distribution, motivated by the previous subsection where the redshift range was shifted from $z=1-2$ to $z=0.7-1.7$."
 Such a shift was found to slightly improve the cosmology constraints. and it also reduces the amount of time needed to observe the galaxies.," Such a shift was found to slightly improve the cosmology constraints, and it also reduces the amount of time needed to observe the galaxies."
 HE we take advantage of this by now looking at a survey plan with four times the number density of ELC inthe range z2—0.7l(andz-1 1.7 unchanged). we find further improvements in determination of 5. wu. ws by2%...4%... relative to the uniform number density in 2=07L7 case of the previous subsection.," If we take advantage of this by now looking at a survey plan with four times the number density of ELG in the range $z=0.7-1$ (and $z=1-1.7$ unchanged), we find further improvements in determination of $\gamma$, $w_0$, $w_a$ by, relative to the uniform number density in $z=0.7-1.7$ case of the previous subsection."
 These caleulations show that the basic point of ground ancl space surveys being capable of delivering comparable cosmology constraints is not. very sensitive (ο these variations in the survey design., These calculations show that the basic point of ground and space surveys being capable of delivering comparable cosmology constraints is not very sensitive to these variations in the survey design.
 Detailed. experiment design and optimization. however. is bevond the scope of this paper.," Detailed experiment design and optimization, however, is beyond the scope of this paper."
 We have not considered other experiments such as the Euclid space mission (Cimattiοἱal.2009).. since it includes other cosmological probes on a par with the power spectrum measurement. and 21 em mapping surveys such as SISA (see Petersonetal.(2009):Morales&Weyithe (2009))). since neutral hydrogen eas measurement techniques and precision constraints are not as fully developed.," We have not considered other experiments such as the Euclid space mission \citep{euclid}, since it includes other cosmological probes on a par with the power spectrum measurement, and 21 cm mapping surveys such as SKA (see \citet{peterson,morales}) ), since neutral hydrogen gas measurement techniques and precision constraints are not as fully developed."
 The three-dimensional distribution of large scale structure contains information on both the cosmological parameters and testing. eravity., The three-dimensional distribution of large scale structure contains information on both the cosmological parameters and testing gravity.
 We have studied: the capabilities of next-generation power spectrum experiments from the ground. BigBOSS. and from space. JDISZM-DP'S. to use the baryon acoustic oscillations. power spectrum shape. ancl redshift space distortions to test standard cosmology.," We have studied the capabilities of next-generation power spectrum experiments from the ground, BigBOSS, and from space, JDEM-PS, to use the baryon acoustic oscillations, power spectrum shape, and redshift space distortions to test standard cosmology."
 The main conclusion is that. the. two experiments could achieve comparable constraints., The main conclusion is that the two experiments could achieve comparable constraints.
 We emphasized the importance of including simultaneously the parameters that allect growth the gravitational growth index characterizing deviations from general relativity. the dark energv equation of state value and. its time variation. and neutrino mass.," We emphasized the importance of including simultaneously the parameters that affect growth – the gravitational growth index characterizing deviations from general relativity, the dark energy equation of state value and its time variation, and neutrino mass."
 Including these and other cosmological parameters we estimate the uncertainty on determination of the gravitational growth index to be 0.043 for BigBOSS. 0.054 for JDIZM-PS. or 0.031 and 0.038 respectively. when combined with nearer-term. Stage LLL experiments.," Including these and other cosmological parameters we estimate the uncertainty on determination of the gravitational growth index to be 0.043 for BigBOSS, 0.054 for JDEM-PS, or 0.031 and 0.038 respectively when combined with nearer-term, Stage III experiments."
 This represents nearly an order of magnitude improvement over Stage LEE knowledge., This represents nearly an order of magnitude improvement over Stage III knowledge.
 We have also studied: the survey characteristics and confirm that the power spectrum at redshifts zz1 has strong leverage., We have also studied the survey characteristics and confirm that the power spectrum at redshifts $z\lesssim1$ has strong leverage.
 This makes the luminous red. galaxy component ofthe survey quite important., This makes the luminous red galaxy component of the survey quite important.
 Furthermore. our results demonstrate that shifting the redshift range of the emission line galaxy survey of BigBOSS from 2=1 2t02—0.7.LT can improve the constraints. while adding benefits such as reduced technical complexity and line confusion anc increased: signal-to-noise ancl the ability. to. crosscorrelate galaxy populations of dilferent. biases.," Furthermore, our results demonstrate that shifting the redshift range of the emission line galaxy survey of BigBOSS from $z=1-2$ to $z=0.7-1.7$ can improve the constraints, while adding benefits such as reduced technical complexity and line confusion and increased signal-to-noise and the ability to crosscorrelate galaxy populations of different biases."
 Lyman-a forest spectra from BigBOSS quasars a >2. which we have neglected. will further advance the determination of cosmological parameters.," $\alpha$ forest spectra from BigBOSS quasars at $z>2$, which we have neglected, will further advance the determination of cosmological parameters."
 The prospects for testing standard cosmology anc in particular general relativity are promising., The prospects for testing standard cosmology and in particular general relativity are promising.
 Improve understanding of the translincar density regime anc velocitics would. further extend. the number of usable, Improved understanding of the translinear density regime and velocities would further extend the number of usable
obtain the results in Table 1..,obtain the results in Table \ref{ages_table}.
 The resulting fit is shown on the right-hand side of Figure 6.., The resulting fit is shown on the right-hand side of Figure \ref{onc}.
" We took the photometry from ?,, and used an uncertainty of 0.02 mags in both magnitude and colours."," We took the photometry from \cite{1982AandAS...47..323C}, and used an uncertainty of 0.02 mags in both magnitude and colours."
 This is an estimate for U—B and corresponds to the deviations for single observations derived by ? from comparison with the data of ?.., This is an estimate for $U-B$ and corresponds to the deviations for single observations derived by \cite{1982AandAS...47..323C} from comparison with the data of \cite{1959MNSSA..18...57F}.
 Although ? often has four observations per star we prefer to take the view that the uncertainty represents the difference between the photometric systems., Although \cite{1982AandAS...47..323C} often has four observations per star we prefer to take the view that the uncertainty represents the difference between the photometric systems.
" We use the membership list of ?,, which is based on proper motions, photometry and spectroscopy, and select only stars with B—V«0.1 to ensure we exclude PMS stars."," We use the membership list of \cite{1982AandAS...47..323C}, which is based on proper motions, photometry and spectroscopy, and select only stars with $B-V < 0.1$ to ensure we exclude PMS stars."
" We found that if we included star 40, which appears to sit just below the MS we obtained an unacceptably low value of Pr(r?)."," We found that if we included star 40, which appears to sit just below the MS we obtained an unacceptably low value of $\Pr(\tau^2)$."
" Furthermore this star is right on the edge of the proper motion distribution of the bulk of the members, so we excluded it."," Furthermore this star is right on the edge of the proper motion distribution of the bulk of the members, so we excluded it."
" We used the data of ?,, excluding starswith B—V>0.0, and HD93163, which lies away from the sequence."," We used the data of \cite{1972ApJ...173...63E}, excluding starswith $B-V>0.0$, and HD93163, which lies away from the sequence."
" Unfortunately ? does not provide uncertainties, but we found a single extinction would yield Pr(7?)—0.79 for uncertainties of 0.014 and 0.014 mags in B—V and U— respectively, which suggests the extinction is uniform."," Unfortunately \cite{1972ApJ...173...63E} does not provide uncertainties, but we found a single extinction would yield $\Pr(\tau^2)$ =0.79 for uncertainties of 0.014 and 0.014 mags in $B-V$ and $U-B$ respectively, which suggests the extinction is uniform."
" UsingB that extinction, and an uncertainty in V of 0.025 mags gives Pr(r?)—0.27 when fitted in V vs B— V."," Using that extinction, and an uncertainty in $V$ of 0.025 mags gives $\Pr(\tau^2)$ =0.27 when fitted in $V$ vs $B-V$ ."
curves.,curves.
" In principle. the RAIS scatter of the S!"" curves gives an estimate of the variability of the sources."," In principle, the RMS scatter of the $S^{\rm final}$ curves gives an estimate of the variability of the sources."
 However. it is important to realize that the division of the input 5 curves by the AZ? light curve is an operation on two correlated quantities.," However, it is important to realize that the division of the input $S^N$ curves by the $M^{(2)}$ light curve is an operation on two correlated quantities."
" That is. each point in the S curves gets scaled by a quantity that includes a contribution from itself,"," That is, each point in the $S^N$ curves gets scaled by a quantity that includes a contribution from itself."
 As a result. the division by the M) curve has the effect. on average. of depressing the measured RAIS of the ομα cupves below their true intrinsic scatter.," As a result, the division by the $M^{(2)}$ curve has the effect, on average, of depressing the measured RMS of the $S^{\rm final}$ curves below their true intrinsic scatter."
" We have estimated the correction for this effect. in a statistical sense. by using the measured RAIS scatter in the SH"" curves."," We have estimated the correction for this effect, in a statistical sense, by using the measured RMS scatter in the $S^{\rm final}$ curves."
 The measured and corrected RAIS scatters [or each source are given in the 7077 RAIS” and “Intrinsic RAIS” cohunus of Table 3.. respectively.," The measured and corrected RMS scatters for each source are given in the $M^{(2)}$ RMS” and “Intrinsic RMS” columns of Table \ref{tab_rms}, respectively."
 The maximum correction is onlv A RRAIS=+0.15% ancl. thus. our conclusion that the CSOs have extremely stable flux densities does not change.," The maximum correction is only $\Delta$ $+$ and, thus, our conclusion that the CSOs have extremely stable flux densities does not change."
" Whether we use the 7/77 or ""Intrinsic values for the RAIS variability of the CSOs. we find that the mean RAIS scatter for the five CSOs is ~0.7%.."," Whether we use the $M^{(2)}$ ” or “Intrinsic” values for the RMS variability of the CSOs, we find that the mean RMS scatter for the five CSOs is $\sim$."
. This is the same value obtained by considering the combined sample of CSOs to be one distribution and calculating its RAIS scatter about (he mean., This is the same value obtained by considering the combined sample of CSOs to be one distribution and calculating its RMS scatter about the mean.
 Finally. we note that the estimated intrinsic variabilities that we have derived above may still include unknown svstematic errors and {hus should be regarcec as upper limits.," Finally, we note that the estimated intrinsic variabilities that we have derived above may still include unknown systematic errors and thus should be regarded as upper limits."
 The CSO light curves can be contrasted wilh those of the phase calibrators. both οἱ which are core-jet sources on the parsec scale1997).. shown in Figure 5..," The CSO light curves can be contrasted with those of the phase calibrators, both of which are core-jet sources on the parsec scale, shown in Figure \ref{fig_pltpcal}."
 The core-jet light curves have been processed in (he same manner as the CSO light curves. including the correction with the C! eurve.," The core-jet light curves have been processed in the same manner as the CSO light curves, including the correction with the $M^{(2)}$ curve."
 Not only do the core-jet calibrator curves have a higher RAIS scatter than do the CSO light curves (Table 4)). but the nature of the light curves is qualitatively different from those of the CSOs.," Not only do the core-jet calibrator curves have a higher RMS scatter than do the CSO light curves (Table \ref{tab_pcrms}) ), but the nature of the core-jet light curves is qualitatively different from those of the CSOs."
 Instead of random scatter about the mean value. the core-jel sources show svstematic changes in flux density during the course of the observations. indicating true variability at the level of nearly105.," Instead of random scatter about the mean value, the core-jet sources show systematic changes in flux density during the course of the observations, indicating true variability at the level of nearly."
.. Thev also exhibit variability from from epoch to epoch., They also exhibit variability from from epoch to epoch.
 Given the nature of the CSO light curves. which show only small ancl random variations about a mean value. we conclude that the CSO sources should make excellent fIux density calibrators for radio monitoring campaigns.," Given the nature of the CSO light curves, which show only small and random variations about a mean value, we conclude that the CSO sources should make excellent flux density calibrators for radio monitoring campaigns."
 If high-precision relative calibration is desired. we recommend that at least four CSOs be observed in each epoch. if possible.," If high-precision relative calibration is desired, we recommend that at least four CSOs be observed in each epoch, if possible."
 With this observing sirategv. it should be possible to account correctly [or svstematic errors in the overall flix density calibration.," With this observing strategy, it should be possible to account correctly for systematic errors in the overall flux density calibration."
 In addition. having at least four CSO calibrators enables the rejection of anv one of the calibrators if something adversely affects its measured. flix density. for either the entire monitoring campaign or a single epoch.," In addition, having at least four CSO calibrators enables the rejection of any one of the calibrators if something adversely affects its measured flux density, for either the entire monitoring campaign or a single epoch."
 We emphasize. again. that CSOs should not be equated with GPS sources. especially for the purpose of Hux density calibration.," We emphasize, again, that CSOs should not be equated with GPS sources, especially for the purpose of flux density calibration."
"spiral arius. and oue smaller. ""local arm.”","spiral arms, and one smaller, “local arm.”"
 Each arm js asstuned to extend through an angele (4. out to a maximi radial distanceof Ryyax=l5 kpc.," Each arm is assumed to extend through an angle $\theta_{\rm ext}$, out to a maximum radial distanceof $R_{\rm max}$ =15 kpc."
 The values of a. Rinne Ομ ANd Oar ave listed in Table 2.. taken directly fro1a. Waiuscoatetal.(1992).," The values of $\alpha$, $R_{\rm min}$, $\theta_{\rm min}$, and $\theta_{\rm ext}$ are listed in Table \ref{tab:spiral}, taken directly from \citet{wain92}."
.. The parameters asstune the Earth is 8.5 kpe from the Calactic ceuter., The parameters assume the Earth is 8.5 kpc from the Galactic center.
 The stellay density along the spiral arias is given by an exponential distribution with radius 2 aud height above the plane + (Wainscoatctal.1992): where 523.5 kpe is the radial scale Απ pc is the scale height of the youngest stars in the ΣΕGalactic plane. and py is à normalization for which the exact value Is uniniportant. because we will divide bv the total mass to obtain the fraction of the arms cucompassed by the survey.," The stellar density along the spiral arms is given by an exponential distribution with radius $R$ and height above the plane $z$ \citep{wain92}: where $h$ =3.5 kpc is the radial scale length, $h_z$ =90 pc is the scale height of the youngest stars in the Galactic plane, and $\rho_0$ is a normalization for which the exact value is unimportant, because we will divide by the total mass to obtain the fraction of the arms encompassed by the survey."
 The density of the spiral aris is assumed to be constant for any eiven A within £375 pc of the ceuter of the arm. and zero outside that radial exteut.," The density of the spiral arms is assumed to be constant for any given $R$ within $\pm$ 375 pc of the center of the arm, and zero outside that radial extent."
 This model for the spiral artis is illustrated schematically iu Figure 7.., This model for the spiral arms is illustrated schematically in Figure \ref{fig:spiral}.
 Iu that figure. we also plot the depth through the Galaxy for which we would detect easilv- aud barely-detectable pulsars in of trials (P2. 18.0) for each of our archival observations.," In that figure, we also plot the depth through the Galaxy for which we would detect easily- and barely-detectable pulsars in of trials $P_{\rm sig}$ =48.0) for each of our archival observations."
 The completeness level would incorporate about more of the Galaxy. but using it would add the complication that a larger fraction of mmagnetars with Ly and lay. above our stated limits would be nissed.," The completeness level would incorporate about more of the Galaxy, but using it would add the complication that a larger fraction of magnetars with $L_{\rm X}$ and $A_{\rm rms}$ above our stated limits would be missed."
 For cach observation. we integrated the mass euclosed along the line of sight out to the depths defined iu 832.1.," For each observation, we integrated the mass enclosed along the line of sight out to the depths defined in 3.1."
 We assumed a field of view of «177 ΠουChandra... which corresponds to the full ACIS-I array.," We assumed a field of view of $\times$ for, which corresponds to the full ACIS-I array."
 We assumed a field-of-view of «20 Που.Newton. which correspouds to the region where vignetting still provides >50% of the on-axis count rate for a source.," We assumed a field-of-view of $\times$ for, which corresponds to the region where vignetting still provides $>$ of the on-axis count rate for a source."
 The fractional mass of tle spiral aruis enclosed by cach observation is plotted as a function of Galactic longitude iu Figure 8.. for the cases of casily- and barely-detectable pulsars.," The fractional mass of the spiral arms enclosed by each observation is plotted as a function of Galactic longitude in Figure \ref{fig:mass}, , for the cases of easily- and barely-detectable pulsars."
 To compute the total fractional mass enclosed by the survey. we identified duplicate observations as those," To compute the total fractional mass enclosed by the survey, we identified duplicate observations as those"
 , 
anallysis.,lysis.
1996).,.
. If the 3.29 HEF arises in small PAHs which are preferentially destroyed near200775.. and if the 2.18 ccontinuum arises either from larger PAHs. from more robust tiny grains. or from larger carbon nanoparticles. none of which are destroyed near200775... then this could explain our observed radial increase in ffor7023.," If the 3.29 IEF arises in small PAHs which are preferentially destroyed near, and if the 2.18 continuum arises either from larger PAHs, from more robust tiny grains, or from larger carbon nanoparticles, none of which are destroyed near, then this could explain our observed radial increase in for."
. If PAHs are the 3.29 IIEF carrier. then PAH i0nization could play a major role in the radial dependence of the ccolor in7023.," If PAHs are the 3.29 IEF carrier, then PAH ionization could play a major role in the radial dependence of the color in."
. The electron density. ο. which depends on the total gas density. is higher at the 3.29 ffilaments than at the 2 ppeak (Fuenteetal.1996:Lemaire1996;Martini1997.1999;Gerin1998;Takami2000).," The electron density, $n_e$, which depends on the total gas density, is higher at the 3.29 filaments than at the 2 peak \citep{FMN96,LFG96,MSH97,MSD99,GPK98,TUS00}."
. More importantly. the UV field. Go. 1s also lower at the 3.29 IIEF filaments than at the 2 ppeak. with Go~77.," More importantly, the UV field, $G_0$, is also lower at the 3.29 IEF filaments than at the 2 peak, with $G_0 \sim r^{-2}$."
" Since the PAH ionization fraction is lower for lower Go/n, (Bakes&Tielens1994).. this could result in à lower PAH ionization fraction in the 3.29 IIEF filaments than at the 2 ppeak."," Since the PAH ionization fraction is lower for lower $G_0/n_e$ \citep{BT94}, this could result in a lower PAH ionization fraction in the 3.29 IEF filaments than at the 2 peak."
 Theoretical calculations and laboratory experiments show that the 3.294 UEF is significantly weaker in ionized PAHs than neutral PAHs (deFreesetal.1993:Szezepanski&Vala1993).," Theoretical calculations and laboratory experiments show that the 3.29 IEF is significantly weaker in ionized PAHs than neutral PAHs \citep{dFMT93,SV93}."
. If the 2 ccontinuum emitters do not change ionization state or their emission is not affected by ionization state. then PAH ionization effects might be sufficient to explain the radial dependence of sshown in Figures 7. and 8..," If the 2 continuum emitters do not change ionization state or their emission is not affected by ionization state, then PAH ionization effects might be sufficient to explain the radial dependence of shown in Figures \ref{f7} and \ref{f8}."
 A third alternative has to do with extinction and the excitation of the 3.294 HEF and the 2 ccontinuum emission., A third alternative has to do with extinction and the excitation of the 3.29 IEF and the 2 continuum emission.
 The stellar radiation from lis systematically reddened with distance from the star. resulting in a softer UV field at larger values of r.," The stellar radiation from is systematically reddened with distance from the star, resulting in a softer UV field at larger values of $r$."
 Sellgren(1984) proposed that the 2 ccontinuum is due to stochastically heated tiny grains. which require energetic UV photons to excite them.," \citet{Se84} proposed that the 2 continuum is due to stochastically heated tiny grains, which require energetic UV photons to excite them."
 The 3.3 IIEF has been proposed to be due to quenched carbonaceous composite. amorphous carbon. or coal (Sakata1988;Papoularetal. 1989).. all substances which absorb well at visible as well as UV wavelengths.," The 3.3 IEF has been proposed to be due to quenched carbonaceous composite, amorphous carbon, or coal \citep{SWT84,SWO87,BBC88,Du88,PCG89}, all substances which absorb well at visible as well as UV wavelengths."
" If the 3.3 HEF could be excited by less energetic photons than the photons required for the 2 ccontinuum emission, then the internal nebular extinction within ccould cause the ccolor to increase with distance from the star."," If the 3.3 IEF could be excited by less energetic photons than the photons required for the 2 continuum emission, then the internal nebular extinction within could cause the color to increase with distance from the star."
 This possibility seems least likely. because Sellgrenetal.(1996) find no evidence that the &—[3.3 jm]]| color depends on oof the illuminating star. over == |1.000-22.000 K. Another exciting result illustrated in Figures 7 and 8 is that the peak value of is ~5.5 mag in the ffilaments.," This possibility seems least likely, because \citet{SWA96} find no evidence that the $K-$ [3.3 ] color depends on of the illuminating star, over = 11,000-22,000 K. Another exciting result illustrated in Figures \ref{f7} and \ref{f8}
 is that the peak value of is $\sim$ 5.5 mag in the filaments."
 Sellgrenetal.(1996) measured or placed upper limits on K—[3.29 pm]] in 14 different reflection nebulae., \citet{SWA96} measured or placed upper limits on $K-$ [3.29 ] in 14 different reflection nebulae.
 In several reflection nebulae. including7023... K-[3.29 jm]] was measured at multiple spatial locations.," In several reflection nebulae, including, $K-$ [3.29 ] was measured at multiple spatial locations."
 The highest value of &—[3.29 um]] measured by Sellgrenetal.(1996) in any reflection nebula. over a wide range of stellar effective temperature and stellar flux. is K—[3.29 um]]2 4.5 mag.," The highest value of $K-$ [3.29 ] measured by \citet{SWA96} in any reflection nebula, over a wide range of stellar effective temperature and stellar flux, is $K-$ [3.29 ]= 4.5 mag."
" Thus the 3.29 ΠΕΡ filaments in aare roughly 2.5 times brighter. compared to the 2 ccontinuum emission, than any other measured value in a reflection nebula."," Thus the 3.29 IEF filaments in are roughly 2.5 times brighter, compared to the 2 continuum emission, than any other measured value in a reflection nebula."
 Care must be taken in comparing our measured values of (Figs., Care must be taken in comparing our measured values of (Figs.
 7. 8)) and published values of K—-[3.29 µπα]]., \ref{f7} \ref{f8}) ) and published values of $K-$ [3.29 ].
 The broadband K measurements of Sellgrenetal.(1996) include," The broadband $K$ measurements of \citet{SWA96}
 include"
In recent vears. observations of high. redshift) universe (2> 6) have become possible.,"In recent years, observations of high redshift universe $z > 6$ ) have become possible."
 Deep imaging surveys with he CHST) and large ground. based elescopes have made the discovery of z76 galaxies almost routine., Deep imaging surveys with the ) and large ground based telescopes have made the discovery of $z\approx 6$ galaxies almost routine.
 Some of those searches (Bunker et 22004. Yan Winclhorst 2004. Stanway. Bunker AleMahon 2003. Douwens et 22006. 2007. Oesch et 22007. Yoshida οἱ 22006) rely on the Lyman break galaxy (LBC) technique. initially used by Steidel and collaborators (Steidel ct 1996) to iclentily galaxies at 2&3 through the large ysorplion produced by the intervening Lyman-a forest Ποιος and the Lyman limit.," Some of those searches (Bunker et 2004, Yan Windhorst 2004, Stanway, Bunker McMahon 2003, Bouwens et 2006, 2007, Oesch et 2007, Yoshida et 2006) rely on the Lyman break galaxy (LBG) technique, initially used by Steidel and collaborators (Steidel et 1996) to identify galaxies at $z\approx 3$ through the large absorption produced by the intervening $\alpha$ forest clouds and the Lyman limit."
 Until recently. working at —igher recshilt (2> 7) was challenging.," Until recently, working at higher redshift $z>7$ ) was challenging."
 Studies were limited o very small deep fields observed from space (e.g. Bouwens et 22008). or to extremely shallow wice-area surveys rom the ground. (e... Stanway et 22008. Llickey et 22010).," Studies were limited to very small deep fields observed from space (e.g. Bouwens et 2008), or to extremely shallow wide-area surveys from the ground (e.g., Stanway et 2008, Hickey et 2010)."
 Phe new Wide Fielel Camera 3 AVECS) instrument. installed on£57 in. Alay 2009. allowed: this technique to o: more ellectively applied to .710. thanks to its near-infrared. channel with significantly larger Ποιά and »etter sensitivity than the previous-ecneration NICALOS instrument.," The new Wide Field Camera 3 (WFC3) instrument, installed on in May 2009, allowed this technique to be more effectively applied to $z\approx 7 - 10$, thanks to its near-infrared channel with significantly larger field and better sensitivity than the previous-generation NICMOS instrument."
" Using WECS broad-band filters at 1.0. 1.25 and 1.6jm (the Y-. J- and Z/-bands) and targetting fields with existing deep Advanced. Camera for Surveys (ACS) data it is possible to identify optical ""drop-outs. objects seen only in the WECS infrared images but not in the optical ones."," Using WFC3 broad-band filters at 1.0, 1.25 and $\mu$ m (the $Y$ -, $J$ - and $H$ -bands) and targetting fields with existing deep Advanced Camera for Surveys (ACS) data it is possible to identify optical “drop-outs"", objects seen only in the WFC3 infrared images but not in the optical ones."
 These are candidate 27 galaxies., These are candidate $z\gtrsim 7$ galaxies.
 Searching for objects with no Hux at. LO and. below (Y-band: clrop-outs. or 7Y-drops) could. lead to the discovery of 2=8 galaxies.," Searching for objects with no flux at $\mu$ m and below $Y$ -band drop-outs, or $Y$ -drops"") could lead to the discovery of $z\approx 8$ galaxies."
" Decp optical images of the observed fields are still necessary to ""clean up” the list of candidates. because. as we will see later. optical detections are useful in ruling out many lower-redshift contaminants."," Deep optical images of the observed fields are still necessary to “clean up"" the list of candidates, because, as we will see later, optical detections are useful in ruling out many lower-redshift contaminants."
 The past) few months have seen several papers presenting high redshift galaxy candidates from 157)WECS imaging of the Ultra Deep Field (UICDE: Bunker et 22010. AleLure et 22010. Oesch et 22010. Bouwens et 22010a. Yan et 22010. Finkelstein et 22010).," The past few months have seen several papers presenting high redshift galaxy candidates from /WFC3 imaging of the Ultra Deep Field (HUDF; Bunker et 2010, McLure et 2010, Oesch et 2010, Bouwens et 2010a, Yan et 2010, Finkelstein et 2010)."
 In the HIUDE. ~10 z'-drops ἐςz 7) have been found. along with ~5r. Y-drops (2& 8).," In the HUDF, $\sim 10$ $z'$ -drops $z\approx 7$ ) have been found, along with $\sim 5$ $Y$ -drops $z\approx 8$ )."
 Spectroscopic confirmation of these candidates in the LUDE will be extremely challenging. as they have magnitudes J2»26.5 (for the z/-drops) and J>28.0 (for the Y -drops)," Spectroscopic confirmation of these candidates in the HUDF will be extremely challenging, as they have magnitudes $J>26.5$ (for the $z'$ -drops) and $J>28.0$ (for the $Y$ -drops)."
 What is needed. are larecr samples over wider areas. which might vield rarer but. brighter candidates more suitable for spectroscopic follow-up.," What is needed are larger samples over wider areas, which might yield rarer but brighter candidates more suitable for spectroscopic follow-up."
 Such ollow-up is important to test the validity. of the Y -drop selection technique. and address the contaminant fraction. as well as exploring the physics of star forming galaxies at zzS (in particular whether Lyman-a emerges during the Cunn-Peterson absorption era).," Such follow-up is important to test the validity of the $Y$ -drop selection technique, and address the contaminant fraction, as well as exploring the physics of star forming galaxies at $z\gtrsim 8$ (in particular whether $\alpha$ emerges during the Gunn-Peterson absorption era)."
" Increasing the survey area of the WECS3 LBC searches will also improve the statistics (and rence the rest-UV. luminosity function constraints). and we rave started to do this by searching [ους -ἄνορς in the larecr- Early Release Science. WEC3 images of some of the GOODS-South field (Wilkins et 22010a) ancl expanding his to include two other deep flanking fields (UDE-DPI2 UDE-D34) close to the LIVDE (Wilkins et 22010b). which das increased. the number of robust z""-drops from ~10 to ~40."," Increasing the survey area of the WFC3 LBG searches will also improve the statistics (and hence the rest-UV luminosity function constraints), and we have started to do this by searching for $z'$ -drops in the larger-area Early Release Science WFC3 images of some of the GOODS-South field (Wilkins et 2010a) and expanding this to include two other deep flanking fields (UDF-P12 UDF-P34) close to the HUDF (Wilkins et 2010b), which has increased the number of robust $z'$ -drops from $\sim 10$ to $\sim 40$."
 In this paper we use our new reductions of the ERS GOODS-South. and UDE-P12 UDE-DP34 to search for 3-drops ats2SO.," In this paper we use our new reductions of the ERS GOODS-South, and UDF-P12 UDF-P34 to search for $Y$ -drops at $z\approx 8 - 9$."
 In Bunker et ((2010) we presented our preliminary list of Y-drops in the HILUDE. and here we also re-analyse this field using à more recent data reduction.," In Bunker et (2010) we presented our preliminary list of $Y$ -drops in the HUDF, and here we also re-analyse this field using a more recent data reduction."
 The evolution of the rest-UV. luminosity function. is key to both understanding the star formation history of the Universe. ancl also to address the role of star-forming ealaxies in reionization.," The evolution of the rest-UV luminosity function is key to both understanding the star formation history of the Universe, and also to address the role of star-forming galaxies in reionization."
 There seems to be strong evolution in the UV luminosity function (UVLE) up to redshift up to 286 (e.g. Stanway. Bunker MeMahon 2003). and recent studies (Bunker et 22010: Wilkins et 22010b: Oesch et 22010) seem to show that this evolution continues up to 2T. although based on small-numboer statistics.," There seems to be strong evolution in the UV luminosity function (UVLF) up to redshift up to $z\approx 6$ (e.g. Stanway, Bunker McMahon 2003), and recent studies (Bunker et 2010; Wilkins et 2010b; Oesch et 2010) seem to show that this evolution continues up to $z\approx 7$, although based on small-number statistics."
 Our goal is to push the measurement of the UVLE further back in cosmic time by assembling a statisticallv-significant sample of probable 2S9 galaxies., Our goal is to push the measurement of the UVLF further back in cosmic time by assembling a statistically-significant sample of probable $z\approx 8 - 9$ galaxies.
 From this we can address the evolution of the star formation rate density. and the ionizing photon budget.," From this we can address the evolution of the star formation rate density, and the ionizing photon budget."
 This paper is organised as follows: in Section 2 we outline the“S57 observations with WECS and the data reduction. and in Section 3 we describe our colour selection to recover high-redshift Lyman break galaxies. and compare our sample with those from other studies.," This paper is organised as follows: in Section 2 we outline the observations with WFC3 and the data reduction, and in Section 3 we describe our colour selection to recover high-redshift Lyman break galaxies, and compare our sample with those from other studies."
 In Section 4 with discuss the evolution. of the star formation rate density. and the implications for reionization. derived from the luminosity function we infer at zS.," In Section 4 with discuss the evolution of the star formation rate density, and the implications for reionization, derived from the luminosity function we infer at $z\sim 8$."
 Our conclusions are presented in Section 5., Our conclusions are presented in Section 5.
" Phroughout. we adopt the standard concordance cosmology of ον=0.3. O4=0.7 and use ll,—τὸ  ft."," Throughout, we adopt the standard concordance cosmology of $\Omega_{M}= 0.3$, $\Omega_{\Lambda}= 0.7$ and use $H_0=70$ $^{-1}$ $^{-1}$."
 All magnitudes are on the AB system (Oke Gunn 1983)., All magnitudes are on the AB system (Oke Gunn 1983).
 In this paper we analyse images from WEC3 onHAST taken in the near-infrared Y-. 7- and 4-bands.," In this paper we analyse images from WFC3 on taken in the near-infrared $Y$ -, $J$ - and $H$ -bands."
 The data come from two cdillerent 4757 programs. both covering areas within. the GOODS-South field. (Ciavalisco et. 22004).," The data come from two different programs, both covering areas within the GOODS-South field (Giavalisco et 2004)."
 TheAST Treasury programme CO-11563 GG. Ulingworth) covers the ΤΗΟΙ and two nearby deep lanking [fields (UDE-PI2 and UDE-P34. also. referred to as HIUDEO5-01. and HIUDEO5-02. in. programme GO-11563).," The Treasury programme GO-11563 G. Illingworth) covers the HUDF and two nearby deep flanking fields (UDF-P12 and UDF-P34, also referred to as HUDF05-01 and HUDF05-02 in programme GO-11563)."
" These llanking fields were imagecl by the Advance Camera for Surveys (ACS) onHST in ο-. /- and. z'""-bands during 20056 in parallel with deep.οί NICALOS NICS observations of the original UDE as part. of. program €GO-10632 MM. Stiavelli)."," These flanking fields were imaged by the Advance Camera for Surveys (ACS) on in $v$ -, $i'$ - and $z'$ -bands during 2005–6 in parallel with deep NICMOS NIC3 observations of the original UDF as part of program GO-10632 M. Stiavelli)."
 In Bunker et ((2010) we analvsed. the single-WNFC3-pointing HUDE data obtained soon-after the commissioning of WECS. and in this paper we study the two new deep. WECS3 pointings on the two deep Hanking fields. and reanalyse the UDE cata using more recent on-orbit calibration of the detector.," In Bunker et (2010) we analysed the single-WFC3-pointing HUDF data obtained soon-after the commissioning of WFC3, and in this paper we study the two new deep WFC3 pointings on the two deep flanking fields, and reanalyse the UDF data using more recent on-orbit calibration of the detector."
 Additionally. we analyse the Earby Release Science. (ERS) program GO/DD-11359 RR. O'Connell) data. covering ten overlapping pointings with (wo orbits in each filter.," Additionally, we analyse the Early Release Science (ERS) program GO/DD-11359 R. O'Connell) data, covering ten overlapping pointings with two orbits in each filter."
 An analvsis of the first 6 pointings for z-drops at 27 was presented in. Wilkins et ((2010a). with the full ERS mosaic and .DPS34 Uanking fields used to select. z-drops in Wilkins et ((2010b).," An analysis of the first 6 pointings for $z$ -drops at $z\approx 7$ was presented in Wilkins et (2010a), with the full ERS mosaic and P34 flanking fields used to select$z$ -drops in Wilkins et (2010b)."
 The infrared channel o£. WECS was used. which is a," The infrared channel of WFC3 was used, which is a"
It is possible to see whether dissipation acts or 1rot by looking at the perturbation of specific vorticity.,It is possible to see whether dissipation acts or not by looking at the perturbation of specific vorticity.
 In the absence of dissipation. the specific vorticity conserves along the streamline. and since the backeround specific vorticity is constant iu the calculation box. we expect that i is also constant in the presence of the planet.," In the absence of dissipation, the specific vorticity conserves along the streamline, and since the background specific vorticity is constant in the calculation box, we expect that it is also constant in the presence of the planet."
 Note that any potential force. whether it is time-dependent or not. docs rot produce specἼπο vorticity.," Note that any potential force, whether it is time-dependent or not, does not produce specific vorticity."
 Therefore. specific vorticity arises ouly if dissipative mechanisnis come into play.," Therefore, specific vorticity arises only if dissipative mechanisms come into play."
 Iu our nunierical calculation. the dissipation is miplemoented iu the shock-capturing scheme.," In our numerical calculation, the dissipation is implemented in the shock-capturing scheme."
 If the formation of specific voricity is driven bv the formation of shock. relation giveu bx equation should be observed at least for the weak. shock cases.," If the formation of specific vorticity is driven by the formation of shock, relation given by equation should be observed at least for the weak shock cases."
" Figure BF shows the evolution of the perturbatio1 of aziuuthallv averaged specific vorticity for calculations witli GAL,Πο=0.1 and 0.1.", Figure \ref{fig:vort_evol} shows the evolution of the perturbation of azimuthally averaged specific vorticity for calculations with $GM_{\rm p}/Hc^2=0.1$ and $0.4$.
 It is possible to see that the specific vorticity is formed around fff~1.5., It is possible to see that the specific vorticity is formed around $x/H\sim 1.5$.
 We later see that his specific vorticity becomes a dominaut source of uass flux. which leads to the formation of a gap.," We later see that this specific vorticity becomes a dominant source of mass flux, which leads to the formation of a gap."
 For the ποΊσα]: calculation: with: Πο2=40.1. we also see the formation of specific vorticity around. ~0.," For the numerical calculation with $GM_{\rm p}/Hc^2=0.1$, we also see the formation of specific vorticity around $x \sim 0$."
" This is because the fluid eleineuts in GAL,the vicinity of the panet orbit around it. aud as a result. a vortex is formed just around the planet."," This is because the fluid elements in the vicinity of the planet orbit around it, and as a result, a vortex is formed just around the planet."
 The formation of a vortex at the planet location causes the vortex circulating in the opposite directiou. which makes a horseshoe orbit in the corotation region.," The formation of a vortex at the planet location causes the vortex circulating in the opposite direction, which makes a horseshoe orbit in the corotation region."
 For the calculation with /ITe=0.1. simular ing happens. but the vortices formed by shock dissipation are stronger.," For the calculation with $GM_{\rm p}/Hc^2=0.4$, similar thing happens, but the vortices formed by shock dissipation are stronger."
" In subsequent sections.GAL, we show that vortices just in the vicinity of the planet location does uot produce a significant amount of mass flix."," In subsequent sections, we show that vortices just in the vicinity of the planet location does not produce a significant amount of mass flux."
 Figure Bs shows the azinuthallutegrated specific vorticity perturbation as a function of Ge(23I)M;USE , Figure \ref{fig:vort_pert} shows the azimuthally-integrated specific vorticity perturbation as a function of $(x-(2/3)H)M_{\rm p}^{2/5}$.
shock dissipation occurs as equation(31).. the ]oeak of the specific vorticity perturbation comes at the same location of 1ο horizontal axis.," If shock dissipation occurs as equation, the peak of the specific vorticity perturbation comes at the same location of the horizontal axis."
" It is possible to observe that the for calculations with GAL,Πο«0.2. equation is mareiually satisfied."," It is possible to observe that the for calculations with $GM_{\rm p}/Hc^2<0.2$, equation is marginally satisfied."
 For calculations with larger planet nase. it is not the case.," For calculations with larger planet mass, it is not the case."
 This is because the shock formation occurs nuuediately after the excitation ofthe wave atcc(2/3)T. and therefore iu the unit of Ge(23I)M; the shock oceurs relatively further away.," This is because the shock formation occurs immediately after the excitation ofthe wave at $x\sim(2/3)H$, and therefore in the unit of $(x-(2/3)H)M_{\rm p}^{2/5}$, the shock occurs relatively further away."
" We now look at the radial mass flux Se, excited by the pauct.", We now look at the radial mass flux $\overline{\Sigma v_x}$ excited by the planet.
 In figure D9.. we show the aziumthally averaged mass Hux obtained by nunerical calculation.," In figure \ref{fig:mdot_fit}, we show the azimuthally averaged mass flux obtained by numerical calculation."
 It is possible to see that there is a spike of the mass flux just in the vicinity of he planet. aud then the uass fux depends linearlv with t1e distance from the plauct within Le/7|<2.," It is possible to see that there is a spike of the mass flux just in the vicinity of the planet, and then the mass flux depends linearly with the distance from the planet within $|x/H|\lesssim 2$."
 The spike in he vicinity of the planct is due to the eas falling onto the planet., The spike in the vicinity of the planet is due to the gas falling onto the planet.
 This causes the spike of the surface density profile iu he vicinity of the planet as shown in figure D5.., This causes the spike of the surface density profile in the vicinity of the planet as shown in figure \ref{fig:gap_evolution}.
 We expect that this feature depends ou the treatiueut of the planet. ancl such mass flux shouk be investigated carefully when ο1ο wants to look at the processes such as gas accretion onto he planet.," We expect that this feature depends on the treatment of the planet, and such mass flux should be investigated carefully when one wants to look at the processes such as gas accretion onto the planet."
 ILowever. as we will see later. the feature in tUs spike region ¢oes not affect the mass flux outside this reeion.," However, as we will see later, the feature in this spike region does not affect the mass flux outside this region."
 Iu the discussion )olow. we focus on the structure ¢nitside this spike reeglon.," In the discussion below, we focus on the structure outside this spike region."
 We first compare the xcsults obtained by nuucvical simulation and analyic calculation., We first compare the results obtained by numerical simulation and analytic calculation.
 Figure DIO compares the nass flux derived by uumuerieal calculation aud Ww cquaticπιC16)., Figure \ref{fig:mdot_comp} compares the mass flux derived by numerical calculation and by equation.
. Since it is not possible to predict the amount of specific vorticity ouly frou linear perturbation tllCOYV. We iive used the results of nunucerical calculation iu obtaining he source terii 5(f..c).," Since it is not possible to predict the amount of specific vorticity only from linear perturbation theory, we have used the results of numerical calculation in obtaining the source term $S(t,x)$."
 It is possible to observe that t16 second-order perturvation theory is valid for calculations with ow-nnass planet. while for calculations with GALII=(V1. the perturbaion theory fails to explain the amount of uass flux.," It is possible to observe that the second-order perturbation theory is valid for calculations with low-mass planet, while for calculations with $GM_{\rm p}/Hc^2=0.4$, the perturbation theory fails to explain the amount of mass flux."
" We find that tje second-order perturbation tliexv can be uxed fey GAL,Πο<0.2.", We find that the second-order perturbation theory can be used for $GM_{\rm p}/Hc^2 \lesssim 0.2$.
 We further investigate how this mass fux is formed., We further investigate how this mass flux is formed.
 We first look at the source term of the mass flux elven by equations aud(12)., We first look at the source term of the mass flux given by equations and.
. We have used the restIts of umuuerical caleulatioi fo caleulate the perturbed values that appear in these two equaions., We have used the results of numerical calculations to calculate the perturbed values that appear in these two equations.
" Figure Bll shows the evolution of the source of mass flux eiven by aud for the calculation with GAL,ΠΟ=0.1.", Figure \ref{fig:source_evol} shows the evolution of the source of mass flux given by and for the calculation with $GM_{\rm p}/Hc^2=0.1$.
" We soe that the terii with ο(#20) is not significant after the planet mass is fully introduced at f£,=12."," We see that the term with $\partial_t S(t,x)$ is not significant after the planet mass is fully introduced at $t\Omega_{\rm p}=12$."
 The term. S).(t..0) depends «πι time strouely in the vicinity of the planet. while nearlv time-independent contribution is observed frou t16 region ΟΠ>1.5.," The term $S_v(t,x)$ depends on time strongly in the vicinity of the planet, while nearly time-independent contribution is observed from the region $|x/H|>1.5$."
 The source arising in the vicinity ofthe planet conies from the vortex making a horseshoe orbit. while the source at e/IT|>1.5 comes from shock formation.," The source arising in the vicinity of the planet comes from the vortex making a horseshoe orbit, while the source at $|x/H|>1.5$ comes from shock formation."
 Iu order to look at which coutribution excites the mass flux more effectively. we calculate the mass flux by artificially cutting the source term at e/IT|>1.," In order to look at which contribution excites the mass flux more effectively, we calculate the mass flux by artificially cutting the source term at $|x/H|>1$."
" Figure BI2. compares tje Inass flux obtained by doing so and the mass fiux obtained by usine the full source ται,", Figure \ref{fig:mdot_sourceterm} compares the mass flux obtained by doing so and the mass flux obtained by using the full source term.
 We have used equation with the source terms obtained by muuerical calculation to derive the mass fiux., We have used equation with the source terms obtained by numerical calculation to derive the mass flux.
 It is clear that the source in the vicinity of the plauct docs not contribute to the lass flux verv much., It is clear that the source in the vicinity of the planet does not contribute to the mass flux very much.
 Therefore. we conclude that the mass fix arises from the specific vorticity ecuerated by the shock dissipation of deusifv wave.," Therefore, we conclude that the mass flux arises from the specific vorticity generated by the shock dissipation of density wave."
" We now discuss the depeudence of ass fux on the box size iu he y-direction. HU£,."," We now discuss the dependence of mass flux on the box size in the $y$ -direction, $L_y$."
" Figureo B13 shows the azimithally inteerated. mass fiux .die, with. GAL,2(fer=0.2 yttor differeutn box leugth Τε.", Figure \ref{fig:variableLy} shows the azimuthally integrated mass flux $\int dy \Sigma v_x $ with $GM_{\rm p}/Hc^2=0.2$ for different box length $L_y$.
 These: mass fuses ave directly: calculated from the uunerical simulations., These mass fluxes are directly calculated from the numerical simulations.
| The lines show a perfect matei for different box sizes., The lines show a perfect match for different box sizes.
" This can be explained if we notice that the augular momentum fux carried by the deusity wave does not depend ou the box size,", This can be explained if we notice that the angular momentum flux carried by the density wave does not depend on the box size.
 As the spiral density wave danips. the aneular momentum carried by the wake is deposited to the background disk to dive the mass flux.," As the spiral density wave damps, the angular momentum carried by the wake is deposited to the background disk to drive the mass flux."
 The total amount of the angular momentum deposied over the y-direction docs uot depend on the box size. sluce the amount of angular momentum fiux carried by the wave docs not depeud ou the box size.," The total amount of the angular momentum deposited over the $y$ -direction does not depend on the box size, since the amount of angular momentum flux carried by the wave does not depend on the box size."
 We now discuss the timescale for the eap-opening in the vicinity of the planet., We now discuss the timescale for the gap-opening in the vicinity of the planet.
 As stated at the end of Section 3.3.. the mass flux in the vicinity of the plauet is expected to be proportional to ww. aud if secoud-order analysis is valid. we expect that the mass flux is proportional to the square of the planet mass.," As stated at the end of Section \ref{subsec:second}, the mass flux in the vicinity of the planet is expected to be proportional to $x$ , and if second-order analysis is valid, we expect that the mass flux is proportional to the square of the planet mass."
 We therefore ft the mass fiux within, We therefore fit the mass flux within
A point is worth mentioning concerning the slope of the CMFEP/IME.,A point is worth mentioning concerning the slope of the CMF/IMF.
 Let us reason out in 3D. for sake of siuplicity.," Let us reason out in 3D, for sake of simplicity."
 In 3D. the case D=Ὁ correspouds iu the k-space to a structured space such that NA)κ ko ic. to a space filling distribution of fluctuations ΕπΠΠ conipactuess).," In 3D, the case $D=3$ corresponds in the k-space to a structured space such that $N(k)\propto k^3$ , i.e. to a space filling distribution of fluctuations (maximum compactness)."
 Since the mass associated with the fluctuation of scale Ris AL=pR?xKk2m (8)), Since the mass associated with the fluctuation of scale $R$ is $M=\rho R^3\propto k^{-3}$ \ref{geo})
increasing the resolution in the inner regions).,increasing the resolution in the inner regions).
 In the relativistic case however this slight departure from numerical hvdrostatic equilibrium is more significant., In the relativistic case however this slight departure from numerical hydrostatic equilibrium is more significant.
 This response is therefore eliminated by solving for the pressure gradient numerically using the same cdillerencing that is contained in the evolution scheme., This response is therefore eliminated by solving for the pressure gradient numerically using the same differencing that is contained in the evolution scheme.
 That. is we solve from the outer boundary condition according to Solving for the pressure in this manner reduces any. spurious response in the initial conditions to below round.olf error., That is we solve from the outer boundary condition $P(r_{\rm max})=K\rho(r_{\rm max})^{\gamma}$ according to Solving for the pressure in this manner reduces any spurious response in the initial conditions to below round–off error.
 The internal energy is then given from (5))., The internal energy is then given from \ref{eq:nreos}) ).
 The pressure calculated using (10)) is essentially indistinguishable from that found using ΩΩ GNP/P~10)., The pressure calculated using \ref{eq:Pnum}) ) is essentially indistinguishable from that found using \ref{eq:polyK}) $\Delta P/P\sim 10^{-5})$.
 Phe initial conditions caleulated using equation (9)). (10)) and. (5)) are shown in Figure 1.," The initial conditions calculated using equation \ref{eq:nrdrhodr}) ), \ref{eq:Pnum}) ) and \ref{eq:nreos}) ) are shown in Figure \ref{fig:nrinit}."
" We use a logarithmic grid with 1001 radial grid points. setting the outer boundary at 7/2,=107."," We use a logarithmic grid with 1001 radial grid points, setting the outer boundary at $r/R_* = 10^3$."
 Using a higher spatial resolution does not allect the simulation results., Using a higher spatial resolution does not affect the simulation results.
 The choice of the shape of the heating profile Cr) is fairly arbitrary since we wish simply to make a comparison between the non-relativistic ancl relativistic results., The choice of the shape of the heating profile $\Lambda(r)$ is fairly arbitrary since we wish simply to make a comparison between the non-relativistic and relativistic results.
" We choose to heat the wind in a spherical shell of a fixed width using a linearly increasing and then decreasing heating rate. symmetric about some heating radius ri which we place at r=2.12,."," We choose to heat the wind in a spherical shell of a fixed width using a linearly increasing and then decreasing heating rate, symmetric about some heating radius $r_{\rm heat}$ which we place at $r=2.1 R_*$."
 The heating profile is spread over a radial zone of width 2/2; (that is the heating zone extends from r=L142; to 3.1A )(see Figure 2)).," The heating profile is spread over a radial zone of width $2R_*$ (that is the heating zone extends from $r=1.1 R_*$ to $3.1
R_*$ )(see Figure \ref{fig:nrresults}) )."
 We choose a heating profile of this form such that it is narrow enough to be associated with a particular radius of heating (necessary since we are looking for scaling laws) whilst being wide enough to avoid the need for high spatial resolution or complicated algorithms (necessary if the heat input zone is too narrow)., We choose a heating profile of this form such that it is narrow enough to be associated with a particular radius of heating (necessary since we are looking for scaling laws) whilst being wide enough to avoid the need for high spatial resolution or complicated algorithms (necessary if the heat input zone is too narrow).
 The important parameter is thus the of the heating with respect to the Schwarzschild radius. so long as the heating profiles are the same in both the relativistic and. non-relativistic cases.," The important parameter is thus the of the heating with respect to the Schwarzschild radius, so long as the heating profiles are the same in both the relativistic and non-relativistic cases."
 Provided that the heating profile is narrow enough to be associated: with a particular racius and wide enough to avoid numerical problems. our results do not depend on the actual shape of the profile we choose.," Provided that the heating profile is narrow enough to be associated with a particular radius and wide enough to avoid numerical problems, our results do not depend on the actual shape of the profile we choose."
 The results of a tvpical non-relativistic simulation with a moderate heating rate are shown in Figure 2 at /=1001 (where / has units of the dynamical time at the inner radius)., The results of a typical non-relativistic simulation with a moderate heating rate are shown in Figure \ref{fig:nrresults} at $t=1001$ (where $t$ has units of the dynamical time at the inner radius).
 We observe the elfect of the heating propagating outwards in the atmosphere in the form of a shock front., We observe the effect of the heating propagating outwards in the atmosphere in the form of a shock front.
 After several huncdred dynamical times the wind structure approaches a steady state in that there is only à small change of the overall wind structure due to the shock continuing to propagate outwards into the surrounding medium., After several hundred dynamical times the wind structure approaches a steady state in that there is only a small change of the overall wind structure due to the shock continuing to propagate outwards into the surrounding medium.
 The small disturbance propagating well ahead of the main shock is a transient. resulting from the response of the atmosphere to the instantaneous switch-on of the heating., The small disturbance propagating well ahead of the main shock is a transient resulting from the response of the atmosphere to the instantaneous switch-on of the heating.
 Phe velocity of the gas begins to asvmptote to à constant value as the shock propagates outwards., The velocity of the gas begins to asymptote to a constant value as the shock propagates outwards.
 Plotting the mass outllow rate Al=4zi7pe and the Bernoulli energy £=5i07|piPoCM/r asa function of radius (Figure 3)). we see that indeed the wind structure is eventually close to that of a steady wind above the heating zone (ice.," Plotting the mass outflow rate $\dot{M} = 4\pi r^2\rho v$ and the Bernoulli energy $E =
\frac{1}{2}v^2 + \rho u + P - GM/r$ as a function of radius (Figure \ref{fig:nrmdoten}) ), we see that indeed the wind structure is eventually close to that of a steady wind above the heating zone (ie."
 AL and E~ constant)., $\dot{M}$ and $E \sim$ constant).
 It is thus computationally inellicient and impractical to compute the time-dependent solution for long enough to determine an accurate velocity as roeox when the wind will continue to have a steady structure., It is thus computationally inefficient and impractical to compute the time-dependent solution for long enough to determine an accurate velocity as $r \rightarrow \infty$ when the wind will continue to have a steady structure.
 Instead we find the steady wind solution for a given amount of energy input to the wind corresponding to the energy. plotted in Figure 3. (top panel)., Instead we find the steady wind solution for a given amount of energy input to the wind corresponding to the energy plotted in Figure \ref{fig:nrmdoten} (top panel).
 Non-relativistic. steady state (0/04= 0) winds with energy input have been well studied by many authors. and the equations describing them can be found in Lamers&Cassinelli(1999).. who credit the original work to Llolzer&Axford(1970).," Non-relativistic, steady state $\partial/\partial t = 0$ ) winds with energy input have been well studied by many authors, and the equations describing them can be found in \citet{lc99}, who credit the original work to \citet{ha70}."
 Phe reader is thus referred to Lamers&Cassinelli(1999) for details of the derivation., The reader is thus referred to \citet{lc99} for details of the derivation.
 As in the usual Bondi/DParker (Bondi1952.. Parker 1958)) wind solution with no heat input. we set οοἱ=0 in (1))-(5)) and combine these equations into one equation for the Mach number AL?=07ο as a function of radius. given by where dOQfdr is the local heating gradient and ete) is the Bernoulli energy which is specified bv integrating the Bernoulli equation," As in the usual Bondi/Parker \citealt{b52}, \citealt{p58}) ) wind solution with no heat input, we set $\partial/\partial t = 0$ in \ref{eq:nrcty}) \ref{eq:nreos}) ) and combine these equations into one equation for the Mach number $M^2 =
v^2/c_s^2$ as a function of radius, given by where $dQ/dr$ is the local heating gradient and $e(r)$ is the Bernoulli energy which is specified by integrating the Bernoulli equation"
"Msn Before which implies that the (AL, A) is only weakly dependent. on the stellar. mass."," , which implies that the $\dot{M}_\star/M_\star$ ) is only weakly dependent on the stellar mass."
 Meanwhile. when studying the same sample of observational estimates. set So the same saniple has been interpreted. on the one hand. as having a strong correlation with stellar mass and. on the other hand. a weakcorrelation’.," Meanwhile, when studying the same sample of observational estimates, set So the same sample has been interpreted, on the one hand, as having a strong correlation with stellar mass and, on the other hand, a weak."
.. What is the reader to conclude from this literature?, What is the reader to conclude from this literature?
 The confusion can be appreciated. by comparing the two panels in Fig. ??.., The confusion can be appreciated by comparing the two panels in Fig. \ref{obs}.
 The trend (??)) does not. seem unreasonable when looking at the top panel. but the problem. is that the observational limit in UV. magnitude creates a corresponding limit in star formation rate (dotted. red. line in bie. ??)).," The trend \ref{trend}) ) does not seem unreasonable when looking at the top panel, but the problem is that the observational limit in UV magnitude creates a corresponding limit in star formation rate (dotted red line in Fig. \ref{obs}) )."
 Because of the greater abundance of fainter galaxies. the population piles-up against this limit.," Because of the greater abundance of fainter galaxies, the population piles-up against this limit."
 Consequently. when the sample is then plotted on the axes in the lower panel (in order to investigate thespecific star formation rate). the dominant feature that translates to the new axes is a dense locus of galaxies around. the observational limit.," Consequently, when the sample is then plotted on the axes in the lower panel (in order to investigate the star formation rate), the dominant feature that translates to the new axes is a dense locus of galaxies around the observational limit."
" As this forms a constant line on the v-axis in the upper panel when divided by the x-axis (stellar mass) to create the lower panel it translates. to ""constant fa. thus giving a the impression of “strong mass-dependence""."," As this forms a constant line on the y-axis in the upper panel, when divided by the x-axis (stellar mass) to create the lower panel it translates to $constant/x$ ”, thus giving a the impression of “strong mass-dependence''."
 Aleanwhile. at lower redshifts. there is similar confusion.," Meanwhile, at lower redshifts, there is similar confusion."
" For example. using far infrared luminosity as à tracer for star formation rate. are Hed to conclude: Conversely. the star. formation rates measured by(2010).. also using the UV. luminosity. SUggest: This result is corroborated. amongst others. by(2009).. but with heavy caveats: On this note. it is clear that. further theoretical interpretation of patterns in the Ad,AL, plane requires an understancing of how the points arrive on these axes."," For example, using far infrared luminosity as a tracer for star formation rate, are led to conclude: Conversely, the star formation rates measured by, also using the UV luminosity, suggest: This result is corroborated, amongst others, by, but with heavy caveats: On this note, it is clear that further theoretical interpretation of patterns in the $M_\star - \dot{M}_\star$ plane requires an understanding of how the points arrive on these axes."
 Ins refTranslation.. we confront the pitfalls in the process of translation between observable ancl physical properties by looking at a plausible model galaxy sample. both in its entirety and through the restrictions of an observational survey.," In \\ref{Translation}, we confront the pitfalls in the process of translation between observable and physical properties by looking at a plausible model galaxy sample, both in its entirety and through the restrictions of an observational survey."
 The moclel we use to generate this mock population is à version of (sce Appendix 22)) which is a development of the mocel applied in(2006)., The model we use to generate this mock population is a version of (see Appendix \ref{Galform}) ) which is a development of the model applied in.
. No claim is mace. in this context. that this is the correct physical picture.," No claim is made, in this context, that this is the correct physical picture."
 All that matters for this exercise is that we are using a realistic moclel. based on current understanding of the physical processes involved. and that this particular observational sample.could have been drawn. from. the model population.," All that matters for this exercise is that we are using a realistic model, based on current understanding of the physical processes involved, and that this particular observational sample have been drawn from the model population."
 This caveat allows us to focus on the investigation in hand: the dillerence between whatcould be inferred from a sample. and the true characteristics of the population from which was drawn.," This caveat allows us to focus on the investigation in hand: the difference between what be inferred from a sample, and the true characteristics of the population from which was drawn."
 In refEvolution.. this investigation is extended to look at the appearance of populations at a range of redshifts.," In \\ref{Evolution}, this investigation is extended to look at the appearance of populations at a range of redshifts."
" Before carrying out these simple but instructive exercises. we momentarily set the issue aside to consider what general hierarchical galaxy formation theory brings to bear on the AZ, relationship. in the absence of any particular mocel or agenda refSSER))."," Before carrying out these simple but instructive exercises, we momentarily set the issue aside to consider what general hierarchical galaxy formation theory brings to bear on the $M_\star - \dot{M}_\star$ relationship, in the absence of any particular model or agenda \\ref{SSFR}) )."
 Clearly this ds. required for a proper interpretation of the observational data: The two quantities that were involved in Fig., Clearly this is required for a proper interpretation of the observational data: The two quantities that were involved in Fig.
" ?? are stellar mass. A. and star formation rate. A,."," \ref{obs} are stellar mass, $M_\star$, and star formation rate, $\dot{M}_\star$."
 These are related by definition: ((2) nar. where fCA0) is the fraction of the initial stellar mass that has been retained by a stellar population after time. AM. since formation.," These are related by definition: (z) = (t) t, where $f(\Delta t)$ is the fraction of the initial stellar mass that has been retained by a stellar population after time, $\Delta t$ , since formation."
 This is related to the recveled fraction. HI. that usually appears in galaxy formation mocdels.," This is related to the recycled fraction, $R$, that usually appears in galaxy formation models."
 In the instantaneous recycling approximation. /? is a constant: Qody fü.," In the instantaneous recycling approximation, $R$ is a constant: $R\equiv 1-\int_0^{t_z} f(t)\dif t$ ."
 Of course. when referring to (77)). one must not forget the hierarchical assembly of the final svstem.," Of course, when referring to \ref{def}) ), one must not forget the hierarchical assembly of the final system."
 Some stars that are present in a galaxy at time ἐς wouldhave formed in a separate. smaller svstem at earlier times.," Some stars that are present in a galaxy at time $t_z$ wouldhave formed in a separate, smaller system at earlier times."
 So a more explicit version of (??)) would be:, So a more explicit version of \ref{def}) ) would be:
cosmological numerical simulation.,cosmological numerical simulation.
" The procedure is more effective than traditional approaches in rejecting interlopers, while still preserving cluster members."," The procedure is more effective than traditional approaches in rejecting interlopers, while still preserving cluster members."
" The galaxy rest-frame velocities with respect to the cluster mean velocity are obtained from the usual relation (?),, where is obtained using the biweight estimator (?)."," The galaxy rest-frame velocities with respect to the cluster mean velocity are obtained from the usual relation , where is obtained using the biweight estimator ."
". We then obtain the galaxy projected distances from the cluster center, defined by its X-ray peak emission, RA-1335""17.965, 6—40?50'55.8""(?)."," We then obtain the galaxy projected distances from the cluster center, defined by its X-ray peak emission, $^h$ $^m$ $^s$, $\delta$ $^{\circ} 59' 55.8''$."
". The algorithm of requires initial estimates of the virial radius, 1200. and circular velocity, vooo, which we obtain from the cluster velocity dispersion estimate of?,, by followingA,, and using the relation of to infer the concentration of the cluster mass-density distribution."," The algorithm of requires initial estimates of the virial radius, $\rm{r}_{200}$, and circular velocity, $\rm{v}_{200}$, which we obtain from the cluster velocity dispersion estimate of, by following, and using the relation of to infer the concentration of the cluster mass-density distribution."
 We run the procedure on the whole sample of 1364 objects with available redshift estimates in the supercluster field., We run the procedure on the whole sample of 1364 objects with available redshift estimates in the supercluster field.
 The procedure is run iteratively until convergence on the number of selected members., The procedure is run iteratively until convergence on the number of selected members.
 We identify 357 supercluster members (they are shown as filled dots in Fig. 1))., We identify 357 supercluster members (they are shown as filled dots in Fig. \ref{f:rv}) ).
 Other algorithms lead to very similar membership definitions., Other algorithms lead to very similar membership definitions.
 The average cluster redshift and velocity dispersion determined for this sample of supercluster members are z=0.2315+0.0003 and oy= km s!., The average cluster redshift and velocity dispersion determined for this sample of supercluster members are $\overline{\rm{z}}=0.2315 \pm 0.0003$ and $\sigma_{\rm{v}}=1051_{-54}^{+51}$ km $^{-1}$.
" We use these values to estimate the cluster virial 1051*3)radius and circular velocity as before, finding 1209=2.066 Mpc and ν2ρρ=1623 km s!, which do not differ significantly from the initially adopted values."," We use these values to estimate the cluster virial radius and circular velocity as before, finding $\rm{r}_{200}=2.066$ Mpc and $\rm{v}_{200}=1623$ km $^{-1}$, which do not differ significantly from the initially adopted values."
" Of the 357 identified supercluster members, 153 are 24 -emitters."," Of the 357 identified supercluster members, 153 are 24 -emitters."
" To estimate the supercluster membership for the subset of galaxies without z, we rely on Zp-estimates."," To estimate the supercluster membership for the subset of galaxies without $\rm{z}$, we rely on $\rm{z}_p$ -estimates."
 We consider six different Zp-estimates for the galaxies in our sample., We consider six different $\rm{z}_p$ -estimates for the galaxies in our sample.
" In particular, we consider the ANNz and EAZY algorithms, as well as a y? minimization fitting of the spectral energy distribution (SED, hereafter) of the galaxies in our sample using SED model templates from?."," In particular, we consider the ANNz and EAZY algorithms, as well as a $\chi^2$ minimization fitting of the spectral energy distribution (SED, hereafter) of the galaxies in our sample using SED model templates from."
. We also consider the three zy estimates directly available from the SDSS DR7., We also consider the three $\rm{z}_p$ estimates directly available from the SDSS DR7.
" Of these six Ζρ estimators, we finally adopt one of those provided in the SDSS DR7, that based on the Artificial Neural Network technique(?)."," Of these six $\rm{z}_p$ estimators, we finally adopt one of those provided in the SDSS DR7, that based on the Artificial Neural Network technique."
". This estimator provides the tightest correlation between z and Zz, for the subsample of galaxies in the A1763 field that have both quantities available (see Fig. 2)).", This estimator provides the tightest correlation between $\rm{z}$ and $\rm{z}_p$ for the subsample of galaxies in the A1763 field that have both quantities available (see Fig. \ref{f:zpz}) ).
" To select the supercluster members in the sample of 24 -emitters on the basis of their zy, we define a zy-range around the mean supercluster redshift."," To select the supercluster members in the sample of 24 -emitters on the basis of their $\rm{z}_p$, we define a $\rm{z}_p$ -range around the mean supercluster redshift."
" The lower and upper z,-limits that define this selection range must be chosen in such a way as to maximize the number of real supercluster members with Ζρ within these limits, and, at the same time, minimize the number of background and foreground galaxies that also happen to have their zy within these limits."," The lower and upper $\rm{z}_p$ -limits that define this selection range must be chosen in such a way as to maximize the number of real supercluster members with $\rm{z}_p$ within these limits, and, at the same time, minimize the number of background and foreground galaxies that also happen to have their $\rm{z}_p$ within these limits."
" The choice of these zp-limits can only be based on the sample of galaxies with zy z, so that we can perform the most robust zy-based membership selection possible based on the well-established spectroscopic membership."," The choice of these $\rm{z}_p$ -limits can only be based on the sample of galaxies with $\rm{z}_p$ z, so that we can perform the most robust $\rm{z}_p$ -based membership selection possible based on the well-established spectroscopic membership."
 We proceed as follows., We proceed as follows.
 We assume that the 153 supercluster members selected on the basis of their z are all real members., We assume that the 153 supercluster members selected on the basis of their $\rm{z}$ are all real members.
" We then determine the zp-distribution of these 153 galaxies (shown as a solid black histogram in Fig. 3)),"," We then determine the $\rm{z}_p$ -distribution of these 153 galaxies (shown as a solid black histogram in Fig. \ref{f:zp_mem}) ),"
 as well as the Zp-distribution of the galaxies with z in either the foreground or the background of the supercluster (dashed blue histogram in Fig. 3))., as well as the $\rm{z}_p$ -distribution of the galaxies with $\rm{z}$ in either the foreground or the background of the supercluster (dashed blue histogram in Fig. \ref{f:zp_mem}) ).
 Using the whole sample of galaxies, Using the whole sample of galaxies
2010).. high Galactic latitude pulsars (Faucher-Giguére&Loeb2010:Stegal-Gaskinsetal.2010).. kilo-parsee (kpe) size AGNjets (Stawarzetal.2006). radio quiet AGNs (Inoueetal.2008:Inoue&Totani2009).. and GeV mass scale DM annihilation or decay (seee.g.Jung- 2009)..,", high Galactic latitude pulsars \citep{fau10,sie10}, kilo-parsec (kpc) size AGN jets \citep{sta06}, radio quiet AGNs \citep{ino08,ino09}, and GeV mass scale DM annihilation or decay \citep[see e.g.][]{jun96,ber00,uli02,oda05,and06,hor06,and07,ahn07,and09,kaw09}."
 Here. has recently detected GeV gamma-ray emissions from 11 misaligned AGNs (ie. radio galaxies). which are one type of AGNs with the direction of a relativistic jetnot comeiding with our line of sight (Abdoetal.2010b)..," Here, has recently detected GeV gamma-ray emissions from 11 misaligned AGNs (i.e. radio galaxies), which are one type of AGNs with the direction of a relativistic jet coinciding with our line of sight \citep{abd10_core}."
 Their average photon index at 0.1-10 GeV is ~2.4 which is same as that of GeV EGRB (Abdoetal.2010e) and blazars (Abdoetal.2010f).., Their average photon index at 0.1-10 GeV is $\sim2.4$ which is same as that of GeV EGRB \citep{abd10_egrb} and blazars \citep{abd10_marco}.
 Although they are fainter than blazars. the expected number in the entire sky is much more than blazars.," Although they are fainter than blazars, the expected number in the entire sky is much more than blazars."
 Then. it is naturally expected that they will make a significant contribution to EGRB.," Then, it is naturally expected that they will make a significant contribution to EGRB."
 Therefore. in this paper. we study the contribution of such gamma-ray loud radio galaxies (not blazars) to EGRB.," Therefore, in this paper, we study the contribution of such gamma-ray loud radio galaxies (not blazars) to EGRB."
 To study the EGRB contribution. of gamma-ray loud radio galaxies. their gamma-ray luminosity function (GLF) is required.," To study the EGRB contribution of gamma-ray loud radio galaxies, their gamma-ray luminosity function (GLF) is required."
 Because of limited samples. it is not a straightforward task to construct it using only samples.," Because of limited samples, it is not a straightforward task to construct it using only samples."
 Therefore. we first investigate the correlation between radio and gamma-ray luminosities of gamma-ray loud radio galaxies.," Therefore, we first investigate the correlation between radio and gamma-ray luminosities of gamma-ray loud radio galaxies."
 In the case of blazars. the correlation between gamma-ray and radio luminosities have been presented in many papers since EGRET era (Padovanietal.1993:Steckeretal. 2010a.b).," In the case of blazars, the correlation between gamma-ray and radio luminosities have been presented in many papers since EGRET era \citep{pad93,ste93,sal94,don95,zha01,nar06,ghi10a,ghi10b}."
. Since the radio luminosity function (RLF) of radio galaxies is well studied (seee.g.Dunlop&Peacock1990;Willottetal. 2001).. we are able to obtain the GLF by converting the RLF to the GLF using a luminosity correlation.," Since the radio luminosity function (RLF) of radio galaxies is well studied \citep[see e.g.][]{dun90,wil01}, we are able to obtain the GLF by converting the RLF to the GLF using a luminosity correlation."
 With that GLF. we evaluate their contribution to EGRB.," With that GLF, we evaluate their contribution to EGRB."
 This work is organized as follows., This work is organized as follows.
 Samples used in this study are shown in $..2.., Samples used in this study are shown in \ref{sec:sam}.
 In $..3.. we will investigate the radio and gamma-ray luminosity correlation and determine our GLF to reproduce the number of detected gamma-ray loud radio galaxies.," In \ref{sec:glf}, we will investigate the radio and gamma-ray luminosity correlation and determine our GLF to reproduce the number of detected gamma-ray loud radio galaxies."
 The EGRB will be calculated and compared with the observed data in §..4.., The EGRB will be calculated and compared with the observed data in \ref{sec:egrb}.
 Discussion and conclusion will be given in §..5 and. §..6.. respectively.," Discussion and conclusion will be given in \ref{sec:dis} and \ref{sec:con}, respectively."
 Throughout this paper. we adopt the standard cosmological parameters of (i.44.04)=(0.7.0.3.0.7).," Throughout this paper, we adopt the standard cosmological parameters of $(h,\Omega_M,\Omega_\Lambda) = (0.7, 0.3, 0.7)$."
Fermi has reported the detection of 11 Fanarof-Riley (FR) radio galaxies including 7 type-I FR (FRI) galaxies and 4 type-II FR (FRIL) galaxies by the entire sky survey for 15 months (Abdoetal.2010b).., has reported the detection of 11 Fanarof-Riley (FR) radio galaxies including 7 type-I FR (FRI) galaxies and 4 type-II FR (FRII) galaxies by the entire sky survey for 15 months \citep{abd10_core}.
 FRI galaxies have decelerating jets. knots at kpe distance from the core and edge-darkened lobes. while FRII galaxies have relativistic jets and brightened radio lobes with bright hotspots (Fanaroff&Ri-ley 1974).," FRI galaxies have decelerating jets, knots at kpc distance from the core and edge-darkened lobes, while FRII galaxies have relativistic jets and edge-brightened radio lobes with bright hotspots \citep{fan74}."
. In the scheme of the AGN jet unification scenario. FRI and FRII galaxies are the misaligned AGN populations of BL Lac objects and flat spectrum radio quasars (FSRQs). respectively (Urry&Padovani1905).," In the scheme of the AGN jet unification scenario, FRI and FRII galaxies are the misaligned AGN populations of BL Lac objects and flat spectrum radio quasars (FSRQs), respectively \citep{urr95}."
 In this study. we use 10 samples (6 FRIs and 4 FRIIs) from Abdoetal.(2010b) which were already reported in 11-month catalog (Abdoetal.2010a.g)..," In this study, we use 10 samples (6 FRIs and 4 FRIIs) from \citet{abd10_core} which were already reported in 11-month catalog \citep{abd10_catalog,abd10_agn}."
 This is because. as discussed in $..3. below. we use the detection efficiency ofFermi shown in Abdoetal.(2010f) which are constructed from the |1-month catalog.," This is because, as discussed in \ref{sec:glf} below, we use the detection efficiency of shown in \citet{abd10_marco} which are constructed from the 11-month catalog."
 Table., Table.
 | lists the gamma-ray loud radio galaxy samples used in this study., 1 lists the gamma-ray loud radio galaxy samples used in this study.
 It gives the object name. the First Source Catalog (IFGL) Fermi-LAT source name. redshift. gamma-ray photon flux above 0.1 GeV. photon index at 0.1-10 GeV. radio flux at 5 GHz. spectral index at 5 GHz. radio classification.," It gives the object name, the First Source Catalog (1FGL) -LAT source name, redshift, gamma-ray photon flux above 0.1 GeV, photon index at 0.1-10 GeV, radio flux at 5 GHz, spectral index at 5 GHz, radio classification."
 The definition of photon index. T. and spectral index. o. is the index of power-law differential photon spectrum. dN/dex€T.. and T—1. respectively.," The definition of photon index, $\Gamma$, and spectral index, $\alpha$, is the index of power-law differential photon spectrum, $dN/d\epsilon\propto\epsilon^{-\Gamma}$, and $\Gamma-1$, respectively."
 From Table., From Table.
 |. the mean photon index of gamma-ray spectra at 0.1—10 GeV. D. is 2.39 and the spread 1s 0.28.," 1, the mean photon index of gamma-ray spectra at 0.1–10 GeV, $\Gamma_c$, is 2.39 and the spread is 0.28."
 This index Is same as that of blazars. 2.40 (Abdoetal.2010f).. and the EGRB spectrum. 2.41 (Abdoetal.2010e)..," This index is same as that of blazars, 2.40 \citep{abd10_marco}, , and the EGRB spectrum, 2.41 \citep{abd10_egrb}."
 From the individual source studies (Abdoetal.2009b.c.2010c).. the typical gamma-ray SEDs are well explained by synchrotron-self-Compton emission models.," From the individual source studies \citep{abd09_ngc1275,abd09_m87,abd10_cena}, the typical gamma-ray SEDs are well explained by synchrotron-self-Compton emission models."
" Here. by taking account of particle cooling effect. the electron spectrum 1s given by 4N/d,x5,"" at ,Xw and 4Nd,xVon at ,>Apr Where +p; is the cooling break lorentz factor."," Here, by taking account of particle cooling effect, the electron spectrum is given by $dN/d\gamma_e \propto \gamma_e^{-p}$ at $\gamma_e \le \gamma_{\rm br}$ and $dN/d\gamma_e \propto \gamma_e^{-(p+1)}$ at $\gamma_e > \gamma_{\rm br}$, where $\gamma_{\rm br}$ is the cooling break lorentz factor."
" The inverse Compton (IC) photon spectrum is given by where ey corresponds to the IC photon energy from electrons with >, (Rybicki&Lightman1979).", The inverse Compton (IC) photon spectrum is given by where $\epsilon_{\rm br}$ corresponds to the IC photon energy from electrons with $\gamma_{\rm br}$ \citep{ryb79}.
 The SED fitting for NGC 1275 and M87 show that the IC peak energy in the rest frame locates at ~5 MeV (Abdoet2009b.c)..," The SED fitting for NGC 1275 and M87 show that the IC peak energy in the rest frame locates at $\sim5$ MeV \citep{abd09_ngc1275,abd09_m87}."
 In this study. weuse the mean photon index. T. as Τ at 0.1—10 GeV and we set a peak energy. ey. in photon spectrum at 5 MeV for all gamma-ray loud radio galaxies as a baseline model.," In this study, weuse the mean photon index, $\Gamma_c$, as $\Gamma$ at 0.1–10 GeV and we set a peak energy, $\epsilon_{\rm br}$ , in photon spectrum at 5 MeV for all gamma-ray loud radio galaxies as a baseline model."
 Then. we are able to define the average SED shape of gamma-ray loud radio galaxies for all luminosities as dNidexεπ at e5 MeV. and dN/dexe? ate «8 MeV by following Equation 1..," Then, we are able to define the average SED shape of gamma-ray loud radio galaxies for all luminosities as $dN/d\epsilon\propto\epsilon^{-2.39}$ at $\epsilon>$ 5 MeV, and $dN/d\epsilon\propto\epsilon^{-1.89}$ at $\epsilon\le$ 5 MeV by following Equation \ref{eq:sed}."
 However. only 3 sources are currently studied with multi-wavelength observational. data.," However, only 3 sources are currently studied with multi-wavelength observational data."
 We need to make further studies of individual gamma-ray loud radio galaxies to understand their SED properties in wide luminosity ranges., We need to make further studies of individual gamma-ray loud radio galaxies to understand their SED properties in wide luminosity ranges.
 We examine other spectral models in the Section 5.2.., We examine other spectral models in the Section \ref{subsec:unc}.
 To estimate the EGRB contribution of gamma-ray loud radio galaxies. we need to construct a GLF.," To estimate the EGRB contribution of gamma-ray loud radio galaxies, we need to construct a GLF."
 However. because of a small sample size. 1t is difficult to construct a GLF using the current gamma-ray data only.," However, because of a small sample size, it is difficult to construct a GLF using the current gamma-ray data only."
 Here. the RLF of radio galaxies is extensively studied by previous works (seee.g.Dunlop&Peacock1990:Willottetal. 2001).," Here, the RLF of radio galaxies is extensively studied by previous works \citep[see e.g.][]{dun90,wil01}."
. If there is a correlation between the radio and gamma-ray luminosities. we are able to convert the RLF to the GLF with that correlation.," If there is a correlation between the radio and gamma-ray luminosities, we are able to convert the RLF to the GLF with that correlation."
 In the case of blazars. it has been suggested that there is a correlation between radio and gamma-ray lummosity from the EGRET era (Padovanietal.1993;ellini1995;Zhangetal.2001:Narumoto&Totani 200600.although it has also been discussed that this correlation cannot be firmly established because of flux limited. samples (Mueckeetal. 1997)..," In the case of blazars, it has been suggested that there is a correlation between radio and gamma-ray luminosity from the EGRET era \citep{pad93,ste93,sal94,don95,zha01,nar06}, although it has also been discussed that this correlation cannot be firmly established because of flux limited samples \citep{muc97}. ."
 Recently. using the samples. Ghirlandaetal.(2010a.b) confirmed that there is a correlation between the radio and gamma-ray luminosities.," Recently, using the samples, \citet{ghi10a,ghi10b} confirmed that there is a correlation between the radio and gamma-ray luminosities."
 To examine a luminosity correlation in gamma-ray loud radio galaxies. we first derive the radioand. gamma-ray luminosity of gamma-ray loud radio galaxies as follows.," To examine a luminosity correlation in gamma-ray loud radio galaxies, we first derive the radioand gamma-ray luminosity of gamma-ray loud radio galaxies as follows."
 Gamma-ray luminosities between the energies ει and e» are, Gamma-ray luminosities between the energies $\epsilon_1$ and $\epsilon_2$ are
20%)) than the solar metallicity values of AG89.,) than the solar metallicity values of AG89.
 Such a result is a little surprising given the debate in the X-ray literature on the correct dust-to-gas ratio., Such a result is a little surprising given the debate in the X-ray literature on the correct dust-to-gas ratio.
" However, it has been known for many years that the ISM metallicity increases toward the Galactic centre and that the ISM metallicity becomes similar to the AG89 solar value at around 6kkpc from the Galactic centre (?).."," However, it has been known for many years that the ISM metallicity increases toward the Galactic centre and that the ISM metallicity becomes similar to the AG89 solar value at around kpc from the Galactic centre \citep{2000A&A...363..537R}."
" Since the ratios derived in X-rays are dominated by high-extinction sightlines, it is perhaps after all not that surprising that the metallicity obtained for a typical sightline through the Galaxy is ~75%, or ddex, higher than the most recent measurements of the solar metallicity (?).."," Since the ratios derived in X-rays are dominated by high-extinction sightlines, it is perhaps after all not that surprising that the metallicity obtained for a typical sightline through the Galaxy is $\sim75\%$, or dex, higher than the most recent measurements of the solar metallicity \citep{2009ARA&A..47..481A}."
 This value is particularly useful since it is a direct measure of the ISM itself without having to use stellar photospheres and it is effectively independent of dust depletion or ionisation in the ISM., This value is particularly useful since it is a direct measure of the ISM itself without having to use stellar photospheres and it is effectively independent of dust depletion or ionisation in the ISM.
" For a typical X-ray sightline through the Galaxy, therefore, a more accurate estimate of the soft X-ray absorption may be obtained by using a metallicity value somewhat higher than that of AG89."," For a typical X-ray sightline through the Galaxy, therefore, a more accurate estimate of the soft X-ray absorption may be obtained by using a metallicity value somewhat higher than that of AG89."
 Certainly it seems that using the current solar metallicities (?) with column densities is likely to lead to a large underestimate of the Galactic soft X-ray absorption., Certainly it seems that using the current solar metallicities \citep{2009ARA&A..47..481A} with column densities is likely to lead to a large underestimate of the Galactic soft X-ray absorption.
" Since the Galaxy is known to showa strong metallicity gradient (?),, if the dust-to-metals ratio is roughly constant (?), one would expect the dust-to-gas ratio to vary in a similar way, aa higher dust-to-gas ratio toward the Galactic centre."," Since the Galaxy is known to showa strong metallicity gradient \citep{2000A&A...363..537R}, if the dust-to-metals ratio is roughly constant \citep{2003ARA&A..41..241D}, one would expect the dust-to-gas ratio to vary in a similar way, a higher dust-to-gas ratio toward the Galactic centre."
 Sightlines toward the Galactic centre will have higher column densities: we therefore may expect a relationship in the Galaxy between the dust-to-gas ratio and the total column density., Sightlines toward the Galactic centre will have higher column densities: we therefore may expect a relationship in the Galaxy between the dust-to-gas ratio and the total column density.
" Such a relationship is possibly indicated by ?,, where the Galactic plane has a significantly higher dust-to-gas ratio than at high-latitudes with the Galactic centre direction being especially high."," Such a relationship is possibly indicated by \citet{1998ApJ...500..525S}, where the Galactic plane has a significantly higher dust-to-gas ratio than at high-latitudes with the Galactic centre direction being especially high."
 In Fig., In Fig.
 [5] the relationship between the Galactic 21ccm and dust column densities is shown.," \ref{fig:nhebv}
 the relationship between the Galactic cm and dust column densities is shown."
" Sightlines toward the Galactic centre (cos(/)cos(b)>0.9, open squares on Fig. B))"," Sightlines toward the Galactic centre $\cos(l)\cos(b)>0.9$, open squares on Fig. \ref{fig:nhebv}) )"
 do indeed seem to show higher dust-to-gas ratio than sightlines with comparable columna densities along other sightlines., do indeed seem to show a higher dust-to-gas ratio than sightlines with comparable column densities along other sightlines.
" The comparison of dust to gas directly yields a non-linear relation, with higher column density sightlines showing a higher dust-to-gas ratio."," The comparison of dust to gas directly yields a non-linear relation, with higher column density sightlines showing a higher dust-to-gas ratio."
 The linear relation 10?!Ay shows clear residuals.," The linear relation $N_\ion{H}{i} =
2.2\times10^{21}A_V$ shows clear residuals."
" However, Ng,=2.00+0.14107! provides a better fit to the data, though the fit is still not 40.773007good."," However, $N_\ion{H}{i} =
2.00\pm0.14\times10^{21} A_V^{0.77\pm0.07}$ provides a better fit to the data, though the fit is still not good."
 Previous studies have shown a similar effect., Previous studies have shown a similar effect.
 ? note that the dust content of low density high velocity clouds is lower than in other regions of the Galaxy.," \citet{1998ApJ...500..525S}
 note that the dust content of low density high velocity clouds is lower than in other regions of the Galaxy."
 The survey of column densities and extinction in the UV using Lya absorption and reddening of stars of ? show the same effect very clearly (their Fig., The survey of column densities and extinction in the UV using $\alpha$ absorption and reddening of stars of \citet{1994ApJ...427..274D} show the same effect very clearly (their Fig.
 4a and to a lesser extent 4b)., 4a and to a lesser extent 4b).
" In principle, a change in the absolute to selective extinction ratio, Ry, could be responsible for the apparent change in gas-to-dust ratio derived from reddening."," In principle, a change in the absolute to selective extinction ratio, $R_V$, could be responsible for the apparent change in gas-to-dust ratio derived from reddening."
" However, since we observe the same effect in Fig."," However, since we observe the same effect in Fig."
" B] where the extinction data are derived from the dust emission in the far-infrared (FIR), not from reddening, this seems unlikely."," \ref{fig:nhebv} where the extinction data are derived from the dust emission in the far-infrared (FIR), not from reddening, this seems unlikely."
" Another possibility is that dust temperatures, which strongly affect the emitted flux in the FIR, might produce such an effect — cooler lines of sight would yield a spuriously lower dust column if the assumed temperature was too high."," Another possibility is that dust temperatures, which strongly affect the emitted flux in the FIR, might produce such an effect – cooler lines of sight would yield a spuriously lower dust column if the assumed temperature was too high."
" However, ? accounted for the dust temperature in their analysis, and more compellingly, we observe the same effect in extinction in the UV data of ?.."," However, \citet{1998ApJ...500..525S} accounted for the dust temperature in their analysis, and more compellingly, we observe the same effect in extinction in the UV data of \citet{1994ApJ...427..274D}."
" Other explanations for the correlation of gas-to-dust ratio with column density, such as ionisation of the hydrogen at low column densities or molecularisation at high column densities, seems unlikely since the gas-to-metals ratio remains effectively constant across the range we study using observations (Fig. p»."," Other explanations for the correlation of gas-to-dust ratio with column density, such as ionisation of the hydrogen at low column densities or molecularisation at high column densities, seems unlikely since the gas-to-metals ratio remains effectively constant across the range we study using observations (Fig. \ref{fig:nxnh}) )."
" It is worth noting, however, that the deviation observed at the high column end of Fig B| is consistent with the factor of two decrease in the column density observed in far-UV molecularisation studies, where a approximately half of the hydrogen exists in molecular form along sightlines with moderate or greater extinctions (??).."," It is worth noting, however, that the deviation observed at the high column end of Fig \ref{fig:nhebv} is consistent with the factor of two decrease in the column density observed in far-UV molecularisation studies, where a approximately half of the hydrogen exists in molecular form along sightlines with moderate or greater extinctions \citep{1978ApJ...224..132B,2009ApJS..180..125R}. ."
" Even if molecularisation or ionisation were partly responsible, however, it does not alter"," Even if molecularisation or ionisation were partly responsible, however, it does not alter"
Llere. we explore a more concentrated halo. a Wi=7 Wine nmiocel. and therefore a sub-maximal disk model.,"Here, we explore a more concentrated halo, a $W_0=7$ King model, and therefore a sub-maximal disk model."
 The Wu=7 halo profile is too centrally concentrated to be an acceptable match to standard rotation curves: the rotation curve rises too steeply and over-supports the disk in the inner galaxy., The $W_0=7$ halo profile is too centrally concentrated to be an acceptable match to standard rotation curves: the rotation curve rises too steeply and over-supports the disk in the inner galaxy.
 The response for both the 16X and No=16 modes are shown in Figures 17 and LS for both clisks., The response for both the 16X and $N=16$ modes are shown in Figures \ref{fig:h437} and \ref{fig:h439} for both disks.
 Phe warp has a feature inside of of &=1 (inside the solar circle in the Milky Way) due to the larger elfect of the halo at smaller radii., The warp has a feature inside of of $R=1$ (inside the solar circle in the Milky Way) due to the larger effect of the halo at smaller radii.
 Phe outer warp profile is more gradual ancl relatively larger at smaller radii., The outer warp profile is more gradual and relatively larger at smaller radii.
 Similar to the standard. model. the warp in Hunter-'loomre 16X disk is stronger than in the Hunter No=16 clisk.," Similar to the standard model, the warp in Hunter-Toomre 16X disk is stronger than in the Hunter $N=16$ disk."
 ‘The semi-analvtic method of re[sec:method.— is ideally suited to N-body simulation., The semi-analytic method of \\ref{sec:method} is ideally suited to N-body simulation.
 The same biorthogonal bases can be used to represent the potential and force. fields. of a particle distribution. (e.g. Clutton-Brock 1972. 1973.. Llernquist Ostriker 21).," The same biorthogonal bases can be used to represent the potential and force fields of a particle distribution (e.g. Clutton-Brock 1972, \nocite{Clut:72,Clut:73}, Hernquist Ostriker \nocite{HeOs:92}) )."
 Because the Poisson equation is linear. each Conmrponen can be represented by an expansion suited to its geometry.," Because the Poisson equation is linear, each component can be represented by an expansion suited to its geometry."
 Similarly. one can casily tailor the inter-component forces to isolate any particular interaction.," Similarly, one can easily tailor the inter-component forces to isolate any particular interaction."
 La particular. the n-bods tests are not. hamverecd bv the cilliculthy in producing a perfect time-dependent equilibrium clisk-halo model: the disk feels the backgroun halo but halo does not react to the background disk. as described in refsec:combined..," In particular, the n-body tests are not hampered by the difficultly in producing a perfect time-dependent equilibrium disk-halo model; the disk feels the background halo but halo does not react to the background disk, as described in \\ref{sec:combined}."
 Vhere are two. dillerences. between. t10 simulation and the perturbation calculation., There are two differences between the simulation and the perturbation calculation.
 First. the clisk mus be thickenecl to keep it stable against local instability (Toomre 1964)).," First, the disk must be thickened to keep it stable against local instability (Toomre \nocite{Toom:64}) )."
 We use a simple isothermal disk with m.=20kms!., We use a simple isothermal disk with $\sigma_z=20\kms$ .
 This disk would also be bar unstable withou a bulge component., This disk would also be bar unstable without a bulge component.
 A rigid Llernquist (1990)) model with scale leneth of 1.4 kpe and. mass of 0.2 Ανν (roughly 12.LOMAL.) suppressed bar. growth., A rigid Hernquist \nocite{Hern:90}) ) model with scale length of 1.4 kpc and mass of 0.2 $M_{disk}$ (roughly $1.2\times10^{10}\msun$ ) suppressed bar growth.
 Second. the direc acceleration by the satellite cülferentiallv accelerates the disk causing the expansion center to drift [rom the center of mass.," Second, the direct acceleration by the satellite differentially accelerates the disk causing the expansion center to drift from the center of mass."
" This technical dillicultly. was circumvented for the purpose of these tests by dividing the original satellite in two anc placing half of of the mass an mirror in the same orbit bu 180"" out of phase.", This technical difficultly was circumvented for the purpose of these tests by dividing the original satellite in two and placing half of of the mass an mirror in the same orbit but $180^\circ$ out of phase.
 Simulations with 100.000 particles with several dilleren partitions between the disk and halo components. were performed on a network parallel n-body code using the LAA implementation (Burns. Daoud Vaigl 1994)) of AIPL (e.g. Cropp. Lusk Skjelum 1990481).," Simulations with 100,000 particles with several different partitions between the disk and halo components were performed on a network parallel n-body code using the LAM implementation (Burns, Daoud Vaigl \nocite{LAM:94}) ) of MPI (e.g. Gropp, Lusk Skjelum \nocite{MPI:94}) )."
 This particular force evaluation scheme lends itself to workstation clusters because the communication overheac is very low (only cocllicients need to. be passed. e.g. Lernquist. Sigurdsson Brvan 1995)) as long as the load per node remains balanced.," This particular force evaluation scheme lends itself to workstation clusters because the communication overhead is very low (only coefficients need to be passed, e.g. Hernquist, Sigurdsson Bryan \nocite{HeSB:95}) ) as long as the load per node remains balanced."
 To suppress transients. the satellite is slowly turned. on over an orbital period.," To suppress transients, the satellite is slowly turned on over an orbital period."
 1n general. the predicted. features. were observed: vertical wakes with midplane heights of roughly 500r. pe in the outer disk in the predicted orientation.," In general, the predicted features were observed: vertical wakes with midplane heights of roughly 500 pc in the outer disk in the predicted orientation."
 Unfortunately even with 100.000. particles and. the approximations above designed to clearly isolate the m=1 wake. the simulation results are difficult to interpret due to discreteness noise.," Unfortunately even with 100,000 particles and the approximations above designed to clearly isolate the $m=1$ wake, the simulation results are difficult to interpret due to discreteness noise."
 Simulations without any satellite reveal that the noise has two elfects., Simulations without any satellite reveal that the noise has two effects.
 First. the disk origin random walks in the fluctuating /=om0 halo component.," First, the disk origin random walks in the fluctuating $l=m=0$ halo component."
 This causes m=0 vertical distortions which lead to scale height thickening., This causes $m=0$ vertical distortions which lead to scale height thickening.
 One should expect these low-order luctuations are amplified above the Poisson amplitude by he global gravitational response as described in. Weinberg (1993. 19973).," One should expect these low-order fluctuations are amplified above the Poisson amplitude by the global gravitational response as described in Weinberg (1993, \nocite{Wein:93,Wein:97}) )."
 Secondly. one finds m=1 height. distortion rom the /=2 noise-excited halo component similar in scale to that expected. [rom the satellite excitation.," Secondly, one finds $m=1$ height distortion from the $l=2$ noise-excited halo component similar in scale to that expected from the satellite excitation."
 In retrospect. this might have been expected.," In retrospect, this might have been expected."
 Any response o à perturbation will feature any cliscrete modes., Any response to a perturbation will feature any discrete modes.
 For the iio. the strongest of these will be weakly clamped.," For the halo, the strongest of these will be weakly damped."
 The halo wake. which is now the self-gravitating response to the disk distortion. will be contain the same weakly daniped mode ound in the response to the satellite.," The halo wake, which is now the self-gravitating response to the disk distortion, will be contain the same weakly damped mode found in the response to the satellite."
 Pherefore. particle luctuation noise can excite a similar with modes and a similar disk response.," Therefore, particle fluctuation noise can excite a similar with modes and a similar disk response."
 The amplitude of the noise excitec distortions was as much as of the amplitude observe with a satellite present., The amplitude of the noise excited distortions was as much as of the amplitude observed with a satellite present.
 However. dillerent Monte. Carlo realizations ofthe same initial model gave vertical warps of arbitrary orientation whereas in the presence of the satellite. the predicted orientation is obtained.," However, different Monte Carlo realizations of the same initial model gave vertical warps of arbitrary orientation whereas in the presence of the satellite, the predicted orientation is obtained."
 A proper n-body investigation of these effects. wil require simulations with many more particles anc will be left for the future., A proper n-body investigation of these effects will require simulations with many more particles and will be left for the future.
 This investigation. however. inadvertently raises the interesting possibility that a satellite may interac," This investigation, however, inadvertently raises the interesting possibility that a satellite may interact"
"In Figure 1 we show the evolution of a binary svstem which ends as à SN Ia. Initially Mi,= O.8.M.. MÀ=L5.M. and log,,(P!/d)=1.9.","In Figure \ref{example} we show the evolution of a binary system which ends as a SN Ia. Initially $M_{\rm WD}^{\rm i}=
0.8\,M_\odot$ , $M_{\rm 2}^{\rm i}= 1.5\,M_\odot$ and $\log_{10}(P^{\rm i}/{\rm d}) = 1.9$."
 The wind enhancement [actor By=10.000.," The wind enhancement factor $B_{\rm W}=10,000$."
 We see three phases of CO WD erowth to L378Al. at which carbon igniles degeneratelv.," We see three phases of CO WD growth to $1.378\,M_\odot$ at which carbon ignites degenerately."
 First. wind accretion becomes important al about 4.7x105 vr when the accretion is sullicient for hydrogen to burn as it aceretes.," First, wind accretion becomes important at about $4.7\times 10^6\,$ yr when the accretion is sufficient for hydrogen to burn as it accretes."
 Stable mass transfer dominates [or a short time of around. 1.02x10* vr.," Stable mass transfer dominates for a short time of around $1.02\times 10^7\,$ yr."
 Finally wind accretion continues alter the svstem has detached because the orbit grows faster than the giant., Finally wind accretion continues after the system has detached because the orbit grows faster than the giant.
 The supernova occurs when the secondarys mass has fallen to 0.353M. just as it is about to leave the red giant branch and shrink to a white dwart.," The supernova occurs when the secondary's mass has fallen to $0.353\,M_\odot$ just as it is about to leave the red giant branch and shrink to a white dwarf."
 At 2.673x10? vvr (1&Tx105 vvr in Figure 1)) the enhaneecl mass-loss rate reaches ils maximum of 150 times Reimers’ rate.," At $2.673 \times 10^9$ yr $t \approx 7
\times 10^6$ yr in Figure \ref{example}) ) the enhanced mass-loss rate reaches its maximum of 150 times Reimers' rate."
" In this case the WD is able to acerete all the wind and Ma,=λος."," In this case the WD is able to accrete all the wind and $\dot {M}_{\rm 2a}=-\dot M_{\rm
2w}$."
 This is an extreme case of small. P. corresponding to the short orbital period edge of the space that leads to SNe Ia for an initially 0.8M. CO WD (see Figure 2 below).," This is an extreme case of small $P^{\rm i}$, corresponding to the short orbital period edge of the space that leads to SNe Ia for an initially $0.8\,M_\odot$ CO WD (see Figure \ref{grid} below)."
 At longer initial periods the WD reaches 1.378M. before RLOF occurs so there is no stable mass (ransler phase.," At longer initial periods the WD reaches $1.378\,M_\odot$ before RLOF occurs so there is no stable mass transfer phase."
 For much. wider svstems and for more massive secondaries. that ienite helium non-degeneralely ancl consequently do not grow very large on their first ascent of the giant branch. similar evolution occurs when the secondary is on (he asymptotic giant branch.," For much wider systems and for more massive secondaries, that ignite helium non-degenerately and consequently do not grow very large on their first ascent of the giant branch, similar evolution occurs when the secondary is on the asymptotic giant branch."
 Figure 2. shows the results of our binary evolution caleulations in an imitial mass plane for various initial WD masses., Figure \ref{grid} shows the results of our binary evolution calculations in an initial period--secondary mass plane for various initial WD masses.
" No SNe In arise when AM,=0.6M..."," No SNe Ia arise when $M_{\rm WD}^{\rm
 i}=0.6\,M_\odot$."
 Whether a CO WD reaches the critical mass to explode as à SN Ia depends on both the amount of mass (transferred and the efficiency al which this can be accreted by the CO WD., Whether a CO WD reaches the critical mass to explode as a SN Ia depends on both the amount of mass transferred and the efficiency at which this can be accreted by the CO WD.
 In each panel contours enclose the progenitors of SNe Ia. Only lor the very. high initial white dwarl masses. of 1.1... can a massive secondary star drive à SN Ia. These stars ignite helium non-cegenerately and so do not grow large enough (ο transfer sufficient mass while on their first ascent of the giant branch.," In each panel contours enclose the progenitors of SNe Ia. Only for the very high initial white dwarf masses, of $1.1\,M_\odot$, can a massive secondary star drive a SN Ia. These stars ignite helium non-degenerately and so do not grow large enough to transfer sufficient mass while on their first ascent of the giant branch."
 Thus. only those initially massive enough to retain enough envelope mass to transfer via a wind on the first ascent of the giant branch are able (ο reach SNe Ia. In this case the initial mass of the secondary. ought not to be larger than the progenitor of the WD.," Thus, only those initially massive enough to retain enough envelope mass to transfer via a wind on the first ascent of the giant branch are able to reach SNe Ia. In this case the initial mass of the secondary ought not to be larger than the progenitor of the WD."
 This determines our upper limit for the upper region in panel (d) and explains why (his region is absent [or lower-mass WDs., This determines our upper limit for the upper region in panel (d) and explains why this region is absent for lower-mass WDs.
 The other regions are more interesting because {μον are more populated by virtue of the stellar mass function., The other regions are more interesting because they are more populated by virtue of the stellar mass function.
 For these the low secondary mass boundary is due to the limited amount of mass available lor transfer [rom the lower-mass companions., For these the low secondary mass boundary is due to the limited amount of mass available for transfer from the lower-mass companions.
 The long period boundary is due to the efficiency ol burning and accumulating the transferred. material., The long period boundary is due to the efficiency of burning and accumulating the transferred material.
 The high secondary. mass and low period boundary are both due to the onset of RLOF and dynamically uistable mass (ransler because CRAP has not removed enough mass., The high secondary mass and low period boundary are both due to the onset of RLOF and dynamically unstable mass transfer because CRAP has not removed enough mass.
Carbon burning then begins more gently in the heated outer lavers of the WD and a supernova is avoided.,Carbon burning then begins more gently in the heated outer layers of the WD and a supernova is avoided.
Strictly speaking. these figures should be regarded: as upper limits. because an increase in numerical resolution or the presence of a dense core of barvonic matter would probably facilitate the survival of satellites.,"Strictly speaking, these figures should be regarded as upper limits, because an increase in numerical resolution or the presence of a dense core of baryonic matter would probably facilitate the survival of satellites."
 Phe relevance of the latter effect is however not clear. as dark matter is the dominant source of gravity already at the optical radius of the galaxy (e.g. Navarro. Frenk White 1996).," The relevance of the latter effect is however not clear, as dark matter is the dominant source of gravity already at the optical radius of the galaxy (e.g. Navarro, Frenk White 1996)."
 Taking meclian values as robust estimators of the distributions. this result on the whole suggests that 50 per cent. of. galaxies in present-day clusters should. have a dark. matter halo truncated at or below zz10r. a radius close to those radii testable by e.g. high precision surface photometry.," Taking median values as robust estimators of the distributions, this result on the whole suggests that 50 per cent of galaxies in present-day clusters should have a dark matter halo truncated at or below $\approx 10 r_e$, a radius close to those radii testable by e.g. high precision surface photometry."
 Of course. some of these galaxies will have lost à substantial part. of their dark matter halo and may themselves be disrupted.," Of course, some of these galaxies will have lost a substantial part of their dark matter halo and may themselves be disrupted."
 Observations indicate that the fraction of morphologically disturbed. galaxies or interacting galaxies in clusters typically increases with redshift (e.g. Lavery Henry. 1988: Ocmler. Dressler 3utcher 1997).," Observations indicate that the fraction of morphologically disturbed galaxies or interacting galaxies in clusters typically increases with redshift (e.g. Lavery Henry 1988; Oemler, Dressler Butcher 1997)."
 Due to the high relative speed: of most encounters. illustrated in Figure 7.. mergers between galaxies are expected to be rare.," Due to the high relative speed of most encounters, illustrated in Figure \ref{fig:coll1}, mergers between galaxies are expected to be rare."
 On the other hand. the numerical simulations of Moore et al. (," On the other hand, the numerical simulations of Moore et al. ("
"1996) have shown that repeated high speed encounters between spirals. at a relative distance less than a few optical radii (e.g. Zi50 kpe for an L, galaxy) can seriously modify the galaxy. morphology.","1996) have shown that repeated high speed encounters between spirals, at a relative distance less than a few optical radii (e.g. $\la 50$ kpc for an $L_*$ galaxy) can seriously modify the galaxy morphology."
 ‘This clistance is also the typical separation of the interacting ealaxies found by Lavery Henry (1988), This distance is also the typical separation of the interacting galaxies found by Lavery Henry (1988).
 We can use the results of the analysis performed. in Sections ?? and 9.1. to estimate the fraction of interacting ealaxies in our simulations., We can use the results of the analysis performed in Sections \ref{sec:coll} and \ref{sec:gsize} to estimate the fraction of interacting galaxies in our simulations.
 Figure 14. shows the fraction of galaxv-size satellites. undergoing close encounters with other satellites. as a function of redshift.," Figure \ref{fig:coll4} shows the fraction of galaxy-size satellites undergoing close encounters with other satellites, as a function of redshift."
" We show results for cdimensionless relative distances b«0.5. b«0.2 and 6«0.1. which correspond to encounters at distances «10r. «4r, and «2r. if one takes the median value rfr.c20 found in the previous section as representative."," We show results for dimensionless relative distances $b<0.5$, $b<0.2$ and $b<0.1$, which correspond to encounters at distances $<10 r_e$, $<4 r_e$ and $<2 r_e$ if one takes the median value $r_v/r_e \simeq 20$ found in the previous section as representative."
 Encounters at such distances already fall in the class discussed by Moore et al., Encounters at such distances already fall in the class discussed by Moore et al.
 We see for example that zz20 per cent of these satellites are, We see for example that $\approx 20$ per cent of these satellites are
and iu r=0.8233 and P(r.5)z92 he Iow-Iuninositv objects.,"and in $r=0.8233$ and $P(r,5)\approx92\%\;(\sim1.7\sigma)$ for the low-luminosity objects."
 The data points in Fie., The data points in Fig.
 E. also include ROSAT poiute observations and Sevfert Ls aud 1.9 galaxies. which colmplete the relation between Lx aud (Q first diseusse by Rafauclli et al. (," \ref{fig_Lx_Q_s1} also include ROSAT pointed observations and Seyfert 1.8 and 1.9 galaxies, which complete the relation between $L_{\rm X}$ and $Q$ first discussed by Rafanelli et al. ("
1997).,1997).
 For Sevfert 2 ealaxies we foun no correlation between the soft N-rav. luuinosity iud the interaction streugth., For Seyfert 2 galaxies we found no correlation between the soft X-ray luminosity and the interaction strength.
 In Sect., In Sect.
 Lo we discuss the problems in deternuning preciscly the X-ray properties of obscure Sevtert 2 ealaxies.," \ref{discussion}
 we discuss the problems in determining precisely the X-ray properties of obscured Seyfert 2 galaxies."
" Tn order to estimate the starburst activity we have investigated the far-infrared Iuninositv Lg, using the far-infrared fluxes fu; at 60 and 100 jan from the IRAS Faint Source Catalogue.", In order to estimate the starburst activity we have investigated the far-infrared luminosity $L_{\rm fir}$ using the far-infrared fluxes $f_{\rm fir}$ at 60 and 100 $\rm \mu m$ from the IRAS Faint Source Catalogue.
" The total far-infrared fluxes fr, (10—120/1u) were computed following IHelou (1985) frou the TRAS 60 jn aud LOO ;12 baud fluxes: where fog aud που are given in Jausky.", The total far-infrared fluxes $f_{\rm fir}$ $40 - 120 \rm \mu m$ ) were computed following Helou (1985) from the IRAS 60 $\rm \mu m$ and 100 $\rm \mu m$ band fluxes: where $f_{60}$ and $f_{100}$ are given in Jansky.
 The far-infrared fluxes were converted to huninosities using Eq., The far-infrared fluxes were converted to luminosities using Eq.
 2 in Sect. 2.3.., \ref{Lx} in Sect. \ref{analysis}.
 For the photon index we assumed E—1.5., For the photon index we assumed $\Gamma = 1.5$.
" The ratio between far-infrared aud soft N-rav huninosity Ly/Lg, aud its dependence on the far-intrared huninosity Lg, is shown iu fie."," The ratio between far-infrared and soft X-ray luminosity $L_{\rm X}/L_{\rm
fir}$ and its dependence on the far-infrared luminosity $L_{\rm fir}$ is shown in fig."
 5 for all Sevtert types., \ref{fig_Lx/Lir_Lir} for all Seyfert types.
 Tuterestinely. NLS1 ealaxies show a sinülu distribution of the far-infrared luminosity as the Sevfert 2 galaxies.," Interestingly, NLS1 galaxies show a similar distribution of the far-infrared luminosity as the Seyfert 2 galaxies."
 The far-infrared huuinositv distribution is significantly different for Seyfert 1 galaxies compared to NLSI1 aud Sevtert 27s., The far-infrared luminosity distribution is significantly different for Seyfert 1 galaxies compared to NLS1 and Seyfert 2's.
 Iu fig., In fig.
" 6 we plot the ratio Ly/Lg, vs. the iuteractiou PAreneth Q for all Sevfert types.", \ref{fig_Lx/Lir_Q} we plot the ratio $L_{\rm X}/L_{\rm fir}$ vs. the interaction strength $Q$ for all Seyfert types.
 For Sevfert 1 galaxies uo correlation between the bhuumositv ratio aud the -iteraction streneth is found., For Seyfert 1 galaxies no correlation between the luminosity ratio and the interaction strength is found.
" Η we cau interprete the far-oeifrared luminosity as mainly caused by starburst activity. uxl the X-ray luminosity as mainly caused by accretion processes, this indicates that starburst and ACN activity increase proportionally."," If we can interprete the far-infrared luminosity as mainly caused by starburst activity, and the X-ray luminosity as mainly caused by accretion processes, this indicates that starburst and AGN activity increase proportionally."
 The interpretations of the results are discussed in Sect. , The interpretations of the results are discussed in Sect. \ref{discussion}.
Below we discuss the loug-teriu (time scales between half a voar up to 8 vears) X-ray and short-term (fime scales of order up to a few days) variability of interacting aud isolated Sevtert 1 aud 2 galaxies., Below we discuss the long-term (time scales between half a year up to 8 years) X-ray and short-term (time scales of order up to a few days) variability of interacting and isolated Seyfert 1 and 2 galaxies.
"algorithm outperforms the WASOBI one, which is to be expected since all signals but one are non-Gaussian.","algorithm outperforms the WASOBI one, which is to be expected since all signals but one are non-Gaussian."
" In the previous section, we have shown that in the case that the astrophysical component 6, is well separated as individual signal, we can create a filter for the raw data that directly filters the lightcurve signal from the noise."," In the previous section, we have shown that in the case that the astrophysical component $\bf{\hat{S}}_{a}$ is well separated as individual signal, we can create a filter for the raw data that directly filters the lightcurve signal from the noise."
" However, in most real data applications, Sa, is not perfectly separated but the components of $5, may be more so."," However, in most real data applications, $\bf{\hat{S}}_{a}$, is not perfectly separated but the components of $\bf{\hat{S}}_{sn}$ may be more so."
 In this case we can construct the noise model Msn given by equation 18 and the diagonal elements of O are fitted as described in section 3.4.., In this case we can construct the noise model $\bf{M}_{sn}$ given by equation \ref{noisemodel2} and the diagonal elements of $\bf{O}$ are fitted as described in section \ref{fitting}.
 The starting position of the algorithm is the same as for the previous example (figure 3))., The starting position of the algorithm is the same as for the previous example (figure \ref{ex1mix}) ).
 The model fit of the first lightcurve in figure 3 and its residuals are shown in figure 7.., The model fit of the first lightcurve in figure \ref{ex1mix} and its residuals are shown in figure \ref{ex1fitted}.
 The autocorrelation function for 100 lags is plotted in figure δ.., The autocorrelation function for 100 lags is plotted in figure \ref{ex1auto}.
" All but two lags are within the 3c confidence limit that the residual is white noise dominated, indicating that all signals have been removed effectively."," All but two lags are within the $\sigma$ confidence limit that the residual is white noise dominated, indicating that all signals have been removed effectively."
 Finally we simulate the convergence properties of both EFICA and WASOBI under varying white noise conditions., Finally we simulate the convergence properties of both EFICA and WASOBI under varying white noise conditions.
 Here we repeatedly run the algorithm until signal separation is completed and record the mean ISRs of the source separation., Here we repeatedly run the algorithm until signal separation is completed and record the mean ISRs of the source separation.
 We performedthis simulation 300 times for Gaussian noise FWHMs varying from 0.0 - 0.3 magnitudes (figure 7 has a gauss = 0.01) and every ISR measurement reported is the mean of 10 iterations., We performedthis simulation 300 times for Gaussian noise FWHMs varying from 0.0 - 0.3 magnitudes (figure \ref{ex1fitted} has a $_{gauss}$ = 0.01) and every ISR measurement reported is the mean of 10 iterations.
 Figure 9 summarises the results., Figure \ref{ex1ISR2} summarises the results.
" Here, the red circles represent the mean ISR or the EFICA algorithm and the blue crosses that of WASOBI."," Here, the red circles represent the mean ISR or the EFICA algorithm and the blue crosses that of WASOBI."
 It can clearly be seen that for this example the EFICA algorithm outperforms WASOBI and on average reaches lower ISR values., It can clearly be seen that for this example the EFICA algorithm outperforms WASOBI and on average reaches lower ISR values.
 We can further note that the blind source separation is not significantly affected by the magnitude of the white noise and performs well under difficult signal to noise conditions., We can further note that the blind source separation is not significantly affected by the magnitude of the white noise and performs well under difficult signal to noise conditions.
 The previous examples illustrated the two methods available to correct the observed data: 1: Filtering the astrophysical signal out, The previous examples illustrated the two methods available to correct the observed data: : Filtering the astrophysical signal out
The structure of the dark matter halo reflects the structure of the total gravitational potential. as prescribed by Eq. (7)).,"The structure of the dark matter halo reflects the structure of the total gravitational potential, as prescribed by Eq. \ref{rhoiso}) )."
 On the one hand. there is an artificial cusp in the vertical dark matter density distribution on the z=O0 plane. which results from the singular (zero-thickness) density distribution assumed for the stellar disk.," On the one hand, there is an artificial cusp in the vertical dark matter density distribution on the $z=0$ plane, which results from the singular (zero-thickness) density distribution assumed for the stellar disk."
 The detailed structure of the cusp can be obtained from the Jeans equation: This feature has no physical relevance and will be naturally eliminated 1n the finite-thickness disk models that we plan to present in a separate paper., The detailed structure of the cusp can be obtained from the Jeans equation: This feature has no physical relevance and will be naturally eliminated in the finite-thickness disk models that we plan to present in a separate paper.
 On the other hand. the halo is characterized by significant flattening.," On the other hand, the halo is characterized by significant flattening."
 This latter feature is gerune and will not disappear in the regular finite-thickness case., This latter feature is genuine and will not disappear in the regular finite-thickness case.
 Figure 2 shows the contours of the total gravitationa| potential. which coincide with those of the dark matter dersity. for the model defined by (a.8)=(1.9.3.4). which. às we will see in the following. is the self-consistent model representative of the correlation in Eq. Gb».," Figure \ref{contours} shows the contours of the total gravitational potential, which coincide with those of the dark matter density, for the model defined by $(\alpha, \beta) = (1.9, 3.4)$, which, as we will see in the following, is the self-consistent model representative of the correlation in Eq. \ref{corr}) )."
 As naturally expected. the system tends to be spherically symmetric in the outer parts (where the gravitational importance of the disk rapidly vanishes). but is highly oblate in the central regions.," As naturally expected, the system tends to be spherically symmetric in the outer parts (where the gravitational importance of the disk rapidly vanishes), but is highly oblate in the central regions."
 The flattening of the dark halo can be quantified in terms of the ellipticity &. defined as where € and 1(&) represent respectively the intersections with the Z=O and &=0 planes of a given contour of the total gravitational potential.," The flattening of the dark halo can be quantified in terms of the ellipticity $\varepsilon$, defined as where $\xi$ and $v(\xi)$ represent respectively the intersections with the $\zeta=0$ and $\xi=0$ planes of a given contour of the total gravitational potential."
 The profile of the ellipticity & as a function of radius is illustrated in Fig. 3.., The profile of the ellipticity $\varepsilon$ as a function of radius is illustrated in Fig. \ref{flattening}.
 The high flattening iside one exponential length may be exaggerated because of the zero-thickness of the disk., The high flattening inside one exponential length may be exaggerated because of the zero-thickness of the disk.
 Figure 4. shows the ellipticity reached by the self-consistent models at 2.2 exponential lengths n the (a.6) plane.," Figure \ref{ellplane} shows the ellipticity reached by the self-consistent models at $2.2$ exponential lengths in the $(\alpha, \beta)$ plane."
 It would be interesting to compare the flattening obtained from our self-consistent models with the empirical determinations based on a variety of dynamical arguments. ranging from the dynamics of warpec disks and polar rings to the flaring of gas layers (see the discussion in the paper by Olling Merrifield 2000: see also the series of papers started by O'Brien et al.," It would be interesting to compare the flattening obtained from our self-consistent models with the empirical determinations based on a variety of dynamical arguments, ranging from the dynamics of warped disks and polar rings to the flaring of gas layers (see the discussion in the paper by Olling Merrifield 2000; see also the series of papers started by O'Brien et al."
 2010)., 2010).
 It would also be interesting to compare the flattening of our self-consistent models with the indications that are expected to be gathered in the near future from weak and strong gravitational lenses (for example. see Trott et al.," It would also be interesting to compare the flattening of our self-consistent models with the indications that are expected to be gathered in the near future from weak and strong gravitational lenses (for example, see Trott et al."
 2010): here. the natural comparison to be made ts in terms of the relevant flattening profile of the projected density distribution.," 2010); here, the natural comparison to be made is in terms of the relevant flattening profile of the projected density distribution."
 A significant feature of the self-consistent models presented in this paper is the unexpected degree of flatness that characterizes their rotation curves., A significant feature of the self-consistent models presented in this paper is the unexpected degree of flatness that characterizes their rotation curves.
 In principle. self-consistent rotation curves are designed to be flat only as an asymptotic condition for R>>/i. that is where the gravitational influence of the stellar disk becomes negligible.," In principle, self-consistent rotation curves are designed to be flat only as an asymptotic condition for $R \gg h$, that is where the gravitational influence of the stellar disk becomes negligible."
 In the intermediate radial range the shape of the rotation curve is instead determined by the mutual interactions between halo and visible disk and thus cannot be ascribed naively to the Maxwellian form of the halo distribution function (especially because in the intermediate radial range an isothermal sphere is known to be associated, In the intermediate radial range the shape of the rotation curve is instead determined by the mutual interactions between halo and visible disk and thus cannot be ascribed naively to the Maxwellian form of the halo distribution function (especially because in the intermediate radial range an isothermal sphere is known to be associated
which were obtained using a variety of methods.,which were obtained using a variety of methods.
 We estimate that the typical uncertainty should be z 0.5 dex 2002).," We estimate that the typical uncertainty should be $\lesssim$ 0.5 dex \citep[e.g. see][]{mclure02,vestergaard02,woo02}."
. In addition. equation 6. can be related to the total jet power. £2).," In addition, equation \ref{eqn_merloni4} can be related to the total jet power, $P_{\rm J}$."
 For llat-spectrum emission from the radio core. (Blancllord&WonielL979): empirical evidence [or this relationship was found by Wording.Fender (2006)..," For flat-spectrum emission from the radio core, \citep[][]{blandford79}; empirical evidence for this relationship was found by \citet*[][]{koerding06b}."
 Thus. at a given value of log(A). a 1 dex dillerence in #& corresponds to a dillerence in jet. power of ezOT dex.," Thus, at a given value of $(\lambda)$, a 1 dex difference in $R$ corresponds to a difference in jet power of $\frac{12}{17} \approx 0.7$ dex."
 Figure 1. demonstrates how the distribution of points in the log(/) log(A) plane changes depending on whether otal or core radio luminosities are used. and if à mass correction term is applied.," Figure \ref{fig:plot1} demonstrates how the distribution of points in the $R$ $\lambda$ ) plane changes depending on whether total or core radio luminosities are used, and if a mass correction term is applied."
 Firstly. we show the original data rom SSLOT in panel (i). though with some slightcations?: the distribution is clearly. bimodal.," Firstly, we show the original data from SSL07 in panel (i), though with some slight; the distribution is clearly bimodal."
 In. panel (ii). racio loucdnesses derived. from. core radio luminosities have »en plotted: though £# still increases with decreasing A. it is immecdiately apparent that the gap between the upper and ower tracks has closed significantly.," In panel (ii), radio loudnesses derived from core radio luminosities have been plotted; though $R$ still increases with decreasing $\lambda$, it is immediately apparent that the gap between the upper and lower tracks has closed significantly."
 However. it is the use of core luminosities and mass corrections that. results in the greatest convergence of the two sequences (panel iii).," However, it is the use of core luminosities and mass corrections that results in the greatest convergence of the two sequences (panel iii)."
 For the three above scenarios. we attempted to quantify any possible dillerences between the distributions of RCs and SCGis/LINERs.," For the three above scenarios, we attempted to quantify any possible differences between the distributions of RGs and SGs/LINERs."
 In the analysis that follows in this section. we first applied alog(A)«— 2cutolfto minimize the effect of varving X-ray states andtheir coupling to jet production at higher Edeington ratios (Fenderetal.2004).," In the analysis that follows in this section, we first applied a $\lambda) < -2$ cutoff to minimize the effect of varying X-ray states andtheir coupling to jet production at higher Eddington ratios \citep[][]{fender04}."
. Secondly. the four PRE RCs with log(A) <6 (three of which have limits in # ancl A) were excluded so that similar baselines in log(A) were covered by both subsets.," Secondly, the four FR I RGs with $\lambda$ ) $< -6$ (three of which have limits in $R$ and $\lambda$ ) were excluded so that similar baselines in $\lambda$ ) were covered by both subsets."
 Nonetheless. the analysis is complicated. by the fact that a number of remaining sources have limits in /? and/or A. especially in the FR LRG subsample.," Nonetheless, the analysis is complicated by the fact that a number of remaining sources have limits in $R$ and/or $\lambda$, especially in the FR I RG subsample."
 We generally have treated any limits as detections: the potentially large uncertaintics associated with a range of datapoints in the Ilog(/?) log(A) plane are discussed. in more detail in Section ??.., We generally have treated any limits as detections; the potentially large uncertainties associated with a range of datapoints in the $R$ $\lambda$ ) plane are discussed in more detail in Section \ref{discussion}.
 The FR E BC lower # limits imply that the average cdilferences in. racio Ioudness between the tracks may be somewhat larger than is suggested here. but because these lower Z? limits result fron upper Lg limits (see table 4 in SSLOT). the gap between the sequences would still be smallest for case (iii) in Figure 1..," The FR I RG lower $R$ limits imply that the average differences in radio loudness between the tracks may be somewhat larger than is suggested here, but because these lower $R$ limits result from upper $L_{B}$ limits (see table 4 in SSL07), the gap between the sequences would still be smallest for case (iii) in Figure \ref{fig:plot1}. ."
 The two-dimensional KolmogorovSmirnov. (x8) was used to evaluate whether the distributions of RCs and SCGs/LINERs are drawn from cdillerent parent. populations:, The two-dimensional Kolmogorov–Smirnov (KS) was used to evaluate whether the distributions of RGs and SGs/LINERs are drawn from different parent populations;
are less massive in simulation MIT. but the intensity of the starburst taking place during the merger is comparable.,"are less massive in simulation M11, but the intensity of the starburst taking place during the merger is comparable."
 As a result. there is less gas available after the merger to forni voung stars and build up an extended thin disc.," As a result, there is less gas available after the merger to form young stars and build up an extended thin disc."
 In most simulations. the merger resulted. in the formation of a ring made of voung stars.," In most simulations, the merger resulted in the formation of a ring made of young stars."
 This implies that prograde gas-rich major mergers have a tendency to form rings., This implies that prograde gas-rich major mergers have a tendency to form rings.
 l'hese rings seem to be signatures of a gas substructure since most of the rings are coplanar with the thin disc., These rings seem to be signatures of a gas substructure since most of the rings are coplanar with the thin disc.
 The large impact parameter use here is quite contrary to the normal scenarios forming a ring remnant (Hernquist&Weil1993:Mapellictal. 2008).," The large impact parameter use here is quite contrary to the normal scenarios forming a ring remnant \citep{hernquistandweil93,mapelli08}."
. That can be a signature of a gas-rich. merger. and more work is needed to certify this assertion.," That can be a signature of a gas-rich merger, and more work is needed to certify this assertion."
 The simulation M12z formed a very complex structure. with a non-coplanar ring connected to a very small thin disc by spiral arms. embedded in an ellipsoid clistribution of old stars (Eig. 3)).," The simulation M12z formed a very complex structure, with a non-coplanar ring connected to a very small thin disc by spiral arms, embedded in an ellipsoid distribution of old stars (Fig. \ref{M12z}) )."
 Also. the face-on views of the mergers for simulations MI290 and rMI2 (top panels of Figs.," Also, the face-on views of the mergers for simulations M1290 and rM12 (top panels of Figs."
 4. for an example ) clearly reveal the presence of a central bar made of both old and voung stars., \ref{M1290} for an example ) clearly reveal the presence of a central bar made of both old and young stars.
 No bars are seen in the other simulations., No bars are seen in the other simulations.
 We can use the surface density brightness to trace the racial Luminosity profiles of the disces., We can use the surface density brightness to trace the radial luminosity profiles of the discs.
 The racial luminosity proliles are. shown in LEο. 5.," The radial luminosity profiles are shown in Fig. \ref{allprof},"
 [or all simulations., for all simulations.
 We calculated. these profiles separately for young stars and old stars., We calculated these profiles separately for young stars and old stars.
 The dotted and dashed lines are fits to the profiles of voung and old stars. respectively.," The dotted and dashed lines are fits to the profiles of young and old stars, respectively."
 In cases where a ring was clearly visible. we exeluded it from the fit.," In cases where a ring was clearly visible, we excluded it from the fit."
 ALL profiles are well-fitted by an exponential profile. except. for simulations MI12z and ALLL. where the voung stars are better-fitted by a de Vaucouleurs profile.," All profiles are well-fitted by an exponential profile, except for simulations M12z and M11, where the young stars are better-fitted by a de Vaucouleurs profile."
 We can use the exponential profiles to caleulate the scale-Iengths of the dises., We can use the exponential profiles to calculate the scale-lengths of the discs.
" In Table 3.. we List the scale-Iength , of the old population. the scale-Iengthfh, of the voung population. and their ratio Pih. except for the simulations MI2z ancl ALLL. for which an exponential profile does not fit the distribution of voung stars."," In Table \ref{tablescales}, we list the scale-length $h_o$ of the old population, the scale-length$h_y$ of the young population, and their ratio $h_o/h_y$, except for the simulations M12z and M11, for which an exponential profile does not fit the distribution of young stars."
 The scale-Iength is usually larger for the old population than the voung one. with ratios varving from 0.98 to 1.60.," The scale-length is usually larger for the old population than the young one, with ratios varying from 0.98 to 1.60."
 This is in agreement with the recent observational work to Yoachim&Dalcanton(2006) if we make a direct. correspondence between old stars and thick-clise stars. d," This is in agreement with the recent observational work to \citet{yd06} if we make a direct correspondence between old stars and thick-disc stars. ,"
efinition. bx the time the merger is completed. old," by the time the merger is completed, old"
In order to clarify the situation and possibly to identify the cause of these problems we undertook the same kind of analvsis from scratch. and for an entirely. new set of data.,In order to clarify the situation and possibly to identify the cause of these problems we undertook the same kind of analysis from scratch and for an entirely new set of data.
 Our present sample consists of 76 RRab variables observed ing Con by Ixaluzny at cl. (, Our present sample consists of 76 $ab$ variables observed in $\omega$ Cen by Kaluzny at el. (
1997) and Ixaluzny et al. (,1997) and Kaluzny et al. (
2003).,2003).
 The photometry in these two papers is of very good quality and shows no systematic differences in the zero point (see Ixaluzny et al., The photometry in these two papers is of very good quality and shows no systematic differences in the zero point (see Kaluzny et al.
 2003 for details)., 2003 for details).
" Following recommendations of WKovaces Ixanbur (1998) for analysis we used only Noten=56 stars with 12),3.", Following recommendations of Kováccs Kanbur (1998) for analysis we used only $N_{\omega Cen}=56$ stars with $D_m<3$.
 A clear advantage of our data is very consistent photometry obtained within the same project ancl using the same telescope., A clear advantage of our data is very consistent photometry obtained within the same project and using the same telescope.
 The vast majority of stars was observed. at. least 500 times. hence we obtained very precise and reliable values of the Fourier coellicients.," The vast majority of stars was observed at least 500 times, hence we obtained very precise and reliable values of the Fourier coefficients."
 To minimize crrors in the cocllicicnts anc their correlation we converted. our projection into orthogonal rigonometric polvnomials (Schwarzenbere-Czerny 1996. Schwarzenbere-Czerny Waluzny 1906).," To minimize errors in the coefficients and their correlation we converted our projection into orthogonal trigonometric polynomials (Schwarzenberg-Czerny 1996, Schwarzenberg-Czerny Kaluzny 1996)."
 As all stars come rom the same cluster we co not suller from the distance indeterminacy and cilferential interstellar reddening because here are no systematic dillerences in (D.V) in the field of w Cen (Schlegel et al., As all stars come from the same cluster we do not suffer from the distance indeterminacy and differential interstellar reddening because there are no systematic differences in $E(B-V)$ in the field of $\omega$ Cen (Schlegel et al.
 1998)., 1998).
 Additionally. because of he significant spread in metallicities within z Cen. our sample is excellent. for. studying metallicity related: cluster cillerences unallected by distance dillerences.," Additionally, because of the significant spread in metallicities within $\omega$ Cen, our sample is excellent for studying metallicity related intra-cluster differences unaffected by distance differences."
" Figure 2 shows the amplitudes 21). amplitude ratios 2, and phase combinations Oj), as the function of the period P? for all Itlteb. variables from our sample."," Figure 2 shows the amplitudes $A_j$, amplitude ratios $R_{j1}$ and phase combinations $\phi_{j1}$ as the function of the period $P$ for all $ab$ variables from our sample."
 Comparing them with the same relations for the INNOI sample (see their Fig., Comparing them with the same relations for the KW01 sample (see their Fig.
 1) we conclude that our relations are significantly tighter and correlate very well with the period., 1) we conclude that our relations are significantly tighter and correlate very well with the period.
" The interesting thing we noted is the clear change of the slope in the Oo, - 2 and oo, - P relations occurring al P=0.75 davs.", The interesting thing we noted is the clear change of the slope in the $\phi_{51}$ - $P$ and $\phi_{61}$ - $P$ relations occurring at $P\approx0.75$ days.
" Arranging the Rab stars from w Con according to the increasing period one can see that it is connected with a disappearance of the ""bump"". clearly seen at phase around. 0.7 in the light curves of variables with periods shorter than 0.75 days."," Arranging the $ab$ stars from $\omega$ Cen according to the increasing period one can see that it is connected with a disappearance of the ""bump"", clearly seen at phase around 0.7 in the light curves of variables with periods shorter than 0.75 days."
 The basic properties of our sample of RRab stars [rom w Con are collected in Table 1., The basic properties of our sample of $ab$ stars from $\omega$ Cen are collected in Table 1.
 We performed: several fits involving P and up to 3 different Fourier. phase and. zumplitude: coellicients: clrawn [rom the first 5 harmonics., We performed several fits involving $P$ and up to 3 different Fourier phase and amplitude coefficients drawn from the first 5 harmonics.
 To remove the constant. term indeterminacy. we adopted as fixed the distance moculus feces=14.09+0.04 mag of Waluzny ct al. (," To remove the constant term indeterminacy, we adopted as fixed the distance modulus $\mu_{\omega Cen} = 14.09\pm0.04$ mag of Kaluzny et al. ("
2002).,2002).
 The results are listed in Table 2., The results are listed in Table 2.
 We explicitly list the fitted formula and its standard deviation D., We explicitly list the fitted formula and its standard deviation $\cal D$.
 To test the numerical self consistency of our fits we use each formula to recalculate [ioco and its standard. deviation o.," To test the numerical self consistency of our fits we use each formula to recalculate $\mu_{\omega
Cen}$ and its standard deviation $\sigma$."
 These are also listed in Table 2., These are also listed in Table 2.
 Its hardly surprising that DezVNG0.," Its hardly surprising that ${\cal D}/\sigma \approx
\sqrt{N_{\omega Cen}}$."
 We shall refer to different fitted. formulae by their consecutive numbers in the Table 2. from (E1) to (E11).," We shall refer to different fitted formulae by their consecutive numbers in the Table 2, from (F1) to (F11)."
 Inspection of Table 2 shows that no formulae involving only amplitudes (e.g. EI F5) are satisfactory., Inspection of Table 2 shows that no formulae involving only amplitudes (e.g. F1 F5) are satisfactory.
 This. is in marked contradiction to expectations from δαν. (8)), This is in marked contradiction to expectations from Eqs. \ref{e:3}) )
 and (9))., and \ref{e:4}) ).
 Ht is particularly. surprising as the latter formula performed best. on the data from. ΑΛΛΟΙ., It is particularly surprising as the latter formula performed best on the data from KW01.
 We observe a strong correlation cllect of type (ii) in Sect. 2?.., We observe a strong correlation effect of type (iii) in Sect. \ref{s311}.
 In F1 F5 only the amplitude coefficients. vary while the rest remains remarkabA stable. and the quality of the fit CD) is unallected.," In F1 F5 only the amplitude coefficients vary while the rest remains remarkably stable, and the quality of the fit $(\cal D)$ is unaffected."
" In FS. contributions from el, and el; simply cancel out to the value in Fl for 24, alone."," In F5, contributions from $A_1$ and $A_3$ simply cancel out to the value in F1 for $A_1$ alone."
 Most. other fits involving boff amplitude and phase appear satisfactory., Most other fits involving amplitude and phase appear satisfactory.
 1 seems that the set of parameters originally selected by 18296 performs quite well in our case. except that our cocllicients in L3 are completely dilferent from those in Eq. (72).," It seems that the set of parameters originally selected by KJ96 performs quite well in our case, except that our coefficients in F3 are completely different from those in Eq. \ref{e:2}) )."
 Formally. our best fit is FG.," Formally, our best fit is F6."
 However. the improvement of 47. for F6 compared to that for F3 yields a Fisher-Snedecor test. value of ΕΙ52)=7.85. only mareinally significant at the level of.," However, the improvement of $\chi^2$ for F6 compared to that for F3 yields a Fisher-Snedecor test value of $F(1,52)=7.85$, only marginally significant at the level of."
 At the face of these values one could say that F2. F3. I6FLO viel fits of similar quality and inclusion of more xwameters are hardly. justifiable.," At the face of these values one could say that F2, F3, F6–F10 yield fits of similar quality and inclusion of more parameters are hardly justifiable."
 It looks like the who »ocedure is incapable of vielding better accuracy than these atter formulae., It looks like the whole procedure is incapable of yielding better accuracy than these latter formulae.
 1n order to reveal any remaining trend in the residuals roni the [it in each panel of Fig., In order to reveal any remaining trend in the residuals from the fit in each panel of Fig.
 3 we plot for all stars their absolute magnitude Ady predicted. by à. given ormula against average apparent magnitude <V7., 3 we plot for all stars their absolute magnitude $M_V$ predicted by a given formula against average apparent magnitude $<V>$.
 Dots correspond. to the formulae from Table 2 and circles. to σας. (S- 10)), Dots correspond to the formulae from Table 2 and circles to Eqs. \ref{e:3}- \ref{e:5}) )
 from IKWOL. the latter shifted by à constant.," from KW01, the latter shifted by a constant."
 The lines mark ideal relations Adj=<V>[aston," The lines mark ideal relations $M_V
= <V>-\mu_{\omega Cen}$."
 Inspection of Fig., Inspection of Fig.
 3 reveals that compared: to. σας. (8- 103) , 3 reveals that compared to Eqs. \ref{e:3}- \ref{e:5}) )
our formulae involving phase perform particularly well [or brighter stars., our formulae involving phase perform particularly well for brighter stars.
 The common feature in all. panels is the markedly. lower inclination of the trend in the points than the ideal relation., The common feature in all panels is the markedly lower inclination of the trend in the points than the ideal relation.
 This is worrisome as apparently the fitted formulae are unable to reproduce the observed span of magnitudes., This is worrisome as apparently the fitted formulae are unable to reproduce the observed span of magnitudes.
 This cllect is also present in similar attempts to predietmagnitudes of cepheids using shapes of, This effect is also present in similar attempts to predictmagnitudes of cepheids using shapes of
above equation is taken over the relative integers denoted by ny.,above equation is taken over the relative integers denoted by $n_y$.
 It is possible to derive a single secoud-order ordinary differcutial equation (Artvinewicz 1993)., It is possible to derive a single second-order ordinary differential equation (Artymowicz 1993).
 aud other perturbed quantities are giveu by . ον The boundary condition for Equation is that wave should propagate away from the plauct., and other perturbed quantities are given by and where The boundary condition for Equation is that wave should propagate away from the planet.
 At the location away frou the effective Lindblad resonance given by the approximate solution cau be written analytically using WKD approximation|., At the location away from the effective Lindblad resonance given by the approximate solution can be written analytically using WKB approximation.
" It takes the form. for |r|>x. where upper sign is for c>0 aud the lower sigu is for c«Q0. aud C(h,) denotes the amplitude (but not necessarily real) of the wave with mode hy."," It takes the form, for $|x|\to\infty$, where upper sign is for $x>0$ and the lower sign is for $x<0$, and $C(k_y)$ denotes the amplitude (but not necessarily real) of the wave with mode $k_y$."
" We note that since we consider the liuear perturbation excited bv the plauet's gravitational potential at the origin of our coordinate system. tho amplitude C(&,) is proportional to the planet mass "," We note that since we consider the linear perturbation excited by the planet's gravitational potential at the origin of our coordinate system, the amplitude $C(k_y)$ is proportional to the planet mass $M_{\rm p}$."
Frou here ou. using the sviunietry of the sheariug-sheet. we ouly cousicder .20 without loss of gencralitv.," From here on, using the symmetry of the shearing-sheet, we only consider $x>0$ without loss of generality."
" Using My.equations(11)...(15).. and (18).. we can derive the asviuptotic form for 9X and de, at |e]»x. where we have retained oulv the leaciug terms in. iu equations aud(15)."," Using equations, and , we can derive the asymptotic form for $\delta \Sigma$ and $\delta v_x$ at $|x|\to\infty$, where we have retained only the leading terms in $x$ in equations and."
". Note that. in the real space. solutions are given by where JJ is the scale height 7I—¢/Q,. 4=1/2 for 6S aud de,. y=1/2 for óc. aud Ελ) is a function of hy."," Note that, in the real space, solutions are given by where $H$ is the scale height $H = c/\Omega_{\rm p}$, $q=1/2$ for $\delta \Sigma$ and $\delta v_x$, $q=-1/2$ for $\delta v_y$, and $F(k_y)$ is a function of $k_y$."
" Therefore. alone the line where yy is coustant. perturbed quantities take the same values except for the depeudence e""."," Therefore, along the line where $y_0$ is constant, perturbed quantities take the same values except for the dependence $x^{q}$."
 Therefore. we cau write the form of the WI&D solutiou in real space. where we write the dependence ou the planet mass explicith. aud f. g. and 7 aye the functious that determines the form of the perturbation.," Therefore, we can write the form of the WKB solution in real space, where we write the dependence on the planet mass explicitly, and $f$, $g$, and $h$ are the functions that determines the form of the perturbation."
 We note that from equation(20).. f aud g are proportional in the place where WIKD approximation is valid.," We note that from equation, $f$ and $g$ are proportional in the place where WKB approximation is valid."
The exact linear solution can be obtained bv solving equations ummerically with nou-cflectiug boundary conditions.,The exact linear solution can be obtained by solving equations numerically with non-reflecting boundary conditions.
" The profiles of density and ce, obtained in such a way are shown in Figure D2..", The profiles of density and $v_x$ obtained in such a way are shown in Figure \ref{fig:linear_profile}.
" Iu this figure. we calculate Dnon-axisviunietrie modes (ky= 0) aud assumed CAL,ΠΟ= 1."," In this figure, we calculate non-axisymmetric modes $k_y\neq 0$ ) and assumed $GM_{\rm p}/Hc^2=1$ ."
 The amplitude of perturbation is proportional to the planet mass., The amplitude of perturbation is proportional to the planet mass.
 Wenote that the results obtained iun equations are based ou the WI&D approximation. and they are applicable ouly in the region [e/I7|z1. ," Wenote that the results obtained in equations are based on the WKB approximation, and they are applicable only in the region $|x/H| \gtrsim 1$ "
Fig.,Fig.
 5., 5.
 The model with à solar-scaled composition can instead be safely excluded., The model with a solar-scaled composition can instead be safely excluded.
 The boxes along the relations mark the interpulse values after each dredge up event., The boxes along the relations mark the interpulse values after each dredge up event.
 Close to these values we should have the highest probability of finding a star., Close to these values we should have the highest probability of finding a star.
 In general. the agreement is remarkably good. with one exception (LET3).," In general, the agreement is remarkably good, with one exception (LE13)."
 Concerning the abundance of the light element F. we observe. as shown in refFabun. à change from an F underabundance to an F overabundance with increasing C/O (relative to the solar value scaled to the iron abundance of the cluster).," Concerning the abundance of the light element F, we observe, as shown in \\ref{Fabun}, a change from an F underabundance to an F overabundance with increasing C/O (relative to the solar value scaled to the iron abundance of the cluster)."
 Accordingly. there is also a similar trend with the luminosity. as found for the C/O ratio.," Accordingly, there is also a similar trend with the luminosity, as found for the C/O ratio."
 Measurements of HF lines are a critical source for obtaining the F abundance in stars., Measurements of HF lines are a critical source for obtaining the F abundance in stars.
 Various hypotheses on the origin of this element have been discussed in the literature (see Schuler et citeSCS07 for a recent overview)., Various hypotheses on the origin of this element have been discussed in the literature (see Schuler et \\cite{SCS07} for a recent overview).
 In. particular. from a correlation of the carbon abundance with the F abundance. Jorisset et al. (1992))," In particular, from a correlation of the carbon abundance with the F abundance, Jorissen et al. \cite{jo92}) )"
 showed that nucleosynthesis in AGB stars is one likely path for the production of this element., showed that nucleosynthesis in AGB stars is one likely path for the production of this element.
 Schuler et al. (2007)), Schuler et al. \cite{SCS07}) )
 come to à similar result. from. F abundance measurements of à carbon-enhanced. metal-poor star.," come to a similar result from F abundance measurements of a carbon-enhanced, metal-poor star."
 A positive correlation between F and C/O has also been acknowledged in a planetary nebula (Zhang Liu citezhang05))., A positive correlation between F and C/O has also been acknowledged in a planetary nebula (Zhang Liu \\cite{zhang05}) ).
 Our data of NGC 1846 AGB stars. clearly support the production and dredge up of F during the AGB evolution., Our data of NGC 1846 AGB stars clearly support the production and dredge up of F during the AGB evolution.
 The two lines in the figure represents the predictions of the reference model., The two lines in the figure represents the predictions of the reference model.
 The only difference between the two lines is in the initial. fluorine abundance., The only difference between the two lines is in the initial fluorine abundance.
 We have assumed [F/Fe]=0 and |F/Fe]=-0.71 at the begirning of the evolutionary sequence. for the solid and the dashed lines. respectively.," We have assumed [F/Fe]=0 and [F/Fe]=-0.71 at the beginning of the evolutionary sequence, for the solid and the dashed lines, respectively."
 The lower value corresponds to the one of the less evolved AGB star in our sample (H39)., The lower value corresponds to the one of the less evolved AGB star in our sample (H39).
 Note that Cunha et al. (2003)), Note that Cunha et al. \cite{cunha03}) )
 report similar fluorine underabundances in LMC giants., report similar fluorine underabundances in LMC giants.
 Our models predict a negligible variation in the surface F abundance after the first dredge up., Our models predict a negligible variation in the surface F abundance after the first dredge up.
" It should be noted that only an ""extreme"" extra mixing during the RGB may induce a sizeable F depletion (see e.g. Denissenkov et al. 2006)).", It should be noted that only an “extreme” extra mixing during the RGB may induce a sizeable F depletion (see e.g. Denissenkov et al. \cite{deni06}) ).
 In contrast. during the AGB fluorine is produced by « captures on N in the convective zone generated by a thermal pulse and. later on. dredged up.," In contrast, during the AGB fluorine is produced by $\alpha$ captures on $^{15}$ N in the convective zone generated by a thermal pulse and, later on, dredged up."
 Part of the N seeds are in the ashes of the CNO burning (about 50%)). while the remaining part is synthesized m the IC pocket.," Part of the $^{15}$ N seeds are in the ashes of the CNO burning (about ), while the remaining part is synthesized in the $^{13}$ C pocket."
 In both cases. N is released by the 'O(p.à) N reaction (for more details see Cristallo et citecriQ6)).," In both cases, $^{15}$ N is released by the $^{18}$ $(p,\alpha)^{15}$ N reaction (for more details see Cristallo et \\cite{cri06}) )."
 However. even if models account for a substantial AGB production. we confirm the previous claim by Jorissen et al.((1992)) that the theoretical predictions underestimate the fluorine overabundance observed in evolved AGB stars.," However, even if models account for a substantial AGB production, we confirm the previous claim by Jorissen et \cite{jo92}) ) that the theoretical predictions underestimate the fluorine overabundance observed in evolved AGB stars."
 A possible solution may be a more efficient. production of PN in the He-rich inter-shell zone., A possible solution may be a more efficient production of $^{15}$ N in the He-rich inter-shell zone.
 Perhaps. an additional and different source of fluorine should be sought.," Perhaps, an additional and different source of fluorine should be sought."
 We have to note. of course. that. as the fluorine abundance in the NGC 1846 stars has been derived from only one line blend. a systematic error cannot be excluded.," We have to note, of course, that, as the fluorine abundance in the NGC 1846 stars has been derived from only one line blend, a systematic error cannot be excluded."
"constant,",constant.
 Ususe our ineasured shifts we performed Monte Carlo experiments and found that the effect of the tutra-order shifts is well modeled by a Caussian dispersion iu waveleneth calibration with a magnitude of around SO120 ms., Using our measured shifts we performed Monte Carlo experiments and found that the effect of the intra-order shifts is well modeled by a Gaussian dispersion in wavelength calibration with a magnitude of around 80–120 $\ms$.
 We found that the effect on depended strongly ou the πα” of lines being compared2e within the spectrum. with the use of a sanall number of lines resulting in larger than expected errors.," We found that the effect on $\delalpha$ depended strongly on the number of lines being compared within the spectrum, with the use of a small number of lines resulting in larger than expected errors."
 Thus. until a correction to these intra-order wavelength nuüscalibrations is found. we reconunuieud against focusing on comparison between pairs of lines or the use of spectra which contain ouly a few lines.," Thus, until a correction to these intra-order wavelength miscalibrations is found, we recommend against focusing on comparison between pairs of lines or the use of spectra which contain only a few lines."
 We sununarized the results of our Monte Carlo experiments ina fitting formula Equation 1). which should be useful n estimating the effect of these (or simular) wavelenetl calibration problems on future fine-structure work.," We summarized the results of our Monte Carlo experiments in a fitting formula Equation \ref{eqn:sigmada}) ), which should be useful in estimating the effect of these (or similar) wavelength calibration problems on future fine-structure work."
 J.D.W. and EK.C. were supported in part by the U.S. Department of Encereyv under erant DE-FCU3-9TER10516., J.B.W. and K.G. were supported in part by the U.S. Department of Energy under grant DE-FG03-97ER40546.
 ALTAL thanks the Australian Research Council for a QETI Research Fellowship (DPO0s77998)., M.T.M. thanks the Australian Research Council for a QEII Research Fellowship (DP0877998).
velocily that the corresponding rarer isotope.,velocity that the corresponding rarer isotope.
 This would be consistent with CO (tvacing the underlying outflow., This would be consistent with CO tracing the underlying outflow.
 In the presence of infall. isotopic line emission would always be expected to be redshifted with respect to the main line (Naravananetal...1995).," In the presence of infall, isotopic line emission would always be expected to be redshifted with respect to the main line \citep{nwb98}."
. In the presence of infall alone. the emergent line intensitv ancl the emergent optical depth profile must be asvimnetric: the line intensity would be greater at blueshifted velocities. and correspondinglv. the line optical depth would be greater at redshilted velocities.," In the presence of infall alone, the emergent line intensity and the emergent optical depth profile must be asymmetric; the line intensity would be greater at blueshifted velocities, and correspondingly, the line optical depth would be greater at redshifted velocities."
 Indeed. the red asvimnetry. in the optical depth profiles of eenission derived from main aud isotopic observations were used to bolster the case lor infall in the IRAS 16293-2422 Class 0 svstem (Naravananetal.1998).," Indeed, the red asymmetry in the optical depth profiles of emission derived from main and isotopic observations were used to bolster the case for infall in the IRAS 16293-2422 Class 0 system \citep{nwb98}."
. In the presence of pure expansion (outflow). the converse would be true: the line profile would be red asvimetric. and the optical depth profile would be blue asviunetric.," In the presence of pure expansion (outflow), the converse would be true: the line profile would be red asymmetric, and the optical depth profile would be blue asymmetric."
 The recently proposed quantitative indicator of fall. OW which is the dillerence in (he velocity of peak emission between main and isotopic lines. normalized by the EWILIM of (the isotopic line (Alardonesοἱal1997).. is based on this effect: OW would be more negative for regions with stronger infall velocity [ields.," The recently proposed quantitative indicator of infall, $\delta V$ which is the difference in the velocity of peak emission between main and isotopic lines, normalized by the FWHM of the isotopic line \citep{mar97}, is based on this effect; $\delta V$ would be more negative for regions with stronger infall velocity fields."
 To determine the nature of the optical depth profiles. we performed an optical depth analvsis of the observed... CS and CO lines.," To determine the nature of the optical depth profiles, we performed an optical depth analysis of the observed, CS and CO lines."
 Figure 2 shows the resultant optical depth profiles towards the central position of SMAI., Figure \ref{tauall} shows the resultant optical depth profiles towards the central position of SMM4.
 The optical depth calculations were performed only over the EWIIM of the isotopic line., The optical depth calculations were performed only over the FWHM of the isotopic line.
" The opacities were estimated [rom (he observed line profile ratios oE1ICO .. CS/C""!S. and CO/CP0."," The opacities were estimated from the observed line profile ratios of , $^{34}$ S, and $^{18}$ 0."
 The opacity. 74 of the more abundant isotope was estimated using Z(Mein)/I(1so)=(1—en1-ereBn where r is the ratio of main to isotopic abundances. and Z(M0/0) and {15ο) are (he line intensities of (he main aud isotopic lines respectively.," The opacity, $\tau_\nu^M$ of the more abundant isotope was estimated using $I(Main)/I(Iso) =
(1-e^{\tau_\nu^M})/(1-e^{\tau_\nu^{M/r}})$, where $r$ is the ratio of main to isotopic abundances, and $I(Main)$ and $I(Iso)$ are the line intensities of the main and isotopic lines respectively."
 The main line is smoothed to the velocity resolution of (he corresponding isotope. and the opacity caleulation is performed for all velocities within ihe FWIIM of the isotopic line.," The main line is smoothed to the velocity resolution of the corresponding isotope, and the opacity calculation is performed for all velocities within the FWHM of the isotopic line."
 This technique assumes that the excitation temperature is the same for the main and isotopic species., This technique assumes that the excitation temperature is the same for the main and isotopic species.
 Iotopic abundance ratios of ]]2 65:1. [CS]:S]2 22.5:1. and [CO[:[CPO]|2 280:1 are assumed (WilsonandRood1994).," Isotopic abundance ratios of $=$ 65:1, $^{34}$ $=$ 22.5:1, and $^{18}$ $=$ 280:1 are assumed \citep{wil94}."
. From Figure 2.. it is seen that all the observed optical depth profiles towards (he central position of SMMA shows a red asymmetry. which is consistent with an infallscenario towards this object.," From Figure \ref{tauall}, it is seen that all the observed optical depth profiles towards the central position of SMM4 shows a red asymmetry, which is consistent with an infallscenario towards this object."
 Moreover. it is seen (hat for similar angular and spectral resolutions.," Moreover, it is seen that for similar angular and spectral resolutions,"
hundred particles “cut” from the glass tiles described above.,"hundred particles “cut"" from the glass tiles described above."
 Each shell is randomly rotated in the vy. and z directions.," Each shell is randomly rotated in the $x, y$, and $z$ directions."
 Although this reduces the smoothness of the outflow. it prevents the occurrence of numerical artefacts.," Although this reduces the smoothness of the outflow, it prevents the occurrence of numerical artefacts."
" The particles are injected at a radius. 10 Rigner~cem. with a constant wind velocity. v, kkmss!."," The particles are injected at a radius, $R_{\rm inner}$$\sim$$10^{15}$ cm, with a constant wind velocity, $v_{\rm w}$$\sim$ $^{-1}$."
 The initial temperature of the particles 1s Tying~ 0000 K. the temperature at Άμος derived from models of Betelgeuse's circumstellar envelope. e.g. ? and 9," The initial temperature of the particles is $T_{\rm wind}$$\sim$ 000 K, the temperature at $R_{\rm inner}$ derived from models of Betelgeuse's circumstellar envelope, e.g. \cite{Glas86} and \cite{Rod91}."
 Radiative cooling plays an important role in determining the temperature structure and emission from the bow shock., Radiative cooling plays an important role in determining the temperature structure and emission from the bow shock.
 Given the large uncertainties in the processes involved. we adopt the approach of ? rather than model the cooling in detail.," Given the large uncertainties in the processes involved, we adopt the approach of \cite{Smi03} rather than model the cooling in detail."
 Their cooling curve consists of analytic solutions and fits for various coolants based on detailed calculations described extensively in the appendices of ? and references therein. e.g. rotational and vibrational transitions of H». CO and H?O. H» dissociative cooling and reformation heating. gas-grain cooling/heating. and an atomic cooling function that includes non-equilibrium effects (see Table. 3)).," Their cooling curve consists of analytic solutions and fits for various coolants based on detailed calculations described extensively in the appendices of \cite{Smi03} and references therein, e.g. rotational and vibrational transitions of $_2$, CO and $_2$ O, $_2$ dissociative cooling and reformation heating, gas-grain cooling/heating, and an atomic cooling function that includes non-equilibrium effects (see Table. \ref{tab: cool}) )."
 First the non-equilibrium molecular and atomic. fractions of hydrogen are calculated according to the prescription of ?.. and a limited equilibrium C and O chemistry 15 used to calculate the CO. OH. and HO abundances (?)..," First the non-equilibrium molecular and atomic fractions of hydrogen are calculated according to the prescription of \cite{Sut97}, and a limited equilibrium C and O chemistry is used to calculate the CO, OH, and $_2$ O abundances \citep{Smi03}."
 We adopt standard solar abundances of hydrogen and helium. and set the abundances of carbon and oxygen to yc-2.5x107 and v076.3x107. respectively (2)...," We adopt standard solar abundances of hydrogen and helium, and set the abundances of carbon and oxygen to $\chi_{\rm C}$$\sim$ $\times10^{-4}$ and $\chi_{\rm O}$$\sim$ $\times 10^{-4}$, respectively \citep{Lam84}."
 We assume that the initial fraction of molecular to atomic hydrogen. f=ng./ng. in the Betelgeuse outflow ts small. f=0.001 (on a scale where 0 is atomic and 0.5 is fully molecular).," We assume that the initial fraction of molecular to atomic hydrogen, $f = n_{\rm H_2}/n_{\rm H}$, in the Betelgeuse outflow is small, $f = 0.001$ (on a scale where 0 is atomic and 0.5 is fully molecular)."
 The hydrogen in the ISM is assumed to be atomic., The hydrogen in the ISM is assumed to be atomic.
 The dust cooling function depends on the temperature of the grains. and we set this temperature to 30 K. the value derived by ?..," The dust cooling function depends on the temperature of the grains, and we set this temperature to 40 K, the value derived by \cite{Ueta08}. ."
 The change in specific internal energy. e. due to radiative cooling is then calculated implicitly for each particle. 7: where A and Γ are the volumetric cooling and heating rates in ccm? ss7!. respectively; Ar is the timestep: and n and a+| are the current and new timesteps. respectively (?)..," The change in specific internal energy, $\epsilon$, due to radiative cooling is then calculated semi-implicitly for each particle, $i$: _i = _i + t, where $\Lambda$ and $\Gamma$ are the volumetric cooling and heating rates in $^{-3}$ $^{-1}$, respectively; $\Delta t$ is the timestep; and $n$ and $n+1$ are the current and new timesteps, respectively \citep{Spr01}."
 The change in specific internal energy is then converted to a change in the entropy of each particle., The change in specific internal energy is then converted to a change in the entropy of each particle.
 We do not include a treatment of dust formation. and destruction. depletion of elements and molecules on to grains. the effects of magnetic or UV background radiation fields. density inhomogeneities in the stellar wind. and ISM.," We do not include a treatment of dust formation and destruction, depletion of elements and molecules on to grains, the effects of magnetic or UV background radiation fields, density inhomogeneities in the stellar wind, and ISM."
 Collisional ionisation. likely important at high temperatures is not explicitly included: instead. hot gas. z10 κ. cools primarily by atomic line. emission (?) and. thermal bremsstrahlung.," Collisional ionisation, likely important at high temperatures is not explicitly included; instead, hot gas, $\gtrsim$ $^4$ K, cools primarily by atomic line emission \citep{Sut93} and thermal bremsstrahlung."
 Although these processes are likely to have an effect on the bow shock properties. both in terms of radiative transfer and cooling. the computational cost of their inclusion in 3D models ts prohibitive.," Although these processes are likely to have an effect on the bow shock properties, both in terms of radiative transfer and cooling, the computational cost of their inclusion in 3D models is prohibitive."
 In the following sections. we explore and discuss possible solutions for Betelgeuse's bow shock with 3D numerical models (see Table. 2)).," In the following sections, we explore and discuss possible solutions for Betelgeuse's bow shock with 3D numerical models (see Table. \ref{tab: models}) )."
" We simulate four basic models. A-D. with medium resolution. and with ISM number densities. nj — 0.3. 1.0. 1.5. and. 1.9 em. and stellar velocities v, = 73. 40. 32. and 29 ! respectively."," We simulate four basic models, A-D, with medium resolution, and with ISM number densities, $_{\rm H}$ = 0.3, 1.0, 1.5, and 1.9 $^{-3}$, and stellar velocities $v_*$ = 73, 40, 32, and 29 $^{-1}$, respectively."
" Several lower resolution models are also caleulated in order to study the long-term evolution of model D (model DL) and the effect of varying the assumed ISM temperature (models C,6so. Cp1600. Οι κους) and the initial molecular hydrogen fraction (model Cj)."," Several lower resolution models are also calculated in order to study the long-term evolution of model D (model $_{\rm L}$ ) and the effect of varying the assumed ISM temperature (models $_{\rm L650}$, $_{\rm L1600}$, $_{\rm L8000}$ ) and the initial molecular hydrogen fraction (model $_{\rm Lf}$ )."
 Model Ay has the same parameters as model A. but is computed with higher resolution.," Model $_{\rm H}$ has the same parameters as model A, but is computed with higher resolution."
 Finally. we havealso computed an adiabatic model (model Bag). discussed in the next section. which provides a useful basis both for comparison to previous studies and to our models with radiative cooling (Sect. 4)).," Finally, we havealso computed an adiabatic model (model $_{\rm ad}$ ), discussed in the next section, which provides a useful basis both for comparison to previous studies and to our models with radiative cooling (Sect. \ref{sec: cool}) )."
with To integrate this equation we must first set its initial condition.,with To integrate this equation we must first set its initial condition.
 We let of0)=co be a free parameter. and ∣⋎⊓∩∶∪⊳∖↓⊔⊓⊾↓⊔⋜↧⊳∖↓≻↓↥∢⊾↓⋅⊔⇍⋜↧↓⊳∖∙∖⇁⊳∖↿∢⋅⊔↓⇂↓↥∢⊾⋏∙≟↓⋅⋜↧∖⇁∐⋜⊔↓∪⊔⋜↧↓∕ ⋠ ⋠ ⋠ ⋠⋠ ⇂⋅∪↓⋅⊓⋅∖⇁⋜⋯," We let $\psi(0)=\psi_0$ be a free parameter, and $\psi'(0)=0$ since in a spherical system the gravitational force vanishes in the centre."
⊲↓⊳∖↓⊔⋅⊳∖⊀↓⊔↿↓↥∢⊾⊓⊾⊔↿↓⋅∢⊾⊳↾∐⊔⊾⊔∪⊔⊓⊾∣⋎↿∖⊽≀⋅↴↕∖↿∖↓⋯⊔↓∢⊾↓⋰⊔⇍⋜↧∐∙∖⇁⊐ ⇂⋅∪⊔⊔∠⇂⊳∖∖⊽∢⊾∐⇀∖∕∣∣⋡∙∖⇁↓⋅⋖⋅⊏↥⊔⊀⊔⋰," Then once $\psi(x)$ is (numerically) found, we fix $\mu$ by requiring that $\Phi(R) = -GM/R$."
↓⊔⋏∙≟↿⇂↥⋜⊔≺↓⋅∪∩∶↙∣⊽∆∪∫↘⋟⊳↾↓∖↓↥⊲↓⊳∖∖∖⋎⋜↧∙∖⇁ we can fine the gravitational potential. ancl thereafter the total mass and energy for any given i ancl co.," This way we can find the gravitational potential, and thereafter the total mass and energy for any given $\beta$ and $\psi_0$."
 The last step is to find the right τὸ and co that would give us AZ and E. Practically. instead. of looking for 3. cu for a specific E and Al choice in sy and. 53. we have picked two dilferent values of 3 and and two corresponding values of cu to satisfy the total mass constraint.," The last step is to find the right $\beta$ and $\psi_0$ that would give us $M$ and $E$ Practically, instead of looking for $\beta$, $\psi_0$ for a specific $E$ and $M$ choice in $s_1$ and $s_3$, we have picked two different values of $\beta$ and and two corresponding values of $\psi_0$ to satisfy the total mass constraint."
 Once oy is fixed it also delines a total energy., Once $\psi_0$ is fixed it also defines a total energy.
" We chose 3,233 in order to obtain ££,«Le.", We chose $\beta_1>\beta_3$ in order to obtain $E_1<E_2$.
 Let us now see how n So4Sy COMparison can be done., Let us now see how the $s_2 \leftrightarrow s_3$ comparison can be done.
 Aceorcing to Sec. 4...," According to Sec. \ref{sec:info},"
 fo(c) is determined by the following set of equations: Aclelitionally. we know that f5(e) is given by and ga(c). 5(r) have been found as described above.," $f_2(\epsilon)$ is determined by the following set of equations: Additionally, we know that $f_3(\epsilon)$ is given by and $g_3(\epsilon)$, $\Phi_3(r)$ have been found as described above."
 Assuming ds 5o= sy. we replace these functions. with foo).geo) ancl Pole) in Eas. (78--580)).," Assuming that $s_2=s_3$ , we replace these functions with $f_2(\epsilon), g_2(\epsilon)$ and $\Phi_2(\epsilon)$ in Eqs. \ref{eq:NK4-con1}- \ref{eq:NK4-f2}) ),"
 and. dillerentiate with respect to e., and differentiate with respect to $\epsilon$.
 Using we get and therefore with C some unknown integration constant., Using we get and therefore with $C$ some unknown integration constant.
 The integral in Ao(c) can be done analytically. viclding Then fromwe find that and therefore Notice how the unknown integration constant C and the climensional constant w are cancelled out.," The integral in $\lambda_0(\epsilon)$ can be done analytically, yielding Then fromwe find that and therefore Notice how the unknown integration constant $C$ and the dimensional constant $\tw$ are cancelled out."
 Next we caleulate fo(e) using and fix 32 such that the οποιον of the svstem is £|Ad., Next we calculate $f_2(\epsilon)$ using and fix $\beta_2$ such that the energy of the system is $E+\Delta E$.
 Once ο is fixed. (c.i) is completely resolved. in terms of δι and 54 [unctions. and we can check if it solves the entropy equations by plugging it into(79).," Once $\beta_2$ is fixed, $K(\epsilon, \eta)$ is completely resolved in terms of $s_1$ and $s_3$ functions, and we can check if it solves the maximum-entropy equations by plugging it into."
. Finally. we should note that as in the LD67 case. the τι). function has à strong peakat oy=go due to the degeneracy.," Finally, we should note that as in the LB67 case, the $\tau_1(\eta)$ function has a strong peakat $\eta=\eta_0$ due to the degeneracy."
" however. this peak is proportional to (nay) as Pfile""=yo lor every 4,00)—6€<qun."," Here, however, this peak is proportional to $\delta(\eta-\eta_0)$ as $f_1(\epsilon)=\eta_0$ for every $\Phi_1(0)<\epsilon<\mu_1$."
" The prefactorin front this delta function is Vig - the volume of phase-space for which P,(0)«οfn. which can he easily. calculated from"," The prefactor in front of this delta function is $V_{deg}$ - the volume of phase-space for which $\Phi_1(0)<\epsilon<\mu_1$, which can be easily calculated from."
 Eherefore. to preform: the integration over τη). in Eqs. (79.. SO))," Therefore, to preform the integration over $\tau_1(\eta)$ in Eqs. \ref{eq:NK4-con2}, \ref{eq:NK4-f2}) )"
 numerically. we first calculate the smooth contribution which comes [rom the miQy) with yp«—qo. and then adel the delta-function contribution by evaluating the integrands at 7=yo ancl multiplying them by Vi.," numerically, we first calculate the smooth contribution which comes from the $\tau_1(\eta)$ with $\eta<\eta_0$, and then add the delta-function contribution by evaluating the integrands at $\eta=\eta_0$ and multiplying them by $V_{deg}$."
 As in the LD67 case. the sy state was constructed as à water- configuration with y given by anc Al=1. R=).=1.," As in the LB67 case, the $s_0$ state was constructed as a water-bag configuration with $\eta$ given by and $M=1$, $R=1$, $G=1$."
" Vhe s, and s5 configurations were then chosen as described in the previous sub-section. by fixing 3 and varving co until the total mass constraint was satisfied."," The $s_1$ and $s_3$ configurations were then chosen as described in the previous sub-section, by fixing $\beta$ and varying $\psi_0$ until the total mass constraint was satisfied."
 The mainnumerical parameters of these configurations are summarised in Table 2., The mainnumerical parameters of these configurations are summarised in Table 2.
 Figure 6. shows the density. profiles of the s; ancl 5; configuration., Figure \ref{fig:rhos-NK} shows the density profiles of the $s_1$ and $s_3$ configuration.
" As expected. the hotter svstem. 85. has a core with a lower density than the 5s, system."," As expected, the hotter system, $s_3$, has a core with a lower density than the $s_1$ system."
" Figure 7. shows the DE. of these systems. ancl compares the AZ(V) functions of these two states. showing that AMa(V)xMj(V) for every V - and therefore the transition 8,755 is allowed."," Figure \ref{fig:fs-NK}
 shows the DF of these systems, and compares the $M(V)$ functions of these two states, showing that $M_3(V) \le M_1(V)$ for every $V$ - and therefore the transition $s_1 \to s_3$ is allowed."
"Finally. to. compare the s» configuration to the δν configuration we have varied 2 in the range 0.1«JJ»<100until we obtained ο=ky,4.306 with 35= 0.6044.","Finally, to compare the $s_2$ configuration to the $s_3$ configuration we have varied $\beta_2$ in the range $0.1<\beta_2<100$until we obtained $E_2=E_3=-4.306$ with $\beta_2=0.6944$ ."
 This was the only solutionin that range. and we believe that it is the only physical solution in general.," This was the only solution in that range, and we believe that it is the only physical solution in general."
 The graph of {ο(1) verses {ο in the range 0.1. is shown in 9.," The graph of $E_2(\beta)$ verses $E_3$ in the range $[0.1,4]$ is shown in ."
. Once do was found. we 4]used the expression of Λίο) in (85).. to caleulate the RLS of and compare," Once $\beta_2$ was found, we used the expression of $K(\epsilon, \mu)$ in , to calculate the RHS of and compare"
1988. transformed using the relation given by COL. [Z/IHH] from Harris 1996).,"1988, transformed using the relation given by C01, [Z/H] from Harris 1996)."
 At metallicities higher than solar the models flatten and the age dependence becomes more important., At metallicities higher than solar the models flatten and the age dependence becomes more important.
 The PaT index varies strongly with age for ages less than a few Gyr., The PaT index varies strongly with age for ages less than a few Gyr.
 Ht reaches a value of z2| aat high ages., It reaches a value of $\approx 1$ at high ages.
 Note. however. the large rms uncertainties of the FFs (0.4 À)).," Note, however, the large rms uncertainties of the FFs $\approx 0.4$ )."
 The blue filled circles show the subsample of the database investigated here where ages and metallicity estimates are available [rom the analvsis of the Fe. Mg and IL? Lick indices (TAIB).," The blue filled circles show the subsample of the database investigated here where ages and metallicity estimates are available from the analysis of the Fe, Mg and $\beta$ Lick indices (TMB)."
 The results discussed in the following do not change if the set of ages and metallicities of Terlevich Forbes (2002) are used instead., The results discussed in the following do not change if the set of ages and metallicities of Terlevich Forbes (2002) are used instead.
 The same applies to (lie effects of errors on the age. metallicity and index. explored. using Monte Carlo simulations.," The same applies to the effects of errors on the age, metallicity and index, explored using Monte Carlo simulations."
 Within the large uncertainties allowed by the FFs. the models reproduce the average value of the measured PaT indices.," Within the large uncertainties allowed by the FFs, the models reproduce the average value of the measured PaT indices."
 In contrast. the models predict values of CaT* and CaT more than 1 larger than the measured ones.," In contrast, the models predict values of $^*$ and CaT more than 1 larger than the measured ones."
 Such a laree discrepancy cannot be explained by calibration errors. which are at least a factor 5 smaller.," Such a large discrepancy cannot be explained by calibration errors, which are at least a factor 5 smaller."
 Uncertainties in the FFs (rms0.5A4)) alone seem also unable to explain it. although at high metallicities (|Z/I]z»0.3) the FFs are based on only a handful of stars.," Uncertainties in the FFs $\approx 0.5$ ) alone seem also unable to explain it, although at high metallicities $>0.3$ ) the FFs are based on only a handful of stars."
 The σα of a high Z SSP is dominated by the contribution of the RGB and the red clump (RC)., The $^*$ of a high Z SSP is dominated by the contribution of the RGB and the red clump (RC).
 IE we set artificially the value of the CaT* FF at [Z/H]—0.35 from the giant branch phase on to 8 ((the lowest value measured lor stars in this phase. most of the stars have CaT*=9—10 A). we obtain CaT*=7.5 [for the SSP. still 0.5 larger than what observed in ellipticals.," If we set artificially the value of the $^*$ FF at $=0.35$ from the giant branch phase on to 8 (the lowest value measured for stars in this phase, most of the stars have $^*=9-10$ ), we obtain $^*=7.5$ for the SSP, still 0.5 larger than what observed in ellipticals."
 The flix contribution of the RC can vary within z30%.. due to the uncertainties on the lifetime of this phase (Zoccali et al.," The flux contribution of the RC can vary within $\approx 30$, due to the uncertainties on the lifetime of this phase (Zoccali et al."
 2000a)., 2000a).
 If we reduce the {hi of the RC bv this amount. we again obtain CaT*=7.5n [for the SSP.," If we reduce the flux of the RC by this amount, we again obtain $^*=7.5$ for the SSP."
 Only a reduction would produce CaT*x7A., Only a reduction would produce $^*\approx7$.
 The SSP Salpeter models translate the averaged observed value of the CaT* into 0.1. or Z=0.840.1 Z..," The SSP Salpeter models translate the averaged observed value of the $^*$ into $=-0.5\pm 0.1$ , or $0.3\pm 0.1$ $_\odot$."
 Taking this result at [ace value. if the T traces the calcium abundance. (his could indicate (hat (his element is underabundant. a suggestion already put [orward by Peletier οἱ al. (," Taking this result at face value, if the $^*$ traces the calcium abundance, this could indicate that this element is underabundant, a suggestion already put forward by Peletier et al. ("
1999) considering 3 ellipticals.,1999) considering 3 ellipticals.
 A similar effect has been suggested bv MeWilliam ancl Rich (1994) and Rich and AleWilliam (2000). who analvse a sample of metal rich bulee stars. suggesting that while Mg and Ti are overabundant with respect to Fe. Ca and Si have nearly solar ratios.," A similar effect has been suggested by McWilliam and Rich (1994) and Rich and McWilliam (2000), who analyse a sample of metal rich bulge stars, suggesting that while Mg and Ti are overabundant with respect to Fe, Ca and Si have nearly solar ratios."
 In addition. modeling the Cat227 Lick index TMD find |Ca/Mg]|g—0.3 in ellipticals (see also Vazdekis et al.," In addition, modeling the Ca4227 Lick index TMB find $\approx -0.3$ in ellipticals (see also Vazdekis et al."
 1997)., 1997).
 However. the issue ol Ca uaiderabundance in high-metallicitv. stars is still controversial (MeWilliam 1997): C02 point out that the CaT index does not correlate with the [Ca/Fe] stellar overabundance: and current modeling of the vields of Type II supernovae (Woosley Weaver 1995) does," However, the issue of Ca underabundance in high-metallicity stars is still controversial (McWilliam 1997); C02 point out that the CaT index does not correlate with the [Ca/Fe] stellar overabundance; and current modeling of the yields of Type II supernovae (Woosley Weaver 1995) does"
In order to investigate the soft. N-ray spectrum (below 2 keV). data restricted. within a small aperture around. the nuclear source are taken from the SIS detectors so that the contamination is minimized.,"In order to investigate the soft X-ray spectrum (below 2 keV), data restricted within a small aperture around the nuclear source are taken from the SIS detectors so that the contamination is minimized."
 A circular region with a 5 arcmin diameter. which corresponds to the half-power diameter of the ASCA ARP PSE. is used instead. of the original photon collection region.," A circular region with a 3 arcmin diameter, which corresponds to the half-power diameter of the ASCA XRT PSF, is used instead of the original photon collection region."
 A contribution from the nearby sources in the band below 1 keV is expected to be about 10 per cent. but should be negligible in the 12 keV banc.," A contribution from the nearby sources in the band below 1 keV is expected to be about 10 per cent, but should be negligible in the 1–2 keV band."
 The count rate ratio in the 12 keV to 2.4.8 keV bancs obtained from the small aperture SIS data is plotted in Fig., The count rate ratio in the 1–2 keV to 2.4–8 keV bands obtained from the small aperture SIS data is plotted in Fig.
 2., 2.
 Phe excess variation in the soft band relative to the hard band is confirmed by the spectral ratio between the active and quiescent states (Fig., The excess variation in the soft band relative to the hard band is confirmed by the spectral ratio between the active and quiescent states (Fig.
 4)., 4).
 The data are consistent with a lux change by a factor of 2 with no spectral variation between the two states above 3 keV. while a large excess variation is evident in the 12 keV band., The data are consistent with a flux change by a factor of 2 with no spectral variation between the two states above 3 keV while a large excess variation is evident in the 1–2 keV band.
 The X-ray source shows a rapid. large amplitude Dux variations even witin the active state.," The X-ray source shows a rapid, large amplitude flux variations even within the active state."
 We next investigated spectral variability associated with the rapid [ux variations. using a normalizec count rate clüagram (Pie.," We next investigated spectral variability associated with the rapid flux variations, using a normalized count rate diagram (Fig."
 5). similar to that used in Papaakis Lawrence (1995) for NCGC4051.," 5), similar to that used in Papadakis Lawrence (1995) for NGC4051."
 The whole 210. keV light curves of the SO and SI detectors were divided into six ancl four count-rate slices. respectively.," The whole 2–10 keV light curves of the S0 and S1 detectors were divided into six and four count-rate slices, respectively."
 Count rates [from cach slice in the 12 keV and 2.48 keV bands were then normalized by the mean count rates in the respective energy. band., Count rates from each slice in the 1–2 keV and 2.4–8 keV bands were then normalized by the mean count rates in the respective energy band.
 Ες plot could. in principle. track spectral variability on a time scale down to the time resolution of the light curve. 128 s. As Fig.," This plot could, in principle, track spectral variability on a time scale down to the time resolution of the light curve, 128 s. As Fig."
 5 shows. a significant excess variation in the 12 keV band occurs at the highest Dux bin.," 5 shows, a significant excess variation in the 1–2 keV band occurs at the highest flux bin."
 Since this bin contains all the three [are-peaks in the active state. the spectral softening appears to be associated with the Πας and may track it with a time lag of less than LO? s. As the image analysis shows. the N-ray. spectrum. of the," Since this bin contains all the three flare-peaks in the active state, the spectral softening appears to be associated with the flaring and may track it with a time lag of less than $10^3$ s. As the image analysis shows, the X-ray spectrum of the"
et al. 1998..,"et al. \cite{halpern},"
 Groot et al. 1998..," Groot et al. \cite{ot_3},"
 Palazzi et al. 1998..," Palazzi et al. \cite{ot_4},"
 Galama et al. 1998.. ," Galama et al. \cite{ot_5}, ,"
Jaunsen et al. 1998..," Jaunsen et al. \cite{ot_6},"
 Hjorth et al. 1998..," Hjorth et al. \cite{ot_7},"
 Bloom et al. 1998..," Bloom et al. \cite{ot_8},"
 Kulkarni et al. 1999.. ," Kulkarni et al. \cite{ot_9}, ,"
"Galama et al. 1999,,"," Galama et al. \cite{ot_10},"
 Palazzi et al. 1999..," Palazzi et al. \cite{ot_11},"
 Bakos et al. 1999))., Bakos et al. \cite{ot_12}) ).
 After the fading of the OT in most cases a faint galaxy was detected., After the fading of the OT in most cases a faint galaxy was detected.
 The detection of the putative host galaxy of GRB971214 is particularly intriguing as the estimate of the redshift is z23.42. locating this event at an extreme cosmological distance (Kulkarni et al. 1998)).," The detection of the putative host galaxy of GRB971214 is particularly intriguing as the estimate of the redshift is z=3.42, locating this event at an extreme cosmological distance (Kulkarni et al. \cite{kulkarni_n}) )."
 We observed with BeppoSAX a GRB on December 4.97272 UT 1997 (Heise et al. 1997))., We observed with BeppoSAX a GRB on December 14.97272 UT 1997 (Heise et al. \cite{heise_grb}) ).
" A follow-up pointing performed 6.67 hours after the main event detected the faint ""£od fading X-ray source (Antonelli et al. 1997)).", A follow-up pointing performed 6.67 hours after the main event detected the faint and fading X-ray source (Antonelli et al. \cite{antonelli}) ).
 After the fading of the optical transient. spectroscopic observations of the associated host galaxy tentatively put it at cosmological distance. às the estimate of its redshift is z=3.42 (Kulkarni et al. 1998)).," After the fading of the optical transient, spectroscopic observations of the associated host galaxy tentatively put it at cosmological distance, as the estimate of its redshift is z=3.42 (Kulkarni et al. \cite{kulkarni_n}) ),"
" that corresponds to a luminosity distance 730 Gpe (for Hy=65 km + ! and Q,20.2).", that corresponds to a luminosity distance $>$ 30 Gpc (for $_0$ =65 km $^{-1}$ $^{-1}$ and $\Omega_0$ =0.2).
 The complete evolutionary history of the emitted spectrum from X to 5 rays up to 2.5 days after the main event suggests that the afterglow in X-rays begins immediately., The complete evolutionary history of the emitted spectrum from X to $\gamma$ rays up to 2.5 days after the main event suggests that the afterglow in X-rays begins immediately.
 The energy output in the afterglow results to be comparable to that in the prompt event., The energy output in the afterglow results to be comparable to that in the prompt event.
 With the new wealth of data on optical counterparts and X-ray afterglows. a major revamping of theoretical models is occurring.," With the new wealth of data on optical counterparts and X–ray afterglows, a major revamping of theoretical models is occurring."
 With the extragalactic origin firmly established on the basis of observations of host galaxies (Metzger et al. 1997..," With the extragalactic origin firmly established on the basis of observations of host galaxies (Metzger et al. \cite{metzger},"
 Kulkarni et al. 1998. 1999)).," Kulkarni et al. \cite{kulkarni_n, ot_9}) ),"
 the cosmological fireball model (e.g. Cavallo Rees 1978.. Mésszárros Rees 1997a)) gives predictions that reasonably fit to observational data.," the cosmological fireball model (e.g. Cavallo Rees \cite{cavallo}, Mésszárros Rees \cite{meszrees1}) ) gives predictions that reasonably fit to observational data."
 In this paper we discuss the details of the prompt and delayed emission from GRB971214. with emphasis on the X and ~ ray spectrum and on its evolution with time.," In this paper we discuss the details of the prompt and delayed emission from GRB971214, with emphasis on the X and $\gamma$ ray spectrum and on its evolution with time."
" Implications on the models of the prompt event and of the afterglow are discussed,", Implications on the models of the prompt event and of the afterglow are discussed.
 was detected in Lateral Shield | of GRBM and in WFC | on December 14.97272 UT., was detected in Lateral Shield 1 of GRBM and in WFC 1 on December 14.97272 UT.
 The burst lasted approximately 30 s. with two leading broad peaks (3s and 10 s FWHM) and a third fainter and sharper peak (1s FWHM) 34s after trigger.," The burst lasted approximately 30 s, with two leading broad peaks (3s and 10 s FWHM) and a third fainter and sharper peak (1s FWHM) 34s after trigger."
 The GRB profile is shown in Fig., The GRB profile is shown in Fig.
 1. as measured by GRBM LSI and WFCI.," 1, as measured by GRBM LS1 and WFC1."
 The analysis of the WFC data was performed using WEC data reduction software version 103106., The analysis of the WFC data was performed using WFC data reduction software version 103106.
 Data reduction. background subtraction and spectral analysis of GRBM data were performed using dedicated SW tools (Amati et al. 1999))," Data reduction, background subtraction and spectral analysis of GRBM data were performed using dedicated SW tools (Amati et al. \cite{amati}) )"
 The latest release of the WFC and GRBM response matrices were used., The latest release of the WFC and GRBM response matrices were used.
 All the spectral fits reported in this article were performed using XSPEC. version 10.0 (Arnaud 1996)).," All the spectral fits reported in this article were performed using XSPEC, version 10.0 (Arnaud \cite{xspec}) )."
 We fitted the joint spectrum with the spectral shape of Band et al. (1993)), We fitted the joint spectrum with the spectral shape of Band et al. \cite{band}) )
" (42,,21.99 for 22 degrees of freedom) and with a power law with exponential cutoff V1, 71.98 for 22 degrees of freedom).", $\chi^2_{\rm dof}$ =1.99 for 22 degrees of freedom) and with a power law with exponential cutoff $\chi^2_{\rm dof}$ =1.98 for 22 degrees of freedom).
 Both give systematic residuals in the WFC energy band., Both give systematic residuals in the WFC energy band.
" The best fit is obtained using a broken power law (\5,4=1.6 for 21 degrees of freedom).", The best fit is obtained using a broken power law $\chi^2_{\rm dof}$ =1.6 for 21 degrees of freedom).
 An F-test shows that the improvement is not significant., An F–test shows that the improvement is not significant.
 The average joint Wide Field Camera/Gamma Ray Burst Monitor spectrum during the burst can be well described by a broken power law with photon indices D420.13 and [2=1.3 and a break energy at ~10 keV. Given the gap between WFC and GRBM spectra. approximately between 10 and 50 keV. a large uncertainty in the position of the break is present and must be added to the statistical uncertainty quoted in Table 1.," The average joint Wide Field Camera/Gamma Ray Burst Monitor spectrum during the burst can be well described by a broken power law with photon indices $\Gamma_1$ =0.13 and $\Gamma_2$ =1.3 and a break energy at $\sim$ 10 keV. Given the gap between WFC and GRBM spectra, approximately between 10 and 50 keV, a large uncertainty in the position of the break is present and must be added to the statistical uncertainty quoted in Table 1."
 The fits with all the above functions are statistically unacceptable. but we estimate that a substantial contribution to the high value of Vos Is due to systematic uncertainties in the spectral deconvolution.," The fits with all the above functions are statistically unacceptable, but we estimate that a substantial contribution to the high value of $\chi^2_{\rm dof}$ is due to systematic uncertainties in the spectral deconvolution."
 Therefore we do not consider to add further components to improve the fit., Therefore we do not consider to add further components to improve the fit.
 The results from all the spectral fits we performed are reported in Table |., The results from all the spectral fits we performed are reported in Table 1.
 In Fig., In Fig.
 2 we report the count rate spectrum from WFC] plus GRBM LSI., 2 we report the count rate spectrum from WFC1 plus GRBM LS1.
 In the same figure we report the joint confidence contours for the two spectral indices of the broken power law., In the same figure we report the joint confidence contours for the two spectral indices of the broken power law.
 The joint confidence contour between Τὸ and the break energy (not reported in Fig., The joint confidence contour between $\Gamma_2$ and the break energy (not reported in Fig.
 2) suggests that the GRB spectrum shows a bending above z 10 keV but the hard X-ray/~ ray spectrum above 50 keV is consistent with a single power law., 2) suggests that the GRB spectrum shows a bending above $\approx$ 10 keV but the hard $\gamma$ ray spectrum above 50 keV is consistent with a single power law.
" A fit with a power law plus exponential cutoff gives an e-folding energy of ~300 keV. This is in the ""hard"" tail of the distribution from statistical studies of BATSE GRB spectra (Band et al. 1993))."," A fit with a power law plus exponential cutoff gives an e-folding energy of $\sim$ 300 keV. This is in the ""hard"" tail of the distribution from statistical studies of BATSE GRB spectra (Band et al. \cite{band}) ),"
 in which a broad intervalof break energies from 50keV to more than | MeV was found. with the majority of GRBs," in which a broad intervalof break energies from 50keV to more than 1 MeV was found, with the majority of GRBs"
"above, we adopt pure density evolution for z=2.","above, we adopt pure density evolution for $z\gtrsim2$."
" We do not show the errors in our predictions, as these are actually dominated by the uncertainty in the fitted i(Lpeax) distribution, not the in The results in unce"," We do not show the errors in our predictions, as these are actually dominated by the uncertainty in the fitted $\nLp$ distribution, not the uncertainty in $\slope(\Lp)$."
"rtaintyFigure 4 /(Lpeak).show that our modeling of the quasar lifetime predicts very accurately the ""luminosity-dependent density evolution"" seen in X-ray samples, at all luminosities and redshifts."," The results in Figure \ref{fig:ldde} show that our modeling of the quasar lifetime predicts very accurately the ``luminosity-dependent density evolution” seen in X-ray samples, at all luminosities and redshifts."
" We underpredict the low-luminosity, high-redshift numbermay of slightlysources, but this is unsurprising, as it is both where the observations are most uncertain and where, for a fixed low L, the break luminosity becomes very much larger than L, meaning that our modeling is based on the quasar lifetime at L well below Lye; where it is most uncertain."," We may slightly underpredict the low-luminosity, high-redshift number of sources, but this is unsurprising, as it is both where the observations are most uncertain and where, for a fixed low $L$, the break luminosity becomes very much larger than $L$, meaning that our modeling is based on the quasar lifetime at $L$ well below $\Lp$ where it is most uncertain."
" Still, the agreement is remarkable, and it is derived almost entirely from the quasar lifetime as a function of peak luminosity."," Still, the agreement is remarkable, and it is derived almost entirely from the quasar lifetime as a function of peak luminosity."
" The distribution which produces the LDDE seen in Figure 4 n(Lpeak)has a simple functional form: a lognormal, with constant narrow width and normalization, and a related to the observed break L,,(z) in the observed center/peakQLF."," The $\nLp$ distribution which produces the LDDE seen in Figure \ref{fig:ldde} has a simple functional form: a lognormal, with constant narrow width and normalization, and a center/peak directly related to the observed break $\lstar(z)$ in the observed QLF."
" In directlykeeping with the interpretation of the QLF from Hopkinsetal.(2005c),, in which the faint-end is made up of brighter sources (dominated, of course, by the peak in the distribution at Lpea~ L.(z)) in dimmer stages of their n(Lpeak)evolution, we have demonstrated that thedistribution."," In keeping with the interpretation of the QLF from \citet{H05c}, in which the faint-end is made up of brighter sources (dominated, of course, by the peak in the $\nLp$ distribution at $\Lp\sim\lstar(z)$ ) in dimmer stages of their evolution, we have demonstrated that the."
 A more detailed prediction of the faint-end slope should account for several points., A more detailed prediction of the faint-end slope should account for several points.
" Sample selection effects from reddening and extinction can be significant, if the fraction of obscured objects is a function ofespecially luminosity (e.g.,Uedaetal.2003;Hopkins2005e)."," Sample selection effects from reddening and extinction can be significant, especially if the fraction of obscured objects is a function of luminosity \citep[e.g.,][]{Ueda03,H05e}."
" Our predictions agree best with observations from the hard X-ray, where the effect of attenuation is minimized, but a more accurate prediction of  in other wavebands must account for the joint evolution of obscuration and luminosity (Hopkinsetal.2005d,e)."," Our predictions agree best with observations from the hard X-ray, where the effect of attenuation is minimized, but a more accurate prediction of $\slope$ in other wavebands must account for the joint evolution of obscuration and luminosity \citep{H05d,H05e}."
" To probe very low accretion rates L«&10? higher-resolution simulations, with more sophisticated Ly,models for low-efficiency accretion (rates well below Bondi or Eddington) and spectral modeling of the corresponding radiatively inefficient accretion flows are needed."," To probe very low accretion rates $L\ll10^{-2}\Lp$, higher-resolution simulations, with more sophisticated models for low-efficiency accretion (rates well below Bondi or Eddington) and spectral modeling of the corresponding radiatively inefficient accretion flows are needed."
" Further, the contributions to the faint-end QLF from quasars With +L, (see Hopkins et 220059) will introduce overall Lyecurvature into the QLF (weakening the observed break, as observed WWolf et 22003; Richards et 22005), which bymay e.g.aid in constraining the n(Lpeak) distribution."," Further, the contributions to the faint-end QLF from quasars with $\Lp\neq\lstar$ (see Hopkins et 2005e) will introduce overall curvature into the QLF (weakening the observed break, as observed by Wolf et 2003; Richards et 2005), which may aid in constraining the $\nLp$ distribution."
" Finally, at low enough L (typical of LINERs and low-L Seyferts), we expect different, possibly stochastic, fueling mechanisms to contribute, which must be modeled to accurately predict the QLF shape below some limit."," Finally, at low enough $L$ (typical of LINERs and $L$ Seyferts), we expect different, possibly stochastic, fueling mechanisms to contribute, which must be modeled to accurately predict the QLF shape below some limit."
" Still, our simple modeling of quasar feedback, and the novel"," Still, our simple modeling of quasar feedback, and the novel"
Besicles the change in the IME for very massive clusters. the most important. parameters in our model are the SEIts of the models (which give the upper mass limit of the forming clusters.Adocuinas). the slope (3) of the IEECME. and the lower mass limit of the ECME. ων.,"Besides the change in the IMF for very massive clusters, the most important parameters in our model are the SFRs of the models (which give the upper mass limit of the forming clusters,$M_\mathrm{ecl,max}$ ), the slope $\beta$ ) of the ECMF, and the lower mass limit of the ECMF, $M_\mathrm{ecl,min}$."
 bor this study of starbursts four SEIS (10. 100. 1000 and. 10000 Al. |) are chosen.," For this study of starbursts four SFRs (10, 100, 1000 and 10000 $M_\odot$ $^{-1}$ ) are chosen."
 Below 10 AL. νι little impact on the IGIME from the top-heavy LMES in. very-massive ‘Lusters is to be expected as only very [ew or none of rem are formed. according to eq. 2.., Below 10 $M_\odot$ $^{-1}$ little impact on the IGIMF from the top-heavy IMFs in very-massive clusters is to be expected as only very few or none of them are formed according to eq. \ref{eq:eclmax}.
 As already discussed in the introduction. SERs of more than 1000. AL. ve+ have recently been found(7).," As already discussed in the introduction, SFRs of more than 1000 $M_\odot$ $^{-1}$ have recently been found."
.. The upper limit for the SERs in the moclels is therefore chosen to be 10000 AL. +., The upper limit for the SFRs in the models is therefore chosen to be 10000 $M_\odot$ $^{-1}$.
 The value of the slope of the ECME is usually given with ao? around 2 with errors between 0.2 and 0.5(?).. hough some studies lind svstematically [latter slopes like 1.8(2).," The value of the slope of the ECMF is usually given with a $\beta$ around 2 with errors between 0.2 and 0.5, though some studies find systematically flatter slopes like 1.8."
. And the mass spectrum of giant. molecular clouds. he precursors of star clusters. shows a slope of 1.7(?).," And the mass spectrum of giant molecular clouds, the precursors of star clusters, shows a slope of 1.7."
. As the identification of embedded clusters in extra-galactic objects is very challenging. we allow a greater range for this yarameter and study ο = 0.5 to 2.35.," As the identification of embedded clusters in extra-galactic objects is very challenging, we allow a greater range for this parameter and study $\beta$ = 0.5 to 2.35."
" The lower mass limit of the ECAIP. Aaa IS even worse constrained than the slope of the κΑΟ,"," The lower mass limit of the ECMF, $M_\mathrm{ecl,min}$, is even worse constrained than the slope of the ECMF."
 We therefore studs a broad. range of yossible Αμα from 5 to 107 AL...," We therefore study a broad range of possible $M_\mathrm{ecl,min}$ from 5 to $^5$ $M_\odot$."
 The lower mass limit of the canonical HIME in each cluster is fixed to 0.01. AZ. and the upper mass linit is determined by the cluster mass, The lower mass limit of the canonical IMF in each cluster is fixed to 0.01 $M_\odot$ and the upper mass limit is determined by the cluster mass.
(?).., Tab.
 ‘Tab. 1 shows the IGLME slopes for stars more massive than 1.8 AJ. lor dillerent. star-formation rates. different values of the ECME slope. 3. and for several lower limits of the ECME. Aou ," \ref{tab:first} shows the IGIMF slopes for stars more massive than 1.3 $M_\odot$ for different star-formation rates, different values of the ECMF slope, $\beta$, and for several lower limits of the ECMF, $M_\mathrm{ecl, min}$."
For clusters above 10° AL. the IME slope For stars above 1 AL. ay. is changed according to eq.," For clusters above $\times 10^5$ $M_\odot$ the IMF slope for stars above 1 $M_\odot$, $\alpha_3$, is changed according to eq."
 while below 10° AZ. as is kept constant at the canonical (Salpeter) index 2.35., \ref{eq:a3M} while below $\times 10^5$ $M_\odot$ $\alpha_3$ is kept constant at the canonical (Salpeter) index 2.35.
 For ay a lower limit of 1 is used because clusters with an as of 1 or less contain more than of the mass in stars more massive than S AL..., For $\alpha_3$ a lower limit of 1 is used because clusters with an $\alpha_3$ of 1 or less contain more than of the mass in stars more massive than 8 $M_\odot$.
 When these stars explode as supernovac the resulting extreme miatss-loss would completely. disperse the star clusters., When these stars explode as supernovae the resulting extreme mass-loss would completely disperse the star clusters.
 1n such a case no globular clusters would survive until today., In such a case no globular clusters would survive until today.
" Lor clusters more massive than z 10"" AZ. this limit is reached and αν is fixed to 1.0 for these objects.", For clusters more massive than $\approx$ $\times 10^6$ $M_\odot$ this limit is reached and $\alpha_3$ is fixed to 1.0 for these objects.
 In Fig., In Fig.
 2 three IGIME examples from Tab., \ref{fig:D1F1} three IGIMF examples from Tab.
 1. are shown ogether with the input canonical IME.," \ref{tab:first}
 are shown together with the input canonical IMF."
 Depending on the »wameters a strong top-heaviness can be seen., Depending on the parameters a strong top-heaviness can be seen.
 In Fie., In Fig.
 3. the results of Tab., \ref{fig:avsm} the results of Tab.
 1. are summarised for 3 = 2.35. 2.0 anc 1.6.," \ref{tab:first} are summarised for $\beta$ = 2.35, 2.0 and 1.6."
 Generally. the ΙΔΗΣ slope decreases with increasing SER. [or a given 2.," Generally, the IGIMF slope decreases with increasing SFR for a given $\beta$."
 Fhis is due to the relation )etween the maximal eluster mass and. the SEIL (eq. 2))., This is due to the relation between the maximal cluster mass and the SFR (eq. \ref{eq:eclmax}) ).
 The higher the SER the more-massive is the upper limit of he ICME., The higher the SFR the more-massive is the upper limit of the ECMF.
 As massive clusters develop a top-heavy ME according to eq. 3...," As massive clusters develop a top-heavy IMF according to eq. \ref{eq:a3M},"
 a larger fraction of massive stars are ormed with increasing SEIts., a larger fraction of massive stars are formed with increasing SFRs.
 Fig., Fig.
 3. shows the dependence of oder on the lower limit of the ECME (Woo).," \ref{fig:avsm} shows the dependence of $\alpha_\mathrm{IGIMF}$ on the lower limit of the ECMF $M_\mathrm{ecl,min}$ )."
 For very Hat EC'MES fines) this dependeney is nearly negligible., For very flat ECMFs ) this dependency is nearly negligible.
" ""his is because for slops of 3 less than 2.0 the ICME is dominated. by massive clusters and reducing the number of low-mass cluster by increasing Αμ does not allect the IGIME significantly."," This is because for slops of $\beta$ less than 2.0 the ECMF is dominated by massive clusters and reducing the number of low-mass cluster by increasing $M_\mathrm{ecl,min}$ does not affect the IGIMF significantly."
 For 3 = 2.35 the opposite is the case., For $\beta$ = 2.35 the opposite is the case.
 For steep slopes. low-mass clusters dominate the ECAIF and therefore have a strong inlluence on the IGLIME.," For steep slopes, low-mass clusters dominate the ECMF and therefore have a strong influence on the IGIMF."
 llere. increasing Moo changes the ΠΟΛΗΣ strongly by eliminating the low-mass clusters.," Here, increasing $M_\mathrm{ecl,min}$ changes the IGIMF strongly by eliminating the low-mass clusters."
 With this contribution the SER dependent. LOLALE theory is extended into the starburst regime., With this contribution the SFR dependent IGIMF theory is extended into the starburst regime.
 The SER. dependent IGLIME. which produces results agreeing with observations [or massive ancl dwarf galaxies.(7272)... leads to top-heavy galaxv-wide [AIFS in massively starbursting galaxies when combined with the cluster-mass dependent high-mass IME slope for. globular clusters anc UCDs (eq... 3))," The SFR dependent IGIMF, which produces results agreeing with observations for massive and dwarf galaxies, leads to top-heavy galaxy-wide IMFs in massively starbursting galaxies when combined with the cluster-mass dependent high-mass IMF slope for globular clusters and UCDs (eq. \ref{eq:a3M}) )"
. by Alarks. WKroupa Dabringhausen (in preparation) and a SER. dependent. lower limit of the EC'ME or Hat. slopes of the ECAIF.," by Marks, Kroupa Dabringhausen (in preparation) and a SFR dependent lower limit of the ECMF or flat slopes of the ECMF."
 This is interesting because some observational results indeed. suggest the IGIME to be top-heavy when SER Z 100 AZ.yr +., This is interesting because some observational results indeed suggest the IGIMF to be top-heavy when SFR $\simgreat$ 100 $M_\odot~yr^{-1}$ .
 Current observational results. from cosmological studies are very cillicult to compare with the models because the observations do not measure IME slopes anc SEIs for individual galaxies but study indirect evidence (luminosities. chemical enrichment. ete.)," Current observational results from cosmological studies are very difficult to compare with the models because the observations do not measure IMF slopes and SFRs for individual galaxies but study indirect evidence (luminosities, chemical enrichment, etc.)"
 for whole populations anc average the results over the galaxy luminosity function., for whole populations and average the results over the galaxy luminosity function.
 The most-massive star cluster for which the IAIF has been determined. by. star, The most-massive star cluster for which the IMF has been determined by star
have ages of approximately 5-7 Car.,have ages of approximately 5-7 Gyr.
 Based on Lick iudices and simple stellar population meocleJf. the derived [a/Fe] ratios are sub-solar to solar. indicatiug a more gradual chemical enrichimen history lor dEs as compared to giant elliptical galaxies in the Virgo Cluster. (," Based on Lick indices and simple stellar population models, the derived $\alpha$ /Fe] ratios are sub-solar to solar, indicating a more gradual chemical enrichment history for dEs as compared to giant elliptical galaxies in the Virgo Cluster. ("
1) We arguee that it is likely that several different. plysical mechanisms played a siguificane role iu the production of the Virgo cluster dE galaxies tuclucing formation. iufall of dEs that were ouce part of Local Group aualogs. aud the conversion of iufalliug cls.,"4) We argue that it is likely that several different physical mechanisms played a significant role in the production of the Virgo cluster dE galaxies including formation, infall of dEs that were once part of Local Group analogs, and the conversion of infalling dIs."
 The present observations support the hypothesis that a large fraction of the Virgo cluster dEs are formed by rai pressure strippiug of gas from iufalliug dI., The present observations support the hypothesis that a large fraction of the Virgo cluster dEs are formed by ram pressure stripping of gas from infalling dIs.
 This research has mace use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Lustitute of Technology. under contract with the National Aeronautics aud Space Acininistration.," 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 the VATT time allocation committee for awarding TBS time to complete this project., We thank the VATT time allocation committee for awarding TBS time to complete this project.
 LvZ acknowledges partial support by luciana University., LvZ acknowledges partial support by Indiana University.
 Support for EJB was provided by NASA through Hubble Fellowship grant #HHST-HF-01135.01 awarded by the Space Telescope Scieuce Institute. which is operated by the Association of Universities for Research in Astronomy. Inc.. for NASA. uncer contract. NAS ," Support for EJB was provided by NASA through Hubble Fellowship grant HST-HF-01135.01 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555."
EDS is grateful for partial support [rom a NASA LTSARP erant No., EDS is grateful for partial support from a NASA LTSARP grant No.
 NAC5-9221 aud the University of Minnesota., NAG5-9221 and the University of Minnesota.
"the intercloud shock sweeps around the cloud, a shear layer forms all around the cloud.","the intercloud shock sweeps around the cloud, a shear layer forms all around the cloud."
" However, a higher level of shear is found in the plane perpendicular to the magnetic field and the flow direction."," However, a higher level of shear is found in the plane perpendicular to the magnetic field and the flow direction."
" As for the parallel shock model, there is a rapid condensation behind the slow-mode shock and a dense boundary layer forms."," As for the parallel shock model, there is a rapid condensation behind the slow-mode shock and a dense boundary layer forms."
" This dense boundary layer, however, does not fragment due to instabilities as the small transverse component of the magnetic field has a stabilising effect."," This dense boundary layer, however, does not fragment due to instabilities as the small transverse component of the magnetic field has a stabilising effect."
" Although the geometrical features of the cloud resemble those of the parallel shock model, the cloud properties resemble those of the perpendicular model (see Sect. ??))."," Although the geometrical features of the cloud resemble those of the parallel shock model, the cloud properties resemble those of the perpendicular model (see Sect.\ref{sect:properties}) )."
" The shock-cloud interaction can thus be separated into two evolutionary tracks, i.e. one that is quasi-parallel and one that is quasi-perpendicular."," The shock-cloud interaction can thus be separated into two evolutionary tracks, i.e. one that is quasi-parallel and one that is quasi-perpendicular."
" From Fig. 6,,"," From Fig. \ref{fig:beta_dep},"
 we see that the transition is associated with the value of 8 downstream of the intercloud shock., we see that the transition is associated with the value of $\beta$ downstream of the intercloud shock.
 For parallel shocks the postshock flow has a 8>1., For parallel shocks the postshock flow has a $\beta > 1$.
" Hence, the magnetic field is dynamically unimportant in the external gas which allows a vorticity layer to form around the cloud."," Hence, the magnetic field is dynamically unimportant in the external gas which allows a vorticity layer to form around the cloud."
" For angles > 20°, the"," For angles $> 20^o$ , the"
gi is the perpendicular component of gravitational force.,$g_\perp$ is the perpendicular component of gravitational force.
" The gravitational force includes not only the traditional Newtonian [force but also an additional ""MOND' [force (mecdiated by a scalar field) which becomes dominant at low accelerations.", The gravitational force includes not only the traditional Newtonian force but also an additional `MOND' force (mediated by a scalar field) which becomes dominant at low accelerations.
 This MOND force may be viewed as arising from a phantom dark halo., This MOND force may be viewed as arising from a phantom dark halo.
 Phe phantom halo begins to make a significant contribution to the gravitational force and hence to the dellection. of photons near the. MOND transition raclius where Al is the true (barvonic) mass of the object., The phantom halo begins to make a significant contribution to the gravitational force and hence to the deflection of photons near the MOND transition radius where $M$ is the true (baryonic) mass of the object.
 In fact. the phantom halo may exhibit an apparent. shell of matter between 1/2 αρ to r; depending upon the form of the function whieh interpolates between the LOND regime and the Newtonian regime (Alilerom&Sanders 2008).," In fact, the phantom halo may exhibit an apparent shell of matter between 1/2 $r_t$ up to $r_t$ depending upon the form of the function which interpolates between the MOND regime and the Newtonian regime \cite{ms08}."
". Phe relevance for the present discussion is that we would expect to find some evidence of ""dark matter” in strong gravitational lensing if the Einstein ring racius is a significant fraction of the MOND transition radius: the larger that. fraction. the larger the apparent contribution of dark matter to the projected. mass detected. by. strong eravitational lensing."," The relevance for the present discussion is that we would expect to find some evidence of “dark matter” in strong gravitational lensing if the Einstein ring radius is a significant fraction of the MOND transition radius; the larger that fraction, the larger the apparent contribution of dark matter to the projected mass detected by strong gravitational lensing."
 The Einstein ring radius. for a point mass. is given by where D. Dy. and Di; are respectively the angular size distances from the observer to the lens. to the source and from the lens to the source.," The Einstein ring radius, for a point mass, is given by where $D_l$, $D_s$, and $D_{ls}$ are respectively the angular size distances from the observer to the lens, to the source and from the lens to the source."
 Combining 77 and S and making use of the fact that ei=felly where fz1/6 we find that where E is a function of the lens and source redshift and depends upon the cosmological mocoel., Combining 7 and 8 and making use of the fact that $a_0=fcH_0$ where $f\approx 1/6$ we find that where F is a function of the lens and source redshift and depends upon the cosmological model.
" ‘This function f(s).24) is shown in 44 as a function of z for three cdillerent values of the source. recishift (2,=0.5.3.5. 100)."," This function $F(z_l,z_s)$ is shown in 4 as a function of $z_l$ for three different values of the source redshift $z_s = 0.5,\,3.5,\,100$ )."
 Vhis is all done for the standard -concordanee cosmology which the relativistic MOND cosmology should mimic to a close approximation., This is all done for the standard “concordance” cosmology which the relativistic MOND cosmology should mimic to a close approximation.
 For the enses in the sample of Bolton et al.," For the lenses in the sample of Bolton et al.,"
 ον&0.5 and z;z0.2 on average: therefore. 7 does not exceed about 0.25. and we mieht expect the contribution of an apparent halo to lensing o be relatively small.," $z_s\approx 0.5$ and $z_l \approx 0.2$ on average; therefore, $F$ does not exceed about 0.25, and we might expect the contribution of an apparent halo to lensing to be relatively small."
 On the other hand for strong lenses considered by Trea Koopmans (2004). z;z land ο.z3.5 implving f£zOA.," On the other hand for strong lenses considered by Treu Koopmans (2004), $z_l\approx 1$ and $z_s\approx 3.5$ implying $F\approx 0.4$."
" The expectation is that there should x: evidence for more ""dark matter"" in these high. redshift systems. as. in fact. is reported by Trea Ixoopmans."," The expectation is that there should be evidence for more “dark matter” in these high redshift systems, as, in fact, is reported by Treu Koopmans."
 We have estimated the contribution of modified graviE o lensing. in the form of projected. phantom dark matter. or all of the objects in the sample of Bolton ct al.," We have estimated the contribution of modified gravity to lensing, in the form of projected phantom dark matter, for all of the objects in the sample of Bolton et al."
 The objects have been modelled as isotropic Jalle spheres with he observed elective racdus., The objects have been modelled as isotropic Jaffe spheres with the observed effective radius.
 Given this density eistribution. he Jeans equation is solved for therun of radial velocity dispersion where the total force. go ds related to. the rewtonian force. gv. by the MOND formula gig)=gx: for) ds the MOND interpolating function (Gr)=r where rox] and por)=1 where vw- 1). taken here to be of he form suggested by Zhao Famaey (2006).," Given this density distribution, the Jeans equation is solved for therun of radial velocity dispersion where the total force, $g$ is related to the Newtonian force, $g_N$, by the MOND formula $g\mu(g)=g_N$; $\mu(x)$ is the MOND interpolating function $\mu(x)=x$ where $x<<1$ and $\mu(x) = 1$ where $x>>1$ ), taken here to be of the form suggested by Zhao Famaey (2006)."
 1n cach case we adjust the mass of the sphere in order to reproduce the observed. Iuminositv-weighted. average line-of-5sight. velocity within οι this mass in most cases agrees closely with, In each case we adjust the mass of the sphere in order to reproduce the observed luminosity-weighted average line-of-sight velocity within $r_{eff}/2$ ; this mass in most cases agrees closely with
The ouly [ree parameter in the eutire technique is the probability threshold used to cletermine cluster membership.,The only free parameter in the entire technique is the probability threshold used to determine cluster membership.
 Optimally. as we have done in this paper. a training set of spectroscopically confirmed. cluster members cau be used to empirically set the threshold value.," Optimally, as we have done in this paper, a training set of spectroscopically confirmed cluster members can be used to empirically set the threshold value."
 When this is uot the case. alternative techniques. such as color-selectiou to identify the early-type sequence at the appropriate redshift. cau be used to identify likely cluster caucdidates.," When this is not the case, alternative techniques, such as color-selection to identify the early-type sequence at the appropriate redshift, can be used to identify likely cluster candidates."
 Ou the other haud. the expected uumber of cluster caudidates can be calculated (roi the statistical backerounc correctiou areuments.," On the other hand, the expected number of cluster candidates can be calculated from the statistical background correction arguments."
 This expected uumber of cluster members cau be used as au independent estimator as we can set the probability threshold value to reproduce the estimated number of cluster galaxies., This expected number of cluster members can be used as an independent estimator as we can set the probability threshold value to reproduce the estimated number of cluster galaxies.
 Based ou our work. we believe that photometric redshifts are au ideal way to study the galaxy populations in high-redshift clusters.," Based on our work, we believe that photometric redshifts are an ideal way to study the galaxy populations in high-redshift clusters."
 For a large number of the tests of common cluster properties the Morphology-Deusity relatiouship). this inethod eliminates tlie need for exteusive spectroscopic surveys and the uncertainty of estimating the background contamination.," For a large number of the tests of common cluster properties the Morphology-Density relationship), this method eliminates the need for extensive spectroscopic surveys and the uncertainty of estimating the background contamination."
 As an additional example ¢ ‘the utility of this approach. consider the maeuituce-limitecd. spectroscopic survey used iu this allalysis.," As an additional example of the utility of this approach, consider the magnitude-limited, spectroscopic survey used in this analysis."
 We cau approxtinate the total number of spectroscopic targets observed by multiplying the utmber of clusters usec in this analysis (live) by the approximate number of targets per cluster fiekl (130). implying that a total of 650 objects were observed. spectroscopically.," We can approximate the total number of spectroscopic targets observed by multiplying the number of clusters used in this analysis (five) by the approximate number of targets per cluster field (130), implying that a total of 650 objects were observed spectroscopically."
 The redshift identification success rate was nearly 77%., The redshift identification success rate was nearly $77\%$.
 Of these redshifts. 50%-85% belong to galaxies.," Of these redshifts, $50\%$ $85\%$ belong to non-cluster galaxies."
 These numbers imply that the spectroscopic survey was ouly L2%—38%e efficient in identifying cluster cauclidates. depeudiug ou the richness of the cluster.," These numbers imply that the spectroscopic survey was only $12\%$ $38\%$ efficient in identifying cluster candidates, depending on the richness of the cluster."
 In addition. our techuique provides the ability to tune the cluster caudidate ideutificatiou to either maximize the completeness or. alternatively. to minimize the contamination.," In addition, our technique provides the ability to tune the cluster candidate identification to either maximize the completeness or, alternatively, to minimize the contamination."
 As a practical example. maximizing Completeness is esseutial for auy observational program which is interested in completely sampling the cluster spectroscopic targeting).," As a practical example, maximizing completeness is essential for any observational program which is interested in completely sampling the cluster spectroscopic targeting)."
 Ou the other hauc. minimizing coutaminatlou is important for selecting a Characteristic set of cluster members for a detailed study of cluster member properties (e.g..thefractionortheMorphology-Deusityrelationship:Lubinefαἱ. 2000).," On the other hand, minimizing contamination is important for selecting a characteristic set of cluster members for a detailed study of cluster member properties \citep[\eg the
Morphological fraction or the Morphology-Density
relationship;][]{lubin00}."
. Furthermore. if a training set of spectroscopically confirmed. galaxies is available. we cau actually characterize the percentages of both the completeness aud. coutamiunatiou that we expect in our final cluster candidate catalog.," Furthermore, if a training set of spectroscopically confirmed galaxies is available, we can actually characterize the percentages of both the completeness and contamination that we expect in our final cluster candidate catalog."
 Like any photometric redshift based technique. our technique is limited in its efficacy by the quality of the photometric data used in the analysis.," Like any photometric redshift based technique, our technique is limited in its efficacy by the quality of the photometric data used in the analysis."
 However. our tecliuique can be applied using a variety of photometric redshift estimation methods.," However, our technique can be applied using a variety of photometric redshift estimation methods."
 Therefore. we expect that. in the uear future. we will be able to fully utilize the capabilities of this techuique for cluster research.," Therefore, we expect that, in the near future, we will be able to fully utilize the capabilities of this technique for cluster research."
 We are very grateful to Bev Oke au Mare Postiuan for the enormous time aud effort. that they put into obtaining and reducing all of the data used in this paper., We are very grateful to Bev Oke and Marc Postman for the enormous time and effort that they put into obtaining and reducing all of the data used in this paper.
 We also wish to thank the anonviuous referee [or a thorough reacing of the original paper aud many interesting comments., We also wish to thank the anonymous referee for a thorough reading of the original paper and many interesting comments.
 This research has made use of NÀSAs Astrophysics Data System Abstract Service., This research has made use of NASA's Astrophysics Data System Abstract Service.
 LML is supported, LML is supported
et al. (,et al. (
2005). who also used spectroscopy aud photomet:y ο classify the object as an ALL star only 5.7 pe away.,"2005), who also used spectroscopy and photometry to classify the object as an M4 star only 5.7 pc away."
 Iu addition. the star shows sigus of activity. through both IIo eudssion aud identification with a bright X-ray source. xossiblv indicating a voung age.," In addition, the star shows signs of activity, through both $\alpha$ emission and identification with a bright X-ray source, possibly indicating a young age."
 Hence. it is of particular interest for high-coutrast imaging surveys. but since it was rot properly classified prior to the publication of Scholz et al. (," Hence, it is of particular interest for high-contrast imaging surveys, but since it was not properly classified prior to the publication of Scholz et al. ("
2005). it has not heen targeted by such survevs.,"2005), it has not been targeted by such surveys."
 For this reason. L 119-1 makes au excelleut test case for iercontrast maging with SINFONI.," For this reason, L 449-1 makes an excellent test case for high-contrast imaging with SINFONI."
 The data of L 119-1. were taken using SINFONI at he VLT diving a visitor mode run at Paranal on the ught of 26 Jan 2007., The data of L 449-1 were taken using SINFONI at the VLT during a visitor mode run at Paranal on the night of 26 Jan 2007.
 Iu order to ect the best possible spatial sampling. the smallest available SINFONT field of vieκ οἱ US.SO87 was used. vieldiug au effective pixel scale of 12.5 imnas/pixel by 25 uas/pixel.," In order to get the best possible spatial sampling, the smallest available SINFONI field of view of $0.8"" \times 0.8""$ was used, yielding an effective pixel scale of 12.5 mas/pixel by 25 mas/pixel."
" The ""IIIK setting was used. covering the soectral range of 1.1 jan to 2.5 qi à atf a spectral resolutiou of abou R=1500."," The “H+K” setting was used, covering the spectral range of 1.4 $\mu$ m to 2.5 $\mu$ m at a spectral resolution of about $R=1500$."
 Adaptive optics was 1sec with the target itsel as the guide star. ale provided good aud stale wavetroit correction the aveyaee Strehl ratio was 3 (Corres»ondius to a waveleugth of 1.95 ji n) as elven w the AO system itself.," Adaptive optics was used with the target itself as the guide star, and provided good and stable wavefront correction – the average Strehl ratio was 34 (corresponding to a wavelength of 1.95 $\mu$ m) as given by the AO system itself."
" The weaher conditinis were al«| good and stable. with au aveoraee seehis o [0,227 at 5X) nim as given by the atuospherie secing monitor at Paranal."," The weather conditions were also good and stable, with an average seeing of 0.72"" at 500 nm as given by the atmospheric seeing monitor at Paranal."
 For the purpose of efficicut subtraction of the stellar PSF. the data were taken at two different instrument Toations.," For the purpose of efficient subtraction of the stellar PSF, the data were taken at two different instrument rotations."
 This enables use of a data reductiou scheme known as roll subtraction (sec» Aucller Weieelt 1987) or aneular differential iaaeiug (ADT. see e.g. Marois ct al.," This enables use of a data reduction scheme known as roll subtraction (see Mueller Weigelt 1987) or angular differential imaging (ADI, see e.g. Marois et al."
 m16)., 2006).
 Our implementation of this technique is described iu Wellner (2005) and Jausou et al. (, Our implementation of this technique is described in Kellner (2005) and Janson et al. (
2007).,2007).
 Five tarect frames aud one sky frame were taken at an angle of 07. and three target frames plus one sky frame at an augle of 907.," Five target frames and one sky frame were taken at an angle of $0^{\circ}$, and three target frames plus one sky frame at an angle of $90^{\circ}$."
 The effective inteeration time per frame was 350 seconds., The effective integration time per frame was 350 seconds.
 ΑΗ the frames generated durig observations were translated into equivalent data cubes. with spatial information along two of the axes. and spectral information alone the third. using the standard ESO data reduction pipeline with the Caseano GUI tool.," All the frames generated during observations were translated into equivalent data cubes, with spatial information along two of the axes, and spectral information along the third, using the standard ESO data reduction pipeline with the Gasgano GUI tool."
 This procedure also performed all basic data reduction steps. such as sky subtraction. flat fielding. bad pixel correction and waveleneth calibration.," This procedure also performed all basic data reduction steps, such as sky subtraction, flat fielding, bad pixel correction and wavelength calibration."
 The output «ata cubes were used in a munuber of further data reduction procedures to generate useful data prodicts. using IDL routiues that were written specifically for these purposes.," The output data cubes were used in a number of further data reduction procedures to generate useful data products, using IDL routines that were written specifically for these purposes."
 The restIts of the basic reduction also iuchided extracted: specra of L119-1 and the tellure standard star. that were also further processed by our IDL routines for spectral type analysis.," The results of the basic reduction also included extracted spectra of L449-1 and the telluric standard star, that were also further processed by our IDL routines for spectral type analysis."
 We note that this procedure. wuch is cletaied below. was designed to correspond as closely as possile to the equivalent procedure for NAC'O-SDI (sec Isell101) 2005 aud Janson et al.," We note that this procedure, which is detailed below, was designed to correspond as closely as possible to the equivalent procedure for NACO-SDI (see Kellner 2005 and Janson et al."
 2007) so that no differeuce in the final performance can be simply attributed to a difference oe1i the wuplemenutation of the technique., 2007) so that no difference in the final performance can be simply attributed to a difference in the implementation of the technique.
" For the SDI. which was our primary purpose. different ""Olnations of image slices were co-adeled το represcut oenages of different filters."," For the SDI, which was our primary purpose, different combinations of image slices were co-added to represent images of different filters."
 In particular. tages denoted by fj. foo aια fs; were created. where fq is an nuage in the wavelength rauge 1.5625 jan to 1.5875 pan. fo iu 1.5875 gun to 1.6125 juu. aud fj in 1.6125 nu to 1.6975 nu. This coustruct was designed in order to create. as close as possible. equivalence to the Fl. F5 and £4 filters of NACO-SDI (see Jauson et al.," In particular, images denoted by $f_1$, $f_2$ and $f_3$ were created, where $f_1$ is an image in the wavelength range 1.5625 $\mu$ m to 1.5875 $\mu$ m, $f_2$ in 1.5875 $\mu$ m to 1.6125 $\mu$ m, and $f_3$ in 1.6125 $\mu$ m to 1.6375 $\mu$ m. This construct was designed in order to create, as close as possible, equivalence to the $F_1$, $F_2$ and $F_3$ filters of NACO-SDI (see Janson et al."
 2007)., 2007).
 The PSF ceuter was determined for every nuage slice in every data cube through eaussian centroidius. and the nuages were shifted to a common position based ou this information.," The PSF center was determined for every image slice in every data cube through gaussian centroiding, and the images were shifted to a common position based on this information."
 Remaining differences in photoceuter positions were minimized via cross-correlation., Remaining differences in photocenter positions were minimized via cross-correlation.
 Sub-pixel shifts were acconmmodated through bilinear iuterpolatio-, Sub-pixel shifts were accommodated through bilinear interpolation.
 The data were also subsampled by a factor 2 to ect the same effective sampling im the x- and v-directiol. and to avoid lage artefacts arising from the doub representation of each saue poiut iji the v-directkna (cach image slice is 61 by 6 pixels iu a SINFONI daa cube. but since the actual sampling is 12.5 nias/pixel in the x-clirection aid. 25.0 uas/pixel iu the v-directio- cach sample poiut is rYopreselned twice in the v-direction). fi.," The data were also subsampled by a factor 2 to get the same effective sampling in the x- and y-direction, and to avoid image artefacts arising from the double representation of each sample point in the y-direction (each image slice is 64 by 64 pixels in a SINFONI data cube, but since the actual sampling is 12.5 mas/pixel in the x-direction and 25.0 mas/pixel in the y-direction, each sample point is represented twice in the y-direction). $f_1$,"
 fo and fa were subsequently rescaled to a comunion A/D scale aud subracted from cach other to produce SDI images., $f_2$ and $f_3$ were subsequently rescaled to a common $\lambda / D$ scale and subtracted from each other to produce SDI images.
 Unsharpanuaski1ο Was apied in order to τος the low spatial frequencics (backeround ancl halo). wlulst retainiic hiegher-frequency features (such as possible companions. but also speckles).," Unsharp-masking was applied in order to remove the low spatial frequencies (background and halo), whilst retaining higher-frequency features (such as possible companions, but also speckles)."
 This was done by convolving each tnage with a gaussian kernel with a FWIM of 110 nas. aud subsequently subtracting the sxinoothi iniage from the original iniage.," This was done by convolving each image with a gaussian kernel with a FWHM of 140 mas, and subsequently subtracting the smooth image from the original image."
" Finally. the resultiie difference images at cach rotation angle were co-acdded. after which. any co-added image corresponding to one augle was subtracted from the otLOY,"," Finally, the resulting difference images at each rotation angle were co-added, after which, any co-added image corresponding to one angle was subtracted from the other."
 The racial profile of t1ο error was calculated for the fina -nage., The radial profile of the error was calculated for the final image.
 This was done for cach separation by seleclue all pixels between an inner aud outer radius of El pixe from the separation of interest. aud talking the stand eviation of those pixels.," This was done for each separation by selecting all pixels between an inner and outer radius of $\pm 1$ pixel from the separation of interest, and taking the standard deviation of those pixels."
 By comparing this radial xofile +o the brightuess of the prunary star itself. the acLever Ontrast as a function of angular separation coild be etermünued.," By comparing this radial profile to the brightness of the primary star itself, the achieved contrast as a function of angular separation could be determined."
 For test purposes. the same procedure as describe above was also performed for three inages in the baud: gj at 2.095 pau to 2.120 quu. go at 2.120 sau to 2.115 jnu and ga at 2.115 jan to 2.170 qi n (Le. wlith the sale type of configuration and the saue bandwidhn ias fi. fo aud fs).," For test purposes, the same procedure as described above was also performed for three images in the K-band: $g_1$ at 2.095 $\mu$ m to 2.120 $\mu$ m, $g_2$ at 2.120 $\mu$ m to 2.145 $\mu$ m and $g_3$ at 2.145 $\mu$ m to 2.170 $\mu$ m (i.e., with the same type of configuration and the same bandwidth as $f_1$, $f_2$ and $f_3$ )."
 These waveleneths are arbitrary from a physical viewpoint. and are not expectec Q COLYTCSDOxd to any particularly interesting spectral features.," These wavelengths are arbitrary from a physical viewpoint, and are not expected to correspond to any particularly interesting spectral features."
 Iustea. the purpose of the analvsis. iu this case. was to test whether the contrast performance is sieuificantly different iu f1e II-," Instead, the purpose of the analysis, in this case, was to test whether the contrast performance is significantly different in the H-"
for dvnamic neutron decoupling to occur.,for dynamic neutron decoupling to occur.
 Because (his is an impossibly hieh Lorentz factor for the collapsar model. dvwnamic neutron decoupling will not occur.," Because this is an impossibly high Lorentz factor for the collapsar model, dynamic neutron decoupling will not occur."
 There max be a detectable neutrino signature of dynamic neutron decoupling., There may be a detectable neutrino signature of dynamic neutron decoupling.
 collisions occurring during decoupling will generate pions., Neutron-proton collisions occurring during decoupling will generate pions.
 In turn these pious will decay and lead to the generation of neutrinos with energies of a few GeV in our reference frame., In turn these pions will decay and lead to the generation of neutrinos with energies of a few GeV in our reference frame.
 These neutrinos should be detectable al the rate of about one per vear in nent eeneralion neutrino telescopes (Dahcall&Mészáros2000)., These neutrinos should be detectable at the rate of about one per year in next generation neutrino telescopes \citep{bah00}.
. In addition. (here may also be a direct electromagnetic signature of neutron decoupling.," In addition, there may also be a direct electromagnetic signature of neutron decoupling."
 For some bursts arising from external shocks. a slow decoupled neutron shell will decav and shock with the outer proton shell as the outer shell plows into the interstellar medium.," For some bursts arising from external shocks, a slow decoupled neutron shell will decay and shock with the outer proton shell as the outer shell plows into the interstellar medium."
 This leads (ο a characteristic tvo-peaked structure in the burst (Pruet&Dalal2002)., This leads to a characteristic two-peaked structure in the burst \citep{pru02}.
. Regardless of whether dvnamic neutron decoupling occurs. neutrons in the jet mar have observable implications for the GRB alterglow.," Regardless of whether dynamic neutron decoupling occurs, neutrons in the jet may have observable implications for the GRB afterglow."
 This is parüceularly true when the shocking radius. i.e. the radius at which the shocks giving rise to the observed 5—ravs occur. is sinaller than the length over which free neutrons decay.," This is particularly true when the shocking radius, i.e. the radius at which the shocks giving rise to the observed $\gamma-$ rays occur, is smaller than the length over which free neutrons decay."
" This condition is where μοι is the shocking radius. 5» is the Lorentz [actor of the outflow in units of 100. and 7,~1000sec is the free neutron lifetime."," This condition is where $r_{\rm shock}$ is the shocking radius, $\gamma_2$ is the Lorentz factor of the outflow in units of 100, and $\tau_n\sim 1000\sec$ is the free neutron lifetime."
 Eq., Eq.
 13. is generally. satisfied [or bursts from internal shocks aud bursts [rom external shocks in a very dense medium., \ref{nafterglow} is generally satisfied for bursts from internal shocks and bursts from external shocks in a very dense medium.
 When Eq., When Eq.
 holds. the neutrons can stream ahead of the slowing proton shell (the complement of the ονπας neutron decoupling discussed above) and deposit energy as they decay.," \ref{nafterglow} holds, the neutrons can stream ahead of the slowing proton shell (the complement of the dynamic neutron decoupling discussed above) and deposit energy as they decay."
 Implications for the resulting afterglow in such a case have been discussed by Beloborodosv.(2002)., Implications for the resulting afterglow in such a case have been discussed by \citet{bel02}.
. In the next section we discuss the r-process in winds and jets from accretion disks., In the next section we discuss the r-process in winds and jets from accretion disks.
 llowever. we first note that GRB jets are characterized bv interesting light element svnthesis.," However, we first note that GRB jets are characterized by interesting light element synthesis."
 Pruet.Guiles.&Fuller(2002) and Lemoine(2002) caleulated the thermal svnthesis of light elements in GRBDB-like outflows., \citet{pgf02} and \citet{lem02} calculated the thermal synthesis of light elements in GRB-like outflows.
 Thev find that the final deuterium mass fraction can be of order154... some three orders of magnitude larger than the primordial vield.," They find that the final deuterium mass fraction can be of order, some three orders of magnitude larger than the primordial yield."
 For kinematically well coupled flows. the nucleosvnthesis depends sensitivelv on Y.. with deuterium vield decreasing with increasing neutron excess.," For kinematically well coupled flows, the nucleosynthesis depends sensitively on $Y_e$, with deuterium yield decreasing with increasing neutron excess."
" For flows in which dynamic neutron decoupling occurs. high energv neutron-a. collisions will spall deuterons and can result in final deuteron mass [fractions as high as (ναοί,Guiles.&Fuller 2002).."," For flows in which dynamic neutron decoupling occurs, high energy $\alpha$ collisions will spall deuterons and can result in final deuteron mass fractions as high as \citep{pgf02}. ."
4.2-m William Llersehel “Telescope (WIUE) at. the. Isaac rewton Group of Telecopes. La Palma.,"4.2-m William Herschel Telescope (WHT) at the Isaac Newton Group of Telecopes, La Palma."
 Ehe observations were obtained simultaneously in the 7. 4. and «' colour xuxds on the 16 May 2002. the 2’. 9. and a! bands on the 19 Alay 2003. and the Z. d. and if bands on subsequent nights.," The observations were obtained simultaneously in the $^{\prime}$ , $^{\prime}$ , and $^{\prime}$ colour bands on the 16 May 2002, the $^{\prime}$, $^{\prime}$, and $^{\prime}$ bands on the 19 May 2003, and the $^{\prime}$, $^{\prime}$, and $^{\prime}$ bands on subsequent nights."
 Data reduction was carried out using the ULTICLACAM xpeline data reduction. software., Data reduction was carried out using the ULTRACAM pipeline data reduction software.
 Unfortunately. we were unable to observe a standard star in the z band using ULPRACAAL so the zeropoint for this filter was chosen o be the same as for the Z band: this will only allect he scale of the z lighteurve. not its shape.," Unfortunately, we were unable to observe a standard star in the $^{\prime}$ band using ULTRACAM, so the zeropoint for this filter was chosen to be the same as for the $^{\prime}$ band; this will only affect the scale of the $^{\prime}$ lightcurve, not its shape."
 MI the data were corrected to zero airmass using the nightlv extinction coefficients measured by the Carlsberg Meridian Telescope on La Palma in the 7 filter. and. converted to other colour bands using the procedure described by 2? and the effective wavelengths of the filters given hy ?..," All the data were corrected to zero airmass using the nightly extinction coefficients measured by the Carlsberg Meridian Telescope on La Palma in the $^{\prime}$ filter, and converted to other colour bands using the procedure described by \citet{king85} and the effective wavelengths of the filters given by \citet{fukugita96}."
 The lighteurves of OU Vir are shown in Figure 1.., The lightcurves of OU Vir are shown in Figure \ref{lightcurve}.
 On 16 Alay 2002 the exposure time was 0.5 seconds and. the data points were separated by approximately 4.9 seconds., On 16 May 2002 the exposure time was 0.5 seconds and the data points were separated by approximately 4.9 seconds.
 ‘These cata were obtained on the first night of commissioning and hence were adversely alfected by typical commissioning problems. chiellv excess noise in the w band and limited time resolution due to the dead-time between exposures.," These data were obtained on the first night of commissioning and hence were adversely affected by typical commissioning problems, chiefly excess noise in the $^{\prime}$ band and limited time resolution due to the dead-time between exposures."
 The data taken in 2003 had no such problems. and hence the dead-time was reduced to 0.025 seconds.," The data taken in 2003 had no such problems, and hence the dead-time was reduced to 0.025 seconds."
 The exposure times for these observations varied according to the seeing on the night. and were 9.2 seconds on 19 May 2003. 5.2 seconds on 20 May. 2003 ancl 4.2 seconds thereafter.," The exposure times for these observations varied according to the seeing on the night, and were 9.2 seconds on 19 May 2003, 5.2 seconds on 20 May 2003 and 4.2 seconds thereafter."
 OU Vir was observed during descent from superoutburst in both 2002 and 2003., OU Vir was observed during descent from superoutburst in both 2002 and 2003.
 ?. found that for OU Vir out of eclipse and during quiescence. V—15.05 and 2V= 0.14. which corresponds to go~0.2 mdy.," \citet{mason02} found that for OU Vir out of eclipse and during quiescence, $V=18.08$ and $B-V=0.14$ , which corresponds to $^{\prime}\sim0.2$ mJy \citep{smith02}."
 (7). 7. quote an outburst amplitude of approximately 4 magnitudes. (corresponding to a peak 4 Dux of ~S4 mJy)., \citet{vanmunster00} quote an outburst amplitude of approximately 4 magnitudes (corresponding to a peak $^{\prime}$ flux of $\sim8.4$ mJy).
 The svstem appears to be significantly. below superouthurst maximum on the 16 Alay 2002. and almost at its quiescent brightness. during the 2003 observations: The maximum superoutburst [ux we have observed is 1.2 my on 16 May. 2002. ancl the out-ol-eclipse quiescent [lux is 0.2 mJy on 22 and 25 May 2003.," The system appears to be significantly below superoutburst maximum on the 16 May 2002, and almost at its quiescent brightness during the 2003 observations: The maximum superoutburst flux we have observed is $\sim1.2$ mJy on 16 May 2002, and the out-of-eclipse quiescent flux is $\sim0.2$ mJy on 22 and 25 May 2003."
 As the descent. from. superoutburst is typically much slower than the ascent. we suspect the 2002 observations took place during the former. state. but. of course we cannot be certain.," As the descent from superoutburst is typically much slower than the ascent, we suspect the 2002 observations took place during the former state, but of course we cannot be certain."
 Phe 2002 cata are. as far as we are aware. the only observations of this superoutburst.," The 2002 data are, as far as we are aware, the only observations of this superoutburst."
 The 2003 superoutburst was first reported on 2 May. (7)..., The 2003 superoutburst was first reported on 2 May \citep{kato03}.
 The superhump is visible in both the 16 May 2002 lishteurve at phase —0.45 and the 20 May. 2003 lighteurve at. phase ~O02. but is not visible in later data. either because it Μας faded or it was at a phase which was not observed.," The superhump is visible in both the 16 May 2002 lightcurve at phase $\sim-0.45$ and the 20 May 2003 lightcurve at phase $\sim-0.2$, but is not visible in later data, either because it had faded or it was at a phase which was not observed."
 The lower three panels of Figure 1. show changes in the eclipse morphology that occur during the descent. from. superoutburst., The lower three panels of Figure \ref{lightcurve} show changes in the eclipse morphology that occur during the descent from superoutburst.
 Importantly. the eclipse morphology changed drastically from a single sharp ingress and egress on 20 May 2003. to separate eclipses of the white dwarf and bright spot in the a and. g bands on 25 May 2003.," Importantly, the eclipse morphology changed drastically from a single sharp ingress and egress on 20 May 2003, to separate eclipses of the white dwarf and bright spot in the $^{\prime}$ and $^{\prime}$ bands on 25 May 2003."
 Phe. bright spot ingress is also visible in the 9g. data of 22 Alay 2003. (, The bright spot ingress is also visible in the $^{\prime}$ data of 22 May 2003. (
The second egress feature visible in this lightcurve is more eracdual than it appears in the compressed scale of Figure 1.. and is mainly due totheegress of the disc.),"The second egress feature visible in this lightcurve is more gradual than it appears in the compressed scale of Figure \ref{lightcurve}, and is mainly due totheegress of the disc.)"
 This evolution of the eclipse morphology is typical for a svstem goingfrom (super) outburst to quiescence (see. for example. ?2)).," This evolution of the eclipse morphology is typical for a system goingfrom (super) outburst to quiescence (see, for example, \citealt{rutten92c}) )."
 The white dwarf eclipse contact phases given in Tables 1 , The white dwarf eclipse contact phases given in Tables \ref{eclipse_times} 
than 1 day.,than 1 day.
 Our interpretation of this phenomenon is that it is à bv-produet of a few unique features of the transit signals we are dealing with., Our interpretation of this phenomenon is that it is a by-product of a few unique features of the transit signals we are dealing with.
 Firstly the duration of the transits. and hence the width of the boxes fitted by the BLS algorithm. is much shorter with respect to both the orbital period and the WASP survey cadence than for transits of main sequence stars.," Firstly the duration of the transits, and hence the width of the boxes fitted by the BLS algorithm, is much shorter with respect to both the orbital period and the WASP survey cadence than for transits of main sequence stars."
 As a consequence the trial bins will contain many fewer data points than for a main sequence transit search. particularly at longer trial periods.," As a consequence the trial bins will contain many fewer data points than for a main sequence transit search, particularly at longer trial periods."
" Secondly as the transit signals are so deep compared to the main sequence case. they are less prone to being ""washed out” when the light curve is folded on an incorrect trial period and the in-transit points spread. across all orbital phases."," Secondly as the transit signals are so deep compared to the main sequence case, they are less prone to being “washed out” when the light curve is folded on an incorrect trial period and the in-transit points spread across all orbital phases."
 In the case illustrated the Earth-sizecl body will cause transits with a depth of θα., In the case illustrated the Earth-sized body will cause transits with a depth of $\sim 70$.
 Even in a trial bin with. for example. 1 in-transit and 10 out-of-transit data points the presence of the single in-transit point would drag down the mean light level in the bin by more than6%.. which could be sullicient to be regarded as a significant detection.," Even in a trial bin with, for example, 1 in-transit and 10 out-of-transit data points the presence of the single in-transit point would drag down the mean light level in the bin by more than, which could be sufficient to be regarded as a significant detection."
 ‘To address this issue we modified equation 5 as follows where d4 is the mean-square deviation of the data points within the bin about their mean., To address this issue we modified equation \ref{sn_unmod} as follows where $\hat{d}^2_j$ is the mean-square deviation of the data points within the bin about their mean.
 This modification will have he elect of strongly. reducing the computed signal-to-noise of bins which contain a mix of in-transit anc out-of-transit data points., This modification will have the effect of strongly reducing the computed signal-to-noise of bins which contain a mix of in-transit and out-of-transit data points.
 Ehe magnitude of this down-weighting will tend o increase as the depth of the transit signal increases. but only in the cases in which the trial period does not match he true period. (or an integer multiple or fraction).," The magnitude of this down-weighting will tend to increase as the depth of the transit signal increases, but only in the cases in which the trial period does not match the true period (or an integer multiple or fraction)."
 Where a bin contains just in-transit points the cdown-weighting will generally be small for all transit depths., Where a bin contains just in-transit points the down-weighting will generally be small for all transit depths.
 Figure shows the BLS periodogram computed using this mocdified prescription4. or the signal-to-noise. for the same transit as in Figure 3..," Figure \ref{new_prdg} shows the BLS periodogram computed using this modified prescription for the signal-to-noise, for the same transit as in Figure \ref{old_prdg}."
 Automated. searches for weak signals in noisy cata are inherently susceptible to false alarms”. whereby a chance alignment of noise fluctuations in the data are nusinterpreted by the search. algorithm as a evidence Likely detection of the signal being hunted.," Automated searches for weak signals in noisy data are inherently susceptible to “false alarms”, whereby a chance alignment of noise fluctuations in the data are misinterpreted by the search algorithm as a evidence likely detection of the signal being hunted."
 Lt is useful therefore to be able to define a filter which can be applied automatically. to weed out these [alse. detections., It is useful therefore to be able to define a filter which can be applied automatically to weed out these false detections.
 We achieved. this by constructing svnthetie light. curves based. on the time-sampling of sample WASP light curves which contain pure white-noise. but no simulated transit signal.," We achieved this by constructing synthetic light curves based on the time-sampling of sample WASP light curves which contain pure white-noise, but no simulated transit signal."
 We then computed. BLS periodograms for these light curves in the same manner as for those containing simulated transits., We then computed BLS periodograms for these light curves in the same manner as for those containing simulated transits.
 7? define a useful metric for assessing the likely. significance of a peak in a BLS periodogram. which they refer to as the Signal Detection Efliciency (SDE): where Shea ds the height of the peak. and S and os are measures of the mean level and. scatter in the noise continuum of the periodogram.," \citet{Kovacs02} define a useful metric for assessing the likely significance of a peak in a BLS periodogram, which they refer to as the Signal Detection Efficiency (SDE): where $\mathcal{S}_{\rm peak}$ is the height of the peak, and $\bar{\mathcal{S}}$ and $\sigma_{\mathcal{S}}$ are measures of the mean level and scatter in the noise continuum of the periodogram."
 We computed the SDE of the highest. peak in cach of the svnthetic. transitless light curves.," We computed the SDE of the highest peak in each of the synthetic, transitless light curves."
 The cumulative distribution function of these SDE measures over the whole sample is plotted in Figure 5.., The cumulative distribution function of these SDE measures over the whole sample is plotted in Figure \ref{PDF_new}.
 This distribution Function allowed us to define a threshold SDE below which we could automatically discount a detection as likely to be a false alarm., This distribution function allowed us to define a threshold SDE below which we could automatically discount a detection as likely to be a false alarm.
 As the size of the sample of WDs observed by WASP is fairly small. just a few hundred. we chose a relatively generous threshold uu= 6.3) which would allow through around of false detections.," As the size of the sample of WDs observed by WASP is fairly small, just a few hundred, we chose a relatively generous threshold $_{\rm thresh}=6.3$ ) which would allow through around of false detections."
 For larger surveys a more strictthreshold might be necessary to avoid being swanipecl by false detections., For larger surveys a more strictthreshold might be necessary to avoid being swamped by false detections.
 Figure 6 and Tables 1.. 2 and 3. sumniarise our recovery," Figure \ref{det_rate} and Tables \ref{tab12}, , \ref{tab13} and \ref{tab15} summarise our recovery"
"some of the 662 ""Neptune-like"" Kepler candidates with radii between 2 and 6 Ro may also fit into the super-Earth category. when defined as in this paper by planets wilh masses between 1 and 10 M..","some of the 662 “Neptune-like” Kepler candidates with radii between 2 and 6 $R_{\earth}$ may also fit into the super-Earth category, when defined as in this paper by planets with masses between 1 and 10 $M_{\earth}$."
" Interestingly. GJ 1214b falls into the latter category of planets that would be defined as ""Neptune-class"" by (he Ixepler standards."," Interestingly, GJ 1214b falls into the latter category of planets that would be defined as “Neptune-class” by the Kepler standards."
 Looking at the current population of 8 (ransiting super-Earths. there seems to be a wide range of implied bulk composition of these planets. ranging from the iron-rich. planet Ixepler-10b. (7)— (0 the hyvdrogen-rich planet Kkepler-11e (2)..," Looking at the current population of 8 transiting super-Earths, there seems to be a wide range of implied bulk composition of these planets, ranging from the iron-rich planet Kepler-10b \citep{bat11} to the hydrogen-rich planet Kepler-11e \citep{lis11}."
 GJ. 1214b. fits in somewhere in the middle of this population of planets. with its middle-o[-the-road. density of 1.9 g/em and implied composition that is either ice-rieh or hyvdrogen-rich. (or somewhere in between these two extremes).," GJ 1214b fits in somewhere in the middle of this population of planets, with its middle-of-the-road density of 1.9 $^3$ and implied composition that is either ice-rich or hydrogen-rich (or somewhere in between these two extremes)."
 Ultimately. a combination of mass and radius measurements along with atmospheric studies such as the one presented here will allow for stronger constraints to be placed on the bulk composition of (hese planets. which will in turi give us a more detailed unelerstanding of the formation and evolution processes that give rise to the observed population of super-Eartls.," Ultimately, a combination of mass and radius measurements along with atmospheric studies such as the one presented here will allow for stronger constraints to be placed on the bulk composition of these planets, which will in turn give us a more detailed understanding of the formation and evolution processes that give rise to the observed population of super-Earths."
 E. M.-H. Ix was supported bv a contract with the California Institute of Technology unded by NASA through the Sagan Fellowship Program., E. M.-R. K was supported by a contract with the California Institute of Technology funded by NASA through the Sagan Fellowship Program.
That the cause of these spectral line shifts could be atmospheric as well as binaries is illustrated by the evolution of the spectrum of the M3 supergiant W237 shown in Figure 3..,That the cause of these spectral line shifts could be atmospheric as well as binaries is illustrated by the evolution of the spectrum of the M3 supergiant W237 shown in Figure \ref{fig:Wd237}.
 Over time the Ca Π line at 8663 is seen to evolve differently from most other lines., Over time the Ca II line at 8663 is seen to evolve differently from most other lines.
" While the Ca II line is blueshifted in the last epoch (red line in Fig 3)) compared to the earlier observations, the other lines are clearly redshifted."," While the Ca II line is blueshifted in the last epoch (red line in Fig \ref{fig:Wd237}) ) compared to the earlier observations, the other lines are clearly redshifted."
 These inconsistent line shifts are repeated throughout the spectrum and are the cause of the relatively large error bars for the relative velocity measurements of W237 compared to the other red supergiant W26 and the yellow hypergiants in Figure 2.., These inconsistent line shifts are repeated throughout the spectrum and are the cause of the relatively large error bars for the relative velocity measurements of W237 compared to the other red supergiant W26 and the yellow hypergiants in Figure \ref{fig:binarity}.
" Another argument for the importance of stellar activity can be made for W11, W23a and to a lesser extent W56."," Another argument for the importance of stellar activity can be made for W11, W23a and to a lesser extent W56."
 These stars show a significant shift of the spectral lines over a 1 day baseline in July 2010., These stars show a significant shift of the spectral lines over a 1 day baseline in July 2010.
" Although this could be explained by a short-period binary, such short-period binaries are expected to have a velocity amplitude of 100 km/s. Such a large velocity shift is not found compared to the other epoch of these stars, observed on June 2010, which could be a coincidence or caused by either a large inclination or a low mass companion."," Although this could be explained by a short-period binary, such short-period binaries are expected to have a velocity amplitude of 100 km/s. Such a large velocity shift is not found compared to the other epoch of these stars, observed on June 2010, which could be a coincidence or caused by either a large inclination or a low mass companion."
" It is unlikely that these scenarios can explain the observations for stars, suggesting that the spectral line shifts are likely to be caused by atmospheric variability."," It is unlikely that these scenarios can explain the observations for stars, suggesting that the spectral line shifts are likely to be caused by atmospheric variability."
" For the other stars, distinguishing between spectral line shifts, caused by binaries or stellar activity, is difficult."," For the other stars, distinguishing between spectral line shifts, caused by binaries or stellar activity, is difficult."
" However, given the high observed binary fraction among massive stars, we do expect a significant portion of the radial velocity variations to be caused by binary companions (?).."," However, given the high observed binary fraction among massive stars, we do expect a significant portion of the radial velocity variations to be caused by binary companions \citep{Sana11}."
 The stars in Table 1 and on the x-axis of Figure 2 have been roughly sorted by spectral type., The stars in Table \ref{tab:vel} and on the x-axis of Figure \ref{fig:binarity} have been roughly sorted by spectral type.
 The LBV is currently in a cool phase and has a lot of lines in common with the A/F hypergiants., The LBV is currently in a cool phase and has a lot of lines in common with the A/F hypergiants.
 Figure 2 shows two trends with spectral type., Figure \ref{fig:binarity} shows two trends with spectral type.
" The first trend is a decrease in the error bars to later spectral types, which is caused by the far larger sample of spectral lines, most of which are less broad, which are available for the later type stars."," The first trend is a decrease in the error bars to later spectral types, which is caused by the far larger sample of spectral lines, most of which are less broad, which are available for the later type stars."
" The main exception on this trend is W237, which has been discussed above (see Fig 3))."," The main exception on this trend is W237, which has been discussed above (see Fig \ref{fig:Wd237}) )."
 The other trend is that the yellow hypergiants and the red supergiants tend to show lower radial velocity variations than the B-supergiants., The other trend is that the yellow hypergiants and the red supergiants tend to show lower radial velocity variations than the B-supergiants.
" This variation stays much larger than the error bars, which means that this trend is consistently found over many different spectral lines."," This variation stays much larger than the error bars, which means that this trend is consistently found over many different spectral lines."
 This could be explained by the fact that we are sensitive to relatively close binaries with periods of at most a few years., This could be explained by the fact that we are sensitive to relatively close binaries with periods of at most a few years.
" ? showed that yellow hypergiants and red supergiants in close binaries evolve more quickly into a Wolf-Rayett star, because they lose their hydrogen atmosphere more effectively in binary-induced mass loss."," \citet{Eld08b} showed that yellow hypergiants and red supergiants in close binaries evolve more quickly into a Wolf-Rayett star, because they lose their hydrogen atmosphere more effectively in binary-induced mass loss."
 So yellow hypergiants and red supergiants in close binaries spend less time in these extended phases before becoming a Wolf-Rayett star than if these stars were in wide binaries or in isolation (?).., So yellow hypergiants and red supergiants in close binaries spend less time in these extended phases before becoming a Wolf-Rayett star than if these stars were in wide binaries or in isolation \citep{Cla11}.
" This creates a selection effect, where observed yellow hypergiants or red supergiants tend to have a low fraction of close binaries."," This creates a selection effect, where observed yellow hypergiants or red supergiants tend to have a low fraction of close binaries."
 We calculate the velocity dispersion of the cluster using only the yellow hypergiants and the LBV., We calculate the velocity dispersion of the cluster using only the yellow hypergiants and the LBV.
 This sample was chosen because these stars show a small amount of radial velocity variations compared to most other stars and they have a large number of spectral lines in common with each other., This sample was chosen because these stars show a small amount of radial velocity variations compared to most other stars and they have a large number of spectral lines in common with each other.
" The large number of lines in common means that we can measure the velocity dispersion on the basis of the cross correlation without having to deal with the systematics, which complicate the measurement of the absolute radial velocity."," The large number of lines in common means that we can measure the velocity dispersion on the basis of the cross correlation without having to deal with the systematics, which complicate the measurement of the absolute radial velocity."
" When trying to include more low variability stars in this sample, we find that"," When trying to include more low variability stars in this sample, we find that"
Found in close-in Another potentially important. effect. we've neglected is the channeling of escaping eas by the stellar. gravity.,found in close-in Another potentially important effect we've neglected is the channeling of escaping gas by the stellar gravity.
 The tical gravity of the host star may cause mass to Low eferentiallvy through the L1 point (??).. ," The tidal gravity of the host star may cause mass to flow preferentially through the L1 point \citep{2003ApJ...588..509G, 2009ApJ...693...23M}."
his elleet would »o especially important during Roche lobe overflow. when a substantial portion of the planet's atmosphere may become unbound from the planet.," This effect would be especially important during Roche lobe overflow, when a substantial portion of the planet's atmosphere may become unbound from the planet."
 Exchange of momentum between he escaping BSgas and the remaining5 planet can counteract he inward. pull of tides. even causingg the |planet to recede rom the star (?)..," Exchange of momentum between the escaping gas and the remaining planet can counteract the inward pull of tides, even causing the planet to recede from the star \citep{2010ApJ...708.1692C}."
 This οσο may significantly. mocitv he orbital evolution we've considered. here and. may. be responsible. at least in part. for the clustering of the orbital »eriods of close-in exoplanets around three days (?)..," This effect may significantly modify the orbital evolution we've considered here and may be responsible, at least in part, for the clustering of the orbital periods of close-in exoplanets around three days \citep{2008PASP..120..531C}."
 The first. discovered. rocky exoplanet. ColtoT-7 b. coute actually be the remnant core of a gas giant.," The first discovered rocky exoplanet, CoRoT-7 b, could actually be the remnant core of a gas giant."
 Phe planets proximity to its host star and strong stellar. insolation suggest that the planet may have lost a significant amoun of mass over its lifetime., The planet's proximity to its host star and strong stellar insolation suggest that the planet may have lost a significant amount of mass over its lifetime.
 The proximity also suggests tides have plaved an important role in the planct’s history. causing it to migrate inward.," The proximity also suggests tides have played an important role in the planet's history, causing it to migrate inward."
 By coupling models of evaporative mass loss and. tidal evolution. we find that the interplay between orbital decay ancl mass loss can lead to a wide variety of evolutionary. pathways.," By coupling models of evaporative mass loss and tidal evolution, we find that the interplay between orbital decay and mass loss can lead to a wide variety of evolutionary pathways."
 Using a moce that couples these two processes. we obtain constraints on the masses anc orbits of gas giants that may. have given rise to the ColtoT-7 b we see today.," Using a model that couples these two processes, we obtain constraints on the masses and orbits of gas giants that may have given rise to the CoRoT-7 b we see today."
 Our results sugges a complex orbital history for the planets in the ColtoT-7 system. possibly including passage through mean-motion resonances. even if ColtoT-7 b has always been a rocky Our calculations have general implications for the uistorics of both close-in rocky and gaseous planets.," Our results suggest a complex orbital history for the planets in the CoRoT-7 system, possibly including passage through mean-motion resonances, even if CoRoT-7 b has always been a rocky Our calculations have general implications for the histories of both close-in rocky and gaseous planets."
 'yevious studies have pointed. out the signatures of evaporation and tidal evolution on the distribution. of masses and semi-major axes for gaseous close-in exoplanets. rut these studies have not considered the coupling of the wo processes.," Previous studies have pointed out the signatures of evaporation and tidal evolution on the distribution of masses and semi-major axes for gaseous close-in exoplanets, but these studies have not considered the coupling of the two processes."
 Although our calculations allow CoRoTl-7 b o be the remnant rocky core of a eas planet. confirming this ivpothesis will require additional evidence.," Although our calculations allow CoRoT-7 b to be the remnant rocky core of a gas planet, confirming this hypothesis will require additional evidence."
 For example. improved constraints on the compositions of gas giant cores nmüsght allow us to distinguish remnant rocky cores on the oisis of their physical properties.," For example, improved constraints on the compositions of gas giant cores might allow us to distinguish remnant rocky cores on the basis of their physical properties."
 More detailed. dynamical studies of ColtoT-7 and other similar svstems will provide important constraints on heir origins and histories., More detailed dynamical studies of CoRoT-7 and other similar systems will provide important constraints on their origins and histories.
 Whatever the details. mass loss and. tidal evolution both probably played: Κον roles in the histories and origins of many close-in exoplanets. rocky or We thank Doug Lamilton. Dan Fabryckv. Alaki Hattori. Diana Valencia. Mare Ixuchner. and John Debes for useful conversations and suggestions.," Whatever the details, mass loss and tidal evolution both probably played key roles in the histories and origins of many close-in exoplanets, rocky or We thank Doug Hamilton, Dan Fabrycky, Maki Hattori, Diana Valencia, Marc Kuchner, and John Debes for useful conversations and suggestions."
 We also thank our referee [or a helpful and thorough review., We also thank our referee for a helpful and thorough review.
 BJ acknowledges support from the NASA Postdoctoral. Program., BJ acknowledges support from the NASA Postdoctoral Program.
 RB acknowledges funding from. NASA Astrobiology Institute's Virtual Planetary Laboratory load team. supported. by NASA under Cooperative Agreement No.," RB acknowledges funding from NASA Astrobiology Institute's Virtual Planetary Laboratory lead team, supported by NASA under Cooperative Agreement No."
 NNIIO5ZDAQQ1C' RG acknowledges support from NASA's Planetary Geology and Geophysics program. grant No.," NNH05ZDA001C. RG acknowledges support from NASA's Planetary Geology and Geophysics program, grant No."
 δλδόσα., NNG05GH65G.
which is a measure of the angular semithickness {1ἐν of the disc at the stellar surface.,which is a measure of the angular semithickness $H/r$ of the disc at the stellar surface.
 Phe three theories then give We therefore consider the generic form where s is a constant., The three theories then give We therefore consider the generic form where $s$ is a constant.
 Lt is convenient to work with dimensionless. rescaled values of the mode frequcney and quadrupole strength. a and Q. defined by which is an eigenvalue problem of SturmLiouville form. when considered together with appropriate boundary conditions.," It is convenient to work with dimensionless, rescaled values of the mode frequency and quadrupole strength, $\tilde\omega$ and $\tilde Q$ defined by Equation \ref{secular}) ) then becomes which is an eigenvalue problem of Sturm–Liouville form, when considered together with appropriate boundary conditions."
 Note that the parameter € drops out. of the equation under the above rescalings., Note that the parameter $\epsilon$ drops out of the equation under the above rescalings.
 For prograde modes (ce> 0). one solution of this equation decays exponentially ascx. while the other solution grows exponoentiallv.," For prograde modes $\tilde\omega>0$ ), one solution of this equation decays exponentially as $x\to\infty$, while the other solution grows exponentially."
 We therefore consider the equation in the domain 1<r< x. requiring solutions to satisfv a rigid. boundary condition Hu—0 at the stellar surface c=1 and to decay as οXe, We therefore consider the equation in the domain $1<x<\infty$ requiring solutions to satisfy a rigid boundary condition $u=0$ at the stellar surface $x=1$ and to decay as $x\to\infty$.
 Reasonable values of Q for Be stars can be estimated Following δι&LIarmanec(2006).., Reasonable values of $\tilde Q$ for Be stars can be estimated following \citet{2006A&A...447..277F}.
 Pheir Table 4 is based on stellar models of intermediate main-sequence age., Their Table 4 is based on stellar models of intermediate main-sequence age.
 There is considerable uncertainty in the applicability of these models because of the rapid rotation of De stars., There is considerable uncertainty in the applicability of these models because of the rapid rotation of Be stars.
 Nevertheless. using these data. we estimate that Q ranges [rom approximately 8 at the lower end (AZ=2.51 AL.) to approximately 12 at the upper end (AZ=15.85AL. }.," Nevertheless, using these data, we estimate that $\tilde Q$ ranges from approximately $8$ at the lower end $M=2.51\,M_\odot$ ) to approximately 12 at the upper end $M=15.85\,M_\odot$ )."
" Fhese values assume. somewhat arbitrarily. a disc temperature of 74,=(2/3)7;. and a stellar rotation rate that is 95% of the critical value."," These values assume, somewhat arbitrarily, a disc temperature of $T_\rmd=(2/3)T_\rme$ and a stellar rotation rate that is $95\%$ of the critical value."
 Similarly. for the stellar models of + Cas and 59C€vg described in Tables 2 and 3 of Eirt&Llarmanec(2006).. we estimate QzzO and 13. respectively.," Similarly, for the stellar models of $\gamma$ Cas and $59$Cyg described in Tables 2 and 3 of \citet{2006A&A...447..277F}, we estimate $\tilde Q\approx9$ and $13$, respectively."
 Lt is clear that significantly larger values of Q cannot be obtained by further increasing the stellar rotation rate. and in fact smaller. values may be more appropriate.," It is clear that significantly larger values of $\tilde
Q$ cannot be obtained by further increasing the stellar rotation rate, and in fact smaller values may be more appropriate."
 The values of€ for all these mocdels are in the range 0.021 0.026. again assuming that 7;= (2/3)1;.," The values of $\epsilon$ for all these models are in the range $0.021$ $0.026$, again assuming that $T_\rmd=(2/3)T_\rme$ ."
 Consider firstthe case without a quadrupole term. Q=0.," Consider firstthe case without a quadrupole term, $\tilde Q=0$."
" The solution that decavs as.r7ox ds then with where A, is the modified Bessel function of the seconc kind. of order v (Abramowitz&Stegun 1965).. ", The solution that decays as $x\to\infty$ is then with where $K_\nu$ is the modified Bessel function of the second kind of order $\nu$ \citep{1965hmfw.book.....A}. .
Note tha > is real and positive for the prograde modes of interest., Note that $z$ is real and positive for the prograde modes of interest.
 ‘This solution has no zeros in z>O i£ £ is real. but does so if v is imaginary.," This solution has no zeros in $z>0$ if $\nu$ is real, but does so if $\nu$ is imaginary."
 To match a rigid boundary. condition a w=] we therefore require £2.«0., To match a rigid boundary condition at $x=1$ we therefore require $\nu^2<0$.
 Phe 2DS theory gives Ss=de. so p=4(07|4) and modes are never confined.," The 2DS theory gives $8s=4\sigma$, so $\nu^2=4(\sigma^2+4)$ and modes are never confined."
 The 2DO theory gives Ss=do|6. so 1D--ασ2) ane modes may be confined for o.<2.," The 2DO theory gives $8s=4\sigma+6$, so $\nu^2=4(\sigma^2-2)$ and modes may be confined for $\sigma^2<2$."
 The 3D theory gives Ss—4o|24. so 57—ασ20) and modes may be confine or a«20.," The 3D theory gives $8s=4\sigma+24$, so $\nu^2=4(\sigma^2-20)$ and modes may be confined for $\sigma^2<20$."
 This analvsis is somewhat misleading because the modes may not be adequately confined to be applicable to he disces of De stars., This analysis is somewhat misleading because the modes may not be adequately confined to be applicable to the discs of Be stars.
 In Fig., In Fig.
 1. we plot. Ai(z) versus ut or p=Nb and p=VSi. choosing ὦ such that Ανρί)=0 abor= |.," \ref{f:knu} we plot $K_\nu(z)$ versus $x$ for $\nu=8\rmi$ and $\nu=\sqrt{8}\rmi$, choosing $\tilde\omega$ such that $K_\nu(z)=0$ at $x=1$ ."
 Only the former case provides an adequately confined mode., Only the former case provides an adequately confined mode.
This shows that the 2DO theory cannot in act produce confined. prograde modes in the absence of a cquacdrupole. even for the most optimistic choice of surface density. profile. because |v] is never large enough.,"This shows that the 2DO theory cannot in fact produce confined prograde modes in the absence of a quadrupole, even for the most optimistic choice of surface density profile, because $|\nu|$ is never large enough."
 However. sulliciently.large imaginary values of v areobtained inthe 3D theory.," However, sufficientlylarge imaginary values of $\nu$ areobtained inthe 3D theory."
 When v is imaginary. confined. solutions are obtained. in principle.when &=25/32 where των is the nth zero of νο) in z 0.," When $\nu$ is imaginary, confined solutions are obtained, in principle,when $\tilde\omega=z_n^2/32$ where $z_{n,\nu}$ is the $n$ th zero of $K_\nu(z)$ in $z>0$ ."
 For example. consider the 3D theory. with ag—2. which is the valueexpected for a steady decretion disc with constant alpha viscosity parameter. far inside its outer radius.," For example, consider the 3D theory with $\sigma=2$, which is the valueexpected for a steady decretion disc with constant alpha viscosity parameter, far inside its outer radius."
 Then s=4 andv= Si. and zeros occur at z= 4.802. 3.067. 2.029. Therefore.in. principle. &=0.720 ," Then $s=4$ and$\nu=8\rmi$ , and zeros occur at $z=4.802$ , $3.067$ , $2.029$ , $\dots$ Therefore,in principle, $\tilde\omega=0.7207$ ,"
"ower thermosphere (S0-100km altitude) due to reactions velween LL"" and Os.",lower thermosphere (80-100km altitude) due to reactions between $^0$ and $_3$.
 The propagation of density and emperature differences through the atmosphere can cause wee variations in both the relative ancl absolute intensity of the ΟΙ lines with periods as short as à few minutes (Aclams Skrutskie 1996)., The propagation of density and temperature differences through the atmosphere can cause large variations in both the relative and absolute intensity of the OH lines with periods as short as a few minutes (Adams Skrutskie 1996).
 In Fig. 3..," In Fig. \ref{OH},"
 we show the temporal dependence of the ΟΙ lines. geocoronalLa. and the skv continuum with respect to local midnight for three consecutive nights.," we show the temporal dependence of the OH lines, geocoronal, and the sky continuum with respect to local midnight for three consecutive nights."
 But the dominant elfect in our 20 min exposures is the increasing average intensity with the zenith angle of the observation (van Rhijn 1921: Ixoncdratvey. 1969)., But the dominant effect in our 20 min exposures is the increasing average intensity with the zenith angle of the observation (van Rhijn 1921; Kondratyev 1969).
 The OLL lines in our bandpass arise from the Py and P» branches and vary in an identical manner., The OH lines in our bandpass arise from the $_1$ and $_2$ branches and vary in an identical manner.
 Osterbrock Alartel (1992) use ΟΙ lines at high spectral resolution to achieve wavelength calibrations to better than but over our bandpass we achieve aat le for the brightest line., Osterbrock Martel (1992) use OH lines at high spectral resolution to achieve wavelength calibrations to better than but over our bandpass we achieve at $\sigma$ for the brightest line.
 There are four discrete components to the rreeion., There are four discrete components to the region.
 In Fig. 3..," In Fig. \ref{OH},"
 the gcocoronal lines reaches a minimum at local midnight and rises exponentially towards dawn., the geocoronal lines reaches a minimum at local midnight and rises exponentially towards dawn.
 Close to twilight or in strong moonlight. Fraunhofer aabsorption is clearly seen in the night sky spectrum.," Close to twilight or in strong moonlight, Fraunhofer absorption is clearly seen in the night sky spectrum."
 This is only apparent in the first few frames of our data on each night and is therefore casily corrected. for., This is only apparent in the first few frames of our data on each night and is therefore easily corrected for.
 There are additional. contributions from the Reynolds laver. and a third. redshifted component due to the high velocity cloud.," There are additional contributions from the Reynolds layer, and a third redshifted component due to the high velocity cloud."
 The absolute variation of the geocoronal comission is extremely well behaved from night to night., The absolute variation of the geocoronal emission is extremely well behaved from night to night.
 We are able to predict the strength of this atmospheric line to better than after the first night., We are able to predict the strength of this atmospheric line to better than after the first night.
 Phe central wavelength was measured at A6562.73 which we could clearly distinguish from the D lamp wavelength A6562.80 at the 36 level (ef., The central wavelength was measured at $\lambda$ 6562.73 which we could clearly distinguish from the D lamp wavelength $\lambda$ 6562.80 at the $\sigma$ level (cf.
 Yelle Roesler 1985)., Yelle Roesler 1985).
 The geocoronal emission arises from. the exosphere at 500 km altituce due to solar exeitation of neutral hydrogen., The geocoronal emission arises from the exosphere at 500 km altitude due to solar $\beta$ excitation of neutral hydrogen.
" Fhis process only excites the 8° Py.547» levels which decay lo 278,ον in contrast to the discharge lamp where all fine structure levels are excited."," This process only excites the $^2$ $_{3/2,1/2}$ levels which decay to $^2$ $_{1/2}$, in contrast to the discharge lamp where all fine structure levels are excited."
 Since galactic emission is seen in all of our cata. it was necessary to difference an observation near twilight with a later observation to measure the central wavelength of the cxospheric contribution.," Since galactic emission is seen in all of our data, it was necessary to difference an observation near twilight with a later observation to measure the central wavelength of the exospheric contribution."
 The radial velocity at. peak intensity of the Revnolds laver aand eemission. using new wavelengths from Spyromilio (1995). provides an independent measurement of the IZarth-Sun motion with respect to the Local Standard of Rest.," The radial velocity at peak intensity of the Reynolds layer and emission, using new wavelengths from Spyromilio (1995), provides an independent measurement of the Earth-Sun motion with respect to the Local Standard of Rest."
 Indeed. ltevnolds (personal communication. 1997) uses this fact to isolate the galactic emission by up to wwith a suitable choice of observing season.," Indeed, Reynolds (personal communication, 1997) uses this fact to isolate the galactic emission by up to with a suitable choice of observing season."
 Apart from extremely precise wavelength: calibration. the geocoronal and Revnolds laver emission (and to some extent. the sky. continuum) are sensitive to the presence of cirrus.," Apart from extremely precise wavelength calibration, the geocoronal and Reynolds layer emission (and to some extent, the sky continuum) are sensitive to the presence of cirrus."
 On the third night (Fig. 3)).," On the third night (Fig. \ref{OH}) ),"
 we stopped observing for, we stopped observing for
rotation velocity is the dominant. component. followed. by non-axisvmuametric and radial components.,"rotation velocity is the dominant component, followed by non-axisymmetric and radial components."
 Phe velocity components perpendicular to the disc are typically the smallest., The velocity components perpendicular to the disc are typically the smallest.
 Altogether. v in Eq.," Altogether, $\textbf{v}$ in Eq."
 1 represents a complex three-dimensional non-axisvmmetrie velocity field. strongly coupled to the global properties of the galaxy. including the dark matter halo. stellar component ancl internal clise activity.," \ref{induktion1} represents a complex three-dimensional non-axisymmetric velocity field strongly coupled to the global properties of the galaxy, including the dark matter halo, stellar component and internal disc activity."
 Deside the large scale components of the gas velocity Leld there are also small scale. velocity Uuctuations of interstellar gas driven by all kinds of local disc activity. ic. stellar winds. supernova explosions. clouc-cloud collisions. ealactic winds. etc (see eg. 2. ?7.. 7T. 2. ?))," Beside the large scale components of the gas velocity field there are also small scale velocity fluctuations of interstellar gas driven by all kinds of local disc activity, i.e. stellar winds, supernova explosions, cloud-cloud collisions, galactic winds, etc (see e.g. \citealp{Ferriere1992}, , \citealp{Efstathiou2000}, \citealp{Johansson&Efstathiou2006}, \citealp{Kulsrud&Zweibel2008}, \citealp{Gressel2008}) )."
 These unordered velocity. components generate two effects. which are known as helicity (in terms of a convective turbulent motion perpencicular to the disc) and turbulent. cillusion (magnetic field. lines with antiparallel direction reconnect and annihilate partially)., These unordered velocity components generate two effects which are known as helicity (in terms of a convective turbulent motion perpendicular to the disc) and turbulent diffusion (magnetic field lines with antiparallel direction reconnect and annihilate partially).
 Lelicity supports the amplification of the magnetic field. whereas turbulent dilfusion reduces the field strength (see. c.g. 2? for a review of nonlinear dynamo theory).," Helicity supports the amplification of the magnetic field, whereas turbulent diffusion reduces the field strength (see, e.g. \citealp{Brandenburg2005} for a review of nonlinear dynamo theory)."
 Therefore. an incorporation of these small scale velocity components into the analysis requires some manipulation of the induction equation. (leq. 1))," Therefore, an incorporation of these small scale velocity components into the analysis requires some manipulation of the induction equation (Eq. \ref{induktion1}) )"
 in terms of a mean-field theory (2... 2.. 2)).," in terms of a mean-field theory \citealp{Steenbeck&Krause1969}, \citealp{Wielebinski&Krause1993}, \citealp{Sur&Shukurov2007}) )."
 Within the frame of the mean-lield description the velocity and magnetic fields are considered: as superpositions of the mean and. Huctuating parts (v=fv|v and B—(B)| B)., Within the frame of the mean-field description the velocity and magnetic fields are considered as superpositions of the mean and fluctuating parts $\textbf{v}=\langle\textbf{v}\rangle+\textbf{v}'$ and $\textbf{B}=\langle\textbf{B}\rangle+\textbf{B}'$ ).
 The lluctuating velocity components are coupled to small-scale Huctuations of the magnetic field., The fluctuating velocity components are coupled to small-scale fluctuations of the magnetic field.
 The coupling terms are then given by Vo αλ. where a=irv(Vv» (003). and by yrALB). where rp now describes the turbulent.o dilfusion. coelTicient οCoufoun. where Chan and fun are the typical velocity and length scale of the turbulent motion. respectively.," The coupling terms are then given by $\nabla\times\alpha\langle\textbf{B}\rangle$ , where $\alpha=\frac{1}{3}\tau\langle\textbf{v}'\cdot(\nabla\times\textbf{v}')\rangle$ \citealp{Zeldovich}) ), and by $\eta_T\Delta \langle\textbf{B}\rangle$, where $\eta_T$ now describes the turbulent diffusion coefficient $\eta_T\propto v_\mathrm{turb}\cdot l_\mathrm{turb}$, where $v_\mathrm{turb}$ and $l_\mathrm{turb}$ are the typical velocity and length scale of the turbulent motion, respectively."
 This leads to the dynamo equation where we have neglected the diffusivity and dropped the mean-brackets for convenience (here. and in the following. D and v refer to their mean values).," This leads to the dynamo equation where we have neglected the diffusivity and dropped the mean-brackets for convenience (here, and in the following, $\textbf{B}$ and $\textbf{v}$ refer to their mean values)."
 Eq., Eq.
 2. is the central equation of cosmic mean field vnanos., \ref{alphadynamo} is the central equation of cosmic mean field dynamos.
 Lt describes the circle. of amplification. of the ilferent components., It describes the circle of amplification of the different components.
" The classical dvnamo nioclel describes 1e amplification of the magnetic field through the following hain of a (convective turbulence) anc © (dillerential rotation) actions: The radial component D, is amplified wough e-action from turbulence: then ds. generated from £2, through O-action from the shear of the galactic illerential rotation.", The classical dynamo model describes the amplification of the magnetic field through the following chain of $\alpha$ (convective turbulence) and $\Omega$ (differential rotation) actions: The radial component $B_r$ is amplified through $\alpha$ -action from turbulence; then $B_\varphi$ is generated from $B_r$ through $\Omega$ -action from the shear of the galactic differential rotation.
 Such an a£ mean Geld dynamo amplifies the magnetic field by repeating the chain of à and 9 actions (sce 7. and ? for à review of dvnamo theory)., Such an $\alpha\Omega$ mean field dynamo amplifies the magnetic field by repeating the chain of $\alpha$ and $\Omega$ actions (see \citealp{Widrow2002} and \citealp{Stefani2008} for a review of dynamo theory).
 However. the origin of the a-elleet is still under discussion (?.. 2.. 2)).," However, the origin of the $\alpha$ -effect is still under discussion \citealp{Cattaneo&Vainshtein1991}, \citealp{Vainshtein&Cattaneo1992}, \citealp{Kulsrud&Anderson1992}) )."
 We emphasize that the ceseribecl classical. cdivinamo models use only one velocity. component. the cüllerentia rotation.," We emphasize that the described classical dynamo models use only one velocity component, the differential rotation."
 To be more precise the role of anv deviation from axisvmmetry is considered to be unimportant for the evolution of the large-scale magnetic field. which is no necessarily true in real galaxies.," To be more precise the role of any deviation from axisymmetry is considered to be unimportant for the evolution of the large-scale magnetic field, which is not necessarily true in real galaxies."
" On this account. there have been three-climensiona numerical simulations using an analytical turbulent velocity Ποια, where deviations [roni axisvnimetry. were WCoLrporalce in the gas- and turbulenee-proliles (2... 23)."," On this account, there have been three-dimensional numerical simulations using an analytical turbulent velocity field, where deviations from axisymmetry were incorporated in the gas- and turbulence-profiles \citealp{Rohde&Elstner&Rudiger1997}, \citealp{Rohde&Elstner1998}) )."
 These studies showed. that even accounting for the a-cllect caleulatec out of the analvtical velocity field an initial magnetic fiel cannot survive for more than 500 Myr.," These studies showed, that even accounting for the $\alpha$ -effect calculated out of the analytical velocity field an initial magnetic field cannot survive for more than 500 Myr."
 Aloreover. 2? performed N--body. simulations. of. two component (collisionless stars and. gaseous. clouds moving in the gravitational potential of the stellar population). eravitating discs embedded in an analytical bulge- ancl halo-potential.," Moreover, \citealp{Elstner&Otmianowska-Mazur2000} performed -body simulations of two component (collisionless stars and gaseous clouds moving in the gravitational potential of the stellar population), self-gravitating discs embedded in an analytical bulge- and halo-potential."
 Phese simulated. clouds provided an already very good approximation of the gas velocity field., These simulated clouds provided an already very good approximation of the gas velocity field.
 However. full ivcirodynamies was not incorporated.," However, full hydrodynamics was not incorporated."
 Ehe obtained velocity ied. was used in an aO-dvnamo description., The obtained velocity field was used in an $\alpha\Omega$ -dynamo description.
 Without including the a-elfect. the non-azimuthal 3D. gas Dow alone did not provide an amplification of the magnetic field.," Without including the $\alpha$ -effect, the non-azimuthal 3D gas flow alone did not provide an amplification of the magnetic field."
 The 101 got amplified by several orders of magnitude within 0.7 Alvr only when the a-ellect was incluced., The field got amplified by several orders of magnitude within 0.7 Myr only when the $\alpha$ -effect was included.
 In addition. they ound an alignment of the magnetic field with the developed spiral pattern of the disc.," In addition, they found an alignment of the magnetic field with the developed spiral pattern of the disc."
 Recently. ο performed three dimensional. full ATID. single and two-component (cold. and hot gas) simulations using smooth particle hyelrodynamic (SPI) methods. to reat MIID.," Recently, \citet{Dobbs&Price2008} performed three dimensional, full MHD, single and two-component (cold and hot gas) simulations using smooth particle hydrodynamic (SPH) methods to treat MHD."
 They applied. a spiral potential to the gas. hus. the self-induced formation of spiral structure was not included.," They applied a spiral potential to the gas, thus, the self-induced formation of spiral structure was not included."
 Their work concentrated on structure formation in the clise. like molecular clouds and inter-arm spurs.," Their work concentrated on structure formation in the disc, like molecular clouds and inter-arm spurs."
 They ound that the main ellect of adding a magnetic field. to hese calculations was to inhibit the formation of structure in the disc., They found that the main effect of adding a magnetic field to these calculations was to inhibit the formation of structure in the disc.
 They did not consider globalenhancement. and structure formation of the magnetic field. but nevertheless. hey found that the global magnetic field was following the arge scale velocity Lele.," They did not consider globalenhancement and structure formation of the magnetic field, but nevertheless, they found that the global magnetic field was following the large scale velocity field."
 ltis the aim of this paper to present further steps owards a more complete dvnamo model., Itis the aim of this paper to present further steps towards a more complete dynamo model.
 We perform. for, We perform for
The discovery in recent vears of many isolated neutron stars (NSs) at the centers of supernova renmauts (SNRs) confirms the long-held notion that these ultra-cdense stellar remmauts are born im supernova explosions(Baace&Zwickv 1931).,The discovery in recent years of many isolated neutron stars (NSs) at the centers of supernova remnants (SNRs) confirms the long-held notion that these ultra-dense stellar remnants are born in supernova explosions\citep{bad34}.
. Most. of these NSs are identified as pulsus. whose enüssion derives either from rotational energv loss. as for the rapidly spinning pulsars in the Crab (P=33 ms) aud Vela (2?=89 mis) roimnauts. or from mmaeuctic feld decay. as posited for the slower (b«Pzx12 s) anomalous N-vav pulsars (ANDPs) and related objects (see Mereghetti 2000 for a review).," Most of these NSs are identified as pulsars, whose emission derives either from rotational energy loss, as for the rapidly spinning pulsars in the Crab $P = 33$ ms) and Vela $P = 89$ ms) remnants, or from magnetic field decay, as posited for the slower $5 < P \leq 12$ s) anomalous X-ray pulsars (AXPs) and related objects (see Mereghetti 2000 for a review)."
 However. the nature of a small but erowiug collection of voung (<105 ves} NSs in SNRs remains a mivstery.," However, the nature of a small but growing collection of young $\simlt 10^4$ yrs) NSs in SNRs remains a mystery."
 These so-called Compact Coutral Objects (CCOs) are ποσο] isolated NSs. distinguished. by their steady flux. predominantly thermal cussion. lack of optical or radio counterparts. and absence of a surrounding pulsar wind nebula (see Pavlov.Sauwal.&Teter2001. for a review}.," These so-called Compact Central Objects (CCOs) are seemingly isolated NSs, distinguished by their steady flux, predominantly thermal emission, lack of optical or radio counterparts, and absence of a surrounding pulsar wind nebula (see \citealt*{pav04}
 for a review)."
 The six fiui examples of CCOs are the central X-ray sources discovered in Cas A (Tananbauim 1999).. Pup A (Petre.Becker.&Winkler1982).. 0.5 (Slaneetal. 1999).. PISS 120951/52 (Ielfaud&Becker198L).. (1266.21.2 (Slaneetal.2001)... aud I&es το103).," The six firm examples of CCOs are the central X-ray sources discovered in Cas A \citep{tan99}, Pup A \citep*{pet82}, $-$ 0.5 \citep{sla99}, PKS 1209–51/52 \citep{hel84}, G266.2–1.2 \citep{sla01}, and Kes 79."
". Their huuinosities range over 1075<<L,c105! cre typical of the vounger pulsars: iowever their spectra are best characterized as hot blackbody emission of Απο~OLkeV. rather than by power-law models."," Their luminosities range over $10^{33} \simlt L_{x} \simlt 10^{34}$ erg $^{-1}$, typical of the younger pulsars; however their spectra are best characterized as hot blackbody emission of $kT_{\rm BB} \sim 0.4$keV, rather than by power-law models."
 This is sóiguificaulv hotter than radio pusuw or other radio-quiet NSs (RONSs:e.g.àYC'araveo.Bignamu.&παρα 1996)..1xt similar to the thermal component of the more Iunos ANPs/SCRs.," This is significantly hotter than radio pulsars or other radio-quiet NSs \citep*[RQNSs; e.g.,][]{car96}, but similar to the thermal component of the more luminous AXPs/SGRs."
 Distinct from the rest. PSR J12105226 in PINS 120951/52 is a121 nis pulsar (Zavlinetal.2000). that cisplavs large deviations in its spin-down rate. a softer spectrum of 1ο=0.22 keV. and evelotrou resonance lines(Samwaletal.2002:Pavlovvin.Pavlov.&Saval 2001).," Distinct from the rest, PSR J1210–5226 in PKS 1209–51/52 is a$424$ ms pulsar \citep{zav00} that displays large deviations in its spin-down rate, a softer spectrum of $kT_{\rm BB} = 0.22$ keV, and cyclotron resonance lines\citep*{san02,pav02,mer02,big03,zav04}."
. These properties suggest that PSR J12105226 is variously awide-binary svsteni. a strongly elitching NS. or au accretor frou fall-hacls material (Zavliuctal. 2001)..," These properties suggest that PSR J1210–5226 is variously awide-binary system, a strongly glitching NS, or an accretor from fall-back material \citep{zav04}. ."
 is the recentlediscovered C'CO in supernova τοι! I&es το | O.1: Sewardetal. 20033)., is the recentlydiscovered CCO in supernova remnant Kes 79 $+$ 0.1; \citealt{sew03}) ).
 The distauce to this unresolved ssource is estimated as Todo kpe.derived from ," The distance to this unresolved source is estimated as $7.1$ kpc,derived from \citep{fra89,gre92} "
the dynamics of the expanding cosmos.,the dynamics of the expanding cosmos.
" This metric was first rigorously derived in the 1930's by Robertson (1935) and (independently) Walker (1936), using the ideas espoused earlier by Weyl."," This metric was first rigorously derived in the 1930's by Robertson (1935) and (independently) Walker (1936), using the ideas espoused earlier by Weyl."
 It is therefore clear that any proper distance in this spacetime is measured on a spacelike hypersurface in the foliated sequence orthogonal to the non-intersecting geodesics., It is therefore clear that any proper distance in this spacetime is measured on a spacelike hypersurface in the foliated sequence orthogonal to the non-intersecting geodesics.
 We have shown in 23 above that the Hubble radius is itself the distance Αι., We have shown in 3 above that the Hubble radius is itself the distance $R_{\rm h}$.
" But according to the definition of Ry in terms of Vy, in Equation (8). Ry must itself be a proper distance with the property that rj is a constant comoving coordinate, otherwise Vy, would not represent the volume within which the particle density is constant in the comoving frame."," But according to the definition of $R_{\rm h}$ in terms of $V_{\rm prop}$ in Equation (8), $R_{\rm h}$ must itself be a proper distance with the property that $r_{\rm h}$ is a constant comoving coordinate, otherwise $V_{\rm prop}$ would not represent the volume within which the particle density is constant in the comoving frame."
 Comparing Equations (11) and (13). wetherefore see that which means that é itself must be constant for consistency with the Weyl postulate.," Comparing Equations (11) and (13), wetherefore see that which means that $\dot{a}$ itself must be constant for consistency with the Weyl postulate."
" This is the most important consequence of our definition of Ay in Equation (8).From Equation (4), we infer that the acceleration @ 1s zero either for an empty universe (in which p= 0) or one characterized by an equation of state ie=—1/3 (refer to the Appendix for some additional insight into why these two conditions are actually related)."," This is the most important consequence of our definition of $R_{\rm h}$ in Equation (8).From Equation (4), we infer that the acceleration $\ddot{a}$ is zero either for an empty universe (in which $\rho=p=0$ ) or one characterized by an equation of state $w=-1/3$ (refer to the Appendix for some additional insight into why these two conditions are actually related)."
" And it istrivial to see from Equation (11) that for all cosmic times f, not just the current value %."," And it istrivial to see from Equation (11) that for all cosmic times $t$, not just the current value $t_0$."
" Within the framework of our proposal, one may then understand why today we ""measure"" Ry(t)) to be equal to cfy (within the observational errors), because in a flat universe (A= 0) consistent with the Weyl postulate and the Cosmological Principle. these two quantities must always be equal."," Within the framework of our proposal, one may then understand why today we “measure"" $R_{\rm h}(t_0)$ to be equal to $ct_0$ (within the observational errors), because in a flat universe $k=0$ ) consistent with the Weyl postulate and the Cosmological Principle, these two quantities must always be equal."
 Let us now see how this result impacts the standard model of cosmology., Let us now see how this result impacts the standard model of cosmology.
" We suppose that where, following convention, we designate the matter, radiation, and dark energy densities, respectively, as og.p;. and Pye."," We suppose that where, following convention, we designate the matter, radiation, and dark energy densities, respectively, as $\rho_{\rm m}$,$\rho_{\rm r}$, and $\rho_{\rm de}$."
" We will also assume that these energy densities scale according to py «a. p,e« a. and py.e. fla). ("," We will also assume that these energy densities scale according to $\rho_{\rm m}\propto a^{-3}$ , $\rho_{\rm r}\propto a^{-4}$ , and $\rho_{\rm de}\propto f(a)$ . ("
Of dark energy is indeed a cosmological constant A. then,If dark energy is indeed a cosmological constant $\Lambda$ then
is nol in isolation. ancl therefore not necessarily expected to reproduce such a low spin parameter.,"is not in isolation, and therefore not necessarily expected to reproduce such a low spin parameter."
 Also. the internal rotation axis changes al 5 kpe are not easily explained with only the monolithic collapse scenario.," Also, the internal rotation axis changes at 5 kpc are not easily explained with only the monolithic collapse scenario."
 In the monolithic collapse model. the inner regions would be expected to have more pronounced rotations.," In the monolithic collapse model, the inner regions would be expected to have more pronounced rotations."
 Yet all four of the galaxies with major kinematic studies presented here do not show a higher rotational signal in (he inner regions., Yet all four of the galaxies with major kinematic studies presented here do not show a higher rotational signal in the inner regions.
 In fact. for NGC 1399. the outer region (22>6) indicates rotation in the metal-poor population that is not evident in the inner regions.," In fact, for NGC 1399, the outer region $R > 6'$ ) indicates rotation in the metal-poor population that is not evident in the inner regions."
 Also. a slightly lower rotational signal is present in the inner regions of NGC 5128 for the metal-poor population (han in (he outer regions.," Also, a slightly lower rotational signal is present in the inner regions of NGC 5128 for the metal-poor population than in the outer regions."
 llierarchical clustering5 of cold dark matter also relies on angular5 momentum in a 5galaxy being5 produced by 5gravitational tidal torques curing5 the 5growth of initial perturbations., Hierarchical clustering of cold dark matter also relies on angular momentum in a galaxy being produced by gravitational tidal torques during the growth of initial perturbations.
 Sugerman.Summers.&loanmionkowski(2000) have demonstrated (hat the tidal torque theory predicts an increase in angular momentum during the collapse. aud with time. the increase in angular momentum slows.," \cite{sugerman00} have demonstrated that the tidal torque theory predicts an increase in angular momentum during the collapse, and with time, the increase in angular momentum slows."
 Accretion οἱ satellites and/or merger events is therefore a possible culprit for moving the angular momentum outward. as major mergers of disks ancl bulges suggest that angular momentum resides largely in the outer regions of the galaxy (Barnes1992:IIerneuist.1993).," Accretion of satellites and/or merger events is therefore a possible culprit for moving the angular momentum outward, as major mergers of disks and bulges suggest that angular momentum resides largely in the outer regions of the galaxy \citep{barnes92,hernquist93}."
. Alternatively. Vitvitskaetal.(2002) examine the change in spin parameter in a scenario where the angular momentum in a galaxy is built up by mass accretion.," Alternatively, \cite{vitvitska02} examine the change in spin parameter in a scenario where the angular momentum in a galaxy is built up by mass accretion."
 Their results show that (he spin parameter changes sharply in major merger events in (he galaxy. and steadily decreases with small satellite accretion events., Their results show that the spin parameter changes sharply in major merger events in the galaxy and steadily decreases with small satellite accretion events.
 Thev also show that the spin parameter for a ealaxv with a major merger alter a redshift of z=3 should be notably larger than a galaxy that did not undergo such a major merger., They also show that the spin parameter for a galaxy with a major merger after a redshift of $z = 3$ should be notably larger than a galaxy that did not undergo such a major merger.
" Their study obtains an average of A=0.045 [rom ACDM N-bodwv simulations for galaxies with halo masses of (1.1—1.5)x1075.! M, with =0.7.", Their study obtains an average of $\Lambda = 0.045$ from $\Lambda$ CDM $N$ -body simulations for galaxies with halo masses of $(1.1-1.5) \times 10^{12} h^{-1}$ $M_{\odot}$ with $h = 0.7$.
 NGC 1399 and MAO9. with their weak rotation signals. are consistent with the model predictions discussed above. whereby (heir major formation events could have occurred al early Gimes and with perhaps only minor accretions happening since then.," NGC 1399 and M49, with their weak rotation signals, are consistent with the model predictions discussed above, whereby their major formation events could have occurred at early times and with perhaps only minor accretions happening since then."
" However. NGC 5128 and M87 have spin parameters 2-9 limes larger (han predicted by (he model averages,"," However, NGC 5128 and M87 have spin parameters 2-3 times larger than predicted by the model averages."
 For NGC 5128. this relatively large rotation (which is nearly independent of both metalliity ancl radius) may. perhaps. be connected with ils history within the Centaurus eroup environment.," For NGC 5128, this relatively large rotation (which is nearly independent of both metallicity and radius) may, perhaps, be connected with its history within the Centaurus group environment."
 The rotation speed aud rotation axis lor ils extended eroup of satellite ealaxies are nearly identical to the NGC 5128 halo (Woocley2006).. much as if the accretion evenis experienced by (he central giant have been taking place preferentially along (he main axis of (he entire group and in the same orientation.," The rotation speed and rotation axis for its extended group of satellite galaxies are nearly identical to the NGC 5128 halo \citep{w06}, much as if the accretion events experienced by the central giant have been taking place preferentially along the main axis of the entire group and in the same orientation."
 The GCS age distribution discussed by Beasleyetal.(2006) and the mean age [or the halo field stars (Rejkubaetal.2005) strongly, The GCS age distribution discussed by \cite{beasley06} and the mean age for the halo field stars \citep{rejkuba05} strongly
and 3342 to UV dominated chemistry in 882.,and 342 to UV dominated chemistry in 82.
 The extremely low LINCO abundance in M3852 and the large abundances of HCO. and support the idea that the IINCO/CS ratio is a measure of the relative importance of the UV heating to shock heating and the evolutionary state of the starburst in galaxies.," The extremely low HNCO abundance in 82 and the large abundances of HCO, $^+$ and $^+$ support the idea that the HNCO/CS ratio is a measure of the relative importance of the UV heating to shock heating and the evolutionary state of the starburst in galaxies."
 The detection of HCO. and in NGC?53 with similar column densities and abundance to those in M82 suggest that the PDR. component is similar in both galaxies as suggested by the similar atomic fine structure line intensities in both galaxies.," The detection of HCO, $^+$ and $^+$ in NGC253 with similar column densities and abundance to those in M82 suggest that the PDR component is similar in both galaxies as suggested by the similar atomic fine structure line intensities in both galaxies."
 The results of model B confirm the observational trends observed in IENCO and the other PDR. molecules in galaxies., The results of model B confirm the observational trends observed in HNCO and the other PDR molecules in galaxies.
" For molecular clouds with 4A,~1—2 (i.e column densities of 1—2x10?!em7) illuminated bv a strong UV radiation field like in the galaxies in our sample. IENCÓO and CIL;OIL are largely photocdissociated and only HCO. and should be observed like in M82 (Martínetal.2006a.2009)."," For molecular clouds with $A_{\rm v}\sim1-2$ (i.e column densities of $1-2\times 10^{21}\rm cm^{-2}$ ) illuminated by a strong UV radiation field like in the galaxies in our sample, HNCO and $_3$ OH are largely photodissociated and only HCO, $^+$ and $^+$ should be observed like in M82 \citep{Martin06a,Martin09}."
. Then. not verv massive molecular elouds aud widelv translucent to the UV. radiation should dominate in 332.," Then, not very massive molecular clouds and widely translucent to the UV radiation should dominate in 82."
 On the other hand. for ealaxies with massive molecular clouds (large visual extinction) or low UV radiation fields. IINCO and CIIOIL are well shielded and (the abundance ratio of IENCO/CS will reach its maximum value.," On the other hand, for galaxies with massive molecular clouds (large visual extinction) or low UV radiation fields, HNCO and $_3$ OH are well shielded and the abundance ratio of HNCO/CS will reach its maximum value."
 Considering (hat 882 and 3342 represent (he stage of galaxies with an extremely low PDR component. the lower INCO/CS ratios measured for 2253. 44945 and 11068 indicate that the PDR component must be substantial. as observed in other PDR. tracers.," Considering that 83 and 342 represent the stage of galaxies with an extremely low PDR component, the lower HNCO/CS ratios measured for 253, 4945 and 1068 indicate that the PDR component must be substantial, as observed in other PDR tracers."
 For 2253 we find that the PDR component is similar to that in M82. but the total column density of dense gas is a [actor of 2-3 larger in 2252 than in M882 from the ow LINCO and CILOII abundance in the latter.," For 253 we find that the PDR component is similar to that in M82, but the total column density of dense gas is a factor of 2-3 larger in 253 than in 82 from the low HNCO and $_3$ OH abundance in the latter."
 Considering the PDR. column densities in boll galaxies are similar. (his component should represent about. 1/3—1/2 of the total nolecular column density in NGC2523.," Considering the PDR column densities in both galaxies are similar, this component should represent about $1/3-1/2$ of the total molecular column density in NGC253."
 This is roughly consistent with the decrease by a actor of 2—3 of the INCO/CS ratio as compared with that of 883 or 13342, This is roughly consistent with the decrease by a factor of $2-3$ of the HNCO/CS ratio as compared with that of 83 or 342
"to pup(OV/X, ds (0.1026x49.32)/(0.001449.87)=1.100. and for the Row 3 model. the ratio of p(0)/X3 to pic(0)/X3, pis (0.2596x49.32)/(0.001483.97)=0.981.","to $\rho_{HF}(0)/\Sigma_{HF}^2$ is $(0.1026\times 49.3^2)/(0.0914\times 49.8^2)=1.100$, and for the Row 3 model, the ratio of $\rho_{3}(0)/\Sigma_{3}^2$ to $\rho_{HF}(0)/\Sigma_{HF}^2$ is $(0.2596\times 49.3^2)/(0.0914\times 83.9^2)=0.981$."
 IL 6? does not change betweenthe ΠΕ and. BEG models. 2y=1.79 and Ry=1.60.," If $\sigma^2$ does not change betweenthe HF and BFG models, $R_1= 1.79$ and $R_3=1.60$."
 Like jj=1.63. Ry and 2 are incompatible with 2=Qs1/2.," Like $R_{HF}= 1.63$, $R_1$ and $R_3$ are incompatible with $R=Q\approx 1/2$."
/ A Poisson-Boltzmann solution is feasible only if 27+WV=0. but this requirement is incompatible with observations: compelling a steady state solution is lanmlamounl {ο compelling (he existence of DAI or non-Newtonian gravity.," A Poisson-Boltzmann solution is feasible only if $2T+V=0$, but this requirement is incompatible with observations; compelling a steady state solution is tantamount to compelling the existence of DM or non-Newtonian gravity."
 Suppose instead that a disk columns vertical profile varies periodically with time., Suppose instead that a disk column's vertical profile varies periodically with time.
 Then 27+ oscillates about 0. so that at anv epoch. 27—V. could be substantially greater or less than zero.," Then $2T+V$ oscillates about $\overline{2T+V}=0$ , so that at any epoch, $2T+V$ could be substantially greater or less than zero."
 In other words. H oscillates about Q.," In other words, $R$ oscillates about $Q$."
 We use this broadened aspect to interpret the HIE. data. and uncover interesting possible ramifications.," We use this broadened aspect to interpret the HF data, and uncover interesting possible ramifications."
 The analvsis so [ar has been quantitative. but [rom here on it will be descriptive audspeculative - aud accordingly less clelensible.," The analysis so far has been quantitative, but from here on it will be descriptive andspeculative - and accordingly less defensible."
" Using dimensional analvsis. we reckon that the > oscillation period is of the order [Gp(0)]""?=50 million vears."," Using dimensional analysis, we reckon that the $z$ oscillation period is of the order $[G\rho(0)]^{-1/2} = 50$ million years."
 The estimated period is roughly a euarter of a galactic vear. but this estimate is inexact because il is based on dimensional considerations only.," The estimated period is roughly a quarter of a galactic year, but this estimate is inexact because it is based on dimensional considerations only."
 It would have been larger if we had used (he mean midplane clensily p over one cevcle instead of the current midplane densitv (which we believe to be near (he maximum value). and there undoubtedly are dimensionless factors that would arise in a precise analvsis. decreasing the estimated period by as much as a [actor of 10. but increasing it no more than [ourfold. (each disk star orbiting the galactic center has a retrograde precession caused by (he other disk stars. so (he z oscillation period must be less than the orbital period).," It would have been larger if we had used the mean midplane density $\overline{\rho(0)}$ over one cycle instead of the current midplane density (which we believe to be near the maximum value), and there undoubtedly are dimensionless factors that would arise in a precise analysis, decreasing the estimated period by as much as a factor of 10, but increasing it no more than fourfold (each disk star orbiting the galactic center has a retrograde precession caused by the other disk stars, so the $z$ oscillation period must be less than the orbital period)."
 What we find puzzling about the stellar orbits is the cause of the svmnieltrie clustering of their ascending and clescencding nodes., What we find puzzling about the stellar orbits is the cause of the symmetric clustering of their ascending and descending nodes.
 Disk column oscillations are exchanges between gravitational. V.x—X'/p(0). and kinetic.. Tx4L7Xo. energy. surfaceB densities.," Disk column oscillations are exchanges between gravitational, $V\propto -\Sigma^3/\rho(0)$, and kinetic, $T\propto \Sigma\sigma^2$, energy surface densities."
. Since. X4 does not vary with. (ime.. oscillations. in p(0) entail oscillations in στ and the p(0) and c? variations are in phase. so that the peaks in midplane mass and kinetic energv densities coincide.," Since $\Sigma$ does not vary with time, oscillations in $\rho(0)$ entail oscillations in $\sigma^2$; and the $\rho(0)$ and $\sigma^2$ variations are in phase, so that the peaks in midplane mass and kinetic energy densities coincide."
 Eq., Eq.
 27. tells us that at the current oscillation phase p(0)o? is about three times higher than its mean value. but it does not tell us how close p(0)o? is (o ils peak value.," \ref{numeq} tells us that at the current oscillation phase $\rho(0)\sigma^2$ is about three times higher than its mean value, but it does not tell us how close $\rho(0)\sigma^2$ is to its peak value."
 Al the peak. there would be no net flow of stars Lowarel or away [rom the midplane.," At the peak, there would be no net flow of stars toward or away from the midplane."
 Unaavare of any evidence for such a flow. we suppose that p(0)o? is close to its peak. and corroborate this with data fom Table À.1 of .. selecting single giants (* tag in Column 24) in the background (g=3 in Column 334) that are in the two zones defined by 100<150 pe.," Unaware of any evidence for such a flow, we suppose that $\rho(0)\sigma^2$ is close to its peak, and corroborate this with data from Table A.1 of \citet{Fetal:05}, , selecting single giants (* tag in Column 24) in the $g=3$ in Column 34) that are in the two zones defined by $100 \le |z|\le 150$ pc."
 There are 467 stars in, There are 467 stars in
mass halos which significantly boost the local potential field. causing satellites to fall into low-mass halos faster than their virial velocity (seealsoFig.8in?.onhowmass.separation.andenvironmentallecthalo mergers).,"mass halos which significantly boost the local potential field, causing satellites to fall into low-mass halos faster than their virial velocity \citep[see also Fig.~8 in][on how mass, separation, and environment affect halo mergers]{WetSchHol08}."
 To highlight the significance of these mass dependencies with respect to the overall orbital distributions. the inset panels of Figs.," To highlight the significance of these mass dependencies with respect to the overall orbital distributions, the inset panels of Figs."
 4 and 5. show the same as the main panels. but the dashed. curves indicate the full cistribution width (stancare deviation).," \ref{fig:circ_rperi_mhost} and \ref{fig:vt_vr_vtot_mhost} show the same as the main panels, but the dashed curves indicate the full distribution width (standard deviation)."
 While mass dependence is significant in each case. note that the mean/median changes by at most one standard deviation across the mass range probed here.," While mass dependence is significant in each case, note that the mean/median changes by at most one standard deviation across the mass range probed here."
 While the above results demonstrate. that satellite orbital parameters depend. on host halo mass. Fig.," While the above results demonstrate that satellite orbital parameters depend on host halo mass, Fig."
 6 explores whether circularity and pericenter cdepencl on satellite halo mass. for host halos of fixed. mass 103275FAL.," \ref{fig:circ_rperi_msat} explores whether circularity and pericenter depend on satellite halo mass, for host halos of fixed mass $10^{14-15}\hmsol$."
 While Fig., While Fig.
 6 suggests a possible drop in circularity. ancl pericenter for very massive satellites. the large scatter across satellite halo mass does not lead to any clear. systematic trends.," \ref{fig:circ_rperi_msat} suggests a possible drop in circularity and pericenter for very massive satellites, the large scatter across satellite halo mass does not lead to any clear, systematic trends."
 Moreover. we found no clear trends with satellite mass for orbital parameters. including varving host halo mass or redshift.," Moreover, we found no clear trends with satellite mass for orbital parameters, including varying host halo mass or redshift."
 Thus. we conclude that the nature of satellite infall is controlled bv host halo mass and is little affected by satellite mass.," Thus, we conclude that the nature of satellite infall is controlled by host halo mass and is little affected by satellite mass."
 This supports the physical. picture that orbital cvnamics are governed by the most massive halo within a region. and that less massive satellites effectively act as massless tracers of the potential Ποια.," This supports the physical picture that orbital dynamics are governed by the most massive halo within a region, and that less massive satellites effectively act as massless tracers of the potential field."
 We now turn to explore the dependence of satellite orbital parameters on redshift., We now turn to explore the dependence of satellite orbital parameters on redshift.
 Since the halo mass function declines significantly with redshift. examining the mergers ofall halos above the resolution limit (71027fh FAL.) would convolve any redshift dependence together with the mass dependence of the previous section.," Since the halo mass function declines significantly with redshift, examining the mergers of all halos above the resolution limit $>10^{10}\hmsol$ ) would convolve any redshift dependence together with the mass dependence of the previous section."
" So to isolate redshift) trends. we examined halos in a fixed mass range: host. halos of mass yoreπαtA, (corresponding to M; halos at z= 0) and satellite halos of mass 10)Hf.+AL."," So to isolate redshift trends, we examined halos in a fixed mass range: host halos of mass $10^{12.0-12.5}\hmsol$ (corresponding to $M_*$ halos at $z=0$ ) and satellite halos of mass $10^{10-11}\hmsol$."
 Figure 7 shows the distribution. of circularity and pericenter at. three redshifts., Figure \ref{fig:circ_rperi_dist_evol} shows the distribution of circularity and pericenter at three redshifts.
 Similar to the dependence on host halo mass in Fig. 3.," Similar to the dependence on host halo mass in Fig. \ref{fig:circ_rperi_dist_mhost},"
 the distributions are skewed to both lower circularity and. lower pericenter at higher redshift., the distributions are skewed to both lower circularity and lower pericenter at higher redshift.
 Figure S demonstrates more explicitly the dependence of average circularity and median pericenter on redshift., Figure \ref{fig:circ_rperi_evol} demonstrates more explicitly the dependence of average circularity and median pericenter on redshift.
 Average circularity falls nearly 30% from z=0 to 5. while pericenter falls more rapidly to less than half of its 2cO0 value.," Average circularity falls nearly $30\%$ from $z=0$ to $5$, while pericenter falls more rapidly to less than half of its $z=0$ value."
 Overall. satellite orbits become more racial and plunge deeper into their host halos with increasing recdshift.," Overall, satellite orbits become more radial and plunge deeper into their host halos with increasing redshift."
 ligue 9 also shows the redshift evolution of satellite velocities., Figure \ref{fig:vt_vr_vtot_evol} also shows the redshift evolution of satellite velocities.
 Tangential velocity declines with recshilt. implying that satellite accretion less cliciently contributes angular momentum growth at higher redshift.," Tangential velocity declines with redshift, implying that satellite accretion less efficiently contributes angular momentum growth at higher redshift."
 Conversely. racial velocity increases with redshift. approaching the hos halo virial value at z5.," Conversely, radial velocity increases with redshift, approaching the host halo virial value at $z\approx5$."
 Interestingly. the contrasting evolutionary trends of racial ancl tangential velocity [ea to no significant evolution in satellite total velocity. which at all redshifts remains “hotter than the host halo viria velocity.," Interestingly, the contrasting evolutionary trends of radial and tangential velocity lead to no significant evolution in satellite total velocity, which at all redshifts remains `hotter' than the host halo virial velocity."
 Note that the widths of the total distributions clo not evolve significantly with redshift. retaining stanclare," Note that the widths of the total distributions do not evolve significantly with redshift, retaining standard"
We have shown that pressure confined clouds at any sub-Keplerian rotational velocity may exist in stable dynamical equilibrium in the BLR.,We have shown that pressure confined clouds at any sub-Keplerian rotational velocity may exist in stable dynamical equilibrium in the BLR.
" Given the significant evidence for a gravitationally bound, flattened, but still of considerable thickness, and disk-like geometry for the BLR (compare sect. ??)),"," Given the significant evidence for a gravitationally bound, flattened, but still of considerable thickness, and disk-like geometry for the BLR (compare sect. \ref{intro}) ),"
 it is reasonable to require a stable dynamical equilibrium for the line-emitting clouds., it is reasonable to require a stable dynamical equilibrium for the line-emitting clouds.
" An essential ingredient for the model is the behaviour of the pressure of the inter-cloud material with radius: A reasonable assumption for the inter-cloud component is an Advection Dominated Accretion Flow (ADAF, e.g. ? ?;; ? 2))."," An essential ingredient for the model is the behaviour of the pressure of the inter-cloud material with radius: A reasonable assumption for the inter-cloud component is an Advection Dominated Accretion Flow (ADAF, e.g. \citeauthor{NY94}
 \citeyear{NY94}; \citeauthor*{YMN08} \citeyear{YMN08}) )."
 A nearly hydrostatic solution is included in the ADAF models for the limit of low accretion rates., A nearly hydrostatic solution is included in the ADAF models for the limit of low accretion rates.
" For this type of solutions, the power law index for the pressure s is between two and three."," For this type of solutions, the power law index for the pressure $s$ is between two and three."
 Outflow solutions have also been considered in the literature., Outflow solutions have also been considered in the literature.
 ? find 1«s1.5., \citet{KK94} find $1<s<1.5$.
" Therefore, s should be between one and three (similar results are obtained by ? 2)."," Therefore, $s$ should be between one and three (similar results are obtained by \citeauthor*{RNF89} \citeyear{RNF89}) )."
 We have considered an isotropic and an anisotropic light source as appropriate for an accretion disk., We have considered an isotropic and an anisotropic light source as appropriate for an accretion disk.
 The former is usually implied in the literature., The former is usually implied in the literature.
" For the isotropic case, the force is central (i.e. conserves angular momentum) and conservative."," For the isotropic case, the force is central (i.e. conserves angular momentum) and conservative."
" We find an equilibrium relation between column density, luminosity of the AGN and rotational velocity."," We find an equilibrium relation between column density, luminosity of the AGN and rotational velocity."
" We show by direct stability analysis that only the part of that relation with high rotational velocities However, by analysis of the effective potential, we show that stable"," We show by direct stability analysis that only the part of that relation with high rotational velocities However, by analysis of the effective potential, we show that stable"
absolute intensities of the well-matchecl lines approaches that of the spectral Uuxine precision (Section 2). with even higher accuracy for relative intensities within a single-band spectrum.,"absolute intensities of the well-matched lines approaches that of the spectral fluxing precision (Section 2), with even higher accuracy for relative intensities within a single-band spectrum."
 However. in many cases the matching is more approximate with consequently. poorer line intensity accuracy.," However, in many cases the matching is more approximate with consequently poorer line intensity accuracy."
 This tends to be an increasing problem at [ater epochs., This tends to be an increasing problem at later epochs.
 Jo assess the precision of a line intensity. given in Table 1 or 2. the reader is advised to examine the quality of the model matches in the spectral plots (Figs. 25).," To assess the precision of a line intensity given in Table 1 or 2, the reader is advised to examine the quality of the model matches in the spectral plots (Figs. 2--5)."
 Model matches were carried out only up to day 2112., Model matches were carried out only up to day 2112.
 The spectra for cays 2952 anc 3158 were judged to be of too low resolution anc S/N to provide useful. constraints on the model parameters., The spectra for days 2952 and 3158 were judged to be of too low resolution and S/N to provide useful constraints on the model parameters.
 We therefore. simply present these spectra. in Figure 6. compared with the final echelle spectrum taken on day 2112.," We therefore simply present these spectra, in Figure 6, compared with the final echelle spectrum taken on day 2112."
 For the epochs covered. by the echelle spectra (days 14692112). the most prominent ejecta emission features included IE E (Pass. Pas. Bre). Hoe LE 1.08. 2.06 yam. Na Lb 1.14. 2.21. 2.34 pm. Si IH] L.61. 1.65 pam. Fe E] L44. L98 jm and Fe LH] 1.26. L.64. 2.05 pm. S 1] LOS. 1.13. yam may also be present. but strong blending with other lines renders this identification less positive.," For the epochs covered by the echelle spectra (days 1469--2112), the most prominent ejecta emission features included H I $\beta$ , $\gamma$, $\gamma$ ), He I 1.08, 2.06 $\mu$ m, Na I 1.14, 2.21, 2.34 $\mu$ m, [Si I] 1.61, 1.65 $\mu$ m, [Fe I] 1.44, 1.98 $\mu$ m and [Fe II] 1.26, 1.64, 2.05 $\mu$ m. [S I] 1.08, 1.13 $\mu$ m may also be present, but strong blending with other lines renders this identification less positive."
 Phere were also regions of emission for which we were unable to find. plausible identifications., There were also regions of emission for which we were unable to find plausible identifications.
 Phese were at 0.920.95. 1.03.1.05. 1.17.1.21 and 2.242.32 pam. The 1.03.1.05 pam feature may be caused xutlv by NL} L04. jam. However. the width ancl shape of the feature indicates that there must be contributions rom other species.," These were at 0.92–0.95, 1.03–1.05, 1.17–1.21 and 2.24–2.32 $\mu$ m. The 1.03–1.05 $\mu$ m feature may be caused partly by [N I] 1.04 $\mu$ m. However, the width and shape of the feature indicates that there must be contributions from other species."
 The 1.17.1.21 pam feature is particularly interesting in that it has persisted [rom as carly as day 112 (Paper D)., The 1.17–1.21 $\mu$ m feature is particularly interesting in that it has persisted from as early as day 112 (Paper I).
 In Papers E and LE we attributed this feature to a blend of allowed lines of Mg 1. Si E and WOOL. However. its relatively unchanging shape between days 112 anc 1822 oompts us to question if it really is a blend of. dilferent species.," In Papers I and II we attributed this feature to a blend of allowed lines of Mg I, Si I and K I. However, its relatively unchanging shape between days 112 and 1822 prompts us to question if it really is a blend of different species."
 We also note that the 2.242.32 jam emission Lies in the same wavelength. region as an unidentified: feature discussed in Paper LL., We also note that the 2.24–2.32 $\mu$ m emission lies in the same wavelength region as an unidentified feature discussed in Paper II.
 The principal CSAL features were due to Lb E: (Pass. Pas. Bro). He L 1.08. 2.06 jan... S HI] 0.91. 0.95 yam and ‘Ve H] 1.26. 1.646. 2.05 jum. Of particular note is the very strong He LE 1.083 yam line which contributes ~20% of the total (ejecta|CSAL) £4 band. flux on cay 1409 and. on davs 1734-2112 (Figure 7).," 			 The principal CSM features were due to H I $\beta$, $\gamma$, $\gamma$ ), He I 1.08, 2.06 $\mu$ m, [S III] 0.91, 0.95 $\mu$ m and [Fe II] 1.26, 1.646, 2.05 $\mu$ m. Of particular note is the very strong He I 1.083 $\mu$ m line which contributes $\sim$ of the total (ejecta+CSM) $IJ$ band flux on day 1469 and on days 1734-2112 (Figure 7)."
 We believe that SS L1) 0.907. 0.953 jam lines have never before been reported. in a supernova spectrum.," We believe that [S III] 0.907, 0.953 $\mu$ m lines have never before been reported in a supernova spectrum."
 Their presence in the spectra of davs 12469 and 1734 is particularly convincing., Their presence in the spectra of days 1469 and 1734 is particularly convincing.
 The lines are less apparent in the day. 1822 and 2112 spectra due to the facing flux and the poorer observing conditions at these epochs., The lines are less apparent in the day 1822 and 2112 spectra due to the fading flux and the poorer observing conditions at these epochs.
 We have also included: narrow line profiles for the νο) 1443. 1.98 jan (and the other lines of these multiplets).," We have also included narrow line profiles for the [Fe I] 1.443, 1.98 $\mu$ m (and the other lines of these multiplets)."
 This line was not anticipated in the work of Luncdevyist Sonnehorn (2001)., This line was not anticipated in the work of Lundqvist Sonneborn (2001).
 Llowever. the observed. line. profile shape on day 1533 in these wavelength regions led us to suspect that CSAL Ee IH] emission may be making a small contribution to these features.," However, the observed line profile shape on day 1533 in these wavelength regions led us to suspect that CSM [Fe I] emission may be making a small contribution to these features."
 At later epochs. the presence of Fe I] emission from the CSM is much less convincing.," At later epochs, the presence of [Fe I] emission from the CSM is much less convincing."
 Finally. we note the presence. of an unidentified narrow feature at à wavelength of 1.485. yam (after blueshifting by 289 km/s) on days 1533 ancl 17234.," Finally, we note the presence of an unidentified narrow feature at a wavelength of 1.485 $\mu$ m (after blueshifting by 289 km/s) on days 1533 and 1734."
 The €CSM spectra will be. discussed. elsewhere., The CSM spectra will be discussed elsewhere.
 Here. we confine our discussion to the ejecta spectra., Here we confine our discussion to the ejecta spectra.
 Phe framework for this section is based upon theoretical descriptions of the physical conditions in the ejecta and line strength predictions at verv late times provided by Kozma Lransson (1992). Fransson lIvozma (1993). Lbransson. Louck ]|xozma (1996) CELIIS96). COT. ΙΙMOS. and I&E98a.b. While dlxLMOS. evolve. their. model. to only 1200. clays 150 days prior to the beginning of our observations) their results ave still relevant to the earlier. part. of the era considered: here.," The framework for this section is based upon theoretical descriptions of the physical conditions in the ejecta and line strength predictions at very late times provided by Kozma Fransson (1992), Fransson Kozma (1993), Fransson, Houck Kozma (1996) (FHK96), C97, dKLM98, and KF98a,b. While dKLM98 evolve their model to only 1200 days 150 days prior to the beginning of our observations) their results are still relevant to the earlier part of the era considered here."
 WEOsa follow the temperature. and ionisation evolution of their model to 2000 clays. covering a significant portion of our era. but. their. line emission calculations (IxF98b) stop at 1200 davs.," KF98a follow the temperature and ionisation evolution of their model to 2000 days, covering a significant portion of our era, but their line emission calculations (KF98b) stop at 1200 days."
 C97 consider the much later epoch of day 2875. which is near the end of our era.," C97 consider the much later epoch of day 2875, which is near the end of our era."
 During the era of the observations described. here. the SN 1987AX ejecta spectrum is produced in a rather exotic manner.," During the era of the observations described here, the SN 1987A ejecta spectrum is produced in a rather exotic manner."
 The energy source of the nebula is the radioactive decay of à number of species created in the explosion (Woosles. Pinto Hartmann 1989: Timmes ct al. (," The energy source of the nebula is the radioactive decay of a number of species created in the explosion (Woosley, Pinto Hartmann 1989; Timmes et al. ("
1996)).,1996)).
" These include ""Co. ""Co. Co. ΤΗ and “Na."," These include $^{56}$ Co, $^{57}$ Co, $^{60}$ Co, $^{44}$ Ti and $^{22}$ Na."
 ALL emit seravs., All emit $\gamma$ -rays.
" Ln addition. ""Co. £pi and Να emit energetic rositrons and """"Co emits energetic electrons."," In addition, $^{56}$ Co, $^{44}$ Ti and $^{22}$ Na emit energetic positrons and $^{60}$ Co emits energetic electrons."
" By day. 1348. 10 most significant⋠⋠⋅ energy sources were wa""Co and το LlepsΤι. 'ontributing about one half and one quarter respectively of 10 deposited energy (Li. MeCray. Sunvacy 1993: Timnmes et al."," By day 1348, the most significant energy sources were $^{57}$ Co and $^{44}$ Ti, contributing about one half and one quarter respectively of the deposited energy (Li, McCray Sunyaev 1993; Timmes et al."
.. 1996)., 1996).
 Around dav 1565. the dominant. source of deposited οποίον became CT; and by about day 2000 more than halt the deposited. ο energy. was in the form of positrons.," Around day 1565, the dominant source of deposited energy became $^{44}$ Ti and by about day 2000 more than half the deposited $^{44}$ Ti energy was in the form of positrons."
 It is generally assumed: that. positrons are deposited “on the spot”., It is generally assumed that positrons are deposited “on the spot”.
 Consequently. given the ~60 vear lifetime of Pi. this means that once positron deposition is dominant. the rate of energy deposition. approaches a constant value of 1.351079 erg/s per 1047 M. of svnthesised “Pi (Wooslev et al.," Consequently, given the $\sim60$ year lifetime of $^{44}$ Ti, this means that once positron deposition is dominant, the rate of energy deposition approaches a constant value of $1.3\times10^{36}$ erg/s per $10^{-4}$ $_\odot$ of synthesised $^{44}$ Ti (Woosley et al."
 1989)., 1989).
 Inorder to reproduce the observed spectra and evolution of SN LOSTA at late times. COT. dlxLMO9S and IxF98sa.b begin with model nebulae having a number of zones of dilfering chemical. composition.," Inorder to reproduce the observed spectra and evolution of SN 1987A at late times, C97, dKLM98 and KF98a,b begin with model nebulae having a number of zones of differing chemical composition."
 These zones are arranged so as to reflect the strong. deep macroscopic mixing in SN 1987 for," These zones are arranged so as to reflect the strong, deep macroscopic mixing in SN 1987A for"
the redshift rauge +6.5 13.,the redshift range $z\approx 6.5$ –13.
 E. Zackrissou. Ον Rydberg aud C. Osstlin acknowledge a grant from the Swedish National Space Board aud the Swedish Research Council.," E. Zackrisson, C.-E. Rydberg and G. Össtlin acknowledge a grant from the Swedish National Space Board and the Swedish Research Council."
 D. Schacrer Is supported bv the Swiss National Science Foundation., D. Schaerer is supported by the Swiss National Science Foundation.
 The authors are indepted to Marcia J. Bieke aud hav Justtanout for giving us access to the NIRCOun and AIIRI broadband filter profiles prior to public release., The authors are indepted to Marcia J. Rieke and Kay Justtanont for giving us access to the NIRCam and MIRI broadband filter profiles prior to public release.
 The anouvmous referee is thanked for useful comments whicha helped to improve the quality of the, The anonymous referee is thanked for useful comments which helped to improve the quality of the
Intermittency in astrophysical plasma turbulence can be analvzed by comparing observed PDFs of fluctuations of the velocity field magnitude in the solar wind with the global theoretical core-halo representation (10)). accounting for nonlocality through entropy generalization.,"Intermittency in astrophysical plasma turbulence can be analyzed by comparing observed PDFs of fluctuations of the velocity field magnitude in the solar wind with the global theoretical core-halo representation \ref{13}) ), accounting for nonlocality through entropy generalization."
 On the other hand. on small scales also the PDFs of interplanetary density. and magnetic field (hictuations are observed to obey (he same leptokurtic core non-Gaussianily along; with pronounced tails or halos. requiring a generalization of Eq. (10)).," On the other hand, on small scales also the PDFs of interplanetary density and magnetic field fluctuations are observed to obey the same leptokurtic core non-Gaussianity along with pronounced tails or halos, requiring a generalization of Eq. \ref{13}) )."
 We introduce a unique. global PDF provided in the context of nonextensive for any physical variable. where nonlocality is associated (to pseudo-acdcditive entropy eeneralization.," We introduce a unique, global PDF provided in the context of nonextensive thermo-statistics for any physical variable, where nonlocality is associated to pseudo-additive entropy generalization."
 Upon normalizing the one-dimensional bi-kappa particle distribution (10)) to unity and assigning a unique distribution variance σ to the thermal spread 0. (he Maxwellian forny of the bi-kappa distribution (10)) transforms with G(&)=1/2 toa Gaussian form! of a global bi-kappa PDF as subject (o a single constant. variance σ (his one-parameter PDF is applicable to the differences of the fluctuations 0.X(7)=X(/+7)—X(/) of any phvsical variable IX. in the astrophysical svstem considered. where X(/) denotes anv characteristic solar wind variable al (me / and 7 is (he time lag.," Upon normalizing the one-dimensional bi-kappa particle distribution \ref{13}) ) to unity and assigning a unique distribution variance $\sigma$ to the thermal spread $v_{t}$, the 'Maxwellian form' of the bi-kappa distribution \ref{13}) ) transforms with $G(\kappa) = 1/2$ to a 'Gaussian form' of a global bi-kappa PDF as Subject to a single constant variance $\sigma$ this one-parameter PDF is applicable to the differences of the fluctuations $\delta X(\tau)=X(t+\tau)-X(t)$ of any physical variable $X$ in the astrophysical system considered, where $X(t)$ denotes any characteristic solar wind variable at time $t$ and $\tau$ is the time lag."
 Ilere & assumes a clear plivsical interpretation defining the degree of nonextensivitv or nonlocalitv in the svstem. thus being a measure of long-range interactions.," Here $\kappa$ assumes a clear physical interpretation defining the degree of nonextensivity or nonlocality in the system, thus being a measure of long-range interactions."
" As &—9x the bi-kappa distribution D,(0.X:&) approaches a single Gaussian.", As $\kappa \longrightarrow \infty$ the bi-kappa distribution $P_{ch}(\delta X;\kappa)$ approaches a single Gaussian.
 In the following we demonstrate the relevance of the nonextensive context by analvzing the observed scale dependence of the PDFs of the dillerences of velocity. density. and magnetic fieldl variables in (he intermittent. turbulent interplanetary medium based on the theoretical elobal bi-kappa PDF (12)).," In the following we demonstrate the relevance of the nonextensive context by analyzing the observed scale dependence of the PDFs of the differences of velocity, density and magnetic field variables in the intermittent, turbulent interplanetary medium based on the theoretical global bi-kappa PDF \ref{16}) )."
 For a proper estimation of empirical PDFs of interplanetary plasma and magnetic field data long sets are needed., For a proper estimation of empirical PDFs of interplanetary plasma and magnetic field data long sets are needed.
 Due to non-stationarityv in driving dissipation conditions. however. the data sets have to be chosen carefully.," Due to non-stationarity in driving dissipation conditions, however, the data sets have to be chosen carefully."
 For the present approach solar wind velocity data are analyzed wilh a time resolution of 92 s and the interplanetary magnetic field strength with a time resolution of 60 s. both available from the WIND spacecralt.," For the present approach solar wind velocity data are analyzed with a time resolution of 92 s and the interplanetary magnetic field strength with a time resolution of 60 s, both available from the WIND spacecraft."
 WIND has a complicated trajectory that also crosses the magnetosphere [rom time to Gime., WIND has a complicated trajectory that also crosses the magnetosphere from time to time.
 Our analysis is based on the entire vear 1997 data set when WIND was in the GSE positions: 150-230 Ry., Our analysis is based on the entire year 1997 data set when WIND was in the GSE positions: 150-230 $R_{E}$ .
The shear viscosity in a differentially rotating chuupy cixk. with accounting for gravitational iuteractions between the clamps of mass in. is given. by Eq. (,"The shear viscosity in a differentially rotating clumpy disk, with accounting for gravitational interactions between the clumps of mass $m$, is given by Eq. ("
60) iu Stewart aula (19580): where O=dO dre? and we; is frequeucy of clup-chluup collisions giveu by Eq. (,60) in Stewart Kaula (1980): where $\Omega^\prime \equiv {\rm d}\Omega/{\rm d}r$ and $\omega_G$ is frequency of clump-clump collisions given by Eq. (
A2) correspouds to Eq. (,A2) corresponds to Eq. (
57) of SIX when one puts lu|l|(a?Ginny22] because in a fat disk the long-range gravitational interactions could be neglected conrpared to the short-ranee ones.,"57) of SK when one puts $\ln [1+(\sigma_v^3/
Gm\Omega)^2]^{1/2}=1$ because in a flat disk the long-range gravitational interactions could be neglected compared to the short-range ones."
 The value of we; is related to the characteristic tine of eravitational eucounters. fe; given by Eq. (," The value of $\omega_G$ is related to the characteristic time of gravitational encounters, $t_G$, given by Eq. ("
2.3) sinply by wer=tof.,2.3) simply by $\omega_G^{-1}=t_G/\sqrt 2$.
 By substituting Eq. (, By substituting Eq. (
A2) iuto Eq. (,A2) into Eq. (
AL). the latter could be written iu the form: where de;=0.83 for a Keplerian disk. e;=1.25 for a solid-body rotating disk. aud 7=Of;.,"A1), the latter could be written in the form: where $A_G=0.83$ for a Keplerian disk, $A_G=1.25$ for a solid-body rotating disk, and $\tau=\Omega t_G$."
 The viscosity cocficicut for cluup-chunp collisions. when the chuup gravity is negligible [Goldreich Tremaine 1978. Eq. (," The viscosity coefficient for clump-clump collisions, when the clump gravity is negligible [Goldreich Tremaine 1978, Eq. ("
16)]. can be written iu the form analogous to Eq. (,"46)], can be written in the form analogous to Eq. ("
43): Eq. (,A3): Eq. (
2.1) unifies the represeutation of viscosity both iu the case when interactions are inclastic. while exavitatiou is negligible [Eq. C,"2.1) unifies the representation of viscosity both in the case when interactions are inelastic, while gravitation is negligible [Eq. ("
AD]and in the case when gravitational encounters are dominating |Eq. (,A4)] in the case when gravitational encounters are dominating [Eq. (
À3)].,A3)].
 Let us consider au incompressible. differcutially rotating. liquid cylinder.," Let us consider an incompressible, differentially rotating, liquid cylinder."
" The linearized equations of motion take the form: Substituting a perturbation in the form of the wave packet f — exp|keling|fhyde] vesults in the following dispersion relation (&.— ifr) As always &? x. 103, aud therefore the condition of instability is b.À. « 0. which correspouds to he erowth of the leading spirals."," The linearized equations of motion take the form: Substituting a perturbation in the form of the wave packet $f$ $\sim$ $\exp[-i\omega+m \varphi+\int k_r dr]$ results in the following dispersion relation $k_\varphi\equiv m/r$ ): As always $\kappa^2$ $\le$ $4\Omega^2,$ and therefore the condition of instability is $k_r k_\varphi$ $<$ 0, which corresponds to the growth of the leading spirals."
 Under this condition the instability is Inonotonous without auv oscillations with epicyelic frequency., Under this condition the instability is monotonous without any oscillations with epicyclic frequency.
 If the rotation is solid-body. one obtains v2 = 0. i.c. the perturbations are stationary.," If the rotation is solid-body, one obtains $\hat \omega$ = 0, i.e. the perturbations are stationary."
 The above solution has a drawback since the 9 component of the eroup velocity for perturbations wader consideration is zero., The above solution has a drawback since the $r$ -component of the group velocity for perturbations under consideration is zero.
 A amore detailed analysis should be performed to fined out what is the role of ν- idence for ο., A more detailed analysis should be performed to find out what is the role of $r$ -dependence for $\Omega$.
 This difficulty can be overcome if one considers the svsteni in a corotating frame of reference., This difficulty can be overcome if one considers the system in a corotating frame of reference.
 Iu this case. ano exact time-dependent solution cau be derive (seco Fridinan. 1989) which cdemioustrates a qualitatively the same behaviour as is obtained above.," In this case, an exact time-dependent solution can be derived (see Fridman, 1989) which demonstrates a qualitatively the same behaviour as is obtained above."
 Specifically. in anv differentially rotating disk whose aneular velocity decreases with radius. the leading spirals erow monotonously.," Specifically, in any differentially rotating disk whose angular velocity decreases with radius, the leading spirals grow monotonously."
 As for a solid-body rotating disk. all perturbations are stationary.," As for a solid-body rotating disk, all perturbations are stationary."
 Note that if one would consider absolutely compressible case. ie. P—0 in the above equations. the continuity equation takes the fori: aud we immediately obtain The coutrast to other work is illuminating.," Note that if one would consider absolutely compressible case, i.e. $P=0$ in the above equations, the continuity equation takes the form: and we immediately obtain The contrast to other work is illuminating."
 Julian Tooure (1966) considered perturbations ia a very thin collisionless sclferavitating stellar disk., Julian Toomre (1966) considered perturbations in a very thin collisionless self-gravitating stellar disk.
 Tn fact. for such perturbations a collisionlessstellar disk is absolutely conipressible. i contrast to incompressible character of perturbations with waveleuegths much smaller than the disks width for a disk cousidered here.," In fact, for such perturbations a collisionless disk is absolutely compressible, in contrast to incompressible character of perturbations with wavelengths much smaller than the disk's width for a disk considered here."
 Coldreich Lyucen-Bell (1965) studied dvnamics of perturbations in a gaseous disk. but only at high frequencies.," Goldreich Lynden-Bell (1965) studied dynamics of perturbations in a gaseous disk, but only at high frequencies."
 Really. perturbations cousidered in their paper demonstrate (asvinptoticaly) oscillations with sone frequency he. where & is the wave umber aud e is the sound speed.," Really, perturbations considered in their paper demonstrate (asymptoticaly) oscillations with sound frequency $kc$, where $k$ is the wave number and $c$ is the sound speed."
 As the scale of perturbatious is stualler than the disk width. Le. kh>1l. their frequency is higher than the epicvclic One.," As the scale of perturbations is smaller than the disk width, i.e. $kh>1$, their frequency is higher than the epicyclic one."
 But as the equations of motions coutai three derivatives with respect to nuc. they describe three modes of perturbations.," But as the equations of motions contain three derivatives with respect to time, they describe three modes of perturbations."
 Besides the two sonic high frequency modes. one mode of low requeney perturbations exists aswell.," Besides the two sonic high frequency modes, one mode of low frequency perturbations exists as well."
 What is examined in our paper is the role offrequency mode in dynamics of the circumuiuelear disk., What is examined in our paper is the role of mode in dynamics of the circumnuclear disk.
 As was shown in Fridiman (1989).this mode does uot demonstrate auv oscillations aud is stationary du a solid-body rotating disk.," As was shown in Fridman (1989),this mode does not demonstrate any oscillations and is stationary in a solid-body rotating disk."
 We start from linearized equations for short-wave. low- perturbations ina barotropic gaseous disk in the," We start from linearized equations for short-wave, low-frequency perturbations in a barotropic gaseous disk in the"
very weaker than that on faint galaxies.,very weaker than that on faint galaxies.
" On the other hand. in faint ellipticals. their colour reflects the feedback ellicienev. 3 —(Vu) ""0n. see eq.(10))]. directly. when the feedback. is elective even in the starburst process."," On the other hand, in faint ellipticals, their colour reflects the feedback efficiency, $\beta$ $=(V/V_{hot})^{-\alpha_{hot}}$ , see \ref{eqn:alphot}) )], directly, when the feedback is effective even in the starburst process."
 In other words. when the value of y is fixed. the evolution of stellar metallicity in faint galaxies is suppressed in the case of high feedback. models. anc the metallicity of luminous ealaxies is almost determined. by the vield. jy. because the Feedback elfect becomes negligible in such luminous galaxies.," In other words, when the value of $y$ is fixed, the evolution of stellar metallicity in faint galaxies is suppressed in the case of high feedback models, and the metallicity of luminous galaxies is almost determined by the yield, $y$, because the feedback effect becomes negligible in such luminous galaxies."
 Therefore. a suppression of growth of stellar metallicity is required in small galaxies for making the slope of CALs.," Therefore, a suppression of growth of stellar metallicity is required in small galaxies for making the slope of CMRs."
 The relationship between the metallicity anc the feedback is discussed in the next section., The relationship between the metallicity and the feedback is discussed in the next section.
" In a chemical evolution of a simple monolithic cloud collapse model. the evolution of metallicity of cold gas for a constant star formation time-scale. τε. is clescribed as where à is a locked-up mass fraction. a=1 HG is the gas fraction. returned by evolved stars). and Z,,,;D is. an initial metallicity of cold gas at /—/,."," In a chemical evolution of a simple monolithic cloud collapse model, the evolution of metallicity of cold gas for a constant star formation time-scale, $\tau_{*}$, is described as where $\alpha$ is a locked-up mass fraction, $\alpha=1-R$ $R$ is the gas fraction returned by evolved stars), and $Z_{cool}^{0}$ is an initial metallicity of cold gas at $t=t_{s}$."
 The rate of increase ol stellar mass is where owe use. the instantaneous recvcling approximation., The rate of increase of stellar mass is where we use the instantaneous recycling approximation.
 From these two equations. the weighted mean stellar metallicity is obtained as where When the star formation time-scale is enough. smaller aan the Llubble time or when the starburst occurs. the final metallicity is determined by £ (ότι5 x).," From these two equations, the mass-weighted mean stellar metallicity is obtained as where When the star formation time-scale is enough smaller than the Hubble time or when the starburst occurs, the final metallicity is determined by $F$ $t/\tau_{*}\to\infty$ )."
 The form of £ shows that when the feedback is strong the final mean stellar metallicitye. becomes small. ἐστιHSoyaZAA as 3Xx.," The form of $F$ shows that when the feedback is strong the final mean stellar metallicity becomes small, $\langle Z_{*}(t/\tau_{*}\to\infty)\rangle_{M_{*}}\to
Z_{cool}^{0}$ as $\beta\to\infty$."
 Moreover. increasing g 1s corresponding to ecreasing the feedback strength 3.," Moreover, increasing $y$ is corresponding to decreasing the feedback strength $\beta$."
 This cllect determines the absolute value of final mean stellar metallicitv. especially for faint galaxies.," This effect determines the absolute value of final mean stellar metallicity, especially for faint galaxies."
 On the other hand. when the feedback is negligible (3« 1). the factor £F is determined by only jy.," On the other hand, when the feedback is negligible $\beta\ll 1$ ), the factor $F$ is determined by only $y$."
 So the ellect o£ y is remarkable in luminous galaxies rather than in faint galaxies when the starburst model shA is adopted. which is the model that the supernova feedback. strength remains even in the starburst.," So the effect of $y$ is remarkable in luminous galaxies rather than in faint galaxies when the starburst model sbA is adopted, which is the model that the supernova feedback strength remains even in the starburst."
 On the other hand. when the starburst model sbl3 is adopted. which is the model that all the cold. eas turns to stars with very shorttime-scale. the," On the other hand, when the starburst model sbB is adopted, which is the model that all the cold gas turns to stars with very shorttime-scale, the"
" ""Deparbmentof Astronomy. Universityofferas. Austin. PΗμ μμ. Alagnesium is one of the few elements lor which the stellar abundance of individual isotopes can be reliably measured.","Department of Astronomy, University of Texas, Austin, TX 78712, Magnesium is one of the few elements for which the stellar abundance of individual isotopes can be reliably measured."
 The relative abundances of Mg isotopes provide a useful probe into the nucleosynthesis history of the Milky Way because they have their origin in dillerent. classes of stars., The relative abundances of Mg isotopes provide a useful probe into the nucleosynthesis history of the Milky Way because they have their origin in different classes of stars.
 According to standard theories of stellar evolution. most of the Ale isotopes originate from massive stars.," According to standard theories of stellar evolution, most of the Mg isotopes originate from massive stars."
 The heavy Mg isotopes behave as secondary elements inside massive stars ancl their production scales with the number of initial “seed” nuclei., The heavy Mg isotopes behave as secondary elements inside massive stars and their production scales with the number of initial “seed” nuclei.
 Consequently. very little is svnthesised by massive stars until an initial of ~ 1 is reached. whereas the generation of operates fairly independently of initial metallicity.," Consequently, very little is synthesised by massive stars until an initial of $\sim$ $-$ 1 is reached, whereas the generation of operates fairly independently of initial metallicity."
 and are detected in metal-poor stars in higher. proportions than one would expect if these neutron-rich isotopes originated. exclusively from. massive stars (Gay Lambert 2000)., and are detected in metal-poor stars in higher proportions than one would expect if these neutron-rich isotopes originated exclusively from massive stars (Gay Lambert 2000).
 Detailed: models of the evolution of Mg isotopic ratios find that massive stars alone are insullicient to account for the values of at Low Vel]. hinting at an additional production site (Times et al.," Detailed models of the evolution of Mg isotopic ratios find that massive stars alone are insufficient to account for the values of at low [Fe/H], hinting at an additional production site (Timmes et al."
 1995: Alibes et al., 1995; Alibes et al.
 2001: CGoswanmi Prantzos 2000)., 2001; Goswami Prantzos 2000).
 Ixarakas Lattanzio (2003a.b) have shown that and," Karakas Lattanzio (2003a,b) have shown that and"
" The oobservatorv performed a survey of the Small Masellauic Cloud (SAIC) in which two sources with unusually soft spectra. TE 0056.8-7151. and TE 0035,7230. were detected. (Seward Mitchell 1981)."," The observatory performed a survey of the Small Magellanic Cloud (SMC) in which two sources with unusually soft spectra, 1E 0056.8-7154 and 1E 0035.4-7230, were detected (Seward Mitchell 1981)."
 LE 0035.1-7230 has been identified iu the optical with a variable blue star with a stroug UV excess aud ai [1 hour orbital period (Orio et al., 1E 0035.4-7230 has been identified in the optical with a variable blue star with a strong UV excess and a 4.1 hour orbital period (Orio et al.
 199Y., 1994).
 The supersoft nature of the source was confirmed by subsequeut ROSAT observations (IKaliabka ct al., The supersoft nature of the source was confirmed by subsequent ROSAT observations (Kahabka et al.
 1991: Kahabka 1996)., 1994; Kahabka 1996).
 Supersoft sources are most xobablv accreting white dwirfs (WDs) which are burning ivdrogen steadily (wan deu Heuvel et al., Supersoft sources are most probably accreting white dwarfs (WDs) which are burning hydrogen steadily (van den Heuvel et al.
 1992)., 1992).
 Au orbital xeriod of 0.1719 davs was found iu optical and X-rav data (Crampton et al., An orbital period of 0.1719 days was found in optical and X-ray data (Crampton et al.
 1997: see van Teescling et al., 1997; see van Teeseling et al.
 1995 ‘Or a recon discussion)., 1998 for a recent discussion).
 The optical προςπα shows xonounced enmüssion at AÍL686 aux ucar Ta., The optical spectrum shows pronounced emission at $\lambda$ 4686 and near $\alpha$ .
 The IL/ line is seen in absorption (Cowley ο al., The $\beta$ line is seen in absorption (Cowley et al.
 1998)., 1998).
 The Mass function derived. from the Af686 line radial velocities indicates a donor star mass of —0.1M. aud a WD nass of οςL.LM5., The mass function derived from the $\lambda$ 4686 line radial velocities indicates a donor star mass of $\sim$${\rm 0.4\ M_{\odot}}$ and a WD mass of $\sim$${\rm0.5-1.4\ M_{\odot}}$.
 A scenario to account for he evolutionary state of the source has been proposed w dFKahabka ποια (1997) in which the svsteii ds a cataclesiiic variable (CV) with a low-mass WD accretiug low the steady-state burniug rate., A scenario to account for the evolutionary state of the source has been proposed by Kahabka Ergma (1997) in which the system is a cataclysmic variable (CV) with a low-mass WD accreting below the steady-state burning rate.
 The recurrent flashes in this system are assumed to be ld aud leave a fraction of the envelope as a nuclear reservoir., The recurrent flashes in this system are assumed to be mild and leave a fraction of the envelope as a nuclear reservoir.
 The WDis heated to, The WDis heated to
"frequency and age, and convolved this with the stellar history of each bin, and related this to the flux at an observed frequency Vo as = aedis ) in units of ergs cm! Ησ s~! and wherez is the shock redshift, d;(z) is the luminosity1 distance, vo/(14-z) is the rest-frame frequency, c and dLv/dM,(vo/(14- is the luminosity per frequency per solar mass of a populationz),t) of stars with an age t, and dM./dt(t) is the star formation history in a given bin.","frequency and age, and convolved this with the stellar history of each bin, and related this to the flux at an observed frequency $\nu_0$ as = dt ) in units of ergs $^{-1}$ $^{-1}$ $^{-1}$ and where$z$ is the shock redshift, $d_l(z)$ is the luminosity distance, $\nu_0/(1+z)$ is the rest-frame frequency, $c$ and $d L\nu /dM_* (\nu_0/(1+z),t)$ is the luminosity per frequency per solar mass of a population of stars with an age $t$, and $dM_{*}/dt(t)$ is the star formation history in a given bin."
" Similarly, we estimate the Lyman alpha flux from our simulations as = dtshe where dL,/dM,(t)=er(1— is the the Lyman alpha luminosity per solar mass of a fac)Q(H)M.,population of stars with an age t Scannapieco 2003), with cr, = 1.04 x10-!! ergs, fa, is the escape fraction of ionizing photons and is taken to be 0.2, is the hydrogen ionizing photon rate in units of Q(H)number per second per solar mass and is taken from the stellar population synthesis code STARBURST99 "," Similarly, we estimate the Lyman alpha flux from our simulations as = dt where $d L_{\alpha}/d M_\star (t) = c_L (1-f_{\rm esc}) Q(H) M_{*},$ is the the Lyman alpha luminosity per solar mass of a population of stars with an age $t$ Scannapieco 2003), with $c_L$ $\equiv$ 1.04 $\times 10^{-11}$ ergs, $f_{\rm esc}$ is the escape fraction of ionizing photons and is taken to be 0.2, $Q(H)$ is the hydrogen ionizing photon rate in units of number per second per solar mass and is taken from the stellar population synthesis code STARBURST99 (Leitherer 1999)."
"Finally, in both the broad and narrow (Leithererband cases we 11999).normalized the flux by the spacing of each bin to get the flux per (physical) kpc."," Finally, in both the broad and narrow band cases we normalized the flux by the spacing of each bin to get the flux per (physical) kpc."
" Figure 16 shows the resulting fluxes for three differentJWST bands (F115W, F150W, and F200W) and the Lyman alpha flux froma selection of simulations spanning a wide range of parameter space."," Figure \ref{jwstflux_fid} shows the resulting fluxes for three different bands (F115W, F150W, and F200W) and the Lyman alpha flux from a selection of simulations spanning a wide range of parameter space."
" Again we note that the fluxes in this figure are computed assuming that all the gas collapsed above py,=1.0x1077? g cm? is converted into stars, and so these fluxes should be scaled by an unknown star formation effciency factor which is <1. Likewise the angular given in this figure assume that that stellar clusters are being viewed edge on, such that angular separation is maximal."," Again we note that the fluxes in this figure are computed assuming that all the gas collapsed above $\rho_{\rm th} = 1.0 \times 10^{-23}$ g $^{-3}$ is converted into stars, and so these fluxes should be scaled by an unknown star formation effciency factor which is $\leq 1.$ Likewise the angular given in this figure assume that that stellar clusters are being viewed edge on, such that angular separation is maximal."
 Table 3 summarizes the observable properties of the stellar clusters generated in all of our models including the total fluxes in theJWST bands and Lyo and the physical and maximal angular scales., Table \ref{msf} summarizes the observable properties of the stellar clusters generated in all of our models including the total fluxes in the bands and ${\alpha}$ and the physical and maximal angular scales.
 Note that the physical and angular scales given are for the extended emission expected at the end of each simulation and not from the final globular cluster., Note that the physical and angular scales given are for the extended emission expected at the end of each simulation and not from the final globular cluster.
" From the values in this figure and table we see that, unfortunately even the wide band filters ofJWST are not expected to have the required sensitivity to detect these objects."," From the values in this figure and table we see that, unfortunately even the wide band filters of are not expected to have the required sensitivity to detect these objects."
" Observations with wide band filters will have typical sensitivities of 10-20 nJy for a 10-σ detection at 10,000 seconds of integration time (Stiavelli 2008), which is roughly an order of magnitude higher than the typical fluxes of zz 1 nJy (see Figure 16)) expected from our objects."," Observations with wide band filters will have typical sensitivities of 10-20 nJy for a $\sigma$ detection at 10,000 seconds of integration time (Stiavelli 2008), which is roughly an order of magnitude higher than the typical fluxes of $\approx$ 1 nJy (see Figure \ref{jwstflux_fid}) ) expected from our objects."
" On the other hand, the narrow band Lya fluxes are over an order of magnitudebrighter than those expected to be obtained with the next generation of ground-based telescopes."," On the other hand, the narrow band ${\alpha}$ fluxes are over an order of magnitude than those expected to be obtained with the next generation of ground-based telescopes."
" The proposed on the for example, will be able to detect such sources down to a flux limit of 1.0x107?? given 25 hours of integration time (McCarthy ergs/s/cm-?,2008; GMT Science Case)."," The proposed on the for example, will be able to detect such sources down to a flux limit of $\times 10^{-20}$ $^{-2},$ given 25 hours of integration time (McCarthy 2008; GMT Science Case)."
" Similarly, the on the will detect Lya sources at z = 7.7 with fluxes of 1.0x10-18 ergs/s/em~? with signal-to-noise (S/N) of 15 in only 1 hour of observation time (Wright Barton 2009; TMT Instrumentation and Performance Handbook)."," Similarly, the on the will detect ${\alpha}$ sources at z = 7.7 with fluxes of $\times 10^{-18}$ $^{-2}$ with signal-to-noise (S/N) of 15 in only 1 hour of observation time (Wright Barton 2009; TMT Instrumentation and Performance Handbook)."
" Finally, for the(Optical-Near-InfraredE-ELT will detect sources with fluxes of 1071? erg/s/cm~? with S/N of 8 in 40 hours of integration time (Hammer 2010)."," Finally, for the will detect sources with fluxes of $^{-19}$ $^{-2}$ with S/N of 8 in 40 hours of integration time (Hammer 2010)."
 This means that the majority of the models studied here are more than bright enough to be detected., This means that the majority of the models studied here are more than bright enough to be detected.
" Beyond being bright in Lya, the unusual, elongated morphology of the stellar distributions formed in outflow-minihalo interactions makes them ideal for study with next generation of ground-based instruments."," Beyond being bright in $\alpha$, the unusual, elongated morphology of the stellar distributions formed in outflow-minihalo interactions makes them ideal for study with next generation of ground-based instruments."
" With expected angular resolutions of 0.1—0.3 arcsec (McCarthy 2008; Wright Barton 2009; Hammer 2010), next generation narrow band images will not only be able to detect the presence of the stars, but show that their distribution is highly-elongated in the direction of the impinging outflow, as illustrated in Figure 17.."," With expected angular resolutions of $0.1-0.3$ arcsec (McCarthy 2008; Wright Barton 2009; Hammer 2010), next generation narrow band images will not only be able to detect the presence of the stars, but show that their distribution is highly-elongated in the direction of the impinging outflow, as illustrated in Figure \ref{narrowband_image}."
" Furthermore, as the starburst galaxies triggering star-formation should have typical solar masses >10°Mo, these will be easily detectable with broad-band JWST measurements."," Furthermore, as the starburst galaxies triggering star-formation should have typical solar masses $\gtrsim 10^8 M_\odot$, these will be easily detectable with broad-band measurements."
" Thus, the detection of a group of elongated Lya emitters which whose axes point directly at a larger broad-band detected starbursting galaxy will provide a unique signature that unambiguously points to the formation of compact stellar clusters by high-redshift"," Thus, the detection of a group of elongated $\alpha$ emitters which whose axes point directly at a larger broad-band detected starbursting galaxy will provide a unique signature that unambiguously points to the formation of compact stellar clusters by high-redshift"
In this research note we focus on polarimetric measurements of Ser A* in the NIR (for polarization properties of Ser A¥ in the mm-regime see Marrone et al. 2006.2007)),"In this research note we focus on polarimetric measurements of Sgr A* in the NIR (for polarization properties of Sgr A* in the mm-regime see Marrone et al. \cite{marrone2, marrone1}) )"
 and their interpretation in terms of the orbiting spot model. i.e. Keplerian motion in strong gravity is adopted as the cause for the sub-flares.," and their interpretation in terms of the orbiting spot model, i.e. Keplerian motion in strong gravity is adopted as the cause for the sub-flares."
 Note that the orbiting blob model can be tested (and perhaps rejected). although the task cannot be achieved now. given the insufficient quality of data available at present.," Note that the orbiting blob model can be tested (and perhaps rejected), although the task cannot be achieved now, given the insufficient quality of data available at present."
 In principle. constraints can be imposed on the model by tracking all four Stokes parameters and comparing their time evolution against the model.," In principle, constraints can be imposed on the model by tracking all four Stokes parameters and comparing their time evolution against the model."
 It is known that general relativity should imprint specific features in the time evolution of a polarized signal when a blob orbits near to à black hole (which is what we suggest here): the direction of the polarization vector should wobble within a range determined by the distance of the blob from the hole and the viewing angle of the observer (e.g.. Connors et al. 1980)).," It is known that general relativity should imprint specific features in the time evolution of a polarized signal when a blob orbits near to a black hole (which is what we suggest here); the direction of the polarization vector should wobble within a range determined by the distance of the blob from the hole and the viewing angle of the observer (e.g., Connors et al. \cite{connors80}) )."
 Here. we discuss in particular the constraints that this modelling sets on the position angle of the normal to the equatorial plane of the spinning BH.," Here, we discuss in particular the constraints that this modelling sets on the position angle of the normal to the equatorial plane of the spinning BH."
 In the next two sections we first report so far unpublished polarimetric data of Ser A* from 2003 that show that the mean polarization angle fluctuated only slightly for at least four years., In the next two sections we first report so far unpublished polarimetric data of Sgr A* from 2003 that show that the mean polarization angle fluctuated only slightly for at least four years.
 Afterwards. this preferred direction 1s interpreted within the blob model.," Afterwards, this preferred direction is interpreted within the blob model."
 The data we present here are polarimetric observations of Ser A* at 2.2jm from October..," The data we present here are polarimetric observations of Sgr A* at $2.2\, \mu$ m from October."
 They have not been published before and are important to identify a favored orientation of the Ser A* system., They have not been published before and are important to identify a favored orientation of the Sgr A* system.
 They have been taken with the near-infrared camera and adaptive optics system NACO at ESO's Very Large Telescope (VLT) in combination with a wire-grid., They have been taken with the near-infrared camera and adaptive optics system NACO at ESO's Very Large Telescope (VLT) in combination with a wire-grid.
 The observations have been conducted in such a way that after ~5 min the wire-grid has been rotated., The observations have been conducted in such a way that after $\sim 5$ min the wire-grid has been rotated.
 While it is now clear (Genzel et al. 2003:;, While it is now clear (Genzel et al. \cite{genzel};
 Eckart et al. 2006)), Eckart et al. \cite{ecki2}) )
 that this time resolution is too low due to the high variability of Ser A* in the NIR. nevertheless a mean polarization angle can be inferred.," that this time resolution is too low due to the high variability of Sgr A* in the NIR, nevertheless a mean polarization angle can be inferred."
 The data are of very high quality and show an exceptionally bright flare., The data are of very high quality and show an exceptionally bright flare.
 We carried out standard reduction techniques. te. sky subtraction. flat fielding and bad pixel correction.," We carried out standard reduction techniques, i.e. sky subtraction, flat fielding and bad pixel correction."
 The point spread function was extracted on each individual image (Diolaiti et al. 2000)), The point spread function was extracted on each individual image (Diolaiti et al. \cite{diolaiti}) )
 and then used for a Lucy-Richard deconvolution., and then used for a Lucy-Richard deconvolution.
 After restoration with a Gaussian beam. aperture photometry on the diffraction limited images for individual sources with known flux and Ser A* was done.," After restoration with a Gaussian beam, aperture photometry on the diffraction limited images for individual sources with known flux and Sgr A* was done."
 For the extinction correction we assumed Ag=2.8 mmag., For the extinction correction we assumed $A_K=2.8$ mag.
 Estimates of uncertainties were obtained from the standard deviation of fluxes from nearby constant sources., Estimates of uncertainties were obtained from the standard deviation of fluxes from nearby constant sources.
 The calibration was performed using the overall interstellar polarization of all sources in the field. which is at 25° (Eckart et al. 1995:;," The calibration was performed using the overall interstellar polarization of all sources in the field, which is at $25\degr$ (Eckart et al. \cite{ecki95};"
 Ott et al. 1999))., Ott et al. \cite{ott}) ).
 The dereddened flux of Sgr A* and of a nearby constant star is shown in Figure 1.., The dereddened flux of Sgr A* and of a nearby constant star is shown in Figure \ref{flux}.
 The flux was calibrated such that each angle seperately matched the total flux of known sources., The flux was calibrated such that each angle seperately matched the total flux of known sources.
 That, That
"axis of +115 AU, in remarkable agreement with Quillen's prediction.","axis of $\approx$ 115 AU, in remarkable agreement with Quillen's prediction."
" The mass predicted by Quillen is lower than the upper limits derived by ?= (~1.7-3.5 however they emphasize that their jum flux M;a5)),may be contaminated by an extensive circumplanetary disk."," The mass predicted by Quillen is lower than the upper limits derived by \citet{Kalas08} $\sim$ 1.7-3.5 ), however they emphasize that their $\mu$ m flux may be contaminated by an extensive circumplanetary disk."
" Young giant planets are predicted to be hot (for My;up>3, , K Tort foragesj500M yr(?))), andtheoreticalspectralenergydistrib 6 und--5 um "," Young giant planets are predicted to be hot (for $_{Jup}>3$, $>$ K for ages $<$ 500 Myr \citep[]{Baraffe03}) ), and theoretical spectral energy distributions (SEDs) predict a strong peak around $\sim$ $\mu$ m \citep[e.g.][]{Burrows97}."
"While direct imaging surveys for substellar companions(e.g.?).. to nearby stars have concentrated on near-IR bands (e.g. H and K), the models predict that L and M-band fluxes for planets should be much brighter than at J, H, and K."," While direct imaging surveys for substellar companions to nearby stars have concentrated on near-IR bands (e.g. $H$ and $K$ ), the models predict that $L$ and $M$ -band fluxes for planets should be much brighter than at $J$ , $H$ , and $K$."
" For example, a jy; object with age GGyr has predicted colors of J—M ~4,H-M ~4, L—M ~ 1 (?)."," For example, a $_{Jup}$ object with age Gyr has predicted colors of $J-M$ $\simeq$ 4, $H-M$ $\simeq$ 4, $L-M$ $\simeq$ 1 \citep{Baraffe03}."
" Motivated by these predictions, we initiated surveys of nearby (d < 25 stars of various types to search for substellar companionspc) at wide separations (>10 AU) using the Clio IR. camera on the 6.5-m MMT telescope with the adaptive secondary mirror (???).."," Motivated by these predictions, we initiated surveys of nearby $d$ $<$ 25 pc) stars of various types to search for substellar companions at wide separations $>$ 10 AU) using the Clio IR camera on the 6.5-m MMT telescope with the adaptive secondary mirror \citep{Lloyd-Hart00,
Wildi03, Brusa04}."
 Here we report observations with MMT/AO and the Clio IR camera sensitive to giant planets at a wide range of orbital radii interior to the companion reported by ?.., Here we report observations with MMT/AO and the Clio IR camera sensitive to giant planets at a wide range of orbital radii interior to the companion reported by \citet{Kalas08}.
 Fomalhaut was imaged 5 December 2006 (02:06 UT) using the Clio 3-5jm imager in conjunction with the adaptive secondary mirror on the 6.5-meter MMT telescope., Fomalhaut was imaged 5 December 2006 (02:06 UT) using the Clio $\mu$ m imager in conjunction with the adaptive secondary mirror on the 6.5-meter MMT telescope.
 The Clio detector is a high well depth Indigo InSb detector with 320x256 pixels and jum size pixels (?).., The Clio detector is a high well depth Indigo InSb detector with 320x256 pixels and $\mu$ m size pixels \citep{Hinz06}.
" Images were taken with a Barr Associates M-band filter with half power wavelength range of 4.47 to 5.06 um with central peak wavelength of 4.77 um?.. The field of view at M-band is 15"".6 x 12"".4 on the Clio array.", Images were taken with a Barr Associates M-band filter with half power wavelength range of 4.47 to 5.06 $\mu$ m with central peak wavelength of 4.77 $\mu$ m. The field of view at $M$ -band is 15”.6 $\times$ 12”.4 on the Clio array.
" The star was nodded 5"".5 along the long axis of the detector after 5 images were taken.", The star was nodded 5”.5 along the long axis of the detector after 5 images were taken.
" Each of the 375 images consists of 50 coadded exposures of 209.1 ms length, for a total coadded duration of 3920 sec."," Each of the 375 images consists of 50 coadded exposures of 209.1 ms length, for a total coadded duration of 3920 sec."
" Exposure times were calculated so as to keep the sky flux counts just below the nonlinearity limit for the detector (around 40,000 ADU)."," Exposure times were calculated so as to keep the sky flux counts just below the nonlinearity limit for the detector (around 40,000 ADU)."
" Short exposures, typically of 64.1 msec were taken after the sequence of deep exposures so as to provide photometric check."," Short exposures, typically of 64.1 msec were taken after the sequence of deep exposures so as to provide photometric check."
" To avoid variations in the pattern of illumination on the Clio detector, the instrument is fixed in orientation with respect to the telescope, resulting in total field rotation of 21? for our Fomalhaut data."," To avoid variations in the pattern of illumination on the Clio detector, the instrument is fixed in orientation with respect to the telescope, resulting in total field rotation of $21^o$ for our Fomalhaut data."
" Conditions were photometric, and the native seeing throughout the Fomalhaut imaging was 7-0"".5-0"".7 at an airmass of 2.1 to 2.8 (as seen with the optical acquisiton camera)."," Conditions were photometric, and the native seeing throughout the Fomalhaut imaging was $\sim$ 0”.5-0”.7 at an airmass of 2.1 to 2.8 (as seen with the optical acquisiton camera)."
 'The pixel scale was determined from images of the A-type binary Castor on UT 7 Dec 2006 (orbitfrom ?).., The pixel scale was determined from images of the A-type binary Castor on UT 7 Dec 2006 \citep[orbit from ][]{Worley96}.
" The observed separation at M-band was + 00.06 pixels, and the orbit predicted an angular separation of 43.445, leading to a pixel scale of -- 00.05 ppixel-!."," The observed separation at M-band was $\pm$ 0.06 pixels, and the orbit predicted an angular separation of 4”.445, leading to a pixel scale of $\pm$ 0.03 $^{-1}$."
" 'The Clio images were reduced using suite of custom C routines (7) that match temporallya adjacent (or nearly adjacent) beam pair observations for background subtraction, then rotate and coadd the background-subtracted images into final images."," The Clio images were reduced using a suite of custom C routines \citep{Heinze07_PhD} that match temporally adjacent (or nearly adjacent) beam pair observations for background subtraction, then rotate and coadd the background-subtracted images into final images."
" Postage stamp images of all of the individual observations (each are typically ~6-25 sec integrations) were inspected, and a small number of observations were rejected (usually during periods of poor seeing, or if the AO system loop was lost, or both)."," Postage stamp images of all of the individual observations (each are typically $\sim$ 6-25 sec integrations) were inspected, and a small number of observations were rejected (usually during periods of poor seeing, or if the AO system loop was lost, or both)."
" Several methods of image combination are run as separate trials to determine the one with the most robust sensitivity, and are discussed in Heinze (2008)."," Several methods of image combination are run as separate trials to determine the one with the most robust sensitivity, and are discussed in Heinze (2008)."
" A separate pipeline, written in IRAF scripts and Perl DataLanguage?,, provides an additional check to the other pipelines."," A separate pipeline, written in IRAF scripts and Perl Data, provides an additional check to the other pipelines."
 We use the method of Angular Differential Imaging (ADI; ?)) to calibrate out the presence of residual speckles in the instrument whilst preserving the flux of any faint companions., We use the method of Angular Differential Imaging (ADI; \citet[]{Marois06}) ) to calibrate out the presence of residual speckles in the instrument whilst preserving the flux of any faint companions.
 The data sets were split according to their beam switch and a master PSF for each beam position created., The data sets were split according to their beam switch and a master PSF for each beam position created.
 Any faint companions at constant position angle will be washed out in the median-combining to form the master PSF., Any faint companions at constant position angle will be washed out in the median-combining to form the master PSF.
 This PSF is then subtracted off all the individual frames., This PSF is then subtracted off all the individual frames.
" The frames are then rotated so that North is up and East to the left, and then combined using various sigma clipping rejection algorithms to produce the final sensitivity image."," The frames are then rotated so that North is up and East to the left, and then combined using various sigma clipping rejection algorithms to produce the final sensitivity image."
" At small separations 2"".0), the images are contrast limited and not sky («background limited, a result of the time varying nature of the aberrations in the telescope optics."," At small separations $(<2''.0$ ), the images are contrast limited and not sky background limited, a result of the time varying nature of the aberrations in the telescope optics."
" Although Fomalhaut is an infrared photometric standard (?),, the core of the star’s PSF in our shortest exposure (64.1 msec) appears to be saturated."," Although Fomalhaut is an infrared photometric standard \citep{vanderBliek96}, the core of the star's PSF in our shortest exposure (64.1 msec) appears to be saturated."
" For this reason, the photometric calibration was tiedto three other A-type stars observed that night: 0 UMa, ι UMa, and ¢ Lep."," For this reason, the photometric calibration was tiedto three other A-type stars observed that night: $\beta$ UMa, $\iota$ UMa, and $\zeta$ Lep."
" The stars do not have published ground-based M-band photometry, but theydo have published fluxes in the um range (?) as well as predicted"," The stars do not have published ground-based M-band photometry, but theydo have published ground-based fluxes in the $\mu$ m range \citep{Gezari99} as well as predicted"
"less than 30,000deg?, one would always choose the maximum survey area possible for SN BAO as opposed to accumulating more SNe in a smaller area.","less than $30,000\,\mbox{deg}^2$, one would always choose the maximum survey area possible for SN BAO as opposed to accumulating more SNe in a smaller area."
" Finally, we illustrate the complementarity between the SN BAO and D, techniques in Figure 3.."," Finally, we illustrate the complementarity between the SN BAO and $D_{\rm L}$ techniques in Figure \ref{fig:snb}."
" Although the 520k BAO technique (dashed line) does not place useful constraints on dark energy, its combination (shaded area) with the Dr, technique (dotted line) reduces the EP by a factor of 5.5 over the Dri-alone EP."," Although the S20k BAO technique (dashed line) does not place useful constraints on dark energy, its combination (shaded area) with the $D_{\rm L}$ technique (dotted line) reduces the EP by a factor of 5.5 over the $D_{\rm L}$ -alone EP."
" Moreover, the combined result (solid line) is not very sensitive to the CMB priors, because the BAO technique can provide adequate constraints on cosmological parameters, such as Wm and CX, for the Dr, technique."," Moreover, the combined result (solid line) is not very sensitive to the CMB priors, because the BAO technique can provide adequate constraints on cosmological parameters, such as $\omega_{\rm m}$ and $\Omega_{\rm k}$, for the $D_{\rm L}$ technique."
 We have demonstrated that SN data can be used to measure BAOs and to constrain cosmological parameters., We have demonstrated that SN data can be used to measure BAOs and to constrain cosmological parameters.
 The BAO constraints on the matter density and the baryon density are sensitive to the priors on the curvature and the scalar spectral index but not to the dark energy parameters., The BAO constraints on the matter density and the baryon density are sensitive to the priors on the curvature and the scalar spectral index but not to the dark energy parameters.
 The dark energy constraints from the SN BAO technique alone are not meaningful., The dark energy constraints from the SN BAO technique alone are not meaningful.
" However, a combination of the SN BAO and Dy techniques reduces the EP considerably, and the priors are no longer crucial."," However, a combination of the SN BAO and $D_{\rm L}$ techniques reduces the EP considerably, and the priors are no longer crucial."
 The SN BAO results in Section 4 are also applicable to galaxy BAOs., The SN BAO results in Section \ref{sec:cons} are also applicable to galaxy BAOs.
 We note that errors are a large uncertainty for SN cosmology., We note that errors are a large uncertainty for SN cosmology.
" Although our assumption about them is conservative compared to the results in Pintoetal.(2004),, further studies are needed to make realistic forecasts."," Although our assumption about them is conservative compared to the results in \citet{pinto04}, further studies are needed to make realistic forecasts."
 Long and non-uniform cadence may result in uneven sampling of the SN spatial distribution., Long and non-uniform cadence may result in uneven sampling of the SN spatial distribution.
" Fortunately, LSST will be likely to always catch the SNe (especially high-z ones) at their maximum owing to its fast sky coverage and rapid sampling."," Fortunately, LSST will be likely to always catch the SNe (especially $z$ ones) at their maximum owing to its fast sky coverage and rapid sampling."
" Furthermore, the effect of the cadence on the SN depth can be simulated and determined, and methods of correcting for uneven depths in galaxy surveys can be applied to the SN data."," Furthermore, the effect of the cadence on the SN depth can be simulated and determined, and methods of correcting for uneven depths in galaxy surveys can be applied to the SN data."
" A spectroscopic SN BAO survey will be impractical, because one would have to revisit the sky many times spectroscopically over thousands of square degrees to catch the SNe that occur at different times."," A spectroscopic SN BAO survey will be impractical, because one would have to revisit the sky many times spectroscopically over thousands of square degrees to catch the SNe that occur at different times."
" However, LSST will be able to obtain SNe in the millions over half the sky photometrically."," However, LSST will be able to obtain SNe in the millions over half the sky photometrically."
 This opens a window for applying the BAO technique to SNe and achieving more robust constraints with SN data., This opens a window for applying the BAO technique to SNe and achieving more robust constraints with SN data.
" Since this SN BAO analysis requires no additional observations than doing the SN Dy analysis alone, it should be a feature of all large-area SN cosmology analyses."," Since this SN BAO analysis requires no additional observations than doing the SN $D_{\rm L}$ analysis alone, it should be a feature of all large-area SN cosmology analyses."
" Moreover, the SN data can also help calibrate the host galaxy zss and the error distribution of other galaxies through the cross-correlation method (Schneideret2006;ZhanNewman 2008)."," Moreover, the SN data can also help calibrate the host galaxy s and the error distribution of other galaxies through the cross-correlation method \citep{schneider06,zhan06d,newman08}."
". We thank J. Frieman, L. Knox, and M. Vasey for useful conversations."," We thank J. Frieman, L. Knox, and M. Wood-Vasey for useful conversations."
 This work was partiallyWood- supported by a UC Davis Academic Federation Innovative Developmental Award., This work was partially supported by a UC Davis Academic Federation Innovative Developmental Award.
"the right hand side of equation (9)) from A,=kya to Ry,=hea.",the right hand side of equation \ref{dmdot2}) ) from $R_m=k_1 a$ to $R_m =k_2 a$.
 This gives Dor σε1 By taking Aya=Ry and hoa>a in equation (14)) we eet the total injection rate of bound mass into (he ellervescent zone A/.., This gives for $k_v \ne 1$ By taking $k_1a=R_0$ and $k_2 a \gg a $ in equation \ref{deltame}) ) we get the total injection rate of bound mass into the effervescent zone $\dot M_e$.
" Using the inequality Aya2Ry. we get then As representative numbers let us take fy=2/3. ο=2. hy,=0. a=20H (sav Ry,=5AU anda100 AU). and let the companion accrete a fraction 29e0.5 of the mass in the shell πια<BR,hea."," Using the inequality $k_1a \gg R_0$, we get then As representative numbers let us take $k_1=2/3$, $k_2=2$, $k_v=0$, $a =20 R_0$ (say $R_0=5 \AU$ and $a=100 \AU$ ), and let the companion accrete a fraction $\beta\sim 0.5$ of the mass in the shell $k_1 a<R_m <k_2 a$."
" The aceretion rate from the ellervescent zone is then Mace=JM,Ryfla0.0252.M,.", The accretion rate from the effervescent zone is then $\dot M_{\rm acc} = \beta \dot M_e {R_0}/{2a}=0.025 \beta M_e$.
" I take the accreting companion to be a main sequence star. (hat ejects (wo jets with a total mass loss rate of M,=0.Λο. and a speed οἱ e;=600kms+."," I take the accreting companion to be a main sequence star, that ejects two jets with a total mass loss rate of $\dot M_j=0.1 \dot M_{\rm acc} $, and a speed of $v_j=600 \km \s^{-1}$."
 The ratio of mass loss rate into the two jets and slow wind for these parameters 1s This ratio is enough for the jets to substantially shape the nebula into a bipolar PN (Akashi 2008)., The ratio of mass loss rate into the two jets and slow wind for these parameters is This ratio is enough for the jets to substantially shape the nebula into a bipolar PN (Akashi 2008).
 An accreting WD companion has much faster jets. ancl can have a much lower accretion rate and still shape the nebula.," An accreting WD companion has much faster jets, and can have a much lower accretion rate and still shape the nebula."
 If the accreting main sequence stars accretes al a much lower rate. it might lead to the formation of an elliptical PN. rather than a bipolar PN (Soker 2001a).," If the accreting main sequence stars accretes at a much lower rate, it might lead to the formation of an elliptical PN, rather than a bipolar PN (Soker 2001a)."
 This paper deals with a phenomenological study of a possible extended region of bound eas around AGB stars experiencing high mass loss rates., This paper deals with a phenomenological study of a possible extended region of bound gas around AGB stars experiencing high mass loss rates.
 The main motivation to propose (he effervescent model is to allow wide binary companions to influence (he morphology of the descendant PN., The main motivation to propose the effervescent model is to allow wide binary companions to influence the morphology of the descendant PN.
 For (that. a wide binary companion should accrete mass. forms an accretion disks. ancl blows jets (Soker 2001a).," For that, a wide binary companion should accrete mass, forms an accretion disks, and blows jets (Soker 2001a)."
 The mass accretion rate and specific angular momentum of (he accreted gas increase wilh decreasing wind speed., The mass accretion rate and specific angular momentum of the accreted gas increase with decreasing wind speed.
 Therefore. accretion from a slowly moving gas. with velocities below the escape velocity from the AGB star. is a more ellicient process (han accretion from a wind.," Therefore, accretion from a slowly moving gas, with velocities below the escape velocity from the AGB star, is a more efficient process than accretion from a wind."
We have performed aperture photometry of both clusters using au aperture with a 6-pixel radius.,We have performed aperture photometry of both clusters using an aperture with a 6-pixel radius.
 The backerouud was measured withiu au aunulis with radii 6 aud 5 pixels and subtractec., The background was measured within an annulus with radii 6 and 8 pixels and subtracted.
" Stellar"" crowcdiug alda highly variable backerouucl Limit he precision of the photometry.", Stellar crowding and a highly variable background limit the precision of the photometry.
" The derived uiaguitudes are co‘rectec for Galactic extinction using Ay = 0.12 mag (Schlegeletal.1998) aud trausforiued to the staudard V2 system using Holtzinaietal(1995b)"" prescriptions."," The derived magnitudes are corrected for Galactic extinction using $A_V$ = 0.12 mag \citep{S98}
 and transformed to the standard $VI$ system using \citet{Ho95b}' ' prescriptions."
 For cluster A we obtain / = 17.97 d- 0.02., For cluster A we obtain $I$ = 17.97 $\pm$ 0.02.
 As for cluster B. V = 18.61 + 0.02. / = 18.92 + 0.02 aud V—/ = —0.28 + 0.03.," As for cluster B, $V$ = 18.64 $\pm$ 0.02, $I$ = 18.92 $\pm$ 0.02 and $V-I$ = –0.28 $\pm$ 0.03."
 Since our V. image of cluster A is satirated. we caunot compare our photometry with that of Drissenetal.(2000).," Since our $V$ image of cluster A is saturated, we cannot compare our photometry with that of \citet{Dr00}."
. However for cluser B our V inagnitude is 0.) mae fainter., However for cluster B our $V$ magnitude is 0.3 mag fainter.
 To check our phooletry. we Lave retrieved [rori theHST archives the Drissenetal.(2000) ünages. aud have derived from them V = 18.66 4E ().03 lor cluster B. iu excellent agreement witli the measurements rou our image.," To check our photometry, we have retrieved from the archives the \citet{Dr00} images, and have derived from them $V$ = 18.66 $\pm$ 0.03 for cluster B, in excellent agreement with the measurements from our image."
 The «il'erence is probably due to a larger aperture used by Drisseretal.(20t(2000) although they do lol precise it in their article., The difference is probably due to a larger aperture used by \citet{Dr00} although they do not precise it in their article.
 With a distauce modulus nm—A1 27.67. the absolute / imagLittces of clusters A and B are respecively —9.70 nag and 8.5);——," With a distance modulus $m-M$ = 27.67, the absolute $I$ magnitudes of clusters A and B are respectively –9.70 mag and –8.75 mag."
 uag., Fig.
 Fig2.0 shows tle CNDs for region slaid UL., \ref{Fig9} shows the CMDs for regions I and II.
 These are dominatedby yourο stellar populatious., These are dominatedby young stellar populations.
 They oth. contain IS sars with ages Z5 10 Myr., They both contain MS stars with ages $\la$ 10 Myr.
 Region IE also coutains two RSCG stars with ages 10 Ivy (the two brieltest stars wlh V—4/-Ls5)., Region I also contains two RSG stars with ages $>$ 10 Myr (the two brightest stars with $V-I$ $\sim$ 1.8).
 Fie., Fig.
 9 shows also as ibstantia population of mo'e evolved AGB and RGB stars. with ages ranging from  100 Myr to Zod Cyr.," \ref{Fig9} shows also a substantial population of more evolved AGB and RGB stars, with ages ranging from $\sim$ 100 Myr to $\ga$ 1 Gyr."
 The remarkable featwe of the CÀD of region IL is the presence of numerois RSG stars., The remarkable feature of the CMD of region II is the presence of numerous RSG stars.
 first notec the presence of these stars aud estimated their age to be ~ 10 Myr.," \citet{Dr00}
 first noted the presence of these stars and estimated their age to be $\sim$ 10 Myr."
 Our comparison with the tlieretical isoch‘oues of Berellietal.(1991) for the metallicity Z = 0.001 shows that the ages o ‘the RSC stars rauge betwe 10 and 30 Myr. in agreement with 000).," Our comparison with the theoretical isochrones of \citet{Be94} for the metallicity $Z$ = 0.001 shows that the ages of the RSG stars range between 10 and 30 Myr, in agreement with \citet{No00}."
. Thus. although there is presently asig burst of star formation. many of the stars iu regions I and II we'e born over a long period of sar formation which started o= ] Gyr ago.," Thus, although there is presently a strong burst of star formation, many of the stars in regions I and II were born over a long period of star formation which started $\ga$ 1 Gyr ago."
 To quantify our statemetts. we have calculated the 1lliber ratios of dillerent stellar types with 4 «€ 25 mag.," To quantify our statements, we have calculated the number ratios of different stellar types with $I$ $\leq$ 25 mag."
 For regions I and IL we obtain respectiveM7 IS/RGB = 3.31 and 2.02. (BLERSG)/RGB 2.16 and 2.17. and ACIB/BRGB = 0.18 aud 0.21.," For regions I and II we obtain respectively MS/RGB = 3.34 and 2.02, (BL+RSG)/RGB = 2.16 and 2.17, and AGB/RGB = 0.18 and 0.24."
 The values of these ratios coufirm our statement that vouug stellar populations are cloninant iu regions I aud II., The values of these ratios confirm our statement that young stellar populations are dominant in regions I and II.
 To study variatious in the spatial cistributious of the stellar populatious 1i the main body located in the WE3 frame. it is convenient to divide it into three regious labelec 3-1 to 3-3. with the latter being closest to regious I aud II discussed in the preceding section (Fig.," To study variations in the spatial distributions of the stellar populations in the main body located in the WF3 frame, it is convenient to divide it into three regions labeled 3-1 to 3-3, with the latter being closest to regions I and II discussed in the preceding section (Fig."
 10aa)., \ref{Fig10}a a).
 Region 3-1 which is outside the cleusest part of the main body is used as comparison., Region 3-4 which is outside the densest part of the main body is used as comparison.
 The fou “nost prominent stellar open clusters are labeled Cl to CL and the circle indicates a compact H region., The four most prominent stellar open clusters are labeled C1 to C4 and the circle indicates a compact H region.
 Regious located to the west of the main body in the ΕΣ frame are shown in Fig., Regions located to the west of the main body in the WF2 frame are shown in Fig.
 10 jb. They will be, \ref{Fig10}b b. They will be
sets of model parameters;,sets of model parameters.
 Namely. we obtain similar values of the reduced 47? (~1.2) for all erain sizes eZ0.Lina.," Namely, we obtain similar values of the reduced $\chi^2$ $(\sim1.2)$ for all grain sizes $a\simgreat 0.4$."
 Over this range of ας inclination auc position anele vary in the intervals 157NU and 6071207. respectively. with lower inclinations for larecr grains.," Over this range of $a$, inclination and position angle vary in the intervals $45^\circ - 80^\circ$ and $60^\circ - 120^\circ$, respectively, with lower inclinations for larger grains."
 The correlation between + aud PA is very strong. aud the uncertainties iu these two paraueters remain very large even for fixed. à.," The correlation between $\iota$ and $PA$ is very strong, and the uncertainties in these two parameters remain very large even for fixed $a$."
 Although the fit is never verv good. the VV Ser SED is better accounted for by large erains (sec the right pancl of Fig.1)) aud in Table 2 we show the best values of the ΡαΠΟΙΟΥΣ ore©1.2;nu.," Although the fit is never very good, the VV Ser SED is better accounted for by large grains (see the right panel of \ref{fig:VVSer_HA}) ) and in Table 2 we show the best values of the parameters for $a\geq 1.2$."
". The rim effective temperature is LLOO Ts. the near-infrared excess is ofL,."," The rim effective temperature is 1400 K, the near-infrared excess is of."
. The lanited number of visibility poiuts does not allow us to constrain all the parameters ofthe disk., The limited number of visibility points does not allow us to constrain all the parameters ofthe disk.
" Fig.5 shows two models. with the sune level of coufidence (42~1): the Wo models have similar orieutatious Guclinatious of 52° and 167 with position angles of 168"" and 1617 respectively) but very different grain sizes (0= 0.340 and oz 12pm) aud radii of the inner rim (0.25AU aud 0.16AU. respecively)."," \ref{fig:CQTau_HA} shows two models, with the same level of confidence $(\chi^2_r \sim 1)$; the two models have similar orientations (inclinations of $^{\circ}$ and $^{\circ}$ with position angles of $^{\circ}$ and $^{\circ}$ respectively) but very different grain sizes $a=0.3\mu$ m and $a \geq 1.2 \mu$ m) and radii of the inner rim (0.25AU and 0.16AU, respectively)."
" For «z 1.2,uu. the effective temperature of the rim (at Z=0) is Ti,=LISON. while εξ1050 for «= n3. The SEDs of the two models are compatible with the observed fluxes. with Lyjg=1354LS."," For $a \geq 1.2 \mu$ m, the effective temperature of the rim (at z=0) is $T_{eff}=1480K$, while $T_{eff}=1050$ for $a=0.3\mu$ m. The SEDs of the two models are compatible with the observed fluxes, with $L_{NIR}=13\%-18\%$."
 All the models with ο within this ranec. aud similar / aud PA. have sinilu 47 values.," All the models with $a$ within this range, and similar $\iota$ and $PA$, have similar $\chi^2$ values."
 Outside this range. models give a much poorer fit to the data.," Outside this range, models give a much poorer fit to the data."
 As for MWC 758. the visibility data coustrain well the orientation of the disk ou the sky.," As for MWC 758, the visibility data constrain well the orientation of the disk on the sky."
 The iuclination. iu particular. has to be quite large. 1075;5557," The inclination, in particular, has to be quite large, $40^{\circ} \simless \iota \simless 55^{\circ}$."
 The PTI observations of V1295 Aq] are characterized by a very small nunber of visibility points and the disk parameters are hardly constrained., The PTI observations of V1295 Aql are characterized by a very small number of visibility points and the disk parameters are hardly constrained.
 Even adding the IOTÀ data does not help due to the big errors that affect these observations., Even adding the IOTA data does not help due to the big errors that affect these observations.
 Note also that PTI and IOTA observations are performed at different waveleugths. Ix and II respectively.," Note also that PTI and IOTA observations are performed at different wavelengths, K and H respectively."
 As for CO Tan. we show the mwels for the two extreme sets of paraicters that eive au equally eood fit (Fig.6)) with 2l1.," As for CQ Tau, we show the models for the two extreme sets of parameters that give an equally good fit \ref{fig:V1295_HA}) ) with $\chi^2_r \sim 1$."
 All the intermediate combinations of e. + aud PA can explain he observations as well.," All the intermediate combinations of $a$, $\iota$ and PA can explain the observations as well."
 Iu order to fit the values of visibility. au inclination ranging between LO and 657 is required.," In order to fit the values of visibility, an inclination ranging between $40^\circ$ and $65^\circ$ is required."
 More face-ou svstenis can not iu general reproduce the visibility spread iu the IOTA data and the V?HA diasiour of the PTT points., More face-on systems can not in general reproduce the visibility spread in the IOTA data and the $V^2-HA$ behaviour of the PTI points.
" The grain radius varies from à2opum (H4,=0 7AU. Tog= l1100A) tog= μαι (Rey,= L.2AU. Topp Οτο} while the position angle cau no be defined at all."," The grain radius varies from $a\geq1.2\mu$ m $\Rrim=0.7$ AU, $T_{eff}=1400K$ ) to $a=0.3\mu$ m $\Rrim=1.2$ AU, $T_{eff}=970K$ ) while the position angle can not be defined at all."
 The right paucl of Fis.6 shows the couparison between the observed aud the predicted SED., The right panel of \ref{fig:V1295_HA} shows the comparison between the observed and the predicted SED.
" More inclined disks can du general reproduce better the photometric iueasureiments around L5jau. The near-infrared emission of disk with an inclination of less than HO’ is peaked at about [pin aud can not reproduce the infrared excess between μι and 2,44: in both models. the integrated near-nfrared Hux is Lyyy~20% L,."," More inclined disks can in general reproduce better the photometric measurements around $\mu$ m. The near-infrared emission of disk with an inclination of less than $^\circ$ is peaked at about $4\mu$ m and can not reproduce the infrared excess between $\mu$ m and $\mu$ m; in both models, the integrated near-infrared flux is $L_{NIR}\sim 20\%$ ."
. Also iu this case. due to the narrow range of available baseliues. the PTI visibilities of NIC. £80 are consistent with different sets of paranueters at the same level of confidence (A?~ 2) ," Also in this case, due to the narrow range of available baselines, the PTI visibilities of MWC 480 are consistent with different sets of parameters at the same level of confidence $(\chi^2_r\sim2)$ ."
Fig.7 shows the two extreme disk configeuratious characterized by quite simular parameters for the dust erai size (αἱ=O.2y;an O.3¢an Πριν 0.G3ÀU-0.53AU aud Ti;gz 1250). but very different values of the inclination (@=35° aud += 607)aud the position angle (¢=607 and c= 1687).," \ref{fig:MWC480_vis2} shows the two extreme disk configurations characterized by quite similar parameters for the dust grain size $a=0.2\mu$ $-0.3\mu$ m; $\Rrim=0.63$ AU-0.53AU and $T_{eff}\simeq
1250K$ ), but very different values of the inclination $\iota=35^{\circ}$ and $\iota=60^{\circ}$ )and the position angle $\psi=60^{\circ}$ and $\psi=168^{\circ}$ )."
 Several intermediate configurations reproduce the observed data, Several intermediate configurations reproduce the observed data
with scale.,with scale.
 It is a matter of taste whether one chooses to describe this scale as one of circular velocity. lass. or potential well depth.," It is a matter of taste whether one chooses to describe this scale as one of circular velocity, mass, or potential well depth."
 It is tempting to attribute this correlation to feedback processes being more effective in objects with sinaller poteutial wells (Dekel&Silk1986)., It is tempting to attribute this correlation to feedback processes being more effective in objects with smaller potential wells \citep{DS}.
. However. the details are heinously complicated (Alaver&Moore2001:eresetal.2009). aud not well understood.," However, the details are heinously complicated \citep{MayerMoore,crazy} and not well understood."
 We would naively expect feedback to be a messy process resulting iu lots of scatter in any correlations that might result., We would naively expect feedback to be a messy process resulting in lots of scatter in any correlations that might result.
 Iustead. the observed relation is remarkably tight.," Instead, the observed relation is remarkably tight."
 Iu principle. the eutire rauge 0xfia< Lois accessible at cach mass. vet only a very particular value is observed.," In principle, the entire range $0 \le f_d \le 1$ is accessible at each mass, yet only a very particular value is observed."
 Moreover. the current potential well is the result of the lierarchical asscuubly of many smaller building blocks.," Moreover, the current potential well is the result of the hierarchical assembly of many smaller building blocks."
 Left to itself. a s12all dark matter halo will have a simall fae," Left to itself, a small dark matter halo will have a small $f_d$."
 TE iucorporated iuto a larger halo. fy goes up.," If incorporated into a larger halo, $f_d$ goes up."
 How does cach building block know to bring the right aiiount of barvous to the final halo?, How does each building block know to bring the right amount of baryons to the final halo?
 We do not see a satisfactory solution to this missing barvon problems at preseut., We do not see a satisfactory solution to this missing baryon problem at present.
 Considerable work reais to be done to obtain a complete understanding of the universe and its contents., Considerable work remains to be done to obtain a complete understanding of the universe and its contents.
 The work of ds supported iu part by NSF erant AST 0505956., The work of is supported in part by NSF grant AST 0505956.
 was supported by an REU supplement from the NSF., was supported by an REU supplement from the NSF.
 The work of iis based upon research supported bv the South African Research Chairs Initiative of the Departineut of Science and Technology and National Research Foundation., The work of is based upon research supported by the South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation.
"calculated magnitude of each asteroid were found for each subtraction, using a custom parallelized Python code that made use of the Minor Planet Center asteroid datatables?.","calculated magnitude of each asteroid were found for each subtraction, using a custom parallelized Python code that made use of the Minor Planet Center asteroid data."
". This code, which typically runs 10x to 100x faster than queries to the minor planet center site, is made available by us for the community as an openwebservice’."," This code, which typically runs $\times$ to $\times$ faster than queries to the minor planet center site, is made available by us for the community as an open."
. We identified 19954 asteroids within the subtraction footprint., We identified 19954 asteroids within the subtraction footprint.
" We created a subsample of those with good («10—15 "")) a priori location accuracy from the catalog, bright enough to have been detected (i.e., the catalog magnitude at least as bright as the limiting magnitude of the image), and which were not close to the edges of the arrays (position >30"" from the nearest edge)."," We created a subsample of those with good $<10-15$ ) a priori location accuracy from the catalog, bright enough to have been detected (i.e., the catalog magnitude at least as bright as the limiting magnitude of the image), and which were not close to the edges of the arrays (position $>30 \arcsec$ from the nearest edge)."
" Further, so as not to identify candidates associated with elongated asteroid observations, we restricted the sample to asteroids calculated to have a proper motion at the time of observation of less than 50 arcsecond per hour, resulting in less than 0.83 arcsecond of total motion during the one minute exposure."," Further, so as not to identify candidates associated with elongated asteroid observations, we restricted the sample to asteroids calculated to have a proper motion at the time of observation of less than 50 arcsecond per hour, resulting in less than 0.83 arcsecond of total motion during the one minute exposure."
 There were 9034 asteroid-associated candidates in this subsample., There were 9034 asteroid-associated candidates in this subsample.
 Figure 4 shows the distribution of asteroids relative to the nearest candidates on the sky., Figure \ref{fig:rocks} shows the distribution of asteroids relative to the nearest candidates on the sky.
 Figure 5 shows a validation of the ML-classified realbogus on these candidates., Figure \ref{fig:rocksrb} shows a validation of the ML-classified realbogus on these candidates.
" Nominally all these candidates are taken to be bona fide “sources,” providing a ground-truth set for us to test the ML-classifier. ["," Nominally all these candidates are taken to be bona fide “sources,” providing a ground-truth set for us to test the ML-classifier. ["
"In practice, however, near the faint end of the distribution there will be some pollution of this set with bad-subtraction candidates: if a known (faint) asteroid happens to be near a poorly-subtracted region, that candidate will be incorrectly included in the sample.]","In practice, however, near the faint end of the distribution there will be some pollution of this set with bad-subtraction candidates: if a known (faint) asteroid happens to be near a poorly-subtracted region, that candidate will be incorrectly included in the sample.]"
 There is a clear trend for brighter candidates to receive a higher realbogus value., There is a clear trend for brighter candidates to receive a higher realbogus value.
 There are many sources with realbogus around 0.35-0.50 that show no trend with magnitude; this locus reflects the distribution of the classifier output convolved with the weighting scheme (eq. 1))., There are many sources with realbogus around 0.35–0.50 that show no trend with magnitude; this locus reflects the distribution of the classifier output convolved with the weighting scheme (eq. \ref{eq:rbi}) ).
" The line near realbogus=0.2 (FNR=0.18) is in rough agreement with, but higher than, the FNR predicted (~0.11) from the training set reffig:rbroc;; blue squares)."," The line near realbogus=0.2 (FNR=0.18) is in rough agreement with, but higher than, the FNR predicted $\sim 0.11$ ) from the training set \\ref{fig:rbroc}; blue squares)."
 This difference might be in part explained by the inclusion of candidates in the asteroid set., This difference might be in part explained by the inclusion of bad-subtraction candidates in the asteroid set.
" Since most asteroids are found far from stars and galaxies on the sky, there is a legitimate concern that this introspection is only validating the ability of the ML-classifier to identify spatially-isolated transients."," Since most asteroids are found far from stars and galaxies on the sky, there is a legitimate concern that this introspection is only validating the ability of the ML-classifier to identify spatially-isolated transients."
" However, by selecting the two dozen candidate asteroids that happen to be near (« 1"") detected objects in the reference images (x symbols in reffig:rocksrb)) we find no clear trend of those sources to be preferentially different in their realbogus values."," However, by selecting the two dozen candidate asteroids that happen to be near $<1 \arcsec$ ) detected objects in the reference images $\times$ symbols in \\ref{fig:rocksrb}) ) we find no clear trend of those sources to be preferentially different in their realbogus values."
 The metrics used in automatically classifying individual subtractions (Table 1)) relate entirely to the candidate itself and not its surroundings (save the parameter)., The metrics used in automatically classifying individual subtractions (Table \ref{tab:features}) ) relate entirely to the candidate itself and not its surroundings (save the parameter).
 Candidates, Candidates
Another method of characterizing nearby clusters is the temperature function. which does not require a mass determination.,"Another method of characterizing nearby clusters is the temperature function, which does not require a mass determination."
 The distribution of cluster temperatures is sensitively dependent on the cosmological model: in Ostrikeretal.(2005).. which used the first-vear WAIAP power spectrum amplitude. the fit to observations was inadequate.," The distribution of cluster temperatures is sensitively dependent on the cosmological model; in \citet{OstrikerBB05}, which used the first-year WMAP power spectrum amplitude, the fit to observations was inadequate."
 Shown in Fig. are (wo measurements of the cumulative temperature function. with different methods of determining (he cluster temperature: Ikebeetal.(2002). excluded cluster cores when fitting for 2. while Henry.(2004). did not.," Shown in $.$ \\ref{fig:noft} are two measurements of the cumulative temperature function, with different methods of determining the cluster temperature: \citet{IkebeRBTK02} excluded cluster cores when fitting for $T$, while \citet{Henry04} did not."
" For purposes of comparison. we took from the simulation a ""light cone” covering one octant of the skv out to z=0.2."," For purposes of comparison, we took from the simulation a “light cone” covering one octant of the sky out to $z=0.2$."
 This covers the redshift range used in the observations. although thev are not volume limited.," This covers the redshift range used in the observations, although they are not volume limited."
 During the simulation. the matter distribution in a series of thin shells was saved: the radius of each shell corresponds to the light travel time from a z=0 observer silting al the origin of the box. and its width corresponds to the time interval between shells.," During the simulation, the matter distribution in a series of thin shells was saved; the radius of each shell corresponds to the light travel time from a $z=0$ observer sitting at the origin of the box, and its width corresponds to the time interval between shells."
 Thus a volume-Inmited mass distribution. including time evolution. is obtained.," Thus a volume-limited mass distribution, including time evolution, is obtained."
 Locating halos and adding gas was done in (he same manner as before., Locating halos and adding gas was done in the same manner as before.
 To compute the star/gas ralio al z>0. the star formation rate was assumed to follow a delaved exponential model (Eqn.1ofNagamineetal. 2006).. with decay time 7= IGvr.," To compute the star/gas ratio at $z>0$, the star formation rate was assumed to follow a delayed exponential model \citep[Eqn. 1 of][]{NagamineOFC06}, , with decay time $\tau=1$ Gyr."
" Both Ένα and 7i, are shown for the ej;=5x10> feedback moclel in Fig. relfig:nolt..", Both $T_{ew}$ and $T_{sp}$ are shown for the $\epsilon_f=5\times 10^{-5}$ feedback model in $.$ \\ref{fig:noft}.
" Because our cosmological parameters were chosen in part to match large-scale structure observations. and the simulated A344,—7 relation matches that of nearby clusters. il is not surprising that our simulated temperature function is a reasonable fit to the observed one."," Because our cosmological parameters were chosen in part to match large-scale structure observations, and the simulated $M_{500}-T$ relation matches that of nearby clusters, it is not surprising that our simulated temperature function is a reasonable fit to the observed one."
 Our ζω. whieh includes the core. gives a higher abundance in the 3—6 keV range than the Henry(2004). data. while our Το. excluding the core. instead gives a lower abundance than Ikebeetal.(2002).," Our $T_{ew}$, which includes the core, gives a higher abundance in the $3-6$ keV range than the \citet{Henry04} data, while our $T_{sp}$, excluding the core, instead gives a lower abundance than \citet{IkebeRBTK02}."
. The zero feedback model appears to give temperatures that are loo low: thus based simply on 2. il appears that some non-gravitational energy input is required io explain the properties of existing clusters.," The zero feedback model appears to give temperatures that are too low; thus based simply on $T$, it appears that some non-gravitational energy input is required to explain the properties of existing clusters."
 The model with feedback and. WMADP 3-vear cosmological parameters now provides a eood fit to the observed temperature function., The model with feedback and WMAP 3-year cosmological parameters now provides a good fit to the observed temperature function.
 Other cluster observables are more dependent on the gas density. most notably X-ray Inminosity.," Other cluster observables are more dependent on the gas density, most notably X-ray luminosity."
" The top panel of Fie. relfig:IxandE shows the £L,—T relation of our simulated catalog for three values of feedback. again with medians shown as lines and shaded regions enclosing of the clusters: here L,, is (he bolometric luminosity inside a projected radius of fij."," The top panel of $.$ \\ref{fig:lxandf} shows the $L_x-T$ relation of our simulated catalog for three values of feedback, again with medians shown as lines and shaded regions enclosing of the clusters; here $L_x$ is the bolometric luminosity inside a projected radius of $R_{500}$."
" Unlike the M—T' relation. Ieedback produces a sienilicant change in L, at a given temperature because (he Brenisstrahlilung enission is proportional to the square ofthe eas density. but otherwise there are similar trends seen."," Unlike the $M-T$ relation, feedback produces a significant change in $L_x$ at a given temperature because the Bremsstrahlung emission is proportional to the square ofthe gas density, but otherwise there are similar trends seen."
 Again the elfect of feedback is less important in the most massive clusters. where," Again the effect of feedback is less important in the most massive clusters, where"
since G2 is composed of (he most massive GC's of the sample. their high mass max be the cause of (he multiple star formation episodes. more massive GCs being able to retain (heir metals for future generations of stars.,"Since G2 is composed of the most massive GCs of the sample, their high mass may be the cause of the multiple star formation episodes, more massive GCs being able to retain their metals for future generations of stars."
 A hint of a mass-metallicity relation can indeed be seen in Fig.10. if one ignores the low-mass GCs (those of G3). in the sense that there are no massive and metal-poor GCs in NGC 5128.," A hint of a mass-metallicity relation can indeed be seen in Fig.10, if one ignores the low-mass GCs (those of G3), in the sense that there are no massive and metal-poor GCs in NGC 5128."
 G3. on the contrary. is composed of low-mass. dvnamically voung GC's. and populates preferentially (he external regions of the galaxy.," G3, on the contrary, is composed of low-mass, dynamically young GCs, and populates preferentially the external regions of the galaxy."
 This suggests that the GCs of this group were lormed in satellite dwarl galaxies which were later progressively accreted into the halo of the galaxy ancl subsequently disrupted., This suggests that the GCs of this group were formed in satellite dwarf galaxies which were later progressively accreted into the halo of the galaxy and subsequently disrupted.
 It is likely that most accretion events occurred recently. since their probability increases with the mass of the attracting galaxy.," It is likely that most accretion events occurred recently, since their probability increases with the mass of the attracting galaxy."
 The metallicity range of the metal-poor component of G3 points to progenitor galaxies of luminosities in the range LOX—LO’L.. assuming that they have the same metallicity and a standarcl Iuminositv-metallicitv relation (e.g. Lamareille et al 2009).," The metallicity range of the metal-poor component of G3 points to progenitor galaxies of luminosities in the range $10^8 - 10^9
L_{\odot}$, assuming that they have the same metallicity and a standard luminosity-metallicity relation (e.g. Lamareille et al 2009)."
 The accretion and disruption of such low-mass galaxies could also explain a tidal stream of voung stars cliscoverecl in the halo of NGC 5128 (Peng et al., The accretion and disruption of such low-mass galaxies could also explain a tidal stream of young stars discovered in the halo of NGC 5128 (Peng et al.
 2002)., 2002).
 Such accretion events may substantially increase the number of GCs in NGC 5128. because the number of GCs per unit galaxv mass (ον) can be verv high in the low-mass galaxies of the Centaurus group (e.g. Sy = 100 for IKIN221. Puzia Sharina. 2008).," Such accretion events may substantially increase the number of GCs in NGC 5128, because the number of GCs per unit galaxy mass $S_N$ ) can be very high in the low-mass galaxies of the Centaurus group (e.g. $S_N$ = 100 for KK221, Puzia Sharina, 2008)."
 The metal-xich. component of G3 might have originated in the accretion of slightly larger galaxies. like the LAIC (see below). or. alternatively. be the low-mass end of GI and/or G2.," The metal-rich component of G3 might have originated in the accretion of slightly larger galaxies, like the LMC (see below), or, alternatively, be the low-mass end of G1 and/or G2."
 The GCs of GI have properties which are intermediate between those of G2 and G3. in mass and denamical evolution.," The GCs of G1 have properties which are intermediate between those of G2 and G3, in mass and dynamical evolution."
 Thev are also marginally vounger than those of G2., They are also marginally younger than those of G2.
 Furthermore. (hese GC's rotate in the same sense as (he gaseous component. but much more slowly so.," Furthermore, these GCs rotate in the same sense as the gaseous component, but much more slowly so."
 They might thus have originated in a galaxy Chat merged with NGC 5128. giving rise lo the dust lane and mavbe also the shells. aud (hat is still in (he process of settling," They might thus have originated in a galaxy that merged with NGC 5128, giving rise to the dust lane and maybe also the shells, and that is still in the process of settling"
The mass conservation equation the adiabatic internal energy. equation. the induction equation op retain their usual forms.,"The mass conservation equation the adiabatic internal energy equation, and the induction equation retain their usual forms."
 The internal energy per particle ο is defined by For an isothermal gas. the energy. equation is replaced with The variables in these equations have their usual meanings.," The internal energy per particle $\epsilon$ is defined by For an isothermal gas, the energy equation is replaced with The variables in these equations have their usual meanings."
 We shall also introduce the constant q. which is a parameter describing the local radial dependence of the angular frequency. Le. qΞdInOfdInA.," We shall also introduce the constant $q$, which is a parameter describing the local radial dependence of the angular frequency, i.e., $q = - {d \ln
\Omega}/{d \ln R}$."
 For a Ixeplerian angular momentum cistribution. q=3/2.," For a Keplerian angular momentum distribution, $q
= 3/2$."
 In this study we have ignored. vertical gravity. ancl have thus dropped. the 7:2 term from equation (1)).," In this study we have ignored vertical gravity, and have thus dropped the $\Omega^2 z \mathbf{\hat{z}}$ term from equation \ref{euler}) )."
 These equations are solved using the time-explicit. operator-split finite dillerencing algorithm of the ZEUS code for hydrodynamics (Stone&Norman1992a) anc MID (Stone&Norman19052:LawleyStone 1995)..," These equations are solved using the time-explicit, operator-split finite differencing algorithm of the ZEUS code for hydrodynamics \citep{sn92a} and MHD \citep{sn92b, hs95}. ."
" The shearing box computational domainextends in .r. jy. and 2 respectively from L./2 to |L,/2. 0 to Ly. 0 to L."," The shearing box computational domainextends in $x$ , $y$, and $z$ respectively from ${-L_{x}}/{2}$ to $+{L_{x}}/{2}$, 0 to $L_{y}$, 0 to $L_{z}$ ."
" The boundary conditions are periodic in both the y and > directions. and. “shearing periodic"" in.r. meaning we equate The azimuthal velocity has an additional correction to ollsct the angular velocity cüllerence between the inner ancl outer racial boundaries: The initial state is one of uniform density απο pressure. and the velocity profile is v=qQuew."," The boundary conditions are periodic in both the $y$ and $z$ directions, and “shearing periodic” in $x$, meaning we equate The azimuthal velocity has an additional correction to offset the angular velocity difference between the inner and outer radial boundaries: The initial state is one of uniform density and pressure, and the velocity profile is ${\mathbf v} = -q\Omega x \mathbf{\hat{y}}$."
 In this paper. our initial magnetic field configurations are either a uniforni toroidal magnetic field. or a vertical magnetic field varving sinusoidally in the radial vw direction.," In this paper, our initial magnetic field configurations are either a uniform toroidal magnetic field, or a vertical magnetic field varying sinusoidally in the radial $x$ direction."
 The magnetic field strength is described by the standard. plasma <7 parameter the ratio of the gas to magnetic pressures., The magnetic field strength is described by the standard plasma $\beta$ parameter the ratio of the gas to magnetic pressures.
 The MIB is triggered by seceding the initial equilibrium state with small pressure and. velocity Huctuations., The MRI is triggered by seeding the initial equilibrium state with small pressure and velocity fluctuations.
 One of the goals of shearing box simulations has been to try to understand what determines the sustained saturation amplitude of the MltlI-driven turbulence., One of the goals of shearing box simulations has been to try to understand what determines the sustained saturation amplitude of the MRI-driven turbulence.
" In accretion clisk applications. the focus is often on the Zi, component of the combined Ievnolds and Maxwell stress tensor. Ilere or, is the azimuthal velocity Ductuation. obtained by subtracting the equilibrium shear Low."," In accretion disk applications, the focus is often on the $T_{r\phi}$ component of the combined Reynolds and Maxwell stress tensor, Here $\delta v_{y}$ is the azimuthal velocity fluctuation, obtained by subtracting the equilibrium shear flow."
 TFhis can be clirectly measured in shearing box simulations., This can be directly measured in shearing box simulations.
 Phe volume-averaged stress is usually normalized. to the averaged: gas pressure. a quantity equivalent to the (Shakura1073) à parameter.," The volume-averaged stress is usually normalized to the averaged gas pressure, a quantity equivalent to the \citep{ss73} $\alpha$ parameter."
 Even with a system as simple as the shearing box. there are many possible factors. both computational as well as physical. that could in principle govern the saturation amplitude.," Even with a system as simple as the shearing box, there are many possible factors, both computational as well as physical, that could in principle govern the saturation amplitude."
 These include the initial field. strength. and geometry. box size and aspect ratio. value of 9. background gas pressure. and numerical resolution.," These include the initial field strength and geometry, box size and aspect ratio, value of $\Omega$, background gas pressure, and numerical resolution."
 Many. of these are physically significant only in relation to others., Many of these are physically significant only in relation to others.
 For example. QO is an arbitrary time scale in the system.," For example, $\Omega$ is an arbitrary time scale in the system."
 The shearing box system is independent of O so long as q remains constant ancl the physical box size changes proportionately., The shearing box system is independent of $\Omega$ so long as $q$ remains constant and the physical box size changes proportionately.
 The formal scaling invariance is that if where e is an arbitrary constant. then the equations remain unchanged if We will make use of this fundamental property in ΚΕ when we explore chaotic behavior.," The formal scaling invariance is that if where $c$ is an arbitrary constant, then the equations remain unchanged if We will make use of this fundamental property in 4 when we explore chaotic behavior."
 For the cases of an initial uniform field oriented. along either the jy or z axes. Lawley.Ganiumic&Balbus(1995) founcd that the saturation. amplitude of the turbulence depended upon both the box size and initial field strength.," For the cases of an initial uniform field oriented along either the $y$ or $z$ axes, \cite{hgb95} found that the saturation amplitude of the turbulence depended upon both the box size and initial field strength."
 When the Ποιά had a vanishing mean value over the computational box volume. the final outcome was much less sensitive to the initial field. energy.," When the field had a vanishing mean value over the computational box volume, the final outcome was much less sensitive to the initial field energy."
 Here. we present a series of zero mean [field simulations designed. to. test how the box size alfects the overall level of the turbulence.," Here, we present a series of zero mean field simulations designed to test how the box size affects the overall level of the turbulence."
" The baseline. calculation. has ¢=1.5 corresponding to a Keplerian background. and a box size of L,=1. Ly,=2a. and L.=1. set so that Le=οὉ where c=Pp."," The baseline calculation has $q = 1.5$ corresponding to a Keplerian background, and a box size of $L_x =1$, $L_y= 2\pi$, and $L_z=1$, set so that $L_z = c_s^2/\Omega$ where $c_s^2=P/\rho$."
 The actual values used are 2?=10' and £=0.001., The actual values used are $P=10^{-6}$ and $\Omega = 0.001$.
 The gas is acdiabatic with 55/3., The gas is adiabatic with $\gamma = 5/3$.
" The initial field is vertical and varies sinusoidally in the we direction. D.xsinGr/L,)."," The initial field is vertical and varies sinusoidally in the $x$ direction, $B_{z} \propto
\sin(x/L_x)$."
 The field strength set so that the volume average magnetic energy corresponds too =SOO., The field strength set so that the volume average magnetic energy corresponds to $\beta = 800$.
 The maximum vertical field. has 1—400. which gives a fastest growing wavelength for the ALBI of Aus=82/157(04/0)046.," The maximum vertical field has $\beta=400$, which gives a fastest growing wavelength for the MRI of $\lambda_{\rm max} = 8\pi/15^{1/2} (v_A/\Omega) = 0.46$."
 The grid resolution is 3202 zones in (Gr.g.2).," The grid resolution is $32 \times 64 \times 32$ zones in $(x,y,z)$."
" This setup corresponds to the so-called ""iducial box” used in Lawley.Gamunieand Brandenburgetal. (1995). "," This setup corresponds to the so-called “fiducial box” used in \cite{hgb95, hgb96} and \cite{betal95}. ."
Inaddition to the fiducialrun. we computed. four additional simulations with cliflerent box dimensions.," Inaddition to the fiducialrun, we computed four additional simulations with different box dimensions."
 In three simulations we doubled each of the box dimensions in turn. and in the final simulation of this set we quadrupled the vertical size.," In three simulations we doubled each of the box dimensions in turn, and in the final simulation of this set we quadrupled the vertical size."
 To maintain a constant resolution number, To maintain a constant resolution number
WIND observations of CGRD 110700D in 82., observations of GRB 110709B in 2.
 Then we present mmmultiavaveleusthn spectroscopy and timing studies in 83., Then we present multi-wavelength spectroscopy and timing studies in 3.
 The plysical implications ou the ceutral eneme properties are discussed in §l., The physical implications on the central engine properties are discussed in 4.
 We draw our couclusions iu 50., We draw our conclusions in 5.
 CRB 110709DB first trigecred the Burst Alert Telescope (BAT: Barthluw ct al., GRB 110709B first triggered the Burst Alert Telescope (BAT; Barthlmy et al.
 2005) on-boardSwift at eee UT on 9 July 2011 (Cunnüugs et al., 2005) on-board at 21:32:39 UT on 9 July 2011 (Cummings et al.
 2011a)., 2011a).
Swift slewed dmunediately to the burst., slewed immediately to the burst.
 The two narrow nld instruments the N-rav Telescope (XRT: Burrows ct al.," The two narrow field instruments, the X-ray Telescope (XRT; Burrows et al."
 2005b) aud the Ultraviolet. Optical telescope (UVOT: Roming et al., 2005b) and the Ultraviolet Optical telescope (UVOT; Roming et al.
 2005) on-board begau to observe the field at Ty|80.5 seconds and Ty|91 secouds. respectively. where Ty is the BAT trigecr time.," 2005) on-board began to observe the field at $T_0+80.5$ seconds and $T_0+91 $ seconds, respectively, where $T_0$ is the BAT trigger time."
 A bright N-aav afterelowwas localized at R.A.(J2000)I05s737.087. Dec(J2000)=2:727/1776 with an uncertainty= of LL confidence. Beardimore et al.," A bright X-ray afterglowwas localized at ${\rm R.A. (J2000)}=10^h58^m37.08^s$, ${\rm Dec. (J2000)}=-23^{\circ}27'17\farcs 6$ with an uncertainty of 4 confidence, Beardmore et al."
 2011)., 2011).
 No reliable optical source was found within the ART error circle (Tolland et al., No reliable optical source was found within the XRT error circle (Holland et al.
 2011α.0).," 2011a,b)."
 Tuterestinely. at 21:13:25. UT on 9 July 2011. 11 nuuutes after the first trieger. the BAT was triegered again and located a second event from the same location (Barthehuy ct al.," Interestingly, at 21:43:25 UT on 9 July 2011, 11 minutes after the first trigger, the BAT was triggered again and located a second event from the same location (Barthelmy et al."
 2011)., 2011).
 The second outburst has conrparable intensity aud light curve characteristics to he first outburst., The second outburst has comparable intensity and light curve characteristics to the first outburst.
 Regarding the two outbursts as two episodes of a oe singleburst. the separation (11 miuuiutes) is the longest compared to other multi-episode. GRBs ucasured bySwift.," Regarding the two outbursts as two episodes of a single burst, the separation (11 minutes) is the longest compared to other multi-episode GRBs measured by."
" In this paper. we use the term ""double must” to stress the unusual nature of this double-trigecr GRB."," In this paper, we use the term “double burst"" to stress the unusual nature of this double-trigger GRB."
" We will use the term ""the first sub-burst to refer o the first outburst and “the second sub-burst to refer o the second outburst."," We will use the term “the first sub-burst"" to refer to the first outburst and “the second sub-burst"" to refer to the second outburst."
 However. as we will show below. he two events are clearly related. indicating that they originated from the same plivsical progenitor svsteni (see Drago Pagliara 2007 for a statistical study of similar GRBs with long quiescent pliases).," However, as we will show below, the two events are clearly related, indicating that they originated from the same physical progenitor system (see Drago Pagliara 2007 for a statistical study of similar GRBs with long quiescent phases)."
 We processed the Swift/BAT data using staudard tools (version 6.11)., We processed the /BAT data using standard tools (version 6.11).
 As shown in Fie. L. ," As shown in Fig. \ref{fig:batlc}, ,"
the first sub-burst lasted from Tj28 seconds to Ty|55 seconds with frouΤουτω=55.643.2 seconds.," the first sub-burst lasted from $T_0-28$ seconds to $T_0+55$ seconds with $T_{90,1st}=55.6\pm 3.2$ seconds."
 The secoud sub-burst lasted Ty|550 seconds to about Ty|865 seconds with Toye.=259.2£8.8 secouds (Cimiuines et al.," The second sub-burst lasted from $\sim T_0+550$ seconds to about $T_0+865$ seconds with $T_{90,2nd}=259.2\pm 8.8$ seconds (Cummings et al."
 20115)., 2011b).
 There was no flux detectable in BAT from about Ty|180 seconds to about Fy|550 seconds., There was no flux detectable in BAT from about $T_0+180$ seconds to about $T_0+550$ seconds.
 We extracted the BAT spectra in several slices., We extracted the BAT spectra in several slices.
 The lower panel in Fig., The lower panel in Fig.
 d. shows the photon iudices obtained bv fitting the spectra with a simple power kaw model., \ref{fig:batlc} shows the photon indices obtained by fitting the spectra with a simple power law model.
 It is obvious that both sub-bursts have strong harcd-to-soft spectral evXution., It is obvious that both sub-bursts have strong hard-to-soft spectral evolution.
 The photon iudices range froii 1.25 to ~1.75., The photon indices range from $\sim 1.25$ to $\sim 1.75$.
" secondThe BAT baud(15-150 ) fluences of the first aud sub-bursts are 8.951025ky0.«10Pereci? aud 1.31!""nκ10erecin? respectively.", The BAT band (15-150 keV) fluences of the first and second sub-bursts are $8.95_{-0.62}^{+0.29} \times 10^{-6}\ {\rm erg} \ {\rm cm}^{-2} $ and $1.34_{-0.07}^{+0.05} \times 10^{-5}\ {\rm erg} \ {\rm cm}^{-2}$ respectively.
 We processed the Suift/NRT data usine our own IDL codes which euiploy the standard WEAsoft analysis tools., We processed the /XRT data using our own IDL codes which employ the standard HEAsoft analysis tools.
 For technical details please refer to Zhang et al., For technical details please refer to Zhang et al.
 2007., 2007.
 Fie., Fig.
 2 shows the NRT light curve aud spectral evolution., \ref{fig:xrtlc} shows the XRT light curve and spectral evolution.
" The prolonged and energetic flaring activity continues up to dy|2000 seconds, which corresponds to the second sub-burst time period."," The prolonged and energetic flaring activity continues up to $T_0+2000$ seconds, which corresponds to the second sub-burst time period."
 The lelt curve after the flare can be fitted by a brokenpower-law with ay=0.98x0.08. o»=1640.13 ane a break time fj=5.94L1«10!s (AP/dof| 338.6/279).," The light curve after the flare can be fitted by a brokenpower-law with $\alpha_1=0.98\pm0.08$, $\alpha_2=1.6\pm 0.13 $ and a break time $t_b=5.9\pm 4.1 \times 10^4\ s$ $\chi^2/dof=338.6/279$ )."
" Assmine GRB 110709D is at the average sedalitt= z~2) ofSwift GRBs. its vest frame break tiae. thpee D~2.0« 10's). and the corresponding N-ray huuinositv. Ly 5«10/00pgs. 1), ave consistent with of the ροκ ζω(~ correlation of previousο) GRBs (Dainotti ct al."," Assuming GRB 110709B is at the average redshift $\sim$ 2) of GRBs, its rest frame break time, $t_{b,rest}$ $\frac{t_b}{1+z}\sim 2.0 \times 10^4 s$ ), and the corresponding X-ray luminosity, $L_{X,b}$ $\sim 5\times 10^{46}erg \ s^{-1}$ ), are consistent with of the $t_{b,rest}$ $L_{x,b}$ correlation of previous GRBs (Dainotti et al."
 2010)., 2010).
 The X-ray. spectra cau e fitted with RU absorbed power-law with total coluunu Ny2ALS3«dOen.2. which includes the Galactic oregrouncd Nh=5.6«10cm? (D'Elia ct al.," The X-ray spectrum can be fitted with an absorbed power-law with total column ${\rm N_H}=2.14_{-0.21}^{+0.22} \times 10^{21} {\rm cm}^{-2}$, which includes the Galactic foreground ${\rm N_H}=5.6\times 10^{20} {\rm cm}^{-2}$ (D'Elia et al."
 2011)., 2011).
 Strong spectral evolution was observed in the second sub-mast phase. where the photon iudices vary significantly roni P~0.9 to P~2.6.," Strong spectral evolution was observed in the second sub-burst phase, where the photon indices vary significantly from $\Gamma \sim 0.9$ to $\Gamma \sim 2.6$."
 The spectrum after Ty|10005 las no significant evolution. with an average photon index P—2.1.," The spectrum after $T_0+4000s$ has no significant evolution, with an average photon index $\Gamma \sim 2.1$."
 The total fuence in NRT baud (0.5-10 seV) is LOF+£0.56«10ereeni2, The total fluence in XRT band (0.3-10 keV) is $4.07\pm0.56 \times 10^{-6} \ {\rm erg} \ {\rm cm}^{-2}$.
 Iu order to check whether the break in the NRT lisht curve is due to curvature caused by au incorrect reference nue Ty effect (e.e.. Yamazaki 2009 and Liane et al.," In order to check whether the break in the XRT light curve is due to curvature caused by an incorrect reference time $T_0$ effect (e.g., Yamazaki 2009 and Liang et al."
 2009. 2010). we plotted the NRT light curve in refercuce to the rieeer time of the secoud sub-burst.," 2009, 2010), we plotted the XRT light curve in reference to the trigger time of the second sub-burst."
 We fouud that the fh. ay and à» do not significantly change within l-sigia range.," We found that the $t_b$, $\alpha_1$ and $\alpha_2$ do not significantly change within 1-sigma range."
 We thus couclude that the break is iutriusic., We thus conclude that the break is intrinsic.
 GRD 110709D trigecred detector Sl of theWIND eanuna-ray spectrometer (Apterke et al., GRB 110709B triggered detector S1 of the gamma-ray spectrometer (Apterkar et al.
 1995) at 21:32:11567 s UT on 9 July 2011 (Colenetzküi et al., 1995) at 21:32:44.567 s UT on 9 July 2011 (Golenetskii et al.
 2011)., 2011).
ISonus-WYNDP recorded the first sub-burst with high-resolution data., recorded the first sub-burst with high-resolution data.
" The Του of the first sub- in WIND euergv baud(20 keV - 5 MeV) is 51.3c7.6 s. BouThe fiuemee in the same cucrev range is 2.60.2«""EPorecin 7.", The $T_{90}$ of the first sub-burst in energy band(20 keV - 5 MeV) is $51.3\pm 7.6$ s. The fluence in the same energy range is $2.6\pm 0.2 \times 10^{-5}\ {\rm erg} \ {\rm cm}^{-2} $ .
 The second sub-burst fell into a telemetry gap but was recorded by the instrument's spare count rate mcasurement channel (Fig. 3))., The second sub-burst fell into a telemetry gap but was recorded by the instrument's spare count rate measurement channel (Fig. \ref{fig:multilc}) ).
 The overlap detection of the first sub-burst allows a, The overlap detection of the first sub-burst allows a
some of the actual clusters are in fact nore massive. sav twice as massive. then following equation 1 again gives another potential increase in the quoted half-light raclii.,"some of the actual clusters are in fact more massive, say twice as massive, then following equation \ref{e:rtide} again gives another potential increase in the quoted half-light radii."
 'Pherefore. for a chwarl irregular galaxy such as 6822 extended clusters with projected half-light radii in the range 0 30pc can be expected to naturally occur (for a range of masses and orbits).," Therefore, for a dwarf irregular galaxy such as $\,6822$ extended clusters with projected half-light radii in the range $10 - 30\,$ pc can be expected to naturally occur (for a range of masses and orbits)."
 Such clusters will evolve slowly., Such clusters will evolve slowly.
 Thev will be dynamically voung. having evolved for approximately wo half-mass relaxation times. and will not show any signs of core-collapse.," They will be dynamically young, having evolved for approximately two half-mass relaxation times, and will not show any signs of core-collapse."
 Any clusters in the outer regions of 6822 with ialf-light. racii less than 10 pe. will need to have started Life relatively compact.," Any clusters in the outer regions of $\,6822$ with half-light radii less than $10\,$ pc will need to have started life relatively compact."
" Certainly they would not be expected o have filled their tidal μασ initially,", Certainly they would not be expected to have filled their tidal radii initially.
 For a cluster in 6822 to exhibit. corc-collapse within a Hubble. time an initial filling factor of less than is required. or an orbit at Aae much [ess than 109κρο," For a cluster in $\,6822$ to exhibit core-collapse within a Hubble time an initial filling factor of less than is required, or an orbit at $R_{\rm gc}$ much less than $10\,$ kpc."
 We have shown hat for a fixed. A. dilferences in initial sizes can translate o dillerences in hall-lieht radii at 12€vr by the same actor.," We have shown that for a fixed $R_{\rm gc}$ differences in initial sizes can translate to differences in half-light radii at $12\,$ Gyr by the same factor."
 We have also shown that primordial binaries do not aleet the evolution of the hall-mass anc hall-light racii, We have also shown that primordial binaries do not affect the evolution of the half-mass and half-light radii.
 This is not surprising for dvnaniucally voung clusters and aas also been demonstrated. for more evolved. clusters in stronger tidal fields (Hurley. 2007)., This is not surprising for dynamically young clusters and has also been demonstrated for more evolved clusters in stronger tidal fields (Hurley 2007).
 Ehe internal evolution characteristic that has the most potential to impact the ιαισα radius evolution is the formation of a central »opulation of DII-DII binaries., The internal evolution characteristic that has the most potential to impact the half-light radius evolution is the formation of a central population of BH-BH binaries.
 Expansion of the half-light racius by this mechanism was shown by Alackey et al. (, Expansion of the half-light radius by this mechanism was shown by Mackey et al. (
2008) ο start. talking ellect after one hall-mass relaxation time. with the effect increasing to a maximum expansion factor of wo bv core-collapse (comparing clusters with and without DII-DII binaries).,"2008) to start taking effect after one half-mass relaxation time, with the effect increasing to a maximum expansion factor of two by core-collapse (comparing clusters with and without BH-BH binaries)."
 So this could be a mild factor for the most extended: clusters in 6822 and potentially play a larger role in determining the observed. hall-leht raclii of initially more compact clusters.," So this could be a mild factor for the most extended clusters in $\,6822$ and potentially play a larger role in determining the observed half-light radii of initially more compact clusters."
 Llowever. this relies on a source of DlIs being retained in the clusters.," However, this relies on a source of BHs being retained in the clusters."
 Overall we ind that cillerences in initial cluster size are the most likely explanation for any measured dilferences in half-light. raclii or clusters that otherwise appear similar., Overall we find that differences in initial cluster size are the most likely explanation for any measured differences in half-light radii for clusters that otherwise appear similar.
 The stochastic ellect of the presence. or not. of a central population of binaries can then possibly play an accded role.," The stochastic effect of the presence, or not, of a central population of BH-BH binaries can then possibly play an added role."
" Our question of ""how. do. similar. clusters. obtain dillerent. structure?""", Our question of “how do similar clusters obtain different structure?”
 now seemingly becomes “can clusters » expected to be born with different sizes?, now seemingly becomes “can clusters be expected to be born with different sizes?”.
 Baunigarelt et al. (, Baumgardt et al. (
2010) asked. a similar question after. showing. that Milkv Way GC's bevond Rae of Skpe fall into. distinct eroups of compact. tidallv-uncderfilling clusters ancl more extended. tidallv-filling elusters.,"2010) asked a similar question after showing that Milky Way GCs beyond $R_{\rm gc}$ of $8\,$ kpc fall into distinct groups of compact, tidally-underfilling clusters and more extended, tidally-filling clusters."
 They concluded it was more likely that the second. &roup formed with large half-mass radi rather than evolving from a more compact state., They concluded it was more likely that the second group formed with large half-mass radii rather than evolving from a more compact state.
 Examining the size distribution of globular clusters in a variety. of Local Croup chvarl galaxies. Da Costa ct al. (," Examining the size distribution of globular clusters in a variety of Local Group dwarf galaxies, Da Costa et al. ("
2009) suggest that there may be two distinct. modes. of cluster formation with typical half-light racit of 3 and 10 pc. analogous to the findings of Baumearcdt et al. (,"2009) suggest that there may be two distinct modes of cluster formation with typical half-light radii of $3$ and $10\,$ pc, analogous to the findings of Baumgardt et al. ("
2010).,2010).
 Lt has been suggested by Ballesteros-Paredes et al. (, It has been suggested by Ballesteros-Paredes et al. (
2009) that ticlal forces may play a role in determining the rate at which stars form within molecular clouds. through compression and possible disruption of the clouds.,"2009) that tidal forces may play a role in determining the rate at which stars form within molecular clouds, through compression and possible disruption of the clouds."
 Their. calculations show that the resultant. star formation ellicieney of a particular cloud depends on its position and orientation in the host galaxy., Their calculations show that the resultant star formation efficiency of a particular cloud depends on its position and orientation in the host galaxy.
 This model is put forward as an alternative to the theory that magnetic field. strength anc radiative feceback regulate. the degree of star. formation within a cloud. (Price Bate 2009)., This model is put forward as an alternative to the theory that magnetic field strength and radiative feedback regulate the degree of star formation within a cloud (Price Bate 2009).
 Either way. if cilferences in star formation clliciency can exist. between proto-clusters [orming in the cores of molecular clouds then Baunmgarelt Ixroupa (2007) have shown that cüllerent mfr values can result for the bound clusters remaining after residual gas is expelled.," Either way, if differences in star formation efficiency can exist between proto-clusters forming in the cores of molecular clouds then Baumgardt Kroupa (2007) have shown that different $r_{\rm h} / r_{\rm t}$ values can result for the bound clusters remaining after residual gas is expelled."
 Furthermore. simulations conducted by Elmegreen (2008) have demonstrated that diffuse star clusters can forni clirectly in regions where the background tidal forces are low.," Furthermore, simulations conducted by Elmegreen (2008) have demonstrated that diffuse star clusters can form directly in regions where the background tidal forces are low."
 Tere star formation elliciecney ds. discussed. in terms of turbulence (or Mach. number) anc cloud pressure (or column density)., Here star formation efficiency is discussed in terms of turbulence (or Mach number) and cloud pressure (or column density).
 Different combinations procluce clusters of dillerent. densities with high-pressure regions making the densest clusters while clouds with low density and. high Mach numbers give rise to cilfuse clusters., Different combinations produce clusters of different densities with high-pressure regions making the densest clusters while clouds with low density and high Mach numbers give rise to diffuse clusters.
 The latter are more likely to form in the outer regions of a galaxy where low-density clouds are expected. to reside and the cdilfuse clusters will not be quickly disrupted (IElmegreen 2008)., The latter are more likely to form in the outer regions of a galaxy where low-density clouds are expected to reside and the diffuse clusters will not be quickly disrupted (Elmegreen 2008).
 So there are. possibilities for variations in environment and/or the properties of molecular clouds producing dilferent. star formation clliclencics and a range of rr values for voung star clusters., So there are possibilities for variations in environment and/or the properties of molecular clouds producing different star formation efficiencies and a range of $r_{\rm h} / r_{\rm t}$ values for young star clusters.
 What is not immediately clear is whether or not clusters forming in the same environment can have a range of ryri values owing to variations in cloud properties (size. shape. orientation) alone.," What is not immediately clear is whether or not clusters forming in the same environment can have a range of $r_{\rm h} / r_{\rm t}$ values owing to variations in cloud properties (size, shape, orientation) alone."
 We now turn our [focus to the M31. extended cluster svstem., We now turn our focus to the M31 extended cluster system.
 Our model All which started. ticdally-Lilline demonstrates the maximum size that a cluster. of Al~15000AL. orbiting at Rue= LOkpe can be expected to have at an age of 12€vr.," Our model M1 which started tidally-filling demonstrates the maximum size that a cluster of $M \sim 15\,000 \, M_\odot$ orbiting at $R_{\rm gc} = 10\,$ kpc can be expected to have at an age of $12\,$ Gyr."
 This is not within the extended cluster size range., This is not within the extended cluster size range.
 Of course we are not claiming that our model MI is a direct representation of a typical star cluster in M31., Of course we are not claiming that our model M1 is a direct representation of a typical star cluster in M31.
 For a start. the mass of the moclel is likely to be an underestimate compared. to actual ΜΟΙ clusters.," For a start, the mass of the model is likely to be an underestimate compared to actual M31 clusters."
 “Phe extended. clusters observed in M31 have masses that range from ~107 to ~LOAL. (Hluxor et al.," The extended clusters observed in M31 have masses that range from $\sim 10^4$ to $\sim 10^5 \, M_\odot$ (Huxor et al."
 2010a: note that masses for ECs in 6822 are not vet. known but. are expected to cover a similar range).," 2010a: note that masses for ECs in $\,6822$ are not yet known but are expected to cover a similar range)."
 Thus we have clirect models at the lower end of this range but could be as much asa factor of ten too small at the upper end., Thus we have direct models at the lower end of this range but could be as much as a factor of ten too small at the upper end.
 A factor of ten increase in mass will lead to a larger tidal racius. but only by à [actor of two and if the internal radii scale in the same way this gives a projected half-light radius in the range of LO pc (see Table 2)).," A factor of ten increase in mass will lead to a larger tidal radius, but only by a factor of two and if the internal radii scale in the same way this gives a projected half-light radius in the range of $10\,$ pc (see Table \ref{t:table2}) )."
 This is right at the low-end of the extended cluster size range., This is right at the low-end of the extended cluster size range.
" However. this still does not help when we are looking at two clusters of the same mass (or luminosity) ab the same Ze, and with very dillerent. half-miass radii. as is observed in the inner regions of M31 (Luxor οἱ al."," However, this still does not help when we are looking at two clusters of the same mass (or luminosity) at the same $R_{\rm gc}$ and with very different half-mass radii, as is observed in the inner regions of M31 (Huxor et al."
 20102), 2010a).
" ""hus it is hard to believe that extended clusters observed in Ίο inner regions of M31. which have hall-lieht radii of about I )pc. evolved in-situ."," Thus it is hard to believe that extended clusters observed in the inner regions of M31, which have half-light radii of about $30\,$ pc, evolved in-situ."
 Lt is possible that extended: clusters observed in the inner regions are actually further out and only appear in the centre owing to projection cllects., It is possible that extended clusters observed in the inner regions are actually further out and only appear in the centre owing to projection effects.
 Such an ellect is not noticeable from the horizontal-branch levels of the few extended clusters that have σους colour-magnitude diagrams (AMlackey ct al., Such an effect is not noticeable from the horizontal-branch levels of the few extended clusters that have good colour-magnitude diagrams (Mackey et al.
 2006) and if there is a projection clleet pushing these clusters into the foreground there is no reason why it shouldn't similarly apply to the compact clusters as well., 2006) and if there is a projection effect pushing these clusters into the foreground there is no reason why it shouldn't similarly apply to the compact clusters as well.
 On the other hand we expect that compact clusters will be more likely to survive in the inner parts of ealaxies than extended clusters and racial distributions of, On the other hand we expect that compact clusters will be more likely to survive in the inner parts of galaxies than extended clusters and radial distributions of
A.,.
"Pv,. In a conical outflow, Ac r?, P« r-?, and Ue is constant."," In a conical outflow, $A \propto r^{2}$ , $P \propto r^{-2}$ , and $v_{\rm c}$ is constant."
" Therefore, the flux produced in a single cloud is independent of its distance from the center of the flow."," Therefore, the flux produced in a single cloud is independent of its distance from the center of the flow."
" However, the total number of clouds is conserved and their decreases as r? for constant velocity of expansion."," However, the total number of clouds is conserved and their space density decreases as $r^{-2}$ for constant velocity of expansion."
"space In densitythis case, then Fy,οςr-!."," In this case, then $F_{\rm H \alpha} \propto r^{-1}$."
" In case (2) of an accelerating outflow, Fugacr-?."," In case (2) of an accelerating outflow, $F_{\rm H \alpha} \propto r^{-2}$."
" In hydrodynamic models by Cooperetal.(2009),, the outflowing filaments are shredded and as are accelerated, so in this case the radial dependence destroyedof the theysurface brightness could be even steeper than r~?."," In hydrodynamic models by \citet{Cooper09}, the outflowing filaments are shredded and destroyed as they are accelerated, so in this case the radial dependence of the surface brightness could be even steeper than $r^{-2}$."
" In Figure 8,, we show the variation of surface brightness in aalong the biconical outflow."," In Figure \ref{fig8}, we show the variation of surface brightness in along the biconical outflow."
" We have presented the measurements using a simple bicone with an opening angle of30°,, which is roughly approximated using our data and the iimages of Meureretal.(2006)."," We have presented the measurements using a simple bicone with an opening angle of, which is roughly approximated using our data and the images of \citet{Meurer06}."
". We assume that the cone originates in the central starburst, which has a radius of 0.26 in the disk corresponding to the size of the central kpcstar-forming concentrationplane seen in the images."," We assume that the cone originates in the central starburst, which has a radius of $\sim 0.26$ kpc in the disk plane corresponding to the size of the central star-forming concentration seen in the images."
" In this case, the starburst lies 0.78 kpc from the origin of the coordinates for each half of the bicone."," In this case, the starburst lies 0.78 kpc from the origin of the coordinates for each half of the bicone."
" Figure 8 shows that the of the surface brightness curve is close to r—?, which would slopetend to support the case for a photoionized outflow within a narrow cone in the polar direction, though this does not rule out the presence of other ionizing sources."," Figure \ref{fig8} shows that the slope of the surface brightness curve is close to $r^{-3}$, which would tend to support the case for a photoionized outflow within a narrow cone in the polar direction, though this does not rule out the presence of other ionizing sources."
 We examine line ratio diagnostic diagrams which use I]/ I]/Haor I]//Horatios against the ratio., We examine line ratio diagnostic diagrams which use / or ratios against the ratio.
 These diagrams were first proposed by Baldwinetal.(1981) and Veilleux&Osterbrock(1987) to determine the ionizing source of emission line in galaxies., These diagrams were first proposed by \citet{BPT81} and \citet{VO87} to determine the likely ionizing source of emission line gas in galaxies.
" The ionizinglikely source classification on these diagramsgas was subsequently updated by Kewleyetal.(2001b,2006) and Kauffmannetal.(2003)."," The ionizing source classification on these diagrams was subsequently updated by \citet{Kewley01b,Kewley06} and \citet{Kauffmann03}."
. These line ratios have the advantage that they can still be used even when reddening corrections are quite uncertain., These line ratios have the advantage that they can still be used even when reddening corrections are quite uncertain.
" In the case of NGC 839, we find a very systematic behavior in the spatial distribution in the line ratios involving the low ionization species as shown in Figure 9.."," In the case of NGC 839, we find a very systematic behavior in the spatial distribution in the line ratios involving the low ionization species as shown in Figure \ref{fig9}."
" Figure 9 shows that the II]// I1]/Ha,, and ratios are systematically lower near the nucleus, somewhat low along the axis of the bicone, and high along the edges of the bicone."," Figure \ref{fig9} shows that the / /, and ratios are systematically lower near the nucleus, somewhat low along the axis of the bicone, and high along the edges of the bicone."
 We will compare the observations with detailed models on the optical diagnostic diagrams in the following section., We will compare the observations with detailed models on the optical diagnostic diagrams in the following section.
 Our results of NGC 839 present unequivocal evidence that within the last Gyr it has undergone a long-lived and massive starburst., Our results of NGC 839 present unequivocal evidence that within the last Gyr it has undergone a long-lived and massive starburst.
" Not only is the disk dominated by an E+A spectrum originating from this starburst, but the starburst is clearly ongoing and is currently actively powering a superwind evidenced by large bulk motions and line splitting."," Not only is the disk dominated by an E+A spectrum originating from this starburst, but the starburst is clearly ongoing and is currently actively powering a superwind evidenced by large bulk motions and line splitting."
" The basic physics of superwinds powered by starbursts is rather simple, and has been described by Chevalier&Oegerle(1979)."," The basic physics of superwinds powered by starbursts is rather simple, and has been described by \cite{Chevalier79}."
". To power a wind, the energy injection per unit area into a fraction, f, of the disk gas must exceed its binding energy."," To power a wind, the energy injection per unit area into a fraction, $f$, of the disk gas must exceed its binding energy."
" As Chevalier&Oegerle(1979) have shown, this means that the gas escaping into the halo has an initial temperature greater than some critical value related to the binding energy."," As \cite{Chevalier79} have shown, this means that the gas escaping into the halo has an initial temperature greater than some critical value related to the binding energy."
 Indeed etal.(2009) have re-iterated how similar a superwindCooper is to a simple stellar wind in an inhomogeneous interstellar medium (ISM)., Indeed \citet{Cooper09} have re-iterated how similar a superwind is to a simple stellar wind in an inhomogeneous interstellar medium (ISM).
" The physical parameters which control the production of a galactic wind can easily be derived, as shown by Dopita(2008),, and we repeat his argument verbatim here."," The physical parameters which control the production of a galactic wind can easily be derived, as shown by \citet{Dopita08}, and we repeat his argument verbatim here."
" The input energy Ei, per unit area is proportional to the surface rate of star formation X, integrated over the lifetime of the starburst, TSB> The escape energy of the gas is where Yeas is the surface density of gas in the disk."," The input energy $E_{\rm in} $ per unit area is proportional to the surface rate of star formation $ \dot{ \Sigma}_* $ integrated over the lifetime of the starburst, $ \tau_{\rm SB}$; The escape energy of the gas is where ${ \Sigma}_{\rm gas} $ is the surface density of gas in the disk."
" The star formation rate is related to the gas surface density through the Kennicutt(1998) star formation law Thus, a galactic wind becomes possible when Therefore, a wind is favored when the escape velocity is low (such as will be the case in small galaxies), when the starburst continues for a significant period (which is not surprising, since long-lived star formation events contribute more energy to removal of gas), and when the gas surface density is high because the energy input per unit mass of ISM is higher in this case."," The star formation rate is related to the gas surface density through the \cite{Kennicutt98} star formation law Thus, a galactic wind becomes possible when Therefore, a wind is favored when the escape velocity is low (such as will be the case in small galaxies), when the starburst continues for a significant period (which is not surprising, since long-lived star formation events contribute more energy to removal of gas), and when the gas surface density is high because the energy input per unit mass of ISM is higher in this case."
 Our observations clearly demonstrate that NGC 839 fulfills all three of these conditions., Our observations clearly demonstrate that NGC 839 fulfills all three of these conditions.
" Given that shock excitation of the filaments in the superwind is implied by the theoretical models of this type of flow, and also by the observed bulk motions, line ratios, and radial dependence of surface weneed to investigate shock models in more brightness,detail."," Given that shock excitation of the filaments in the superwind is implied by the theoretical models of this type of flow, and also by the observed bulk motions, line ratios, and radial dependence of surface brightness, weclearlyneed to investigate shock models in more detail."
 The clearlyshock velocities which are suggested by observation (100-250 km s!) are much lower than the fast shock models described by, The shock velocities which are suggested by observation (100-250 km $^{-1}$ ) are much lower than the fast shock models described by
Powerful radio emission is rare in the population of active galactic nuclei (AGN).,Powerful radio emission is rare in the population of active galactic nuclei (AGN).
 This phenomenon. only found. in about of the AGNs. is associated with the presence of relativistic particles produced in the central regions of the AGN. and then channelled through the jets out to distances of hundreds. of kpe up to a few Alpe.," This phenomenon, only found in about of the AGNs, is associated with the presence of relativistic particles produced in the central regions of the AGN, and then channelled through the jets out to distances of hundreds of kpc up to a few Mpc."
 Such relativistic particles are responsible for the svnchrotron radiation at the origin of the radio emission., Such relativistic particles are responsible for the synchrotron radiation at the origin of the radio emission.
 Furthermore. they may scatter low cncrey photons to high energy bands by inverse Compton (1€) processes. suggesting a connection between radio and high energy οταν emission.," Furthermore, they may scatter low energy photons to high energy bands by inverse Compton (IC) processes, suggesting a connection between radio and high energy $\gamma$ -ray emission."
 Indeed. all the 5-rav AGN detected by EGRET are radio-Ioud sources. strongly supporting this scenario.," Indeed, all the $\gamma$ -ray AGN detected by EGRET are radio-loud sources, strongly supporting this scenario."
 No racio-quict ACGNs were firmly detected in 5-rays by the Large Area Telescope (LAT) on, No radio-quiet AGNs were firmly detected in $\gamma$ -rays by the Large Area Telescope (LAT) on
peculiar velocities indicating απ eusenmible average temperature T. the average galaxy ass is 5). and & is the two-galaxy correlation function.,"peculiar velocities indicating an ensemble average temperature $T$, the average galaxy mass is $m$ , and $\xi$ is the two-galaxy correlation function."
 Since the volume V oauav be a cone with apex at the observer which projects the galaxies in its volume iuto à cell of area A on the sky. the same form of the distribution fiction in equation (1)) applies to counts of galaxies in two-dimensional cells on the sk.," Since the volume $V$ may be a cone with apex at the observer which projects the galaxies in its volume into a cell of area $A$ on the sky, the same form of the distribution function in equation \ref{eq:GQED}) ) applies to counts of galaxies in two-dimensional cells on the sky."
 This form of equation (3)) asstunes that evolution is negligible within the voluue. which is reasonable for a narrow redshift baud as in the 2\TASS catalog (0<2X 0.1).," This form of equation \ref{eq:b}) ) assumes that evolution is negligible within the volume, which is reasonable for a narrow redshift band as in the 2MASS catalog $0 \le z \lesssim 0.1$ )."
 For volunes covering wide redshift bauds. evolution may be incladed as described in ancl(2000).," For volumes covering wide redshift bands, evolution may be included as described in and."
. Although the form of equation (1)) is independent of the shape aud size of randomly located volumes which are not pathological (0.9.. not fractal or chosen o avoid ealaxies). the value of 5 will depeud ou volume and shape.," Although the form of equation \ref{eq:GQED}) ) is independent of the shape and size of randomly located volumes which are not pathological (e.g., not fractal or chosen to avoid galaxies), the value of $b$ will depend on volume and shape."
 This was found in carly N-body simulations and explicitly calculated for squarexojected. cones usine equation (3))1992).., This was found in early N-body simulations and explicitly calculated for squareprojected cones using equation \ref{eq:b}) ).
 Comparisons of different values of N and b or cells of the same shape aud size. but for different subsamples of galaxies. can be used to explore possible vasesIn these subsauiples.," Comparisons of different values of $\overline{N}$ and $b$ for cells of the same shape and size, but for different subsamples of galaxies, can be used to explore possible biasesin these subsamples."
 If the bias is known priori. it can be incorporated iuto equations (1)) aud (3)) as described iu detail previously2000).," If the bias is known , it can be incorporated into equations \ref{eq:GQED}) ) and \ref{eq:b}) ) as described in detail previously."
. In principle. an uuknowan bias coutaimed In subsaniples eau also be recovered from the results. but ifs undqueness is more dificult to establish.," In principle, an unknown bias contained in subsamples can also be recovered from the results, but its uniqueness is more difficult to establish."
 The value of N cau be determined directly from the catalog and the value of 5 follows for equation (1)) from the observed variance of counts in cells of amy particular volume ancl shape: Therefore in principle the theory coutaüus no free paralucters for comparing equation (1)) with the observations., The value of $\overline{N}$ can be determined directly from the catalog and the value of $b$ follows for equation \ref{eq:GQED}) ) from the observed variance of counts in cells of any particular volume and shape: Therefore in principle the theory contains no free parameters for comparing equation \ref{eq:GQED}) ) with the observations.
 We can also fit N and b in equation (1)) directly to the observed distribution function. aud see if the slieht difference between these two methods of determine NV aud b provides useful information.," We can also fit $\overline{N}$ and $b$ in equation \ref{eq:GQED}) ) directly to the observed distribution function, and see if the slight difference between these two methods of determining $\overline{N}$ and $b$ provides useful information."
 After deriving cquation (1)). its predicted form was found to agree well with counts in cells aud void probabilitics in several galaxy surveys including the Zwickv Catalog1991).. the UGC and ESO Catalogs and the IRAS Catalog1).. all projected outo the sky. as well as for the SSRS Catalog1).. aud the Disces-Perseus Supercluster iu three dineusions.," After deriving equation \ref{eq:GQED}) ), its predicted form was found to agree well with counts in cells and void probabilities in several galaxy surveys including the Zwicky Catalog, the UGC and ESO Catalogs and the IRAS Catalog, all projected onto the sky, as well as for the SSRS Catalog, and the Pisces-Perseus Supercluster in three dimensions."
 All previous conrpurisons have involved catalogs coutaimine at most several tens of thousands of galaxies., All previous comparisons have involved catalogs containing at most several tens of thousands of galaxies.
 The new catalogs becoming available have about 10100 times as many galaxies. with different levels of sky coverage. homoecucity. aud information about galaxy properties.," The new catalogs becoming available have about 10–100 times as many galaxies, with different levels of sky coverage, homogeneity, and information about galaxy properties."
 These new larger catalogs are nÓauportant because their nuproved statistics may reveal departures from equation (1)) resulting. from citterent distributious of ealaxies aud dark matter. mcreing. lass segregation. or other cuviromuental effects;," These new larger catalogs are important because their improved statistics may reveal departures from equation \ref{eq:GQED}) ) resulting from different distributions of galaxies and dark matter, merging, mass segregation, or other environmental effects."
 Section 2. describes the 2ATASS Catalog and our method of analysis. Section 3 eives our results. aud Section |. describes some of their implications.," Section \ref{sec:analysis_2MASS_dist} describes the 2MASS Catalog and our method of analysis, Section \ref{sec:results_2MASS_dist} gives our results, and Section \ref{sec:discussion_2MASS_dist} describes some of their implications."
" The Two Micron All Sky Survey. eiiploved. telescopes in the Northern and Southern lemispheres to observe in the three infrared bands J (1.111.96:40). II (1.501.580,00) aud A,(2.00.—2.32100)."," The Two Micron All Sky Survey employed telescopes in the Northern and Southern hemispheres to observe in the three infrared bands J $(1.11 - 1.36 \mu m)$, H $(1.50 - 1.80\mu m)$ and $K_{s} (2.00 - 2.32\mu m)$."
 Most. of the sources are points. but 1.617.509 are resolved with respect to the observed 2ALASS point spread function and they constitute the Exteuded Source Catalog (ASC).," Most of the sources are points, but 1,647,599 are resolved with respect to the observed 2MASS point spread function and they constitute the Extended Source Catalog (XSC)."
 About of these extended somcees aregalaxies?., About of these extended sources are.
 Exanunation of the Abell 262 cluster sugeests that inost of the 2ATASS galaxies are local with :=0.1 (Skrutskie. private conunununication).," Examination of the Abell 262 cluster suggests that most of the 2MASS galaxies are local with $z \lesssim 0.1$ (Skrutskie, private communication)."
 Iu addition to the local population. the Catalog coutaius more distaut very Inmunous ealaxies and about of the catalog may be quasars with redshifts <52001).," In addition to the local population, the Catalog contains more distant very luminous galaxies and about of the catalog may be quasars with redshifts $\le 5$."
. The low redshifts for nearly all the sources indicate that evolutionary corrections will not be significant for our statistics using this sample., The low redshifts for nearly all the sources indicate that evolutionary corrections will not be significant for our statistics using this sample.
" To select our samples. we adopted Kvon magnitudes following and dereddeued them using the reddening maps of assuiaiug AQ)=OSPR(BV). AGIT)=OSE,BV). and ACN.)=O23E(BV)2003)?."," To select our samples, we adopted Kron magnitudes following and dereddened them using the reddening maps of assuming $A(J) = 0.82 E(B-V)$, $A(H) = 0.48 E_(B-V)$, and $A(K_{s}) = 0.28 E(B-V)$."
" We required all galaxies brighter than Aij=12 to have JyNoy between 0.7 aud 1.1 and all candidate galaxies to have star-galaxy separation mdices typical of galaxies (65,<<lb and ο:1.1) to avoid confusion with nearby galactic sources."," We required all galaxies brighter than $K_{s,0} = 12$ to have $J_{0} - K_{s,0}$ between 0.7 and 1.4 and all candidate galaxies to have star-galaxy separation indices typical of galaxies $e_{score} < 1.4$ and $g_{score}<1.4$ ) to avoid confusion with nearby galactic sources."
 We also require that a candidate is not | asa possible anomaly (e.g. artifact. cluster/ealaxy piece. Calactic object or star) and that if a candidate is among the ~25% visually verified sources. it is not indicated as nou-exteuded (ecx 2).," We also require that a candidate is not ] as a possible anomaly (e.g. artifact, cluster/galaxy piece, Galactic object or star) and that if a candidate is among the $\sim 25\%$ visually verified sources, it is not indicated as non-extended $vc \neq 2$ )."
 To uumimize the relative contribution of stars in the siuuples. we usually remove cells at low Calactic latitude. δω]<207.," To minimize the relative contribution of stars in the samples, we usually remove cells at low Galactic latitude, $|\delta_{gal}| < 20 \degr$."
 Iu some cases we choose higher Galactic latitude cutoffs for comparison. as shown in Table 1 aud Figure 3..," In some cases we choose higher Galactic latitude cutoffs for comparison, as shown in Table \ref{tbl:GQED} and Figure \ref{fig:GQED_mag}."
 We also remove cells with high stellar density. or in very clustyregions. as described below.," We also remove cells with high stellar density, or in very dustyregions, as described below."
 Although this does not explicitly avoid the Magellanic clouds. the lueh stellar density cutoffs remove their central regions.," Although this does not explicitly avoid the Magellanic clouds, the high stellar density cutoffs remove their central regions."
" To examine the completeness of the ealaxy sample. we have measured (V/1,,,? as a function of A, magnitude."," To examine the completeness of the galaxy sample, we have measured $\langle V/V_{max} \rangle$ as a function of $K_{s,0}$ magnitude."
 The results are essentially coustaut between about 0.52 aud 0.51 for 10.0<Ay13.7 aud we cluploy a conservative truncation ofthe galaxy sample at Au= 13.5.," The results are essentially constant between about 0.52 and 0.51 for $10.0 < K_{s,0} <
13.7$ and we employ a conservative truncation ofthe galaxy sample at $K_{s,0} = 13.5$ ."
" To obtain the distribution functiou frou, counuts-in- we imap the sources onto a Tamuncr-Aitof equal area projection (c.g... 2002)): Tere (a . 8) is the Galactic coordinate in radians aud Gr. g) is the projected coordinate."," To obtain the distribution function from counts-in-cells, we map the sources onto a Hammer-Aitoff equal area projection (e.g., ): Here $\alpha$ , $\delta$ ) is the Galactic coordinate in radians and $x$ , $y$ ) is the projected coordinate."
 Figure 1 shows the suuple of galaxy candidates with A513.5 on a," Figure \ref{fig:GQED_allsky} shows the sample of galaxy candidates with $K_{s,0} < 13.5$ on a"
data are needed to confirm the correlation and study its possible implications.,data are needed to confirm the correlation and study its possible implications.
 A recent paper suggest that the HEG/LEG nature of a radio galaxy could be related to the black hole spin instead of the different accretion mechanism 2007)., A recent paper suggest that the HEG/LEG nature of a radio galaxy could be related to the black hole spin instead of the different accretion mechanism .
". However, the definitions of high and low excitation sources used in these two papers are slightly different than the definitions used by and adopted for our sample."," However, the definitions of high and low excitation sources used in these two papers are slightly different than the definitions used by and adopted for our sample."
" While searching for HEG and LEG differences in the samples we used, we also found that they show differences in X-ray emission."," While searching for HEG and LEG differences in the samples we used, we also found that they show differences in X-ray emission."
" LEGs have X-ray luminosities below 10*? erg/s while HEG X-ray emission cover a wider range 10??t01.4x10*,2010)."," LEGs have X-ray luminosities below $10^{42}$ erg/s while HEG X-ray emission cover a wider range to $1.4\times10^{44}$,."
" Although there is an overlap around 1041-33, there are no LEGs with X-ray luminosities higher than 107 erg/s. We see the same behaviour in [OIIIJA50007 luminosity (with a similar overlap around 10*'erg/s, see Figure 1 c and d)."," Although there is an overlap around $10^{41-42}$, there are no LEGs with X-ray luminosities higher than $^{42}$ erg/s. We see the same behaviour in $\lambda50007$ luminosity (with a similar overlap around $^{41}$ erg/s, see Figure 1 c and d)."
 A detailed study about the origin of the HEG and LEG X-ray properties is however beyond the scope of this paper., A detailed study about the origin of the HEG and LEG X-ray properties is however beyond the scope of this paper.
 Figure 1cc shows that the division for HEGs and LEGs described for FRIII/FRII sources by is also visible among CSS sources (i.e. earlier phases of AGN evolution)., Figure \ref{OIIIandRadio}c c shows that the division for HEGs and LEGs described for I sources by is also visible among CSS sources (i.e. earlier phases of AGN evolution).
" The FRIII HEG and CSS HEG, as well as the FRIII LEG and CSS LEG show a wide range of radio powers, but it seems they follow different [ΟΠΠ] luminosity versus radio power correlation."," The II HEG and CSS HEG, as well as the II LEG and CSS LEG show a wide range of radio powers, but it seems they follow different III] luminosity versus radio power correlation."
" FRII sources could be completely different group of objects concerning the photoionization, or follow the LEG IIII] luminosity versus radio power correlation."," I sources could be completely different group of objects concerning the photoionization, or follow the LEG III] luminosity versus radio power correlation."
 As has been noted by all FRIIs for which they were able to derive a spectral type are LEGs., As has been noted by all Is for which they were able to derive a spectral type are LEGs.
 We considered separately the populations of HEGs and LEGs and we have obtained the following linear correlations (plotted in Fig., We considered separately the populations of HEGs and LEGs and we have obtained the following linear correlations (plotted in Fig.
 1cc): HEG logLioI=0.59(+0.07)xLa.s5Guz+26.77(+1.75) ," \ref{OIIIandRadio}c c): HEG $\log{L_{[\rm O\,III]}}=0.59(\pm 0.07)\times\log{L_{\rm 4.85\,GHz}}+26.77(\pm
1.75)$ "
"From standard shock jump conditions, we have In addition, the Riemann invariant connecting states 2 and 3 through the rarefaction, along with the relation pxP'/% inside the rarefaction give while These can be combined to give the following equationfor ji— M,/M;:","From standard shock jump conditions, we have In addition, the Riemann invariant connecting states 2 and 3 through the rarefaction, along with the relation $\rho \propto P^{1/\gamma_i}$ inside the rarefaction give while These can be combined to give the following equationfor $\mu = \mathcal{M}_b/\mathcal{M}_i$ :"
these parameters variable. we can expect a requirement lor spectroscopic accuracy less than the signal sizes (hemselves.,"these parameters variable, we can expect a requirement for spectroscopic accuracy less than the signal sizes themselves."
 Bear in mind however. (hat this depends on (he number of data points.," Bear in mind however, that this depends on the number of data points."
 The inclusion of astrometric data to the fitting procedure will help relax the accuracy. bound., The inclusion of astrometric data to the fitting procedure will help relax the accuracy bound.
 Observationallv. the Galaetic-center. stars are of course observable onlv in infrared.," Observationally, the Galactic-center stars are of course observable only in infrared."
 For the most massive stars. including $2. the Brackett-> line al 2.16jm is (he most prominent available spectral feature. ancl has an intrinsic dispersion of ~lO0kms! (seee.g..?)..," For the most massive stars, including S2, the $\gamma$ line at $2.16\,\mu\rm m$ is the most prominent available spectral feature, and has an intrinsic dispersion of $\sim100\kms$ \citep[see e.g.,][]{martins}."
 For low-mass stars. the edges of the CO molecular bands (the so-called CO band heads) ave excellent sharp features lor redshift measurements.," For low-mass stars, the edges of the CO molecular bands (the so-called CO band heads) are excellent sharp features for redshift measurements."
 The SINFONI spectrograph. an instrument at the VET. has a spectral resolution of T5kms.+.," The SINFONI spectrograph, an instrument at the VLT, has a spectral resolution of $75\kms$."
 Redshift errors are currently estimated at 108 of kins! (seeSection but expected to improve., Redshift errors are currently estimated at 10s of $\kms$ \citep[see Section 4.1 of][]{gillessen} but expected to improve.
 Measurements by (his instrument during 92's next pericenter passage in 2016 could sullice to provide data rom which the Schwarzschild signals could be extractec., Measurements by this instrument during S2's next pericenter passage in 2016 could suffice to provide data from which the Schwarzschild signals could be extracted.
 Spectral measurements seeking the spin-dependent signals are far bevond the capabilities of existing infrared spectrographs., Spectral measurements seeking the spin-dependent signals are far beyond the capabilities of existing infrared spectrographs.
 On the other haud. recent developments such as laser-comb spectrographs (seee.g..7) suggest optimism (hat the spectral resolutions of next-generation instrumentis will prove adequate.," On the other hand, recent developments such as laser-comb spectrographs \citep[see e.g.,][]{steinmetz} suggest optimism that the spectral resolutions of next-generation instruments will prove adequate."
 Meanwhile. there are some theoretical issues (hat require further research.," Meanwhile, there are some theoretical issues that require further research."
because it is crucial to be sure that the +21 sample is statistically — a worry that is less siguificaut at το0.5 since the claimed effect is of dimming rather than brightening.,because it is crucial to be sure that the $z>1$ sample is statistically – a worry that is less significant at $z\sim0.5$ since the claimed effect is of dimming rather than brightening.
" Au interealactic dust distribution would also diii other distant objects,", An intergalactic dust distribution would also dim other distant objects.
 Dust has been proposed several tines as an explanation for the dropoff iu quasar uuuber counts for :>3 (e.g. Ostriker Heisler 1981: Wright 1986)., Dust has been proposed several times as an explanation for the dropoff in quasar number counts for $z\ga 3$ (e.g. Ostriker Heisler 1984; Wright 1986).
 While this poiut is still controversial. observation of the dropoff in racdio-selected quasars (Shaver et al.," While this point is still controversial, observation of the dropoff in radio-selected quasars (Shaver et al."
 1996) shows this explanation to be uulikely., 1996) shows this explanation to be unlikely.
 The models of this paper would not predict the dropoff (unless substautial population III dust exists also)snee e(l)xmOd for all c., The models of this paper would not predict the dropoff (unless substantial population III dust exists also)since $A_V(z) \la 1$ for all $z$.
 Galaxy counts in contrast to quasar studies. show an excess in B-baud counts at high + as compared to some evolution models (see Shimasalku Fukugita 1998 for a summnaiuv).," Galaxy counts, in contrast to quasar studies, show an excess in $B$ -band counts at high $z$ as compared to some evolution models (see Shimasaku Fukugita 1998 for a summary)."
" For B-baud observations probing 20.5E0.3. this ""excess. amounts to a deviation of up to 1l mas from the predicted curve."," For $B$ -band observations probing $z\sim 0.5\pm0.3$, this `excess' amounts to a deviation of up to $\sim
1$ mag from the predicted curve."
 The dust extinction of <(0.1 mag for :<1 would cularec this discrepancy. but not ereath.," The dust extinction of $\la 0.4$ mag for $z \la 1$ would enlarge this discrepancy, but not greatly."
 This holds for £ aud A- xuxl surveys as well., This holds for $I$ and $K$ -band surveys as well.
 Because of uucertaünties iu the uodels at high +. Shimasaku Fukueita are reluctant ο draw couclusious about cosmological parameters from he galaxy counts.," Because of uncertainties in the models at high $z$, Shimasaku Fukugita are reluctant to draw conclusions about cosmological parameters from the galaxy counts."
 But with rapid progress in the field this nay soon become a useful test of the dust model., But with rapid progress in the field this may soon become a useful test of the dust model.
 Several claims of dust detection im clusters lave been uade. but remain controversial.," Several claims of dust detection in clusters have been made, but remain controversial."
 The model of A99 wecdicted that cluster dust should be more ervey than ealactic dust: the aremmenuts of this paper reimforce this xediction., The model of A99 predicted that cluster dust should be more grey than galactic dust; the arguments of this paper reinforce this prediction.
 The intracluster gas destrovs dust efficicutly: since sputtering destrovs simall evaius more efficicutly than aree eraius. it is likely that whatever grains survive in clusters are laree. aud thus supply grey opacity (this may iclp explain the controversy suuroundiue the existence on intracluster dust).," The intracluster gas destroys dust efficiently; since sputtering destroys small grains more efficiently than large grains, it is likely that whatever grains survive in clusters are large, and thus supply grey opacity (this may help explain the controversy surrounding the existence on intracluster dust)."
 Determunation of the extinetion curve of dust in clusters (Gf dust indeed exists) would be au imuportant test of the key idea of the imterealactic dust model. although erey dust in clusters would not necessarily iuplv that dust in the diffuse ICM is also ervey.," Determination of the extinction curve of dust in clusters (if dust indeed exists) would be an important test of the key idea of the intergalactic dust model, although grey dust in clusters would not necessarily imply that dust in the diffuse IGM is also grey."
 Dust confined to galactic halos might also be detectable by its IR cinission or by studies of objects seen through the halo., Dust confined to galactic halos might also be detectable by its IR emission or by studies of objects seen through the halo.
 Zaritsky (1991) has preseuted preliminary evideuce for halo dust in NGC 2835 and NGC 3521 at ~ GOkpe using 6B τοσο if coufirmmed this would be au inportant dust component. as the inferred mass is large.," Zaritsky (1994) has presented preliminary evidence for halo dust in NGC 2835 and NGC 3521 at $\sim 60\,$ kpc using $B-I$ reddening; if confirmed this would be an important dust component, as the inferred mass is large."
 As discussed in refsec-auetals.. fairly strong arguneuts sugecst that the universe currently has O2~(1.5.3)410. Hin inetals.," As discussed in \\ref{sec-metals}, fairly strong arguments suggest that the universe currently has $\Omega_Z \approx (1.5-3) \times
10^{-4}$ in metals."
 This metal cannot all be contained in the stars aud gas in known ealaxies. so unless nietals are well hidden in uuobserved ealaxies. a ictal deusitv QU~(0.752.25)ς1a! should exist in the more uniforii ICAL or in exteuded halos.," This metal cannot all be contained in the stars and gas in known galaxies, so unless metals are well hidden in unobserved galaxies, a metal density $\Omega_Z^{igm} \approx (0.75-2.25) \times 10^{-4}$ should exist in the more uniform IGM or in extended halos."
 Moreover. nost of this metal was probably in place by ~0.5.," Moreover, most of this metal was probably in place by $z\sim0.5$."
" Some fraction d,, of this metal must be in dust.", Some fraction $d_m$ of this metal must be in dust.
 There are several good reasons to expect that the erain size distribution of this dust should be cdiffercut thau for dust in galaxies: (1) Ejection by radiation pressure favors higher opacity. less reddening erains C99).," There are several good reasons to expect that the grain size distribution of this dust should be different than for dust in galaxies: (1) Ejection by radiation pressure favors higher opacity, less reddening grains (A99)."
 Within the DL model. this means huge erains are preferentially ejected. (," Within the DL model, this means large grains are preferentially ejected. ("
2) As dust leaves galaxies (where it is alinost certainly created). sanall eras are prefercutially destroved by sputtering.,"2) As dust leaves galaxies (where it is almost certainly created), small grains are preferentially destroyed by sputtering."
 This prefercutial destruction occurs also iu the ICM. but the οποιος is rather uncertain. (," This preferential destruction occurs also in the IGM, but the efficiency is rather uncertain. ("
3) Sinall eraims are eenerallv assuued to form from the shattering of larecr erains.,3) Small grains are generally assumed to form from the shattering of larger grains.
 This shattering will not occur in the IGAL due to the low densities. nor can simall eraius erow from the vapor.," This shattering will not occur in the IGM due to the low densities, nor can small grains grow from the vapor."
 The principal assumption of this paper (supported by what detailed calenlatious are available) is that very small dust erains leaving the galaxy comprising a fraction (lf) of the total dust deusitv are removed from the erain-size distribution. while huge eraius are not.," The principal assumption of this paper (supported by what detailed calculations are available) is that very small dust grains leaving the galaxy – comprising a fraction $(1-f)$ of the total dust density – are removed from the grain-size distribution, while large grains are not."
 Dust as inodeled by DL. with grains of radius (<0.10) renioved Cfz0.1). reddens very little vet has a visual opacity jg25«10cu?ο|.," Dust as modeled by DL, with grains of radius $\la 0.1\mic$ ) removed $f \approx 0.4$ ), reddens very little yet has a visual opacity $\kappa \approx 5\times 10^4\,{\rm cm^2\,g^{-1}}$ ."
 Uniformly distributed dust of coustaut comoving deusity im an 9=0.2 open universe provides an extinction to +=0.5 of hence if can account for the dinunine of type Ta supernovae at 2~0.5 in a wav fully consistent with observations., Uniformly distributed dust of constant comoving density in an $\Omega=0.2$ open universe provides an extinction to $z=0.5$ of hence it can account for the dimming of type Ia supernovae at $z\sim 0.5$ in a way fully consistent with observations.
" The fact that the expected dust density of OSFOU""~(0.252.25)ν10.!«(0.5)(0.1)=(1.5L5)«107 is so close to the density required is very interesting."," The fact that the expected dust density of $0.5 f \Omega_Z^{igm} \simeq (0.25-2.25)\times 10^{-4} \times
(0.5) \times (0.4) = (1.5-4.5) \times 10^{-5}$ is so close to the density required is very interesting."
 According to these estimates (sec also refsec-inetals aud 8refsec-dustdeus)) it is possible. but rather unlikely. that there is sufficieut dust (QUIC—(k5)~9«10 7) to allow conrpatibilitv with a closed. iatter-doninated uuiverse.," According to these estimates (see also \\ref{sec-metals} and \\ref{sec-dustdens}) ) it is possible, but rather unlikely, that there is sufficient dust $\Omega_{dust}^{igm}(z=0.5) \sim 9 \times 10^{-5}$ ) to allow compatibility with a closed, matter-dominated universe."
 The arguueuts of this paper show that there may be an iutergalactic dust component which is important vet has evaded earlier attempts at its discovery: from this point of view the supernova observations are telling us uot about cosmic acceleration. but about cosmic opacity.," The arguments of this paper show that there may be an intergalactic dust component which is important yet has evaded earlier attempts at its discovery; from this point of view the supernova observations are telling us not about cosmic acceleration, but about cosmic opacity."
 If the arguments of this paper are substantially correct. an intergalactic dust distribution of some imaguitude is inevitable. so if is worth pointing out the chief caveats (which maintain rough consistenev with other observations) under which the obscurationwould not be sufficieut to to account for the supernova dinuiue:," If the arguments of this paper are substantially correct, an intergalactic dust distribution of magnitude is inevitable, so it is worth pointing out the chief caveats (which maintain rough consistency with other observations) under which the obscurationwould not be sufficient to to account for the supernova dimming:"
As a similar inequality of (3.1)) is already shown ou E? (see inequality (1.2) |). the idea of tlT proof of (3.1)) lies in using (1.2)) lor a special extension of the function «€W.2(6dy) to the entirT space ?.,"As a similar inequality of \ref{prop1_eq}) ) is already shown on $\R^{2}$ (see inequality \ref{cara_eq2}) )), the idea of the proof of \ref{prop1_eq}) ) lies in using \ref{cara_eq2}) ) for a special extension of the function $u\in W_{2}^{2,1}(\Omega_{T})$ to the entire space $\R^{2}$."
 For this reason. we demaud that the exteuded function stays dn wiüR2) which is cotτ via the following arguments.," For this reason, we demand that the extended function stays in $W_{2}^{2,1}(\R^{2})$ which is done via the following arguments."
 Remark first that the function « can be extended by continuity to tltT boundary OQ; of Op., Remark first that the function $u$ can be extended by continuity to the boundary $\partial \Omega_{T}$ of $\Omega_{T}$.
 Take 9 as the function defiued over as follows: ancl A direct consequence of this extension is the following lemuna., Take $\tilde{u}$ as the function defined over as follows: and A direct consequence of this extension is the following lemma.
 The proof of tliislenuma is direct by the extension., The proof of thislemma is direct by the extension.
" α Another important consequence of the extension (3.2)) aud (3.3)) is the fact that i€Wil,). aud that we have (see for instance [?])) Let Z4CZ» be the two subsets of Qj defined by: and Taking the cut-off function ΨfCX E). Q€Wx1 satisfying:"," $\hfill{\blacksquare}$ Another important consequence of the extension \ref{first_ext}) ) and \ref{second_ext}) ) is the fact that $\tilde{u}\in
W_{2}^{2,1}(\widetilde{\Omega}_{T})$, and that we have (see for instance \cite{EVANS}) ) Let $\mathcal{Z}_{1}\subset\mathcal{Z}_{2}$ be the two subsets of $\widetilde{\Omega}_{T}$ defined by: and Taking the cut-off function $\Psi\in C^{\infty}_{0}(\R^{2})$ , $0\leq
\Psi\leq 1$ satisfying:"
of Blazhko stars can be quite complex in some cases (see e.g. ig.,of Blazhko stars can be quite complex in some cases (see e.g. fig.
 Sin Daeetal.(2006). and fig., 8 in \citet{ssc} and fig.
 12 in Jurcsikοἱal.(2008a)))., 12 in \citet{mwI}) ).
 —Therefore. we suppose that V29 is probably a DIazhko with modulation either with a period very close to one vear or on à very long (zc7000 d) time-scale.," Therefore, we suppose that V29 is probably a Blazhko variable, with modulation either with a period very close to one year or on a very long $\approx7000$ d) time-scale."
 The CCD V amplitude of 00 is 0.05-mag smaller han that in the Stormetal.(1991). data., The CCD $V$ amplitude of K00 is 0.05-mag smaller than that in the \cite{s91} data.
 The star is zw from the centre., The star is far from the centre.
 Maximunm-brightness variation in the hotographic and CCD £2 (Stormetal.1991). data between 1971 and 1993 is also probable., Maximum-brightness variation in the photographic and CCD $B$ \citep{s91} data between 1971 and 1993 is also probable.
 Phe Fourier spectrum of his data set indicates a modulation. frequency of 0.0011 ed+ (900 d). however. a vearly alias solution (621. d) is equally possible (see. Fig. 16)).," The Fourier spectrum of this data set indicates a modulation frequency of 0.0011 $^{-1}$ (900 d), however, a yearly alias solution (621 d) is equally possible (see Fig. \ref{v30sp}) )."
 The pulsation period of V30 was constant during the centurs-ong time base of the observations., The pulsation period of V30 was constant during the century-long time base of the observations.
 The light curves are dillerent in the ROG and KOO data as shown in Fig. 17.., The light curves are different in the R96 and K00 data as shown in Fig. \ref{v38}.
 Companions at 5r107 alfect some of the photometric data.," Companions at 5""–10"" affect some of the photometric data."
 Because of irregular. Huctuations in the pulsation period. we failed. to find the period of the modulation from the photographic data.," Because of irregular fluctuations in the pulsation period, we failed to find the period of the modulation from the photographic data."
 Phe pulsation period. varied irregularly with a dE0.00002 c amplitude., The pulsation period varied irregularly with a $\pm0.00002$ d amplitude.
 Very faint stars are close to V52. a brighter star is at 127 distance.," Very faint stars are close to V52, a brighter star is at 12"" distance."
 The light. curve of V52 is somewhat anomalous. with smaller. amplitude ancl less steep rising branch than that other RR Lyrac stars with similar period have.," The light curve of V52 is somewhat anomalous, with smaller amplitude and less steep rising branch than that other RR Lyrae stars with similar period have."
 The pulsation-periocd variation is complex: abrupt and continuous changes of the period are detected., The pulsation-period variation is complex; abrupt and continuous changes of the period are detected.
Oo41 classified. the star as irregular.,Oo41 classified the star as irregular.
 The CCD data shown in Fig., The CCD data shown in Fig.
 IS indicate light-curve. variability., \ref{v52lc} indicate light-curve variability.
 “Phe Fourier spectrum of the residual photographic data between 19741993 show mocdulation-frequency components at fofu. folfu and 2fo|fu with fü=0.00104  (95 d) (Vig. 19)).," The Fourier spectrum of the residual photographic data between 1974--1993 show modulation-frequency components at $f_0-f_{\mathrm{m}}$, $f_0+f_{\mathrm{m}}$ and $2f_0+f_{\mathrm{m}}$ with $f_{\mathrm{m}}=0.00104$ $^{-1}$ (95 d) (Fig. \ref{v52sp}) )."
 The modulation is the most. prominent in the ;ohase and steepness of the rising branch., The modulation is the most prominent in the phase and steepness of the rising branch.
 The CCD light curves of ROG and KOO iwe dilferent shapes and amplitudes., The CCD light curves of R96 and K00 have different shapes and amplitudes.
 The maximunm- variation is about O.2-mae in V band., The maximum-brightness variation is about 0.2-mag in $V$ band.
 A very aint close companion does not allect the photometry seriously., A very faint close companion does not affect the photometry seriously.
 The photographie data show strong maximunm-xiehtness variation. too.," The photographic data show strong maximum-brightness variation, too."
 Mocdulation-[requeney components corresponding to the same. a 115-d. modulation. period appear in the residual spectra of both the 19711993 and 195219¢3 photographic data. however. a 170-d. alias solution cannot be excluded (Eis. 20)).," Modulation-frequency components corresponding to the same, a 115-d modulation period appear in the residual spectra of both the 1971–1993 and 1952–1963 photographic data, however, a 170-d alias solution cannot be excluded (Fig. \ref{v56sp}) )."
 The CCD data do not contradict the 115-d. modulation. period., The CCD data do not contradict the 115-d modulation period.
 Phe period changes indicate long-term. evelic variation.," The period changes indicate long-term, cyclic variation."
 A separate star. far from the cluster centre.," A separate star, far from the cluster centre."
 No CCD observation is available., No CCD observation is available.
By cramiuing a iiediau shift between magnitudes of stars detected im a proerain frame and template maenitudes for he same stars in auv 200ς pixcl area. oue obtains a correction to the photometry of stars in the defined macro-xxel.,"By examining a median shift between magnitudes of stars detected in a program frame and template magnitudes for the same stars in any $200\times200$ pixel area, one obtains a correction to the photometry of stars in the defined macro-pixel."
 Stars for which the scatter is more than [ times the uedian error bar are rejected as potentially variable., Stars for which the scatter is more than 4 times the median error bar are rejected as potentially variable.
 The iranues are then divided iuto macro-pixcls. cach covering 200« detector pixels. to obtain 10« maps.," The frames are then divided into macro-pixels, each covering $200\times200$ detector pixels, to obtain $10\times10$ maps."
 The map records relative photometry corrections. the scatter of all naenitude differences in a miacro-pixol aud the unuuber of objects available for those calculations.," The map records relative photometry corrections, the scatter of all magnitude differences in a macro-pixel and the number of objects available for those calculations."
 The global scatter of the map is also recorded., The global scatter of the map is also recorded.
 All these characteristics cau 0 used to assess the quality of the data., All these characteristics can be used to assess the quality of the data.
 The pipeline will assign a value to a macro-pixel in cases when there are fewer than 10 stars to work with. available stars cover ess than half of the macro-pixel area. or the value of the correction or its error are unreasonablv high (21.0 mae).," The pipeline will assign a value to a macro-pixel in cases when there are fewer than 10 stars to work with, available stars cover less than half of the macro-pixel area, or the value of the correction or its error are unreasonably high $>1.0$ mag)."
 Applving relative photometry corrections and building intermediate database files is the final stage in the data reduction process., Applying relative photometry corrections and building intermediate database files is the final stage in the data reduction process.
 Tudividual corrections are obtained bv bi-lincarly interpolating the maps., Individual corrections are obtained by bi-linearly interpolating the maps.
 In the case of a niüssius niacro-pixel surrounded by valid ones. we allow a patch based ou linear interpolation to be applied.," In the case of a missing macro-pixel surrounded by valid ones, we allow a patch based on linear interpolation to be applied."
 Such mcasurements are flageed accordingly but were observed to remain reliable., Such measurements are flagged accordingly but were observed to remain reliable.
 We also flag measurements with large corrections (=0.1 inag). large scatter of magnitude ifereuces used to derive the correction (20.2 mag). and lurge scatter of all macro-pixels iu the map (>0.1 nae).," We also flag measurements with large corrections $>0.1$ mag), large scatter of magnitude differences used to derive the correction $>0.2$ mag), and large scatter of all macro-pixels in the map $>0.1$ mag)."
 If the patch cannot be computed. there is sufficient oeiforniation to derive the correction.," If the patch cannot be computed, there is insufficient information to derive the correction."
 This condition sets ιοNOCORR flag signaling a very unreliable measurement., This condition sets the flag signaling a very unreliable measurement.
 Table 2.) describes all the data processing flags., Table \ref{tab:flags} describes all the data processing flags.
 The correction could uot be calculated for fewer than of ιο database measurements., The correction could not be calculated for fewer than of the database measurements.
 For most frames of all correction values are distributed within £0.05 mae., For most frames of all correction values are distributed within $\pm$ 0.05 mag.
 Iu case of a frame affected by a shutter elitch the distribution can e stronelv non-Gaussian with the interval typically extending to 0.1 mae., In case of a frame affected by a shutter glitch the distribution can be strongly non-Gaussian with the interval typically extending to $\pm$ 0.1 mag.
 Iu both cases there is a small tail of high correction values exteuding to about £1.0 mae., In both cases there is a small tail of high correction values extending to about $\pm$ 1.0 mag.
" Measurements that can be associated with the position of a template object to within 1e are άσσος, with the object ID and frame ID and stored in the main light curve database file.", Measurements that can be associated with the position of a template object to within $\sigma$ are tagged with the object ID and frame ID and stored in the main light curve database file.
 The error estinate is available frou the template list., The error estimate is available from the template list.
 There are no additional restrictions on detections adimitted to the main light curve database., There are no additional restrictions on detections admitted to the main light curve database.
 The final umuuber of database light curves is almost 2410/ (the same as the nuuber of teiiplate objects)., The final number of database light curves is almost $\times10^7$ (the same as the number of template objects).
 There are ~3.35 «10? individual observations with identified pareut objects., There are $\sim$ $\times10^9$ individual observations with identified parent objects.
 Remaining observations are in the “orphan” category., Remaining observations are in the “orphan” category.
" We decided to keep ouly high S/N orphan measurements, those with maenitudes 11.5 or brighter and magnitude errors below 0.1."," We decided to keep only high S/N orphan measurements, those with magnitudes 14.5 or brighter and magnitude errors below 0.1."
 The database contains over «105 orphan nuieasureiments., The database contains over $\times10^8$ orphan measurements.
 All measuremeuts are treated individually. iu particular joined detection iu paired exposures (Section 2.3)) is uot required.," All measurements are treated individually, in particular joined detection in paired exposures (Section \ref{sec:observing}) ) is not required."
 Such criteria. based solely ou frame epochs. can always be applied to the data as a post processing step.," Such criteria, based solely on frame epochs, can always be applied to the data as a post processing step."
 At this point we formed a revised catalog ofobjects with average properties based ou the fully processed light curve files., At this point we formed a revised catalog of objects with average properties based on the fully processed light curve files.
 For cach teiiplate object we examine a corrected set of mieasurenmients and recalculate the median magnitude. magnitude scatter (significantly improved in niost cases). mecian error bar and other useful characteristics.," For each template object we examine a corrected set of measurements and recalculate the median magnitude, magnitude scatter (significantly improved in most cases), median error bar and other useful characteristics."
 Ouly the subset of “eood™” measurements defined in Table 3. is used in these calculations., Only the subset of “good” measurements defined in Table \ref{tab:good} is used in these calculations.
 These criteria primarily reject error codes and several fags associated with known problems., These criteria primarily reject error codes and several flags associated with known problems.
 Cinreuth. it is a recommended choice for working with NSVS data that offers a scusible compromise between the amount of data and data quality.," Currently, it is a recommended choice for working with NSVS data that offers a sensible compromise between the amount of data and data quality."
 Other equally good or better selection cuts may be possible., Other equally good or better selection cuts may be possible.
" A small fraction of all objects below the equator and at the far field edees have fewer than 15 ""eood measurements and. as such. their data are of Lanited use."," A small fraction of all objects below the equator and at the far field edges have fewer than 15 “good” measurements and, as such, their data are of limited use."
 Correspouding catalog eutries have liebt curve statistics copied from the template list aud are fHagged as havingTPLSTATS., Corresponding catalog entries have light curve statistics copied from the template list and are flagged as having.
 Pointing imperfections im repeated exposures of a given field result in object detectious outside the area around the field ceuter covered by a single CCD format (Table 1))., Pointing imperfections in repeated exposures of a given field result in object detections outside the area around the field center covered by a single CCD format (Table \ref{tab:specs}) ).
 This effectively extends cach template by a iarein of X150 pixels on all sides., This effectively extends each template by a margin of $\pm150$ pixels on all sides.
 Together with similarly sized oeiteuded overlap between the fields. this causes iultiple etectious of the same physical objects iu more than one field.," Together with similarly sized intended overlap between the fields, this causes multiple detections of the same physical objects in more than one field."
 Overlap regions teud to erow closer to the celestial north pole for simple gcometric reasons., Overlap regions tend to grow closer to the celestial north pole for simple geometric reasons.
 About of the database elt curves belong to object refereuces of second order or higher., About of the database light curves belong to object references of second order or higher.
 In Section L2 πο use those independent light curves to assess svsteniatie errors du positions and magnitudes., In Section \ref{sec:database} we use those independent light curves to assess systematic errors in positions and magnitudes.
 On the other haud. removing multiple references to the same objects requires perfect coutrol over svstematic effects.," On the other hand, removing multiple references to the same objects requires perfect control over systematic effects."
 Even if the influence of shutter problems aud atimospheric eracdieuts were kuowu with certainty. some irreducible effects would remain.," Even if the influence of shutter problems and atmospheric gradients were known with certainty, some irreducible effects would remain."
 The problemi is not trivial in the case of unfiltered photometry. especially for fast variable sources. but it becomes much easier to handle for a few sources of particular interest after the data has been extracted from the database.," The problem is not trivial in the case of unfiltered photometry, especially for fast variable sources, but it becomes much easier to handle for a few sources of particular interest after the data has been extracted from the database."
 This is why a elobal meree of the plysical database las not been performed., This is why a global merge of the physical database has not been performed.
 We provide a database table with pairs of object IDs that refer to the same phlivsical object (Section. L.2))., We provide a database table with pairs of object IDs that refer to the same physical object (Section \ref{sec:database}) ).
 Implementation details of this incl cau be hidden by the user interface to the database by defining adnappime between the low level database structures aud the top level view where object data appear as merged (Section 41.21)., Implementation details of this kind can be hidden by the user interface to the database by defining a mapping between the low level database structures and the top level view where object data appear as merged (Section \ref{sec:database}) ).
 That approach provides full flexibility to refine the definition of what is the same. aud what is not. as more is known about the data set.," That approach provides full flexibility to refine the definition of what is the same, and what is not, as more is known about the data set."
 Our Northern Sky Variabilitv Survey covers the eutire sky visible οι Los Alamos. New Mexico.," Our Northern Sky Variability Survey covers the entire sky visible from Los Alamos, New Mexico."
 This iucludes the cutive region north of the declination 62δι more than 30.000 square degrees. of the celestial spliere.," This includes the entire region north of the declination $\delta\simeq-38\arcdeg$; more than 30,000 square degrees, of the celestial sphere."
 The completeness. quality of the data aud the ΠΡΟ of available measurements are noticeably lower at low declinatious and low Galactic latitude.," The completeness, quality of the data and the number of available measurements are noticeably lower at low declinations and low Galactic latitude."
 The overall quality ofthe survey measurements is sumniauizediu Table 1.., The overall quality of the survey measurements is summarized in Table \ref{tab:quality}.
 Iu Figure 2 we show positious of roughly 5«10° NSVS stars brighter than 11 mae out of about 11 1nillion stars brighter than 15.5 mag preseut in the simvex., In Figure \ref{fig:sky} we show positions of roughly $5\times10^5$ NSVS stars brighter than 11 mag out of about 14 million stars brighter than 15.5 mag present in the survey.
 The main feature, The main feature
This should. modify the shape of the continuum. emission via absorption. emission ancl scattering. producing a Lully thermalised. blackbods-like component.,"This should modify the shape of the continuum emission via absorption, emission and scattering, producing a fully thermalised, blackbody-like component."
 Here however. the spectral shape of M33. N-8. ijs. unlikely. to. be described solely by a photosphere covering a hot disc. as the peak temperatures of the observed spectra are implausibly high for a pure photosphere (c.f," Here however, the spectral shape of M33 X-8 is unlikely to be described solely by a photosphere covering a hot disc, as the peak temperatures of the observed spectra are implausibly high for a pure photosphere (c.f."
 Ixing 2004)., King 2004).
 We therefore arrive at. the model of an. Eddington ‘slimy disc (Mineshige et al., We therefore arrive at the model of an Eddington `slim' disc (Mineshige et al.
 2000)., 2000).
 Several authors (Poschini et al., Several authors (Foschini et al.
 2006: Weng et al., 2006; Weng et al.
 2009) iwe shown this model to be a reasonable description. of he mocerate signal-to-noise data of individual observations. with a reported requirement for an adclitional soft power-law continuum to high energies in some cases.," 2009) have shown this model to be a reasonable description of the moderate signal-to-noise data of individual observations, with a reported requirement for an additional soft power-law continuum to high energies in some cases."
" Here however. we it thebinned data with an absorbed. ρου dise model in NSPEC). where the index of he temperature profile p is a [ree parameter (£xHE"" or disc temperature Z/ ancl radius 2)."," Here however, we fit the data with an absorbed $p$ -free disc model in ), where the index of the temperature profile $p$ is a free parameter $T\propto R^{-p}$ for disc temperature $T$ and radius $R$ )."
 Such a model has oen used. as evidence for slim dise spectra in ULNs. as a wedieted change in the profile from p=0.75 for standard discs to p—0.5 for slim disces is indeed seen in some objects (c.g. Vierdavanti et al.," Such a model has been used as evidence for slim disc spectra in ULXs, as a predicted change in the profile from $p = 0.75$ for standard discs to $p = 0.5$ for slim discs is indeed seen in some objects (e.g. Vierdayanti et al."
 2006: although also sce Gladstone et al., 2006; although also see Gladstone et al.
 2009)., 2009).
" ""he best-fit parameters and their confidence imits are shown in Table 3.", The best-fit parameters and their confidence limits are shown in Table 3.
 The model provides à. very acceptable description of the low and medium flux binned datasets. and the peak temperature is constrained. to drop with the increase in Dux.," The model provides a very acceptable description of the low and medium flux binned datasets, and the peak temperature is constrained to drop with the increase in flux."
 The model is a poorer. although μαill marginally adequate description of the high flux data: lowever its parameters are not significantly different from. 1e medium IDux bin.," The model is a poorer, although still marginally adequate description of the high flux data; however its parameters are not significantly different from the medium flux bin."
 Although a slim disc by its very definition does not ollow the same radial temperature profile as the standard in disc (Shakura Sunvaey 1973). we would not expect the temperature X the inner edge to drop with increasing [lux unless vw radius had moved: substantially outwards (contrary o what is seen in Galactic black bole N-rav. binaries).," Although a slim disc by its very definition does not follow the same radial temperature profile as the standard thin disc (Shakura Sunyaev 1973), we would not expect the temperature of the inner edge to drop with increasing flux unless the radius had moved substantially outwards (contrary to what is seen in Galactic black hole X-ray binaries)."
 Similarlv. we would not expect the index of the racial emperature dependence p to increase significantlv with lux either.," Similarly, we would not expect the index of the radial temperature dependence $p$ to increase significantly with flux either."
 We can see from Table 3 that the temperature drops by more than 0.3. keV vet. the p value. increases significantly., We can see from Table 3 that the temperature drops by more than 0.3 keV yet the $p$ value increases significantly.
 Thus the change here is contrary to what we, Thus the change here is contrary to what we
Incorporating different galaxy models in numerical simulations. the fitting values οἱ A and D are obtained [or each model by Hevmans et al. (,"Incorporating different galaxy models in numerical simulations, the fitting values of $A$ and $B$ are obtained for each model by Heymans et al. ("
2004: Ilexians et al.,2004; Heymans et al.
 2006)., 2006).
 Comparing wilh SDSS observations. Mandelbaunm et al. (," Comparing with SDSS observations, Mandelbaum et al. ("
2006) present their fitting results with B=Ih!Mpe. and l=0.57£0.72 (see also Hevmans οἱ al.,"2006) present their fitting results with $B=1h^{-1}\hbox{Mpc}$, and $A=0.57\pm 0.72$ (see also Heymans et al."
 2006)., 2006).
 To investigate their influence on weak lensing elfects. we need to analvze the angular correlation of intrinsic ellipticities. which is related to the three dimensional correlation e;;(r) through the following equation where ó(r) and £(7) ave the selection function aud the two-point correlation function for background galaxies. aid ry and π are the comoving separations of (wo galaxies perpendicular and along the line of sight. respectively.," To investigate their influence on weak lensing effects, we need to analyze the angular correlation of intrinsic ellipticities, which is related to the three dimensional correlation $c_{ij}(\vec r)$ through the following equation where $\phi(r)$ and $\xi(r)$ are the selection function and the two-point correlation function for background galaxies, and $r_p$ and $\pi$ are the comoving separations of two galaxies perpendicular and along the line of sight, respectively."
" Since (he correlations decrease quickly on large scales. in the small-angle limit we have (e.g.. Jing 2002). where For weak lensing elfeets. both the convergence # and (he shear 5 are determined by the second derivatives of the lensine potential ó. and where 6;;=O;0, o."," Since the correlations decrease quickly on large scales, in the small-angle limit we have (e.g., Jing 2002), where For weak lensing effects, both the convergence $\kappa$ and the shear $\gamma$ are determined by the second derivatives of the lensing potential $\phi$, and where $\phi_{,ij}=\partial_i\partial_j \phi$ ."
 Concerning weak lensing detections of mass concentrations. we locus on the convergence & lield.," Concerning weak lensing detections of mass concentrations, we focus on the convergence $\kappa$ field."
" In the weak lensing limit. it is related {ο the shear 5 in Fourier space through where the summation over a=(1.2) is implied. and e,οsin(2,/)] with (cosy.siny) (INaiser Squires 1993)."," In the weak lensing limit, it is related to the shear $\gamma$ in Fourier space through where the summation over $\alpha=(1,2)$ is implied, and $c_{\alpha}=[\cos (2\varphi),\sin (2\varphi)]$ with $\vec k=k(\cos \varphi,\sin \varphi)$ (Kaiser Squires 1993)."
 Observationallv. the shear + can be estimated from (he ellipticities of galaxy images.," Observationally, the shear $\gamma$ can be estimated from the ellipticities of galaxy images."
 Inthe weak lensing limit. we have," Inthe weak lensing limit, we have"
For the case of a point mass lous the total maguification of both images is eiven by fp277|2/ryr?tok pcorpRon.D.Di).,"For the case of a point mass lens the total magnification of both images is given by $\tilde{\mu}=\hat{r}^2 +2/\hat{r}\sqrt{\hat{r}^2 +4}$ ; $\hat{r} \equiv r_\perp/R_e(m,D,D_s)$."
 The Einstein radius of the lens is given by Re=IGinDiDi;/Di., The Einstein radius of the lens is given by $R_e^2= 4Gm \tilde{D}_l \tilde{D}_{ls}/\tilde{D}_s$.
 The single lens distribution fiction is then The probability in (5)) is not uormalizable: it diverges at siuall pi., The single lens distribution function is then The probability in \ref{pointprob}) ) is not normalizable; it diverges at small $\delta\tilde{\mu}$.
 This can be handled by introducing a cutoff iu either fr space or in ry., This can be handled by introducing a cutoff in either $\delta\tilde{\mu}$ space or in $r_\perp$.
 The nature of this cutoff is not important as long as it is at sufficiently: small df) or large rp., The nature of this cutoff is not important as long as it is at sufficiently small $\delta\tilde{\mu}$ or large $r_\perp$.
 This will be clear when the total magnification distribution due to multiple lenses is considered., This will be clear when the total magnification distribution due to multiple lenses is considered.
 If the dark matter consists of microscopic particles clumped into halos. the eutire halo will act as a siuele leus.," If the dark matter consists of microscopic particles clumped into halos, the entire halo will act as a single lens."
 Iu this case the Ricci focusing contribution to the magnification strongly dominates over shear distortions produced by mass outside of the beam (Holz&Wald(1998).Premadi.MartelMatzuer 1998)) and is then a function of only the local dimensionless surface deusitv. &(y).," In this case the Ricci focusing contribution to the magnification strongly dominates over shear distortions produced by mass outside of the beam \cite{HW98,PMM98}) ) and is then a function of only the local dimensionless surface density, $\kappa({\bf y})$."
 Furthermore the lensing of the ereat majoritv of SNe will be quite weak which allows us to coufideutly make the linear approximation: àp=2lsCy.Dj.D.)|Ky].," Furthermore the lensing of the great majority of SNe will be quite weak which allows us to confidently make the linear approximation: $\delta\mu = 
2[\kappa({\bf y},D_l,D_s)+\kappa_b]$."
 This assuuiption has been well justified by many authors aud will be comfirmecdt by results iu reftotal.., This assumption has been well justified by many authors and will be confirmed by results in \\ref{total}.
 For the purposes of this paper it will suffice to use a simple model for the surface deusitv of halos., For the purposes of this paper it will suffice to use a simple model for the surface density of halos.
 We use models with surface censitics given by This model behaves like a singular isothermal sphere out to 4429re where it is smoothly cut off., We use models with surface densities given by This model behaves like a singular isothermal sphere out to $y_\perp \simeq r_s$ where it is smoothly cut off.
 Iu the following calculations. cach halo is assumed to harbor a galaxy.," In the following calculations, each halo is assumed to harbor a galaxy."
 At all redshifts a Schechter huuinosity function fit to local galaxies is asuued witha=107 aud o?=(010.|5?Ape I., At all redshifts a Schechter luminosity function fit to local galaxies is assumed with $\alpha=-1.07$ and $\phi^*=0.01(1+z)^3h^3\mpc^{-3}$ .
" The huninositics are then related to the circular velocity. V. by the local Tully-Fisher relation. V,2VGL/L,)*?? where V;=200kns.4."," The luminosities are then related to the circular velocity, $V_c$ by the local Tully-Fisher relation, $V_c=V_*(L/L_*)^{0.22}$ where $V_*=200\kms$."
 The scale lengths axe related to the huuinositv through à.—r(L/L.)!7 with p.=220kpc., The scale lengths are related to the luminosity through $r_c=r_*(L/L_*)^{1/2}$ with $r_*=220\kpc$.
 The precise values used for these parameters do not have a siguificaut effect on the results of this paper., The precise values used for these parameters do not have a significant effect on the results of this paper.
 The total magnification of a source includes contributions from all the lenses surrounding the liebt path., The total magnification of a source includes contributions from all the lenses surrounding the light path.
 To find the true path connecting a source to ux. the lensing equation must be solved with iuultiple deflections (see Schucider.Ehlers&Faleo (1992))).," To find the true path connecting a source to us, the lensing equation must be solved with multiple deflections (see \cite{sch92}) )."
 The maguifications due to differcut leus planes are in general nonlinearly coupled., The magnifications due to different lens planes are in general nonlinearly coupled.
 However. if the deflectiousdue to no more than one of the lenses is very weak the coupling between lenses can be ignored aud their maguifications. ὃμ or df). will add linearly.," However, if the deflectionsdue to no more than one of the lenses is very weak the coupling between lenses can be ignored and their magnifications, $\delta\mu$ or $\delta\tilde{\mu}$, will add linearly."
 This is a good approximation for the vast majority of light paths in realistic mocels., This is a good approximation for the vast majority of light paths in realistic models.
 The validity of this assuniptiou will be justified by the results aud is further investigated in Moetealf(1999)., The validity of this assumption will be justified by the results and is further investigated in \cite{Met99}.
.. Furthermore munerical simulations aud analytic arguineuts show that for both kinds of DM it is a good approximation to take the lenses to be uucorrelated iu space (sce Holz&Wald(1998).Aletcalf 1L998b)).," Furthermore numerical simulations and analytic arguments show that for both kinds of DM it is a good approximation to take the lenses to be uncorrelated in space (see \cite{HW98,Met98b}) )."
" If inaddition we take the lenses internal properties to be uncorrelated. the probability that thetotal magnification. ὃς, of a point source is between ofr, aud of,|dófr; is"," If inaddition we take the lenses internal properties to be uncorrelated, the probability that thetotal magnification,$\delta\tilde{\mu}_s$ , of a point source is between $\delta\tilde{\mu}_s$ and $\delta\tilde{\mu}_s+d\delta\tilde{\mu}_s$ is"
halo is anchored to that of the observed one (essentially by scaling the number density of CRp in simulated clusters).,halo is anchored to that of the observed one (essentially by scaling the number density of CRp in simulated clusters).
 We tind that: Considering all these results. as well as the outcome from our earlier work on the Coma cluster (?).. we conclude that aadronic models alone are not able to explain the observed woperties of giant radio haloes. in terms of their radial extension. observed clusters’s radiobi-modality. scaling relations and spectral roperties.," We find that: Considering all these results, as well as the outcome from our earlier work on the Coma cluster \citep{2010MNRAS.401...47D}, we conclude that hadronic models alone are not able to explain the observed properties of giant radio haloes, in terms of their radial extension, observed clusters's radio, scaling relations and spectral properties."
 Therefore we conclude that radio emission observed in galaxy clusters in form of giant radio halos are a powerful tool o infer the amount of cosmic ray protons within galaxy cluster. confirming previous results that the energy content of cosmic ray »rotons in clusters can not exceed percent level (e.g.9090Pi.," Therefore we conclude that radio emission observed in galaxy clusters in form of giant radio halos are a powerful tool to infer the amount of cosmic ray protons within galaxy cluster, confirming previous results that the energy content of cosmic ray protons in clusters can not exceed percent level \citep[e.g.][]{2007ApJ...670L...5B,2008MNRAS.388.1062C}."
 The problem of halo's extension could be alleviated in hadronic models. where the contribution from primary (shock accelerated) electrons at the cluster outskirts is combined in the simulations with that from secondary electrons (2))).," The problem of halo's extension could be alleviated in hadronic models, where the contribution from primary (shock accelerated) electrons at the cluster outskirts is combined in the simulations with that from secondary electrons \citet{2008MNRAS.385.1211P}) )."
 However. as shown in Sect. ??..," However, as shown in Sect. \ref{rradprof},"
" the problem of the halo profiles arises at distances Q.1 — 0.3 Ay, from cluster centers where. based on the same simulations. the contribution to the diffuse synchrotron emission from these shock accelerated electrons is not yet dominant."," the problem of the halo profiles arises at distances 0.1 – 0.3 $R_\mathrm{vir}$ from cluster centers where, based on the same simulations, the contribution to the diffuse synchrotron emission from these shock accelerated electrons is not yet dominant."
 Further we would like to note that the detailed morphology of the radio emission caused by electrons injected at shocks (e.g.?) will be significantly different from the morphology of giant radio halos and therefore is in general unlikely able to mimic large scale. cluster centric radio emission.," Further we would like to note that the detailed morphology of the radio emission caused by electrons injected at shocks \citep[e.g.][]{1999ApJ...518..603R}
 will be significantly different from the morphology of giant radio halos and therefore is in general unlikely able to mimic large scale, cluster centric radio emission."
 Thus additional physieal processes are required to explain observations., Thus additional physical processes are required to explain observations.
 The problem of the radio in massive clusters can be alleviated by assuming that MHD turbulence (and the rms magnetic field) decays as soon as clusters approach a relaxed state. after a major merger (22)...," The problem of the radio in massive clusters can be alleviated by assuming that MHD turbulence (and the rms magnetic field) decays as soon as clusters approach a relaxed state after a major merger \citep{2009A&A...507..661B,2009JCAP...09..024K}."
 In this case it might also be hought that CRp in these relaxed clusters would undergo less scattering on Magnetic field irregularities escaping from the cluster volume and reducing the source of secondary electrons., In this case it might also be thought that CRp in these relaxed clusters would undergo less scattering on magnetic field irregularities escaping from the cluster volume and reducing the source of secondary electrons.
 All these wrocesses are not properly included in our MHD cosmologica simulations., All these processes are not properly included in our MHD cosmological simulations.
 However. 2) have shown that the fast decay ofthe rms Ποιά in galaxy clusters. that is necessary to explain the observecbi-modality. would imply a situation where the magnetic field power spectrum peaks at the smaller scales. anc eads to the consequence that an large flux of energy in clusters goes into magnetic field amplification/dissipation.," However, \citet{2009A&A...507..661B} have shown that the fast decay of the rms field in galaxy clusters, that is necessary to explain the observed, would imply a situation where the magnetic field power spectrum peaks at the smaller scales, and leads to the consequence that an large flux of energy in clusters goes into magnetic field amplification/dissipation."
 In addition. because turbulent cascade should start to decay on larges scales. which are resolved by Faraday rotation measurements. this scenario would predict abi-modality in rotation measures. and depolarisation in largest clusters. which is not observed (Govoni e al.," In addition, because turbulent cascade should start to decay on largest scales, which are resolved by Faraday rotation measurements, this scenario would predict a in rotation measures and depolarisation in largest clusters, which is not observed (Govoni et al."
 The discovery of giant radio halos with steep spectrum (Q0Ls2) in merging clusters proves that particle acceleration mechanisms are responsible for the origin of these sources and. based on simple energy arguments. disfavours hadronic models (2)...," The discovery of giant radio halos with steep spectrum $\alpha \sim 1.8-2$ ) in merging clusters proves that particle acceleration mechanisms are responsible for the origin of these sources and, based on simple energy arguments, disfavours hadronic models \citep{2008Natur.455..944B}."
 Observations of the best studied halo. in the Coma cluster. have shown that its spectrum steepens at higher frequencies (2).. due to the competition between energy losses and acceleration of the emitting particles. in which case the particle acceleration time-scale would be of the order of 0.1 Gyr.," Observations of the best studied halo, in the Coma cluster, have shown that its spectrum steepens at higher frequencies \citep{2003A&A...397...53T}, due to the competition between energy losses and acceleration of the emitting particles, in which case the particle acceleration time-scale would be of the order of 0.1 Gyr."
 More recently we have shown that the steepening cannot be a result of the inverse Compton (SZ) decrement (2).. confirming these previous finding and supporting a scenario of particle acceleration mechanisms at the origin of the halo.," More recently we have shown that the steepening cannot be a result of the inverse Compton (SZ) decrement \citep{2010MNRAS.401...47D}, confirming these previous finding and supporting a scenario of particle acceleration mechanisms at the origin of the halo."
 Particle acceleration due to micro-turbulence in merging galaxy clusters has been proposed for the origin of radio halos (e.g. ?2)..," Particle acceleration due to micro-turbulence in merging galaxy clusters has been proposed for the origin of radio halos \citep[e.g.][]{2001MNRAS.320..365B,2001ApJ...557..560P}."
 In this case particle acceleration mechanisms would generate radio halos in connection with (massive) cluster mergers. while the radio emission would decay as soon as clusters approach a relaxed state. due to dissipation of tat least a fraction of) this turbulence and the fast electron radiative cooling.," In this case particle acceleration mechanisms would generate radio halos in connection with (massive) cluster mergers, while the radio emission would decay as soon as clusters approach a relaxed state, due to dissipation of (at least a fraction of) this turbulence and the fast electron radiative cooling."
 It will therefore be necessary to consider these processes in future simulations used to study radio halos., It will therefore be necessary to consider these processes in future simulations used to study radio halos.
 That includes an estimation of the locally merger injected turbulence as well as a more detailed description of CR electron spectra., That includes an estimation of the locally merger injected turbulence as well as a more detailed description of CR electron spectra.
 1. D. kindly acknowledges the support of ESF/Astrosim Exchange grant 2065 and thanks the INAF/IRA in Bologna for the hospitality., J. D. kindly acknowledges the support of ESF/Astrosim Exchange grant 2065 and thanks the INAF/IRA in Bologna for the hospitality.
 K. D. acknowledges the supported by the DFG Priority Programme 1177., K. D. acknowledges the supported by the DFG Priority Programme 1177.
 Here we provide additional sealing relations to substantiate the scalings shown before., Here we provide additional scaling relations to substantiate the scalings shown before.
 In figure ΑΙ we show bolometric X-ray luminosity over mass weighted temperature for the simulated cluster sample at redshift zero (diamonds) and 0.48 (triangles)., In figure \ref{lx_t} we show bolometric X-ray luminosity over mass weighted temperature for the simulated cluster sample at redshift zero (diamonds) and 0.48 (triangles).
 We include band-corrected he observed relation from 2). (broken line) and a the same correlation normalised to the simulated Coma cluster (black line)., We include band-corrected the observed relation from \citet{2008arXiv0809.3784P} (broken line) and a the same correlation normalised to the simulated Coma cluster (black line).
 It is well known that non radiative simulations tend to over predict he x-Ray luminosity by a fair amount (see for example (230)., It is well known that non radiative simulations tend to over predict the x-Ray luminosity by a fair amount (see for example \citep{2006MNRAS.367.1641B}) ).
 In addition the effect of K-correction can be seen in comparison with he cluster at high redshift., In addition the effect of K-correction can be seen in comparison with the cluster at high redshift.
 Still. after re-normalizing the x-Ray luminosity there is a reasonably good agreement of with observations We therefore conclude. that our simulated clusters sample shows similar thermal properties than the observations.," Still, after re-normalizing the x-Ray luminosity there is a reasonably good agreement of with observations We therefore conclude, that our simulated clusters sample shows similar thermal properties than the observations."
 In figure A2. we present the scaling of radio power at 1.4 GHz, In figure \ref{timevo} we present the scaling of radio power at 1.4 GHz
average electron energy is set by the balance between Coulomb heating and Compton cooling rates: The resulting electron temperature is of a few hundred keV. and thus Compton cooling of the hot electrons gives rise to emission.,"average electron energy is set by the balance between Coulomb heating and Compton cooling rates: The resulting electron temperature is of a few hundred keV, and thus Compton cooling of the hot electrons gives rise to X-ray emission."
 In Paper I. we distinguished two classes of objects. Class S and Class Q. depending on the volume filling factor of the expanding clouds with respect to the local region size.," In Paper I, we distinguished two classes of objects, Class S and Class Q, depending on the volume filling factor of the expanding clouds with respect to the local region size."
" The volume filling factor e was defined as Class Q objects have large black hole mass (Mp=10? M.) for which the volume filling factor is small (e« 1). while Class S objects are characterized by a large filling factor (e~ 1). associated with smaller black hole masses (Maj,x 105M..)."," The volume filling factor $\epsilon$ was defined as Class Q objects have large black hole mass $M_{BH} \gtrsim 10^{9} M_{\odot}$ ) for which the volume filling factor is small $\epsilon \ll 1$ ), while Class S objects are characterized by a large filling factor $\epsilon \sim 1$ ), associated with smaller black hole masses $M_{BH} \lesssim 10^{8} M_{\odot}$ )."
 We identified Class Q objects with massive and luminous quasars. and Class S sources with less luminous Seyfert galaxies.," We identified Class Q objects with massive and luminous quasars, and Class S sources with less luminous Seyfert galaxies."
" In Class S. the black hole mass is expressed in units of M. and the aceretion rate in units of M.— IM../yr: in Class Q. the black hole mass is expressedin units of Mig=MoxI0M.. and the aceretion rate in units of M=M,x10Ma/yr."," In Class S, the black hole mass is expressed in units of $M_{BH} = M_{8} \times 10^{8} M_{\odot}$ , and the accretion rate in units of $\dot{M} = \dot{M}_{0} \times 1 M_{\odot}/\textrm{yr}$ ; in Class Q, the black hole mass is expressedin units of $M_{BH} = M_{9} \times 10^{9} M_{\odot}$, and the accretion rate in units of $\dot{M} = \dot{M}_{1} \times 10 M_{\odot}/\textrm{yr}$."
 We further defined two subcases. Cases A and B. comparing the electron aceretion and radiation time scales.," We further defined two subcases, Cases A and B, comparing the electron accretion and radiation time scales."
" The separation depends on whether the ratio of the Compton cooling time (£,,;) over the local dynamical time (54) 1s smaller or greater than unity.", The separation depends on whether the ratio of the Compton cooling time $t_{cool}$ ) over the local dynamical time $t_{dyn}$ ) is smaller or greater than unity.
 In Class S. this condition can be written as (see Eq. (," In Class S, this condition can be written as (see Eq. ("
22) in Paper D) We see that the time scale condition translates into a condition on the ratio of accretion rate to central mass. 1/Mpy).,"22) in Paper I) We see that the time scale condition translates into a condition on the ratio of accretion rate to central mass, $\dot{M}/M_{BH}$."
 This parameter can be related to the Eddington ratio L/Le. since where Ly 1s the Eddington luminosity.," This parameter can be related to the Eddington ratio $L/L_{E}$, since where $L_{E}$ is the Eddington luminosity."
" Case A is defined by the condition £4,>£44. and Case B by the opposite condition. £4,,/<tan."," Case A is defined by the condition $t_{cool} > t_{dyn}$, and Case B by the opposite condition, $t_{cool} < t_{dyn}$."
 In other words. for a given black hole mass. there are two cases divided into lower accretion rate (Case A) and higher accretion rate (Case B) systems.," In other words, for a given black hole mass, there are two cases divided into lower accretion rate (Case A) and higher accretion rate (Case B) systems."
 As shown in Paper 1. the time scale condition implies that only Case A is appropriate for Class Q objects.," As shown in Paper I, the time scale condition implies that only Case A is appropriate for Class Q objects."
 In Paper II. we introduced a characteristic X-ray time scale and calculated that its dependence on black hole mass and accretion rate is of the form The model time seale is thus shorter for small black hole mass and/or high accretion rate.," In Paper II, we introduced a characteristic X-ray time scale and calculated that its dependence on black hole mass and accretion rate is of the form The model time scale is thus shorter for small black hole mass and/or high accretion rate."
 We have shown that this model dependence on black hole mass and accretion rate is in excellent agreement with the empirical relation obtained by ?.., We have shown that this model dependence on black hole mass and accretion rate is in excellent agreement with the empirical relation obtained by \citet{McH_et_2006}.
 The spectral shape of the X-ray emission. and in particular the value of the spectral slope. is determined by two plasma physical parameters: the electron temperature and the medium optical depth.," The spectral shape of the X-ray emission, and in particular the value of the spectral slope, is determined by two plasma physical parameters: the electron temperature and the medium optical depth."
 The dimensionless electron temperature 15 defined as and is given by the balance between Coulomb heating and Compton cooling rates., The dimensionless electron temperature is defined as and is given by the balance between Coulomb heating and Compton cooling rates.
" The optical depth of the cloud is give by where 71, is the electron number density. σ the Thomso cross section. and R the typical size of the upscattering region."," The optical depth of the cloud is given by where $n_{e}$ is the electron number density, $\sigma_{T}$ the Thomson cross section, and $R$ the typical size of the upscattering region."
 We compute the power law spectral slope using estimatePA of the electron temperature and optical depth obtained withi our model., We compute the power law spectral slope using estimates of the electron temperature and optical depth obtained within our model.
 We follow ? who give the exact analytical solutio for the spectral index without restriction on plasma temperature and optical depth., We follow \citet{T_L_1995} who give the exact analytical solution for the spectral index without restriction on plasma temperature and optical depth.
 In the non-relativistic limit the spectral slope is given by where the parameter f is only a function of the optical depth and the geometry (plane or spherical)., In the non-relativistic limit the spectral slope is given by where the parameter $\beta$ is only a function of the optical depth and the geometry (plane or spherical).
" The spectral index in the relativistic case is given by where the coefficient dja) is computed through a transcendental equation,", The spectral index in the relativistic case is given by where the coefficient $d_{0}\left( \alpha \right)$ is computed through a transcendental equation.
" The electron temperature in Class S was calculated in Paper I and is on the order of We Meeralso estimated the typical electron density. which we parametrize here as n,2ng-1.2x105m."," The electron temperature in Class S was calculated in Paper I and is on the order of We also estimated the typical electron density, which we parametrize here as $n_{e} = n_{S} \cdot 1.2 \times 10^{8} \mathrm{cm^{-3}}$."
 In Case A. the cooling time scale is longer than the dynamical time scale. and the size of the upscattering region is therefore given by the size of the shock region. R=10Zi Msem.," In Case A, the cooling time scale is longer than the dynamical time scale, and the size of the upscattering region is therefore given by the size of the shock region, $R \cong 3 \times 10^{15} \zeta_{UV} M_{8} \mathrm{cm}$ ."
" In Case B. the cooling time scale is shorter than the dynamical time scale. the size of the Comptonization region is then given by the distance over which electrons travel at the local free-fall speed during the cooling time. R=v,12x108nCMS! Miem."," In Case B, the cooling time scale is shorter than the dynamical time scale, the size of the Comptonization region is then given by the distance over which electrons travel at the local free-fall speed during the cooling time, $R = v_{ff} \cdot t_{cool} \cong 1.2 \times 10^{15} \eta_{1/3}^{-1} \zeta_{UV}^{5/2} \dot{M}_{0}^{-1} M_{8}^{2} \mathrm{cm}$ ."
 The optical depths for the two cases are obtained with Eq. (8) , The optical depths for the two cases are obtained with Eq. \ref{tau}) )
We can now use these estimatesMg of the optical depth to compute the parameterB in the spherical geometry. following ?..," We can now use these estimates of the optical depth to compute the parameter $\beta$ in the spherical geometry, following \citet{T_L_1995}. ."
 Inserting the value of the electron temperature (eq. 11)), Inserting the value of the electron temperature (eq. \ref{T_e}) )
 and the respective values of the 6 parameter in eq. (9).," and the respective values of the $\beta$ parameter in eq. \ref{NR_alpha})),"
 we obtain the spectral slopes in the two cases, we obtain the spectral slopes in the two cases
is present on the same J frame as JS4 9 in the RGO La Palma archive.,is present on the same $I$ frame as JS4 9 in the RGO La Palma archive.
 Our magnitudes for JS4 9 agree within 0.03 mag with JS., Our magnitudes for JS4 9 agree within $0.03$ mag with JS.
 The relative magnitude offset to Teidel in the archive frame gave /.=19.5. in good agreement with our F=19.26.," The relative magnitude offset to Teide1 in the archive frame gave $I=19.3$, in good agreement with our $I=19.26$."
 Since two of the measurements give almost identical magnitudes and the third deviates. it is likely that the explanation to the discrepancy sits in the photometry of ZRM and not m intrinsic variability.," Since two of the measurements give almost identical magnitudes and the third deviates, it is likely that the explanation to the discrepancy sits in the photometry of ZRM and not in intrinsic variability."
 This conclusion ts supported by the ./ magnitude staying roughly constant., This conclusion is supported by the $J$ magnitude staying roughly constant.
 woulc be the lowest mass BD found so far in the Pleiades (~0.01 T.) if it can be confirmed as a member., would be the lowest mass BD found so far in the Pleiades $\sim0.04$ $_{\odot}$ ) if it can be confirmed as a member.
 are probably not Pleiades members. but still of interest.," are probably not Pleiades members, but still of interest."
 NPL43 45 have A magnitudes which place them as GD165B-type objects. re. possible field All the JS candidates except JS9. fall outside our Pleiades limits. confirming the result of ZRM.," NPL43 45 have $K$ magnitudes which place them as GD165B-type objects, i.e. possible field All the JS candidates except JS9, fall outside our Pleiades limits, confirming the result of ZRM."
 JS9 itself has a proper motion inconsistent with membership (Hamblyetal, JS9 itself has a proper motion inconsistent with membership \cite{hambly91}.
.1991).., In Fig.
 In Fig. 8 we show the derived Pletades LF., \ref{Figimf} we show the derived Pleiades LF.
 The included objects are listed in Table 3.., The included objects are listed in Table \ref{Tabimf}.
 Pin Fig., in Fig.
 8 treats the proposed binaries NPL22 and 32 as separate components. with magnitudes as in Sect. 5.2..," \ref{Figimf} treats the proposed binaries NPL22 and 32 as separate components, with magnitudes as in Sect. \ref{individual}."
 rejects NPL22 and 32 as nonmembers. since if they are not binaries they are too bright to be members.," rejects NPL22 and 32 as nonmembers, since if they are not binaries they are too bright to be members."
 Both treat PPL15 as two separate components., Both treat PPL15 as two separate components.
 The theoretical LF was derived from evolutionary models in Baraffe et al. (1998).," The theoretical LF was derived from evolutionary models in Baraffe et al. \cite*{baraffe98},"
. which are based on the latest generation of non-grey atmosphere models (Allard& 1997)., which are based on the latest generation of non-grey atmosphere models \cite{allard97}.
". Three different MF-indices were considered .n=0. Land 2 (o ts defined by ον=constin""din. an = mass and /.N = the number of stars per mass interval din)."," Three different MF-indices were considered, $n=0$, 1 and 2 $n$ is defined by $dN=const*m^{-n}dm$, $m$ = mass and $dN$ = the number of stars per mass interval $dm$ )."
 We normalized to 7.5 stars in the interval 15<[κα16. the mean density of HHJ stars (corrected for the Figure 8. suggests a rising MF towards lower masses with a power-law index between 0 and |. but there are several uncertainties one should be aware of.," We normalized to 7.5 stars in the interval $15 < I_\mathrm{KC} < 16$, the mean density of HHJ stars (corrected for the Figure \ref{Figimf} suggests a rising MF towards lower masses with a power-law index between 0 and 1, but there are several uncertainties one should be aware of."
 The observed number of objects is small. but it remains clear that the LF drops from 7=15 to the survey limit.," The observed number of objects is small, but it remains clear that the LF drops from $I=15$ to the survey limit."
 We cannot say how many Pleiades BDs that are lost in unresolved binaries., We cannot say how many Pleiades BDs that are lost in unresolved binaries.
 However. we estimate a likely upper limit by assuming that the There is also a normalization error. which does not affect the falling trend. however.," However, we estimate a likely upper limit by assuming that the There is also a normalization error, which does not affect the falling trend, however."
 The model in Baraffe et al., The model in Baraffe et al.
 (1998) 1s state-of-the-art and based on the latest generation of non-grey atmospheres and should provide the best possible mass-luminosity relations for the Pleiades BD sequence., \cite*{baraffe98} is state-of-the-art and based on the latest generation of non-grey atmospheres and should provide the best possible mass-luminosity relations for the Pleiades BD sequence.
 Since it has not yet been possible to derive an empirical mass-luminosity relation for substellar objects. we do not try to estimate the uncertainties in mass that may arise from the model.," Since it has not yet been possible to derive an empirical mass-luminosity relation for substellar objects, we do not try to estimate the uncertainties in mass that may arise from the model."
 We have performed a deep 850 aremin? RIA survey in the central area of the Pletades cluster., We have performed a deep 850 $^{2}$ $RIJK$ survey in the central area of the Pleiades cluster.
 Photometry in 7. J or A is presented for 32 previously known and 7 new likely members.," Photometry in $I$, $J$ or $K$ is presented for 32 previously known and 7 new likely members."
 Four of those are below the BD limit. and the faintest one would be the lowest mass BD found in the Pleiades so far. if its membership could be confirmed.," Four of those are below the BD limit, and the faintest one would be the lowest mass BD found in the Pleiades so far, if its membership could be confirmed."
 The overall agreement in the photometry with other surveys is satisfactory., The overall agreement in the photometry with other surveys is satisfactory.
 Teidel is an exception., Teide1 is an exception.
 We find J=19.26. ~ 00.5 mag fainter than ZRM.," We find $I=19.26$, $\sim$ 0.5 mag fainter than ZRM."
 Based on RGO archive data and a roughly constant 7 magnitude we conclude that the reason for this discrepancy most likely sits in the photometry of ZRM and not in intrinsic variability., Based on RGO archive data and a roughly constant $J$ magnitude we conclude that the reason for this discrepancy most likely sits in the photometry of ZRM and not in intrinsic variability.
 A number of very red faint objects were found below the Pleiades sequence., A number of very red faint objects were found below the Pleiades sequence.
 Two of those were measured in J.J and Iv and fit in as GD165B-type objects. possible field BDs.," Two of those were measured in $I$, $J$ and $K$ and fit in as GD165B-type objects, possible field BDs."
 After splitting PPLI5 and two other probable binaries into components. the Pleiades LF was compared to model LFs derived from the most recent theoretical mass-Iuminosity relations.," After splitting PPL15 and two other probable binaries into components, the Pleiades LF was compared to model LFs derived from the most recent theoretical mass-luminosity relations."
 The observed LF supports an MF-index between 0 and |., The observed LF supports an MF-index between 0 and 1.
 Thus. even if the MF seems to rise for low-mass BDs in the Pleiades. it is not steep enough to leave more than a few percent of the cluster's mass in BDs. which is consistent with dynamical findings (Pinfieldetal. 1997)..," Thus, even if the MF seems to rise for low-mass BDs in the Pleiades, it is not steep enough to leave more than a few percent of the cluster's mass in BDs, which is consistent with dynamical findings \cite{pinfield97b}. ."
 assunptious to be mace., assumptions to be made.
 One of the ireas where it can be effücieutle used aud which at present cau not be accessed by the conveutional spectroscopy is studving the fast variability. of the reflected cunission., One of the areas where it can be efficiently used and which at present can not be accessed by the conventional spectroscopy is studying the fast variability of the reflected emission.
 Indeed. variation of the parameters in the Comptonization region. for ustauce. lead to variations of the spectral shape of the Couptonized radiation which would be imprinted in the Fourier frequency resolved spectra.," Indeed, variation of the parameters in the Comptonization region, for instance, lead to variations of the spectral shape of the Comptonized radiation which would be imprinted in the Fourier frequency resolved spectra."
 Their shape. however. muüght differ significantl from any of the Coniptonized spectra they resulted from and no easily interpretable results could be obtained via the conventional spectral fits.," Their shape, however, might differ significantly from any of the Comptonized spectra they resulted from and no easily interpretable results could be obtained via the conventional spectral fits."
 The shape of the reflection signatures. on the other," The shape of the reflection signatures, on the other"
"where the subscripts “WSR” aud ""WS"" here indicate that the terms are taken from different models in WSR and Wong&Sarazin(2009).. respectively.","where the subscripts “WSR” and “WS” here indicate that the terms are taken from different models in \citetalias{WSR+08} and \citet{WS09}, respectively."
 Tn this work. since we are interested in the relative effects onu SZ surveys and cosmological parameter estimation introduced by the non-equipartition effects instead of the precise Y A velation which depends on details of nunerical siuulations. in principle. we cau take iu equilibrimu Y A relation from simulations aud apply our non-cquipartition bias to the equilibria Y A7 relation.," In this work, since we are interested in the relative effects on SZ surveys and cosmological parameter estimation introduced by the non-equipartition effects instead of the precise $Y$ $M$ relation which depends on details of numerical simulations, in principle, we can take any equilibrium $Y$ $M$ relation from simulations and apply our non-equipartition bias to the equilibrium $Y$ $M$ relation."
" The reasou forusing the equilibiuu Y A relation iu WSR to model the non-equipartition 3 A relation instead of the Y M. relation in Woug&Sarazin is that the formerrelation takes iuto account the dependence of Y on gas fraction fai where fea,xM!5m for Mogy2101!AF..."," The reason forusing the equilibrium $Y$ $M$ relation in \citetalias{WSR+08} to model the non-equipartition $Y$ $M$ relation instead of the $Y$ $M$ relation in \citet{WS09} is that the formerrelation takes into account the dependence of $Y$ on gas fraction $f_{\rm gas}$ , where $f_{\rm gas}\propto M^{1/3}$ for $M_{200}\gtrsim 10^{14} M_{\odot}$."
 The uuncerical solutions in Wong&Sarazin(2009). assiune a constant fi. and a self argunient shows that YXAPOfaxADUS.," The numerical solutions in \citet{WS09} assume a constant $f_{\rm gas}$, and a self-similar argument shows that $Y \propto M^{5/3} f_{\rm gas} 
\propto 
M^{5/3}$."
 The equilibrium Y AL relation i WSR has a power-law index close to 2., The equilibrium $Y$ $M$ relation in \citetalias{WSR+08} has a power-law index close to 2.
" On the other haud. the nuou- effects on the integrated } depend weakly onu fea, and hence we can assume the Y bias of the constant fe models in Wong&Sarazin(2009). cau be applied to the varving Fa model in WSR.."," On the other hand, the non-equipartition effects on the integrated $Y$ depend weakly on $f_{\rm gas}$ and hence we can assume the $Y$ bias of the constant $f_{\rm gas}$ models in \citet{WS09} can be applied to the varying $f_{\rm gas}$ model in \citetalias{WSR+08}."
 Another advantage of using the equilibrimim Y M relation in WSR is that we can compare the effect of uou-equipartition onu cosmolosical paraiueters estimations to the merecr effects calculated in WSR.., Another advantage of using the equilibrium $Y$ $M$ relation in \citetalias{WSR+08} is that we can compare the effect of non-equipartition on cosmological parameters estimations to the merger effects calculated in \citetalias{WSR+08}. .
 The equipartition Y A relation and the integrated- SZ bias introduced by the nuon-equipartitiou effect we used in this paper are plotted in Figure L.., The equipartition $Y$ $M$ relation and the integrated SZ bias introduced by the non-equipartition effect we used in this paper are plotted in Figure \ref{fig:YvsM}.
 Clusters with higher masses are hotter. aud hence. the equipartition timescales are longer.," Clusters with higher masses are hotter, and hence, the equipartition timescales are longer."
 Thus. the non-equipartitiou effects are stronger mb more inassive clusters (Fox&Loeb1997:WongSaraziu2009).," Thus, the non-equipartition effects are stronger in more massive clusters \citep{FL97, WS09}."
. For our non-equipartition model in the ACDM universe. the integrated SZ bias decreases as redshift decreases.," For our non-equipartition model in the $\Lambda$ CDM universe, the integrated SZ bias decreases as redshift decreases."
 This is probably due to the decreasing rate of accretion outo clusters in the ACDAI universe during the cosmological acceleration. Which results in a longer time for ion equilibration (Wong&Sarazin2009).," This is probably due to the decreasing rate of accretion onto clusters in the $\Lambda$ CDM universe during the cosmological acceleration, which results in a longer time for electron--ion equilibration \citep{WS09}."
. Iu order to quantity the effect of nou-equipartitiou ou the SZ versus nass relation. we fit a power-law fiction to the integrated SZ bias of the form to all the clusters with Mogy between Lot! and ενLOPAL..," In order to quantify the effect of non-equipartition on the SZ versus mass relation, we fit a power-law function to the integrated SZ bias of the form to all the clusters with $M_{200}$ between $10^{14}$ and $4 \times 
10^{15} M_{\odot}$."
 The range is consistent with the cluster lnass range uxed to study the mass function m N-rav observations (Vikhliuiuetal.2009)., The range is consistent with the cluster mass range used to study the mass function in X-ray observations \citep{Vik+09}.
. We also ft over the wider range of 1007 to 1010A7.. for comparison., We also fit over the wider range of $10^{13}$ to $10^{16} M_{\odot}$ for comparison.
 The fitted coefficieuts. AN aud Aq correspoud to the biases in the fitted SZ versus nass relation if the non-equipartitiou effect is not taken iuto account., The fitted coefficients $\Delta N$ and $\Delta\alpha$ correspond to the biases in the fitted SZ versus mass relation if the non-equipartition effect is not taken into account.
 The clusters in our sample are distributed roughly mniformiy in the logarithia of the mass., The clusters in our sample are distributed roughly uniformly in the logarithm of the mass.
 The fitted results are listed in Table 1.., The fitted results are listed in Table \ref{tab:YMfit}. .
 The effect of nom-equipartition is to decrease Y. for the ligh-iass clusters. aud lence the effect ou the SZ versus mass relation is to lower the power-law iudex by 0.01 to 0.016. which corresponds to a decrease of for the SZ versus mass relation with power-law index a=2.," The effect of non-equipartition is to decrease $Y$ for the high-mass clusters, and hence the effect on the SZ versus mass relation is to lower the power-law index by 0.01 to 0.016, which corresponds to a decrease of for the SZ versus mass relation with power-law index $\alpha = 2$."
 This is comparable to the wneertainty of the power-law index derived from simmlations combined with observations within Moy (Arnaudetal.2009)., This is comparable to the uncertainty of the power-law index derived from simulations combined with observations within $M_{500}$ \citep{APP+09}.
. The normalization is biased to compensate for the chauge in power-law index. aud the bias is about for the scaled mass of LOMAL...," The normalization is biased to compensate for the change in power-law index, and the bias is about for the scaled mass of $10^{15} M_{\odot}$."
 For SZ surveys which measure Y out to the shock radius. ee. observations with a spatial resolution poorer than typical shock radii. we have shown that the non-equipartition effect can introduce a small deviation in the measured Y M relation.," For SZ surveys which measure $Y$ out to the shock radius, e.g., observations with a spatial resolution poorer than typical shock radii, we have shown that the non-equipartition effect can introduce a small deviation in the measured $Y$ $M$ relation."
 The deviationρα are small. but future SZ surveys with sufficient statisticy. may be able to detect such signatures.," The deviations are small, but future SZ surveys with sufficient statistics may be able to detect such signatures."
 Ou the other haud. if clusters are spatially resolved and Y are measured withiu Rogy. we have shown that nou-equipartitiou effect is stnaller than for all clusters. aud hence the bias 1- the Y A relation is negligible (Wong&Sarazin2009).," On the other hand, if clusters are spatially resolved and $Y$ are measured within $R_{200}$, we have shown that non-equipartition effect is smaller than for all clusters, and hence the bias in the $Y$ $M$ relation is negligible \citep{WS09}."
. A bias in measurement out to the shock radii but not within ~Royy will indicate that cbluster outer regions nay be in non-equipartition., A bias in measurement out to the shock radii but not within $\sim R_{200}$ will indicate that cluster outer regions may be in non-equipartition.
 The παο of galaxy clusters expected to be found per unit comoving volume depends seusitivelv on cosinology., The number of galaxy clusters expected to be found per unit comoving volume depends sensitively on cosmology.
 The quantity which is convenient to describe the cluster nuniber deusitv is the mass function. (Al.i). where MALMM. gives the number of clusters per unit colmoving volume with masses in the rauge Af>AL dM. and + is the redshift.," The quantity which is convenient to describe the cluster number density is the mass function, $n(M,z)$, where $n(M,z)dM$ gives the number of clusters per unit comoving volume with masses in the range $M\rightarrow M+dM$ , and $z$ is the redshift."
 While the exact form of the mass function can be found most accurately from cosmological simulations (Spriugeletal. 2005).. a senii-analytic form of the mass function eiven by theextended PressSchechter theory (Press&Schechter1971:Boud provides a more convenient wav to understand the dependence of the niass function on cosmological parameters. especially when we are interested iu the relative effect imustead of the precise values of the mass function itself.," While the exact form of the mass function can be found most accurately from cosmological simulations \citep{Spr+05}, , a semi-analytic form of the mass function given by theextended Press–Schechter theory \citep{PS74, BCE+91, LC93} provides a more convenient way to understand the dependence of the mass function on cosmological parameters, especially when we are interested in the relative effect instead of the precise values of the mass function itself."
 Although thePressSchechter theory cannotreproduce the mass function found in cosmological simulations at very high redshifts aud low cluster masses (Sheth&Tounuueu1999: 2007).. it is more than sufficient over the," Although thePress–Schechter theory cannotreproduce the mass function found in cosmological simulations at very high redshifts and low cluster masses \citep{ST99, LHH+07}, , it is more than sufficient over the"
have been a visually biiliaut object.,have been a visually brilliant object.
 For example. at a distance between 1.0 aud 1.3 kpe aud an Ay = 3.0. a SN would have beeu an. = 3.5 to 5.0 for AA = 17 to. Ls.," For example, at a distance between 1.0 and 1.3 kpc and an $A_{\rm V}$ = 3.0, a SN would have been $m_{\rm v}$ = $-3.5$ to $-5.0$ for $M_{\rm V}$ = $-17$ to $-18$."
 Iu fact. it would have been a bright guest star almost regardless of the specific SN subtype. i0. Type Ta. IL. Ποιο. or Tn uuless it was a very subliinous event.," In fact, it would have been a bright guest star almost regardless of the specific SN subtype, i.e., Type Ia, II, Ib,c, or IIn unless it was a very subluminous event."
" Pushing the nuubers toward fainter apparen magnitudes lanits by adopting the largest distance recently estimated for RN JL713.7-3916. namely 1.7 kpe. and an ely = LONy27«107 cm7: Cassani-Chenai 2001)). aud a As of =16.0 equal to the faintest Type Ib.c SNe (Droutctal.2011).. the supernova would stil have been quite bright with i,z1 aud should have remained visible well iuto 391 AD."," Pushing the numbers toward fainter apparent magnitudes limits by adopting the largest distance recently estimated for RX J1713.7-3946, namely 1.7 kpc, and an $A_{\rm V}$ = 4 $N_{H} = 7 \times 10^{21}$ $^{-2}$; \citealt{CC04}) ), and a $M_{\rm V}$ of $-16.0$ equal to the faintest Type Ib,c SNe \citep{Drout11}, the supernova would still have been quite bright with $m_{\rm v} \approx -1$ and should have remained visible well into 394 AD."
 Simaller distances of around 1 kpe as suggested by Fukuietal.(2003). aac Moriguchietal.(2005) but keeping ly = LO leads to apparent mmaenitudes around 2. or about as bright as Jupiter.," Smaller distances of around 1 kpc as suggested by \citet{Fukui03} and \citet{Moriguchi05} but keeping $A_{\rm
V}$ = 4.0 leads to apparent magnitudes around $-2$, or about as bright as Jupiter."
 To place these brightness estimates im context. we list in Table 1 the reported peak visual maguitucdes (to the nearest half magnitude where possible) of all Galactic SN over the last two millennia based on aucieut records (Stepheuson&Cween2002).," To place these brightness estimates in context, we list in Table 1 the reported peak visual magnitudes (to the nearest half magnitude where possible) of all Galactic SN over the last two millennia based on ancient records \citep{SG02}."
. The listed peas magnitudes. especially for the older SNe. ire often uncertain due to the sometimes fragmentary nature of the existing records aud possible observer error or exageeration.," The listed peak magnitudes, especially for the older SNe, are often uncertain due to the sometimes fragmentary nature of the existing records and possible observer error or exaggeration."
 For example. whereas the estimated istance and visual extinction to the SN 1006 remmnaut oeuplics a iiaxiunun apparent visual brightness around 7.5 (Winkleretal.2003). analyses of reported escriptious sugeest values 2 mae higher or lower Stephenson2010).," For example, whereas the estimated distance and visual extinction to the SN 1006 remnant implies a maximum apparent visual brightness around $-7.5$ \citep{Winkler03}, analyses of reported descriptions suggest values 2 mag higher or lower \citep{Stephenson10}."
. This plus uncertainty iu remnant istances has led to somewhat different values listed iu Table 1 from other authors (c.¢.. Schaefer 1996)).," This plus uncertainty in remnant distances has led to somewhat different values listed in Table 1 from other authors (e.g., \citealt{Schaefer96}) )."
" Despite these caveats. one finds that the peas magnitude estimates from ancient descriptions is. πι ost cases, m rough agreement with visual magnitude estimates based upon the likely SN event."," Despite these caveats, one finds that the peak magnitude estimates from ancient descriptions is, in most cases, in rough agreement with visual magnitude estimates based upon the likely SN event."
 We have identified core-collapse παράπονα events m cases where a compact central object is prescut im the likely associated SNR., We have identified core-collapse supernova events in cases where a compact central object is present in the likely associated SNR.
 Listed in Table 1. are the current estimates for remnant distances and line of sight visual extinctions., Listed in Table \ref{tab:hist} are the current estimates for remnant distances and line of sight visual extinctions.
 Besides the 393 SN. the worst aerecment between the predicted and reported brightness is perhaps that of SN Lisi with the remnant 3€58 about which there has been considerable debate as to that renimant'*s age aud distance estinates (sce Fesenetal.2008 aud Isothes2010. aud refereuces therein).," Besides the 393 SN, the worst agreement between the predicted and reported brightness is perhaps that of SN 1181 with the remnant 3C58 about which there has been considerable debate as to that remnant's age and distance estimates (see \citealt{Fesen08} and \citealt{Kothes10} and references therein)."
 As noted above. the Chinese records include no cohunent about the stars briehtuess.," As noted above, the Chinese records include no comment about the star's brightness."
 This leaves |one to wonder why they didut iuclude a conmuuenut about brightuess especially if SN 3925 is related to RN. J1712.7-3916 it απο have rivaled Jupiter or even Veuus at ---s brightest., This leaves one to wonder why they didn't include a comment about brightness especially if SN 393 is related to RX J1713.7-3946 it might have rivaled Jupiter or even Venus at its brightest.
 One possible solution might simply lie in the extreme brevity of the existing Chinese records., One possible solution might simply lie in the extreme brevity of the existing Chinese records.
 The escription is about as short as one could write a record oncerming the appearance of a guest star., The description is about as short as one could write a record concerning the appearance of a guest star.
 Iu considering this peak brightuess issue. dt is oeuportaut to note that the records that have survived from this period in China are condensed sununuiuies of the Jin dynasty history written by imperial scholars nanny decades and even centuries after the actual events.," In considering this peak brightness issue, it is important to note that the records that have survived from this period in China are condensed summaries of the Jin dynasty history written by imperial scholars many decades and even centuries after the actual events."
 Moreover. trying to interpret the meaning of the lack of a note about the stars brightuess is made more difficult eiven the fact that no mention is made in the existing records on the brightuesses of either of the other two possible guest stars of 369 and 386.," Moreover, trying to interpret the meaning of the lack of a note about the star's brightness is made more difficult given the fact that no mention is made in the existing records on the brightnesses of either of the other two possible guest stars of 369 and 386."
 Iu the absence of any indication iu the Chinese records reearding the brightuess for the 393 guest star. ClarkStephenson(1977). estimated a peak visual niaguitude 0.," In the absence of any indication in the Chinese records regarding the brightness for the 393 guest star, \citet{CS77} estimated a peak visual magnitude $\simeq 0$ ."
 They arrived at this value from the lack of aay remark. about any extraordinary brightuess aud a consideration of atinospheric extinction since observers at Nanjiug could view the enest star no more than 20 degrees above the horizon., They arrived at this value from the lack of any remark about any extraordinary brightness and a consideration of atmospheric extinction since observers at Nanjing could view the guest star no more than 20 degrees above the horizon.
 Iu like fashion. Wangctal.(1997). estimated it could have been no brighter than 2 maenitude. reasoning that had the guest star been brighter than this the Chinese astronomers would have compared it to the plaucts Saturn. Mars and Jupiter.," In like fashion, \citet{Wang97} estimated it could have been no brighter than $-2$ magnitude, reasoning that had the guest star been brighter than this the Chinese astronomers would have compared it to the planets Saturn, Mars and Jupiter."
" All three plaucts were. in fact. visible in the morning sky in the carly Spring of 393 AD with apparent visual maeuitudes of | 0.27. | 0.25, aud 2.1. respectively. aud located within 15 degrees of the reported euest star iu Scorpius."," All three planets were, in fact, visible in the morning sky in the early Spring of 393 AD with apparent visual magnitudes of $+$ 0.27, $+$ 0.25, and $-$ 2.4 respectively, and located within 45 degrees of the reported guest star in Scorpius."
 Wangetal.(1997). further argued that if its peak magnitude had been fainter than 0 mag then it would have not been visible to the uaked eve for as long as ὃ mouths., \citet{Wang97} further argued that if its peak magnitude had been fainter than 0 mag then it would have not been visible to the naked eye for as long as 8 months.
 Adopting a distance of 1.1 kpe. an ly = 2.0. and a peak visual imaeuitude of 2 to 0. they estimated a RX J1713.7-3916 supernova to have been Ay = 12to0. 1.," Adopting a distance of 1.1 kpc, an $A_{\rm V}$ = 2.0, and a peak visual magnitude of $-2$ to $0$, they estimated a RX J1713.7-3946 supernova to have been $M_{\rm V}$ = $-12$ to $-14$."
 Towever. this would mean SN 393 was an uumsually low-huninosity supernova event similar to SN 1987À. 190011. aud 2O005cs with AA>15 (Richardsonctal.2002: 2006).," However, this would mean SN 393 was an unusually low-luminosity supernova event similar to SN 1987A, 1999br, and 2005cs with $M_{\rm V} > -15$ \citep{Richardson02,Pastorello2004,Pastorello2006}."
. Ou the other haud. if the RAN JL713.7-3916 supernova had a more conmnon My: for core-collapse SNe of 17 to. Ls. it then should have beeu easily visible into early 391 AD.," On the other hand, if the RX J1713.7-3946 supernova had a more common $M_{\rm V}$ for core-collapse SNe of $-17$ to $-18$, it then should have been easily visible into early 394 AD."
 Yet there is no mention of this in the existing Chinese records., Yet there is no mention of this in the existing Chinese records.
 So. if the 393 event only reached =2 to O mae and was connected to RX J17123.7-3916. then at the distance aud visual extinction assumed by Wangctal.(1997). it must have been a very subhuuimous event (MA> 15) similar to SN IL/Th.c events occupving the faint cud of CCSNe (Richardsonetal. 2002).," So, if the 393 event only reached $-2$ to $0$ mag and was connected to RX J1713.7-3946, then at the distance and visual extinction assumed by \citet{Wang97} it must have been a very subluminous event $M_{\rm V} > -15$ ) similar to SN II/Ib,c events occupying the faint end of CCSNe \citep{Richardson02}."
. Tn March 393 when the Chinese reported the first sielting of the 393 euest star. astrouoniers in Naujiug (latitude | 327) would have been able to see the stars colmprising Scorpius. tail rise above the horizon around Lai local time auc reach euliiiuation 22 degrees above he southern horizon iu the morning by 5 am. roughly a wf hour before the begining of astronomical twilieht.," In March 393 when the Chinese reported the first sighting of the 393 guest star, astronomers in Nanjing (latitude $+32\arcdeg$ ) would have been able to see the stars comprising Scorpius' tail rise above the horizon around 1 am local time and reach culmination 22 degrees above the southern horizon in the morning by 5 am, roughly a half hour before the beginning of astronomical twilight."
 If he euest star was as brilliant as we estimate if it were the RAN JL713.7-3916 supernova L5 mae). it would have con easy to follow from night into twilieht aud then iuto davtine.," If the guest star was as brilliant as we estimate if it were the RX J1713.7-3946 supernova $-4.5$ mag), it would have been easy to follow from night into twilight and then into daytime."
 Such a guest star in Scorpius would remain visible at elt for the next several mouths right wp until the time it would set in evening twilight around mid-September., Such a guest star in Scorpius would remain visible at night for the next several months right up until the time it would set in evening twilight around mid-September.
 A star about as bright or brighter than the niue stars coluprising the Scorpius’s tail asterisia. all but one of which are fainter than 2ud magnitude. mielt stay visible a little longer.," A star about as bright or brighter than the nine stars comprising the Scorpius's tail asterism, all but one of which are fainter than 2nd magnitude, might stay visible a little longer."
 Thus it might have still been visible duriug carly twilight a week or two longer aud ποιος possibly into carly October., Thus it might have still been visible during early twilight a week or two longer and hence possibly into early October.
 This would still fall short of the, This would still fall short of the
Sct and y Dor pulsators.,Sct and $\gamma$ Dor pulsators.
 Using the formalism there it can be shown that the pulsation constant of WASP-33 (logQwasp-33=— 1.45) perfectly corresponds to the 6 Sct domain.," Using the formalism there it can be shown that the pulsation constant of WASP-33 $\log Q_{\rm 
WASP-33}=-1.45$ ) perfectly corresponds to the $\delta$ Sct domain."
" The power spectrum of ó Sct pulsators is usually very rich, as illustrated by the 754 frequencies identified for FG Vir (Bregeretal. 2005),, but asteroseismic modelling is especially difficult for fast rotators as WASP-33."," The power spectrum of $\delta$ Sct pulsators is usually very rich, as illustrated by the 75+ frequencies identified for FG Vir \citep{2005A&A...435..955B}, but asteroseismic modelling is especially difficult for fast rotators as WASP-33."
" Given this evidence, a different scenario considering that WASP-33 belongs to the relatively rare class of hybrid pulsators, showing simultaneous ó Sct and y Dor oscillations (Handleretal.2002;Handler2009),, may be possible."," Given this evidence, a different scenario considering that WASP-33 belongs to the relatively rare class of hybrid pulsators, showing simultaneous $\delta$ Sct and $\gamma$ Dor oscillations \citep{2002MNRAS.333..262H,2009MNRAS.398.1339H}, may be possible."
 One scenario that should be explored in spite of all the evidence is the possibility that the photometric variations are ellipsoidal in nature and are not caused by pulsations., One scenario that should be explored in spite of all the evidence is the possibility that the photometric variations are ellipsoidal in nature and are not caused by pulsations.
" Indeed, the tidal bulge travels particularly fast over the stellar surface, because the orbital motion of the planet is retrograde with respect to the stellar rotation."," Indeed, the tidal bulge travels particularly fast over the stellar surface, because the orbital motion of the planet is retrograde with respect to the stellar rotation."
 Note that there is an indeterminacy in the stellar rotation velocity because it is not a given assumption that the inclination of the stellar spin axis corresponds to the planet's orbital inclination., Note that there is an indeterminacy in the stellar rotation velocity because it is not a given assumption that the inclination of the stellar spin axis corresponds to the planet's orbital inclination.
" But a simple calculation, equalling the pulsation frequency found here to that of the relative orbital motion of WASP-33 b above the star surface, renders the ellipsoidal variation scenario as physically not valid since the star would have to rotate at a largely super- speed in terms of gravitational break-up."," But a simple calculation, equalling the pulsation frequency found here to that of the relative orbital motion of WASP-33 b above the star surface, renders the ellipsoidal variation scenario as physically not valid since the star would have to rotate at a largely super-critical speed in terms of gravitational break-up."
" It is more likely that the tidal bulge rotates over the stellar surface with a frequency of about 2 d!, which is the net combination of the orbital and rotation frequencies, and is far from the frequencies we find relevant in the periodogram."," It is more likely that the tidal bulge rotates over the stellar surface with a frequency of about 2 $^{-1}$, which is the net combination of the orbital and rotation frequencies, and is far from the frequencies we find relevant in the periodogram."
" As seen above, the periodogram is still not defined sufficiently well to assess the true pulsation spectrum of WASP-33."," As seen above, the periodogram is still not defined sufficiently well to assess the true pulsation spectrum of WASP-33."
" However, given the potential interest, we find it appropriate to briefly address here the possibility of the coupling between the pulsation and the orbit."," However, given the potential interest, we find it appropriate to briefly address here the possibility of the coupling between the pulsation and the orbit."
" If the pulsation frequency of 21.311+0.004 d! turned out to be real, this could suggest the existence of some kind of star-planet interactions that lead to a high-order commensurability of 26 between the pulsation and orbital periods."," If the pulsation frequency of $\pm$ 0.004 $^{-1}$ turned out to be real, this could suggest the existence of some kind of star-planet interactions that lead to a high-order commensurability of 26 between the pulsation and orbital periods."
 Very few cases are known to date of a ó Sct variable belonging to a close binary system (Willems&Claret 2005).., Very few cases are known to date of a $\delta$ Sct variable belonging to a close binary system \citep{2005ASPC..333...52W}.
" The best described candidate for tidally-induced oscillations is HD 209295, which simultaneously presents y Dor and ó Sct-type pulsations, and which was photometrically found to show several p-modes directly related to the orbital motion of its companion (Handleretal.2002).."," The best described candidate for tidally-induced oscillations is HD 209295, which simultaneously presents $\gamma$ Dor and $\delta$ Sct-type pulsations, and which was photometrically found to show several p-modes directly related to the orbital motion of its companion \citep{2002MNRAS.333..262H}."
" This poses the tantalizing possibility of a similar situation occurring in WASP-33, which will certainly be much clearer when additional photometry is acquired and puts constraints on the 6 Sct frequency spectrum."," This poses the tantalizing possibility of a similar situation occurring in WASP-33, which will certainly be much clearer when additional photometry is acquired and puts constraints on the $\delta$ Sct frequency spectrum."
" High-precision R-band photometry has allowed us to present the discovery of photometric oscillations in WASP-33, thus becoming the first transiting planet host with ó Sct pulsations."," High-precision $R$ -band photometry has allowed us to present the discovery of photometric oscillations in WASP-33, thus becoming the first transiting planet host with $\delta$ Sct pulsations."
 These oscillations have a period of about 68 minutes and a semi-amplitude of 1 mmag., These oscillations have a period of about 68 minutes and a semi-amplitude of 1 mmag.
 The frequency spectrum of WASP-33 is still not well defined because the size and significance of the peaks depends on the scheme used to weigh the data., The frequency spectrum of WASP-33 is still not well defined because the size and significance of the peaks depends on the scheme used to weigh the data.
" In a particular weighing criterion, the most significant period comes out to be commensurable with the orbital period at a factor of 26."," In a particular weighing criterion, the most significant period comes out to be commensurable with the orbital period at a factor of 26."
" If this association is assumed to be physically relevant, the multiplicity hints at the existence of planet-star interactions."," If this association is assumed to be physically relevant, the multiplicity hints at the existence of planet-star interactions."
" In any case, gaining insight into the nature of WASP-33 will necessarily require the collection of additional data (possibly multi-colour) with longer time baseline and to carry out pulsation and dynamical modelling."," In any case, gaining insight into the nature of WASP-33 will necessarily require the collection of additional data (possibly multi-colour) with longer time baseline and to carry out pulsation and dynamical modelling."
" The WASP-33 system now represents a new benchmark in the world of exoplanets that can provide valuable information on stellar pulsations (through, e.g., transit surface mapping), on the tidal interactions between planets and stars, and on the dynamical evolution of planetary systems."," The WASP-33 system now represents a new benchmark in the world of exoplanets that can provide valuable information on stellar pulsations (through, e.g., transit surface mapping), on the tidal interactions between planets and stars, and on the dynamical evolution of planetary systems."
the f-component of the angular momoentum of photon and a comma followed by a variable as subscript to a quantity. represents à derivative of the quantity with respect to the,"the $t$ -component of the angular momentum of photon and a comma followed by a variable as subscript to a quantity, represents a derivative of the quantity with respect to the"
the spacing reduces to that of the incompressible case. Άμος=11ΠΠ.,"the spacing reduces to that of the incompressible case, $\lambda_{max} = 11 R$."
 We now compare (he observations of Nessie to this Caeory under the assumption that Nessie is well approximated by an isothermal evlinder., We now compare the observations of Nessie to this theory under the assumption that Nessie is well approximated by an isothermal cylinder.
 HE Nessie lies in the limit f«H. the theory reduces to Chat of an incompressible fIuid. ancl predicts cores spaced at a characteristic length scale ~114.," If Nessie lies in the limit $R \ll H$, the theory reduces to that of an incompressible fluid, and predicts cores spaced at a characteristic length scale $\sim 11R$."
 One can estimate the radius /2 of Nessie [rom the radial extent of the sharp extinction edges evident in the GLIMPSE and. MIPSGAL images., One can estimate the radius $R$ of Nessie from the radial extent of the sharp extinction edges evident in the GLIMPSE and MIPSGAL images.
 This suggests a racius of ~~0.017 or 0.5 pe at the kinematic distance of 3.1 kpc (Clemens1985)., This suggests a radius of $R \sim 0.01 ^\circ$ or $\sim 0.5$ pc at the kinematic distance of 3.1 kpc \citep{Clemens1985}.
. Thus. one would expect cores to form at a spacing of 5.5 pc. in satisfactory agreement with the observations if the filament axis is mostly perpendicular to the line of sight.," Thus, one would expect cores to form at a spacing of $\sim 5.5$ pc, in satisfactory agreement with the observations if the filament axis is mostly perpendicular to the line of sight."
" If Nessie is treated as an isothermal gas evlinder with a central volume density η=LO! ""and T=10 K. appropriate for cold. dense. molecular gas traced by emission. (hen the isothermal scale heieht is J=0.05 pe."," If Nessie is treated as an isothermal gas cylinder with a central volume density $n = 10^4$ $^{-3}$ and $T = 10$ K, appropriate for cold, dense, molecular gas traced by emission, then the isothermal scale height is $H = 0.05$ pc."
" Thus. Nessie would bein the regime RosLT. and the theoretical spacing between cores should be À,,,,=22/1~1 pe."," Thus, Nessie would be in the regime $R \gg H$, and the theoretical spacing between cores should be $\lambda_{max} = 22 H \sim 1$ pc."
 This is smaller than the observed spacing by about a factor of 5., This is smaller than the observed spacing by about a factor of 5.
 This discrepaney may. arise from the Lact that turbulent pressure dominates over thermal pressure., This discrepancy may arise from the fact that turbulent pressure dominates over thermal pressure.
 Theoretical studies of sell-gravitating evlinders usually assume that (thermal pressure is the dominant gas pressure., Theoretical studies of self-gravitating cylinders usually assume that thermal pressure is the dominant gas pressure.
 However. because the observed linewidths in most molecular clouds tvpically exceed the thermal sound speeds by laree factors. turbulent pressure usually dominates over thermal pressure.," However, because the observed linewidths in most molecular clouds typically exceed the thermal sound speeds by large factors, turbulent pressure usually dominates over thermal pressure."
" Ilf one replaces the sound speed c, with the velocity dispersion σ to account for turbulent pressure (Fiege&Pudritz2000).. the effective scale height [ppp is increased considerably over the thermal scale height /7."," If one replaces the sound speed $c_s$ with the velocity dispersion $\sigma$ to account for turbulent pressure \citep{Fiege2000}, the effective scale height $H_{eff}$ is increased considerably over the thermal scale height $H$."
" Assuming a central volume density again of ηcLO! 7. and a FWIIM linewidth of 2.5!.. typically observed toward Nessie. the ellective scale height is 77,jj0.17 pe. which leads to a spacing Ol Amer=22H,py~4 pc between the cores."," Assuming a central volume density again of $n \sim 10^4$ $^{-3}$, and a FWHM linewidth of 2.5, typically observed toward Nessie, the effective scale height is $H_{eff} \sim 0.17$ pc, which leads to a spacing of $\lambda_{max} = 22 H_{eff} \sim 4$ pc between the cores."
 Again. the theoretical prediction is in satisfactory agreement with the observations. especially since the central densitv and hence (he scale heieht // is uncertain.," Again, the theoretical prediction is in satisfactory agreement with the observations, especially since the central density and hence the scale height $H$ is uncertain."
 Moreover. the theoretical assumption of a unilorm. isothermal cxlinder (sometimes embedded in a uniform pressure external medium) is obviously idealized.. ancl the fragmentation length scale may well οπου in more realistic treatments.," Moreover, the theoretical assumption of a uniform, isothermal cylinder (sometimes embedded in a uniform pressure external medium) is obviously idealized, and the fragmentation length scale may well differ in more realistic treatments."
 The theory also predicts that sell-gravitating evlinders in equilibrium have a maximum. critical linear mass density (mass per unit length along the evlinder's axis).," The theory also predicts that self-gravitating cylinders in equilibrium have a maximum, critical linear mass density (mass per unit length along the cylinder's axis)."
 Above the critical value. the cvlinder would collapse racially into a line.," Above the critical value, the cylinder would collapse radially into a line."
" This critical linear mass densitvis given bv CU/D),,,,=2072/6: where v is the sound speed c; in the case of thermal support (Stodolkiewicez 1963. Ostriker 1964) and the turbulent velocity. dispersion c in (he case of turbulent support (Fiege&Pudiitz2000)."," This critical linear mass densityis given by $(M/l)_{max} = 2v^{2}/G$; where $v$ is the sound speed $c_s$ in the case of thermal support (Stodolkiewicz 1963, Ostriker 1964) and the turbulent velocity dispersion $\sigma$ in the case of turbulent support \citep{Fiege2000}."
". I£ turbulent pressure dominates over thermal pressure in Nessie. (he critical linear mass density can be estimated as (M/I),,,,=84GMV)? M. pet. where AV is in units of !.."," If turbulent pressure dominates over thermal pressure in Nessie, the critical linear mass density can be estimated as $(M/l)_{max} = 84 (\Delta V)^2$ $M_\odot$ $pc^{-1}$, where $\Delta V$ is in units of ."
 For typical line widths observed in Nessie, For typical line widths observed in Nessie
Understanding the assembly of stellar mass in galaxies is a fundamental step towards a description of galaxy evolution.,Understanding the assembly of stellar mass in galaxies is a fundamental step towards a description of galaxy evolution.
 Key tools to study this process through cosmic time are the galaxy stellar mass funetion (GSMF) and its integral over masses (the stellar mass density. SMD hereafter).," Key tools to study this process through cosmic time are the galaxy stellar mass function (GSMF) and its integral over masses (the stellar mass density, SMD hereafter)."
 Therefore. it is no surprise that most extragalactic surveys in the past decade have been used to determine the shape and evolution of the GSMF as a function of redshift.," Therefore, it is no surprise that most extragalactic surveys in the past decade have been used to determine the shape and evolution of the GSMF as a function of redshift."
 The earliest results based on small field surveys revealed that the SMD decreases with increasing redshift. as expected in the framework of the currently accepted cosmological hierarchical scenario. both in terms of integrated SMD 2003). as well as of the detailed GSMF (e.g.Fontanaetal.2004;Droryetal.2004. 2005).," The earliest results based on small field surveys revealed that the SMD decreases with increasing redshift, as expected in the framework of the currently accepted cosmological hierarchical scenario, both in terms of integrated SMD \citep[e.g.][]{giallongo98,dickinson03,fontana03,rudnick03}, as well as of the detailed GSMF \citep[e.g.][]{fontana04,drory04,drory05}."
. There have since been many indications that the evolution of the GSMF occurs more rapidly for more massive galaxies than for low mass ones (e.g.FontanaKajisawaetal.2009:Marchesini 2009).. a behaviour known as downsizing in stellar mass (seeFontanotetal.2009.andreferencestherein)..," There have since been many indications that the evolution of the GSMF occurs more rapidly for more massive galaxies than for low mass ones \citep[e.g.][]{fontana06,pozzetti07,perezgonzalez08,kajisawa09,marchesini09}, a behaviour known as downsizing in stellar mass \citep[see][and references therein]{fontanot09}."
 The advent of near- and mid-infrared facilities. above all the Spitzer telescope. has allowed the uncertainties in stellar mass estimates to be reduced and the extension of their analysis to z>3 (e.g.Fontanaetal.2006;Kajisawaetal.2009:Caputi 2011).," The advent of near- and mid-infrared facilities, above all the Spitzer telescope, has allowed the uncertainties in stellar mass estimates to be reduced and the extension of their analysis to $z\gtrsim3$ \citep[e.g.][]{fontana06,kajisawa09,caputi11}."
 In parallel. wide-field surveys have provided large samples with more accurate statistics (Droryetal.2009;Pozzetti2010:Bolzonellaetal.2010:Marchesini2010;Hbert 2010).," In parallel, wide-field surveys have provided large samples with more accurate statistics \citep{drory09,pozzetti10,bolzonella10,marchesini10,ilbert10}."
. One of the key results of these surveys has been the demonstration that the shape of the GSMF cannot be deseribed by a (widely adopted) single Schechter function at least up ίος=1.5.LA but that it departs from this parametric. form because of the superposition of individual distributions for the red and blue galaxy populations or/and because of a change with stellar mass either in star formation efficiency or galaxy assembly rate (Droryetal.2009)..," One of the key results of these surveys has been the demonstration that the shape of the GSMF cannot be described by a (widely adopted) single Schechter function at least up to $z\simeq 1.5$, but that it departs from this parametric form because of the superposition of individual distributions for the red and blue galaxy populations or/and because of a change with stellar mass either in star formation efficiency or galaxy assembly rate \citep{drory09}."
 An accurate knowledge of the GSMF is also a sensitive test of modern galaxy evolutionary models., An accurate knowledge of the GSMF is also a sensitive test of modern galaxy evolutionary models.
 From its initial studies. much interest in the GSMF has been triggered by the possibility of constraining the physies of the evolution of more massive galaxies. which. according to the hierarchical structure formation scenario. are the results of the merging of lower mass objects at earlier times (Coleetal.1994).," From its initial studies, much interest in the GSMF has been triggered by the possibility of constraining the physics of the evolution of more massive galaxies, which, according to the hierarchical structure formation scenario, are the results of the merging of lower mass objects at earlier times \citep{cole94}."
. In addition. to achieve a complete view of the galaxy formation picture. an important goal is a robust knowledge of the properties of low mass galaxies at high redshift.," In addition, to achieve a complete view of the galaxy formation picture, an important goal is a robust knowledge of the properties of low mass galaxies at high redshift."
 The slope of the GSMF at low masses may also represent a eritical benchmark for current galaxy formation models., The slope of the GSMF at low masses may also represent a critical benchmark for current galaxy formation models.
 There is growing evidence that the number of low mass galaxies in the Universe is systematically overpredicted bymost or all theoretical models (Fontanaetal.2006:Fontanotetal.2009:Marchesini 2009).," There is growing evidence that the number of low mass galaxies in the Universe is systematically overpredicted bymost or all theoretical models \citep{fontana06,fontanot09,marchesini09}."
.. Very similar evidence also appears in the analysis of the luminosity functions (Polietal.2001:Marchesint&vanDokkum2007;LoFaroetal.2009;Henriques201 1).," Very similar evidence also appears in the analysis of the luminosity functions \citep{poli01,marchesini07,lofaro09,henriques11}."
. A particularly striking aspect of the mismatch is that it appears 1n different renditions of theoretical models. suggesting that it marks some fundamental incompleteness in our theoretical understanding of galaxy formation and growth.," A particularly striking aspect of the mismatch is that it appears in different renditions of theoretical models, suggesting that it marks some fundamental incompleteness in our theoretical understanding of galaxy formation and growth."
 While a global picture is emerging from these investigations. many outstanding questions are still to. be addressed.," While a global picture is emerging from these investigations, many outstanding questions are still to be addressed."
 In general. the various GSMFs presented in the literature agree reasonably well at z=0-5. although disagreements exist. somewhat increasing at high redshift (Caputietal.2011:GonzálezMarchesini2010;Mortlocketal. 2011). that cannot be explained by merely field-to-field variance.," In general, the various GSMFs presented in the literature agree reasonably well at $z=0-5$, although disagreements exist, somewhat increasing at high redshift \citep{caputi11,gonzalez11,marchesini10,mortlock11}, that cannot be explained by merely field-to-field variance."
 At even higher redshift. the available estimates of the SMD are based on UV-selected samples. hence are potentially incomplete in mass. and/or are often derived by adopting average mass-to-light ratios for the whole population rather than detailed object-by-object estimates (Gonzálezetal. 2011)..," At even higher redshift, the available estimates of the SMD are based on UV-selected samples, hence are potentially incomplete in mass, and/or are often derived by adopting average mass-to-light ratios for the whole population rather than detailed object-by-object estimates \citep{gonzalez11}. ."
 Finally. and particularly," Finally, and particularly"
result of heating [rom massive stars (220M. ). while cool dust. could. be powered by intermediate mass. stars (5-20 AM.) and the interstellar radiation field.,"result of heating from massive stars $>20 M_{\odot}$ ), while cool dust could be powered by intermediate mass stars (5-20 $M_{\odot}$ ) and the interstellar radiation field."
 Phe nonthermal-racio/cool-dust. correlation could not be explained through a dependence on the same energy. source., The nonthermal-radio/cool-dust correlation could not be explained through a dependence on the same energy source.
 LIBN suggest a possible scenario involving coupling of gas. cold. dust. and magnetic fields.," HBX suggest a possible scenario involving coupling of gas, cold dust and magnetic fields."
 In this paper we present the first detection. of high-latitude dust for NGC 5775., In this paper we present the first detection of high-latitude dust for NGC 5775.
 Observing with SCUBA. we map the cold dust in the cüsk and halo.," Observing with SCUBA, we map the cold dust in the disk and halo."
 We also present racio continuum observations of the galaxy taken with the Giant Aletrewave Radio Telescope (GARD). which trace largely the non-thermal svnchrotron emission.," We also present radio continuum observations of the galaxy taken with the Giant Metrewave Radio Telescope (GMRT), which trace largely the non-thermal synchrotron emission."
 The observations from SCUBA and GMBLE are spatially compared with one another in an elfort to investigate whether a cold dust/non-thermal racio emission correlation exists in the disk and halo of this galaxy., The observations from SCUBA and GMRT are spatially compared with one another in an effort to investigate whether a cold dust/non-thermal radio emission correlation exists in the disk and halo of this galaxy.
" NGC 5775 is an edge-on spiral galaxy at a distance of 24.8 Alpe (11,275 kim s1 Alpe ly oand with an inclination angle of SG (Irwin L994)."," NGC 5775 is an edge-on spiral galaxy at a distance of 24.8 Mpc $_o$ =75 km $^{-1}$ $^{-1}$ ), and with an inclination angle of $^\circ$ (Irwin 1994)."
" NGC 5775 is found on the FIR/raclio correlation at log Dau, = 22.32 W + and log (Lire fl.) = 10.44.", NGC 5775 is found on the FIR/radio correlation at log $_{20 cm}$ = 22.32 W $^{-1}$ and log $_{FIR}$ $_\odot$ ) = 10.44.
 The results in this paper are the first ones of an ongoing project to investigate a possible sub-mim/metre wavelength correlation in the disks and halos of galaxies., The results in this paper are the first ones of an ongoing project to investigate a possible sub-mm/metre wavelength correlation in the disks and halos of galaxies.
 Observations of NGC 5775. were mace on 2001. January 4 and 5. at the JCAPP using SCUBA.," Observations of NGC 5775 were made on 2001 January 4 and 5, at the JCMT using SCUBA."
 SCUBA images a 2.3. region of sky simultaneously at 450 and. 850. pam. Our observations provide fully sampled. images by moving the secondary mirror in the G4pt jigele map mode., SCUBA images a $2.3^{\prime}$ region of sky simultaneously at 450 and 850 $\mu$ m. Our observations provide fully sampled images by moving the secondary mirror in the 64pt jiggle map mode.
 We performed pointing checks every hour against a bright source., We performed pointing checks every hour against a bright source.
 Skydip measurements were also made to determine the atmospheric ranspareney by change in elevation (opacity was about 0.27 at 850 jum and 1.67 at 450. sem), Skydip measurements were also made to determine the atmospheric transparency by change in elevation (opacity was about 0.27 at 850 $\mu$ m and 1.67 at 450 $\mu$ m).
 Alars was mapped twice each night for calibration of our source and to determine he beam shape., Mars was mapped twice each night for calibration of our source and to determine the beam shape.
 Our observations of NGC 5775 consisted of three exposures of 45 minutes each over two overlapping ields. since our galaxy is larger than the diameter of the region that the telescope can image.," Our observations of NGC 5775 consisted of three exposures of 45 minutes each over two overlapping fields, since our galaxy is larger than the diameter of the region that the telescope can image."
 The software package SURE was used to reduce the SCUBA cata., The software package SURF was used to reduce the SCUBA data.
 All maps were reduced using typical reduction tasks., All maps were reduced using typical reduction tasks.
 SURE was used to clean and. [lat-field. the images., SURF was used to clean and flat-field the images.
 Dirty bolometers were removed and the image noise was reduced using a SURE task which compensated for spatially correlated emission., Dirty bolometers were removed and the image noise was reduced using a SURF task which compensated for spatially correlated emission.
 The pointing drifts were corrected and the images were calibrated. using Mars., The pointing drifts were corrected and the images were calibrated using Mars.
 Finally all the observations were combined into a single map., Finally all the observations were combined into a single map.
 The resulting map has a resolution of 14.6 and an rms noise of 4 mJy/beam., The resulting map has a resolution of $^{\prime\prime}$ and an rms noise of 4 mJy/beam.
 NGC 5775 was observed with the GAIRT on 2000 July 1 and 16 at 617 Mllz using à bandwidth of 16 Mllz., NGC 5775 was observed with the GMRT on 2000 July 1 and 16 at 617 MHz using a bandwidth of 16 MHz.
 Phe GMIECE consists of thirty steerable. 45-metre diameter. antennas. of which 14 are located. randomly in a central 1 km 1 km diameter region referred to as the Central Square.," The GMRT consists of thirty steerable, 45-metre diameter antennas, of which 14 are located randomly in a central 1 km $\times$ 1 km diameter region referred to as the Central Square."
" The remaining antennas lie along 3 arms of an approximately ""X"" configuration. with cach arm extending to a length of about 12 Km."," The remaining antennas lie along 3 arms of an approximately `Y' configuration, with each arm extending to a length of about 14 km."
 This provides we coverage for imaging both the compact and extended emission., This provides $uv$ coverage for imaging both the compact and extended emission.
 A more detailed description of the GMIE can be found in Swarup et al. (, A more detailed description of the GMRT can be found in Swarup et al. (
1991).,1991).
 These observations were mace during the commissioning phase of the GMBBE and typically 25 to 27 antennas were available for cach day., These observations were made during the commissioning phase of the GMRT and typically 25 to 27 antennas were available for each day.
 The source was observed on two dillerent cays for checking consistency of the images., The source was observed on two different days for checking consistency of the images.
 “Phe primary fux density calibrator was 3€286 while the phase calibrator was ὃς208., The primary flux density calibrator was 3C286 while the phase calibrator was 3C298.
 The total time spent on the source was approximately 120 minutes on each observing cay., The total time spent on the source was approximately 120 minutes on each observing day.
 The analysis of the cata was done using the Astronomical Image Processing System (ALPS) from the National Badio Astronomy Observatory., The analysis of the data was done using the Astronomical Image Processing System (AIPS) from the National Radio Astronomy Observatory.
 Ehe data. editing itself was done within the ALPS environment using the task UVELCG., The data editing itself was done within the AIPS environment using the task UVFLG.
 However. the identification of bad data was done outside the ALPS environment. with algorithms developed by J. Stil in a package called ‘bore’.," However, the identification of bad data was done outside the AIPS environment with algorithms developed by J. Stil in a package called `borg'."
 The bore allows the user to define what constitutes bad data., The borg allows the user to define what constitutes bad data.
 For our data. bore identified all points that had. near zero flux. density at cach channel for the flux density ancl phase calibrator.," For our data, borg identified all points that had near zero flux density at each channel for the flux density and phase calibrator."
 The routine also identified the spikes in the data while observing the calibrators by finding points that deviate more than. approximately 3 sigma from the modal amplitude for a particular baseline. channel and source.," The routine also identified the spikes in the data while observing the calibrators by finding points that deviate more than, approximately 3 sigma from the modal amplitude for a particular baseline, channel and source."
 I£ any baseline had a significant number of points Dlageed. it was subsequently µασσο from all sources.," If any baseline had a significant number of points flagged, it was subsequently flagged from all sources."
 The bore package helped to ease the editing of the data because the GAIN did not have any utomatic ageing of bad. data. including bad antennas at the time of these observations.," The borg package helped to ease the editing of the data because the GMRT did not have any automatic flagging of bad data, including bad antennas at the time of these observations."
 The ALPS tasks CALID. CLCAL and BPASS were used on the Ilagged data set to calibrate the source.," The AIPS tasks CALIB, CLCAL and BPASS were used on the flagged data set to calibrate the source."
 The central 100 channels of the total of 128 channels were used in the analysis., The central 100 channels of the total of 128 channels were used in the analysis.
 Phe channels were averaged and Fourier inversion and cleaning were performed on the NGC 5775 data using IALAGR., The channels were averaged and Fourier inversion and cleaning were performed on the NGC 5775 data using IMAGR.
 A series of self-calibration and cleaning procedures were then conducted to produce two maps. one from each day of observations.," A series of self-calibration and cleaning procedures were then conducted to produce two maps, one from each day of observations."
 After determining that the two maps were virtually identical we used the ALPS task DBCON to combine the UV. plane data from cach observation and produced a final single map to increase our signal-to-noise ratio., After determining that the two maps were virtually identical we used the AIPS task DBCON to combine the UV plane data from each observation and produced a final single map to increase our signal-to-noise ratio.
 Using the brightest source visible in our observation and the rms noise of the map. 0.9 mJv/heam. we calculate a dynamic range of 119.," Using the brightest source visible in our observation and the rms noise of the map, 0.9 mJy/beam, we calculate a dynamic range of 112."
" Although the angular resolution using the entire GMIC is approximately 6 aresec. we have tapered the GMICE images to 14.6"" to be comparable with the S50 jun SCUBA map."," Although the angular resolution using the entire GMRT is approximately 6 arcsec, we have tapered the GMRT images to $^{\prime\prime}$ to be comparable with the 850 $\mu$ m SCUBA map."
 In Fig., In Fig.
 1 we show our final SSO pam map of the edge-on spiral galaxy NGC 5775., 1 we show our final 850 $\mu$ m map of the edge-on spiral galaxy NGC 5775.
 Phe 450 jin map (not shown) has avery similar disk morphology with poorer signal-to-noise ratio., The 450 $\mu$ m map (not shown) has a very similar disk morphology with poorer signal-to-noise ratio.
 SCUBA maps of NGC 5775 reveal a bright central source and a number of additional peaks of bright emission. approximately along the disk (Note that the figure-S outline is an artifact due to combining the data from the two fields used.).," SCUBA maps of NGC 5775 reveal a bright central source and a number of additional peaks of bright emission, approximately along the disk (Note that the figure-8 outline is an artifact due to combining the data from the two fields used.)."
Figure 9 shows the time evolution of the total number of n-bodies within the grid.,Figure 9 shows the time evolution of the total number of $n$ -bodies within the grid.
 During (he transition from runaway growth to oligarchic growth. ἂν peaks aud remains constant for Q.11 Myr.," During the transition from runaway growth to oligarchic growth, $N_o$ peaks and remains constant for 0.1–1 Myr."
" Once orbital interactions begin. AV, declines."," Once orbital interactions begin, $N_o$ declines."
 The rate of decline is fastest in the most massive svstenis., The rate of decline is fastest in the most massive systems.
 The [ill parameter also shows the rapid transition Irom oligarchyto chaos., The Hill parameter also shows the rapid transition from oligarchyto chaos.
 When ἂν peaks. pj reaches a maximum.," When $N_o$ peaks, $p_H$ reaches a maximum."
 Ho declines sharply when mergers reduce (he number of ορατό»., It declines sharply when mergers reduce the number of oligarchs.
 After a merger or series of mergers. py rises slowly as the remaining oligarchs accrete leftover planetesinials.," After a merger or series of mergers, $p_H$ rises slowly as the remaining oligarchs accrete leftover planetesimals."
 To examine the sensitivity of these results to mp4. we consider a broad range of promotion mass.," To examine the sensitivity of these results to $m_{pro}$, we consider a broad range of promotion mass."
 For Xy = 116 g ? at 0.81.2 AU. caleulations with inproρωOS x10? (Xu/4gcm 7) ο cannot follow the evolution of the most massive coagulation particles accurately.," For $\Sigma_0$ = 1–16 g $^{-2}$ at 0.8–1.2 AU, calculations with $m_{pro} \gtrsim$ $2 \times 10^{25}$ $\Sigma_0 / {\rm 4~g~cm^{-2}}$ ) g cannot follow the evolution of the most massive coagulation particles accurately."
 Thus. the production rate of oligarchs is inconsistent.," Thus, the production rate of oligarchs is inconsistent."
 Once a few oligarchs form. (he models provide a poor treatment of interactions among oligarchs and therefore vield poor estimates of the merger rate and (he Gimescale for the transition from oligarchy to chaos.," Once a few oligarchs form, the models provide a poor treatment of interactions among oligarchs and therefore yield poor estimates of the merger rate and the timescale for the transition from oligarchy to chaos."
 Calculations with smaller Προ provide better solutions to the evolution of the largest objects., Calculations with smaller $m_{pro}$ provide better solutions to the evolution of the largest objects.
" To measure (he quality of the results for the transition from oligarchy (o chaos. we define /s: as the time when oligarchs with m=10?(X,/8eem7) ο contain half of the initial mass and /,, as the time when these oligarchs start tomerge and the number of oligarchs starts to decline."," To measure the quality of the results for the transition from oligarchy to chaos, we define $t_{\Sigma}$ as the time when oligarchs with $m \gtrsim 10^{26} (\Sigma_0 / {\rm 8~g~cm^{-2}})$ g contain half of the initial mass and $t_m$ as the time when these oligarchs start tomerge and the number of oligarchs starts to decline."
" The scaling of the oligarch mass with X, provides a clean way to compare models with different initial conditions.", The scaling of the oligarch mass with $\Sigma_0$ provides a clean way to compare models with different initial conditions.
" Our caleulations show clear trends for /,, and ἐν as a function of X, (Figure 11).", Our calculations show clear trends for $t_m$ and $t_{\Sigma}$ as a function of $\Sigma_0$ (Figure 11).
" The limescale for oligarchs to contain half of the initial mass roughly. varies as fexX,77 ith very littledispersion?..", The timescale for oligarchs to contain half of the initial mass roughly varies as $t_{\Sigma} \propto \Sigma_0^{-2/3}$ with very little.
" The transition [rom oligarchic growth to chaotic grwoth at /=Ly, also depends on My.", The transition from oligarchic growth to chaotic grwoth at $t = t_m$ also depends on $\Sigma_0$.
" Our results vield an approximate relation. /4,xA."," Our results yield an approximate relation, $t_m \propto \Sigma_0^{-3/2}$."
 |lowever. this (rend appears to have inflection points for V 2g ?andX> 8 g 7.," However, this trend appears to have inflection points for $\Sigma \lesssim$ 2 g $^{-2}$ and$\Sigma \gtrsim$ 8 g $^{-2}$."
 Caleulations in progress will allow usto test this relation and its origin in more detail., Calculations in progress will allow usto test this relation and its origin in more detail.
" There are no large trends for /,, and /s; with my.", There are no large trends for $t_m$ and $t_{\Sigma}$ with $m_{pro}$.
" Although caleulations with smaller Nyro Vield smaller dispersions in /,, and ἐν al each Xj. the median values for /,, and /s; are fairly independent of ,;."," Although calculations with smaller $m_{pro}$ yield smaller dispersions in $t_m$ and $t_{\Sigma}$ at each $\Sigma_0$ , the median values for $t_m$ and $t_{\Sigma}$ are fairly independent of $m_{pro}$ ."
" A Spearman rank test (Pressetal.1992). suggests a weak inverse correlation between /,4. /« and m pros which we plan to test with additional calculations."," A Spearman rank test \citep{pre92} suggests a weak inverse correlation between $t_m$ , $t_{\Sigma}$ and $m_{pro}$ , which we plan to test with additional calculations."
with the subclump distribution is given by a simple counting argument: The subchunp distribution on smaller scales can be estimated. if one assumes a model for the density run of subclumps around. their parent. halos.,with the subclump distribution is given by a simple counting argument: The subclump distribution on smaller scales can be estimated if one assumes a model for the density run of subclumps around their parent halos.
 For instance. one might assume that they trace the density profile. of the mass. or that this distribution is a non-singular isothermal sphere.," For instance, one might assume that they trace the density profile of the mass, or that this distribution is a non-singular isothermal sphere."
 Once this density profile has been specified. the small scale distribution of the subelumps can be described rather compactly using the halo model of large scale structure (see the recent review in Cooray Sheth 2002).," Once this density profile has been specified, the small scale distribution of the subclumps can be described rather compactly using the halo model of large scale structure (see the recent review in Cooray Sheth 2002)."
 ]t is sometimes of interest. to estimate the. distribution of subclumps as a function. of local density., It is sometimes of interest to estimate the distribution of subclumps as a function of local density.
 We develop (wo approximations for this quantity., We develop two approximations for this quantity.
 Phe first is a simple counting argument which exploits the [act that the number of m-subelumps of an Ad-parent does not depend on any «quantities other than m ancl AZ., The first is a simple counting argument which exploits the fact that the number of $m$ -subclumps of an $M$ -parent does not depend on any quantities other than $m$ and $M$.
 LW the local overdensity 9 is defined on sullicientlv large scales that As=pl(1|9) is much larger than the mass of anv parent halo. then the density of subelumps in such regions is where the density dependent parent halo mass function n(AM.T|8) can be estimated. following Mo White (19: Ixaullmann Lemson (1999) and Sheth Tormen (2002).," If the local overdensity $\delta$ is defined on sufficiently large scales that $M_\delta\equiv \bar\rho V(1+\delta)$ is much larger than the mass of any parent halo, then the density of subclumps in such regions is where the density dependent parent halo mass function $n(M,T|\delta)$ can be estimated following Mo White (1996), Kauffmann Lemson (1999) and Sheth Tormen (2002)."
 On very laree scales. Als Al. the parent. halo mass function reduces to nC.T|o)⋅1|b(AL)3]n(AdT).," On very large scales, $M_\delta\gg M$ , the parent halo mass function reduces to $n(M,T|\delta) \to [1 + b(M)\delta]\,n(M,T)$."
 Thus. on these scales. maa(m.T9)Ldboar.28)nasCMT). with buon.2) given. by the expression. derived. in the previous subsection.," Thus, on these scales, $n_{\rm sub}(m,T|\delta)\to [1 + b_{\rm sub}(m,T)\delta]\,n_{\rm sub}(M,T)$, with $b_{\rm sub}(m,T)$ given by the expression derived in the previous subsection."
 On. intermediate. scales. this simple expression for n(A.T|9) is no longer valid. but equation (19)) will remain accurate provided that the full expression for ΠΑΛΙ.119} is used.," On intermediate scales, this simple expression for $n(M,T|\delta)$ is no longer valid, but equation \ref{nsubdelta}) ) will remain accurate provided that the full expression for $n(M,T|\delta)$ is used."
 Equation (19)) becomes inaccurate once the cell size V on which 3 is evaluated is comparable to the diameter of a tvpical halo., Equation \ref{nsubdelta}) ) becomes inaccurate once the cell size $V$ on which $\delta$ is evaluated is comparable to the diameter of a typical halo.
 On such small scales. some cells may only contain portions of parent halos. and hence the simple counting argument is no longer accurate.," On such small scales, some cells may only contain portions of parent halos, and hence the simple counting argument is no longer accurate."
" Then it is more accurate to simply compute Nau(m[Ms.25). where 75 is obtained by using the spherical collapse relation for the inear and nonlinear overdensities. d)(0) (Mo White 1996 eive a convenient fitting formula for this relation). and then set o,(25)=60(O)."," Then it is more accurate to simply compute $N_{\rm sub}(m|M_\delta,T_\delta)$, where $T_\delta$ is obtained by using the spherical collapse relation for the linear and nonlinear overdensities, $\delta_0(\delta)$ (Mo White 1996 give a convenient fitting formula for this relation), and then set $\delta_{\rm sc}(T_\delta) = \delta_0(\delta)$."
 Note that. in contrast to equation (16)). rere the upper limit of the integral. 7. is not the same as the ime when the parent halo is identified. 73.," Note that, in contrast to equation \ref{nsubmM}) ), here the upper limit of the integral, $T$, is not the same as the time when the parent halo is identified, $T_\delta$."
 Εις is because not all the subelumps which will form within Ms bv 75 have ormed at P<75., This is because not all the subclumps which will form within $M_\delta$ by $T_\delta$ have formed at $T\le T_\delta$.
 Thus. Dividing this quantity by naa(m.ZV provides an estimate of how biased the subcelump distribution. in dense cells is relative to the average.," Thus, Dividing this quantity by $n_{\rm sub}(m,T)V$ provides an estimate of how biased the subclump distribution in dense cells is relative to the average."
 Writing the density-dependent abundance this way shows explicitlv— that subhalos of a given mass in dense regions formed at earlier times than did subhalos of the same mass in less dense regions., Writing the density-dependent abundance this way shows explicitly that subhalos of a given mass in dense regions formed at earlier times than did subhalos of the same mass in less dense regions.
 For the parent halo mass function in equation (11)). all the integrals above can be performed analytically: (note that. this is independent of. 7) and so the abundance of subcelumps Is The halo bias factor associated with equation (11)) is (Cole Iwaiser 1989: MoWhite 1996: Sheth Tormen 1999). so the large scale. bias [actor of the subclumps. computed. using the simple counting argument of equation (18)) is," For the parent halo mass function in equation \ref{nmps}) ), all the integrals above can be performed analytically: (note that this is independent of $T$ ) and so the abundance of subclumps is The halo bias factor associated with equation \ref{nmps}) ) is (Cole Kaiser 1989; MoWhite 1996; Sheth Tormen 1999), so the large scale bias factor of the subclumps, computed using the simple counting argument of equation \ref{halobias}) ) is"
reduce the sensitivity of the final images.,reduce the sensitivity of the final images.
 A further analysis using a different imaging approach may be required., A further analysis using a different imaging approach may be required.
 We performed a sanity check on the flux calibration making use of photometric 100-μπι IRAS coverage in the field., We performed a sanity check on the flux calibration making use of photometric $\mu$ m IRAS coverage in the field.
 We select 14 IRAS sources (robustly detected at zm) with clear detections in our PACS image., We select 14 IRAS sources (robustly detected at $\mu$ m) with clear detections in our PACS image.
 A full description of the source extraction for the ssurvey is presented in Rigby et ((in preparation)., A full description of the source extraction for the survey is presented in Rigby et (in preparation).
" For this test, we perform a source extraction using aperture photometry within SEXtractor auto) and correcting flux densities using Fig. 9.."," For this test, we perform a source extraction using aperture photometry within SEXtractor ) and correcting flux densities using Fig. \ref{Fap_corr}."
 We find a bootstrapped median of (S100-PAcCs/S100-1RAs)=1.034t0.08 for the flux density ratio.," We find a bootstrapped median of $(S_{\rm
 100-PACS}/S_{\rm 100-IRAS}) = 1.03\pm0.08$ for the flux density ratio."
" Despite the small number of sources, this roughly confirms the quality of the flux calibration withiin HIPE."," Despite the small number of sources, this roughly confirms the quality of the flux calibration within HIPE."
" According to an ICC report (footnote 9)), these calibrations are still under development within HIPE."," According to an ICC report (footnote \ref{fnscanning}) ), these calibrations are still under development within HIPE."
 Note that monochromatic flux densities quoted from broadband photometry are dependent on the shape of the SED (colour corrections)., Note that monochromatic flux densities quoted from broadband photometry are dependent on the shape of the SED (colour corrections).
" Indeed, based on the PACS filter profiles (see Fig. 1)),"," Indeed, based on the PACS filter profiles (see Fig. \ref{filters}) ),"
" small variations of the order of x,5 pper cent have to be applied to the observed flux density at the reference wavelength.", small variations of the order of $\ls5$ per cent have to be applied to the observed flux density at the reference wavelength.
 These variations are significant for cold («20 K)) sources (?))., These variations are significant for cold $<$ ) sources \citealt{poglitsch10}) ).
 The pipeline-reduced maps are already astrometrically calibrated., The pipeline-reduced maps are already astrometrically calibrated.
" We confirmed and checked the accuracy of the astrometric solution of the PACS green and red maps against the FIRST catalogue, the parallel SPIRE catalogue (Rigby et al,"," We confirmed and checked the accuracy of the astrometric solution of the PACS green and red maps against the FIRST catalogue, the parallel SPIRE catalogue (Rigby et al.,"
 in preparation) and with respect to each other., in preparation) and with respect to each other.
 Catalogue sources were deemed to be matches if an association was found within 6aarcsec., Catalogue sources were deemed to be matches if an association was found within arcsec.
 The mean offsets are summarised in Table 2 along with the number of matches between the input catalogues used to determine the offsets., The mean offsets are summarised in Table \ref{tab:ast} along with the number of matches between the input catalogues used to determine the offsets.
 The mean offsets and standard deviations are smaller than the search radius used for the matching., The mean offsets and standard deviations are smaller than the search radius used for the matching.
" This, together with the negligible sub-pixel change in astrometric offset for association radii between 5 and aarcsec, supports the idea that the quoted offsets and standard deviations are representative of the astrometric accuracy of the maps."," This, together with the negligible sub-pixel change in astrometric offset for association radii between 5 and arcsec, supports the idea that the quoted offsets and standard deviations are representative of the astrometric accuracy of the maps."
 Both green and red maps were seen to be well aligned with each other and to the SPIRE and FIRST catalogues., Both green and red maps were seen to be well aligned with each other and to the SPIRE and FIRST catalogues.
" An analysis of the direction of the offsets suggests that there is a systematic offset between the PACS green map and SPIRE catalogue of —1 and aarcsec in aand Dec., respectively."," An analysis of the direction of the offsets suggests that there is a systematic offset between the PACS green map and SPIRE catalogue of $-$ 1 and arcsec in and Dec., respectively."
" This might be related to recent ICC findings relating to a 50-ms time shift in science data MMülller, ccomm.)."," This might be related to recent ICC findings relating to a 50-ms time shift in science data Mülller, comm.)."
 As all of the mean offsets are close to the size of a single PACS pixel (and significantly smaller than an individual SPIRE pixel — see, As all of the mean offsets are close to the size of a single PACS pixel (and significantly smaller than an individual SPIRE pixel – see
Carbon monoxide is found in a variety of astrophysical environments usually being the most abundant molecule with the exception of Η».,Carbon monoxide is found in a variety of astrophysical environments usually being the most abundant molecule with the exception of $_2$.
 It is typically observed in absorption in the UV and near-IR and in emission in the far-IR to millimeter wavelengths., It is typically observed in absorption in the UV and near-IR and in emission in the far-IR to millimeter wavelengths.
 For example. the detected a large number CO rovibrational lines toward Orion Peak | and 2 (Gonzálex-Alfonzoetal. 2002)) while pure rotational lines were observed in the planetary nebulae NGC 7027 (Cernicharoetal. 1997)).," For example, the detected a large number CO rovibrational lines toward Orion Peak 1 and 2 \cite{gon02}) ) while pure rotational lines were observed in the planetary nebulae NGC 7027 \cite{cer97}) )."
 —n most environments. the molecular level populations are not in equilibrium. so that predicting spectral line intensities depends crucially on the magnitude of collisional excitation rate coefficients due to the dominant species H». He. and H. Adopting semiempirical potentials. Green Thaddeus (1976) performed one of the earliest quantal scattering calculations for the CO-H:;. CO-He. and CO-H systems at astrophysically relevant temperatures.," In most environments, the molecular level populations are not in equilibrium, so that predicting spectral line intensities depends crucially on the magnitude of collisional excitation rate coefficients due to the dominant species $_2$, He, and H. Adopting semiempirical potentials, Green Thaddeus (1976) performed one of the earliest quantal scattering calculations for the $_2$, CO-He, and CO-H systems at astrophysically relevant temperatures."
 Their results suggested that the rate coefficients for atomic hydrogen collisions were significantly less than those due to H>. so that CO-H collisions were usually neglected in modeling studies of CO spectra.," Their results suggested that the rate coefficients for atomic hydrogen collisions were significantly less than those due to $_2$, so that CO-H collisions were usually neglected in modeling studies of CO spectra."
 The H-CO complex has been extensively studied by the chemical physics community for the past three decades including early ab initio PES calculations by Botschwinna (1974)., The H-CO complex has been extensively studied by the chemical physics community for the past three decades including early ab initio PES calculations by Botschwinna (1974).
 A later ab initio PES by Bowman. Bittman. and Harding (1986. BBH) was construeted and used in subsequent scattering. calculations (Lee&Bowman 1987)).," A later ab initio PES by Bowman, Bittman, and Harding (1986, BBH) was constructed and used in subsequent scattering calculations \cite{lee87}) )."
 The H+CO system has a barrier to the formation of the HCO complex at a H-CO internuclear separation of 4.2 ag with a calculated height of 0.125-0.17 eV. but measured to be 0.087(17) eV (700 em! or 1000 K) (Wangetal. 1973)).," The H+CO system has a barrier to the formation of the HCO complex at a H-CO internuclear separation of 4.2 $_0$ with a calculated height of 0.125-0.17 eV, but measured to be 0.087(17) eV $\sim$ 700 $^{-1}$ or 1000 K) \cite{wan73}) )."
 Lee Bowman (1987) found that for collision energies below the barrier. and not coincident with tunneling resonances. rotational excitation cross sections displayed an even AJ propensity. 1.8. homonuclear-like behavior at long-range.," Lee Bowman (1987) found that for collision energies below the barrier, and not coincident with tunneling resonances, rotational excitation cross sections displayed an even $\Delta J$ propensity, i.e. homonuclear-like behavior at long-range."
 Another H-CO surface was computed at the MRCI level of theory by Keller et al. (, Another H-CO surface was computed at the MRCI level of theory by Keller et al. (
1996). the so-called WKS PES.,"1996), the so-called WKS PES."
 This PES was found to reproduce H-CO spectroscopic measurements better than that of the BBH surface., This PES was found to reproduce H-CO spectroscopic measurements better than that of the BBH surface.
 It was also noted by Green et al. (, It was also noted by Green et al. (
1996) that the WKS and BBH surfaces gave different rotational excitation cross sections with the difference being most significant for the 0—1 transition.,1996) that the WKS and BBH surfaces gave different rotational excitation cross sections with the difference being most significant for the $0\rightarrow 1$ transition.
 This discrepancy was ascribed to the differences in the treatment of the long-range portion of the potentials., This discrepancy was ascribed to the differences in the treatment of the long-range portion of the potentials.
 Balakrishnan. Yan. Dalgarno (2002) later confirmed this difference in the rotational excitation cross sections and therefore utilized the WKS surface for large-scale calculations of rotational excitation rate coethciets for astrophysical modeling applications.," Balakrishnan, Yan, Dalgarno (2002) later confirmed this difference in the rotational excitation cross sections and therefore utilized the WKS surface for large-scale calculations of rotational excitation rate coefficients for astrophysical modeling applications."
 Recetly. Liszt (2006) adopted the new CO-H rotational excitatio rate coefficients of Balakrishnan et al. (," Recently, Liszt (2006) adopted the new CO-H rotational excitation rate coefficients of Balakrishnan et al. ("
2002) in an investigation of the non-equilibrium rotational populations of CO in environments typical of the diffuse interstellar medium (ISM).,2002) in an investigation of the non-equilibrium rotational populations of CO in environments typical of the diffuse interstellar medium (ISM).
 He concluded that the increase in the rotational excitatior rate coefficients for CO-H substantially enhanced CO rotational brightness and excitation temperatures and that CO-H collisions should not be neglected in future models., He concluded that the increase in the rotational excitation rate coefficients for CO-H substantially enhanced CO rotational brightness and excitation temperatures and that CO-H collisions should not be neglected in future models.
 However. what has been previously overlooked is that the new large 0—{ rate coefficient results in a departure from the homonuclear-like even AJ. propensity which has been argued on reasonable physical grounds to be valid for the H-CO collision system (Lee&Bowman 1987)).," However, what has been previously overlooked is that the new large $0\rightarrow 1$ rate coefficient results in a departure from the homonuclear-like even $\Delta J$ propensity which has been argued on reasonable physical grounds to be valid for the H-CO collision system \cite{lee87}) )."
 As the scattering results have been confirmed m a number of theoretical investigations. a possible explanation is a subtle deficiency in the long-range portion of the WKS. surface.," As the scattering results have been confirmed in a number of theoretical investigations, a possible explanation is a subtle deficiency in the long-range portion of the WKS surface."
 In this letter. we explore this issue by computing two new," In this letter, we explore this issue by computing two new"
"1c, which for the post-break slope can largely be attributed to the overshoot in slope directly after the break (see also section 3)).","$1
\sigma$, which for the post-break slope can largely be attributed to the overshoot in slope directly after the break (see also section \ref{results_section}) )."
" the of the pre-break slope inferred from Although(synthetic) light inaccuracycurves will be smaller when earlier time data is available, which is often the case for light curves, a systematic difference will remain (see also ?))."," Although the inaccuracy of the pre-break slope inferred from (synthetic) light curves will be smaller when earlier time data is available, which is often the case for light curves, a systematic difference will remain (see also \citealt{Johannesson2006}) )."
 This emphasizes the importance of numerical modeling for the proper interpretation of data., This emphasizes the importance of numerical modeling for the proper interpretation of data.
 The situation gets worse when we move the observer off-axis., The situation gets worse when we move the observer off-axis.
 As Fig., As Fig.
" 10 shows, even thougha jet break is clearly detected on-axis for our physics settings, it can become hard to distinguish from a single power law for an observer positioned at 0;/2."," \ref{Fproblog_figure} shows, even though a jet break is clearly detected on-axis for our physics settings, it can become hard to distinguish from a single power law for an observer positioned at $\theta_j / 2$."
" The average observer angle one would expect when observing jets oriented randomly in the sky is 20;/3 (for small jet opening angles, and assuming that the observer angle lies between zero and the jet opening angle)."," The average observer angle one would expect when observing jets oriented randomly in the sky is $2\theta_j /3$ (for small jet opening angles, and assuming that the observer angle lies between zero and the jet opening angle)."
 Larger observer angles will lead to that we discuss separately below., Larger observer angles will lead to that we discuss separately below.
 It therefore follows that a significant number of jet breaks may remain hidden in the data due to the jets not being observed directly on-axis., It therefore follows that a significant number of jet breaks may remain hidden in the data due to the jets not being observed directly on-axis.
 In table 2. the classifications for the individual Monte Carlo iterations are also counted., In table \ref{break_times_results_table} the classifications for the individual Monte Carlo iterations are also counted.
" Assuming again that jets are oriented randomly in the sky and that jets are only observed up to observer angles equal to 0;, we can calculate how often an afterglow with the physical parameters of the simulation would be classified as showing a jet break."," Assuming again that jets are oriented randomly in the sky and that jets are only observed up to observer angles equal to $\theta_j$, we can calculate how often an afterglow with the physical parameters of the simulation would be classified as showing a jet break."
 For each angle 0; we have classified n; out of 1000 synthetic curves as showing a jet break., For each angle $\theta_i$ we have classified $n_i$ out of 1000 synthetic curves as showing a jet break.
 This means that we will classify the afterglow described by the simulation as showing a jet break only 1000sin(0;)x100%~29% of the time.," This means that we will classify the afterglow described by the simulation as showing a jet break only $\sum_i n_i
\sin( \theta_i ) / \sum_i 1000 \sin( \theta_i ) \times 100 \% \approx
29 \%$ of the time."
" This2 value;n;sin(0))/ is only>>; a very rough estimate, for it depends on the S10? criterion, that is to some extent arbitrary."," This value is only a very rough estimate, for it depends on the $F_{prob} \lesssim 10^{-5}$ criterion, that is to some extent arbitrary."
" Also,PF, as noted before, the off-axis curves are relatively brighter due to the fixed count rate."," Also, as noted before, the off-axis curves are relatively brighter due to the fixed count rate."
 The requirement of having data up to ten days introduces a selection effect as well., The requirement of having data up to ten days introduces a selection effect as well.
" For all results above, it should be kept in mind that they have been obtained for a single half opening angle of 0.2 radians (approx."," For all results above, it should be kept in mind that they have been obtained for a single half opening angle of 0.2 radians (approx."
 11.5?) which is relatively large (although not extremely so and within the range of jet opening angles observationally inferred from data)., $11.5^\circ$ ) which is relatively large (although not extremely so and within the range of jet opening angles observationally inferred from data).
 This results in a later jet break than a smaller opening angle would lead to., This results in a later jet break than a smaller opening angle would lead to.
" On the other hand we have set z=0, which again moves the jet break to earlier observer times and thereby compensates for the large opening angle."," On the other hand we have set $z = 0$, which again moves the jet break to earlier observer times and thereby compensates for the large opening angle."
 The general effect of higher observer angles is that both jet edges become observable at different times., The general effect of higher observer angles is that both jet edges become observable at different times.
 The reason that a broken power law did not always produce significantly better fit than a single power law is mainly becausea the full drop in count rate associated with the further edge got pushed out beyond ten days for off-axis observers (Section 3))., The reason that a broken power law did not always produce a significantly better fit than a single power law is mainly because the full drop in count rate associated with the further edge got pushed out beyond ten days for off-axis observers (Section \ref{results_section}) ).
 For strongly collimated jets with small opening angles this effect is therefore expected to be less severe., For strongly collimated jets with small opening angles this effect is therefore expected to be less severe.
 The often large difference between the physical parameters like p (affecting the slope of the light curve) and 0; (affecting the break time) used in a model and the values for these parameters when inferred from synthetic data created from that model has been discussed in detail by ?.., The often large difference between the physical parameters like $p$ (affecting the slope of the light curve) and $\theta_j$ (affecting the break time) used in a model and the values for these parameters when inferred from synthetic data created from that model has been discussed in detail by \citet{Johannesson2006}.
" They also include the observer angle as a model parameter, but do not discuss it further in their paper."," They also include the observer angle as a model parameter, but do not discuss it further in their paper."
 The existence of orphan afterglows is an important and general prediction of current afterglow theories., The existence of orphan afterglows is an important and general prediction of current afterglow theories.
" Regardless of the GRB launching mechanism and the initial baryon content of the jet, eventually synchrotron emission from a decelerating baryonic blast wave should be observable for observer "," Regardless of the GRB launching mechanism and the initial baryon content of the jet, eventually synchrotron emission from a decelerating baryonic blast wave should be observable for any observer angle."
"For this reason, various groups have anylooked for orphan angle.afterglows, both at the optical and radio frequencies (e.g. ????))."," For this reason, various groups have looked for orphan afterglows, both at the optical and radio frequencies (e.g. \citealt{Levinson_etal_2002_ApJ,
 Gal-Yam_etal_2006_ApJ, Soderberg2006, Malacrino_etal_2007_AA}) )."
 Few positive detections have been reported and surveys and archival studies have mainly served, Few positive detections have been reported and surveys and archival studies have mainly served
More importantly. the {lis is independent of the ambient densitv and weakly dependent on ἐμ.,"More importantly, the flux is independent of the ambient density and weakly dependent on $\epsilon_B$."
 For all well modeled afterglows. the cooling Lequency at hhr is below the X-ray baad.," For all well modeled afterglows, the cooling frequency at hr is below the X-ray band."
 Thus. Fx44 can be utilized (to vield information about the kinetic energv of GRBs.," Thus, $F_{X,10}$ can be utilized to yield information about the kinetic energy of GRBs."
 Earlier work (Piranefal.2001). [focussed on statistical studies of Fxyy and found the very surprising result that itis narrowly clustered.," Earlier work \citep{pkp+01} focussed on statistical studies of $F_{X,10}$ and found the very surprising result that it is narrowly clustered."
" By assuming that the true kinetic energy. Ey=byud,xLxLy nd. fj (the beaming factor) are uncorrelated. the authors deduced that £y and thus ZZ; are even more strongly. clustered."," By assuming that the true kinetic energy, $E_b=E_{b,\rm
iso}f_b\propto L_X = L_{X,\rm iso}f_b$, and $f_b$ (the beaming factor) are uncorrelated, the authors deduced that $L_X$ and thus $E_b$ are even more strongly clustered."
 However. (his approach is weakened by assuming (in effect) (he answer.," However, this approach is weakened by assuming (in effect) the answer."
 Furthermore. the approach of Piran which relies on subtracting variances is very sensitive {ο measurement errors.," Furthermore, the approach of \citet{pkp+01} which relies on subtracting variances is very sensitive to measurement errors."
 To illustrate: (his: point.: we note συ)2=0.68“oy(LTag Dorp the entire: sample presented here. ee2tosy," To illustrate this point, we note $\sigma_l^2(L_{X,\rm iso})=0.68^{+0.17}_{-0.09}$ for the entire sample presented here, whereas $\sigma_l^2(f_b)=0.52^{+0.13}_{-0.12}$."
yThus. OLS:o7(Ly) =2I0.1652;SOU.S0may be negative- using-.: the−↽ statistical −− approach.," Thus, $\sigma^2_l(L_X)=0.16^{+0.30}_{-0.21}$ may be negative using the statistical approach."
" In contrast to the statistical approach. we take the direct approach and estimate the true kinetic energv. FyxLyis,fp. by using the measured Ly44, and inferred. fj."," In contrast to the statistical approach, we take the direct approach and estimate the true kinetic energy, $E_b \propto L_{X,\rm iso}f_b$, by using the measured $L_{X,\rm iso}$ and inferred $f_b$."
 The advantage of our approach is Chat we do not make assumptions of correlations (or lack thereof) ancl more importantlv we do not subtract. variances., The advantage of our approach is that we do not make assumptions of correlations (or lack thereof) and more importantly we do not subtract variances.
 We directly compute the variance of the desired physical quantitv. namely Ly. and find that it is strongly. clustered.," We directly compute the variance of the desired physical quantity, namely $L_X$, and find that it is strongly clustered."
" Even more importantly. wilh our direct approach we have uncovered (he plvsical reason for the wide dispersion in £yi4, and (the clustering of Ly. namely the dispersion in jet opening angles."," Even more importantly, with our direct approach we have uncovered the physical reason for the wide dispersion in $L_{X,{\rm iso}}$ and the clustering of $L_X$ , namely the dispersion in jet opening angles."
 Ly is related to the physical «quantities as follows (Freedinan&Waxamnan2001): where lere e=(p—2)/(p1). as well as A and D depend to some extent on the details οἱ the electron distribution (power law versus relativistic \Mlaxwellian: the value of power law index. p).," $L_X$ is related to the physical quantities as follows \citep{fw01}: where Here $\epsilon\equiv(p-2)/(p-1)$, as well as $A$ and $B$ depend to some extent on the details of the electron distribution (power law versus relativistic Maxwellian; the value of power law index, $p$ )."
 There is no reason to expect that Ly should be clustered., There is no reason to expect that $L_X$ should be clustered.
" ILowever. one can argue that (he microphlvsics should be the same for each GRB afterglow. in particular e, ancl p."," However, one can argue that the microphysics should be the same for each GRB afterglow, in particular $\epsilon_e$ and $p$."
 The best studied afterglows appear to favor p—2.2 (e.g. Frail.Waxman&Kulkarnial. 1993)). a value also [nvored by our current theoretical knowledge of shock acceleration (see Ostrowski&Dednarz2002 and references therein).," The best studied afterglows appear to favor $p=2.2$ (e.g. \citealt{fwk00,gwb+98}) ), a value also favored by our current theoretical knowledge of shock acceleration (see \citealt{ob02} and references therein)."
 In addition. as already indicated by the 5-rav observations. there is evidence supporting strong clustering of explosion energies in GRBs (Fraile£af... 2001)..," In addition, as already indicated by the$\gamma$ -ray observations, there is evidence supporting strong clustering of explosion energies in GRBs \citep{fks+01}. ."
solution was added in quadrature to each the knot’s estimated wncertainty.,solution was added in quadrature to each the knot's estimated uncertainty.
 If the rns scatter was less than lO mas. if was set to LO mas to account for systematics.," If the rms scatter was less than 40 mas, it was set to 40 mas to account for systematics."
 Transformed kuot positions were automatically collated with the exposure epochs for the images. vieldiug a time series of positious for cach knot.," Transformed knot positions were automatically collated with the exposure epochs for the images, yielding a time series of positions for each knot."
 Finally. cach knots trajectory was fitted with a straielt linc. where fy is the weighted mean epoch of observation. and similarly for Y.," Finally, each knot's trajectory was fitted with a straight line, where $t_0$ is the weighted mean epoch of observation, and similarly for $Y$."
 Uncertainties were propagated iuto the coefficieuts in a standard manner., Uncertainties were propagated into the coefficients in a standard manner.
 Table 3 gives the results of this procedure., Table 3 gives the results of this procedure.
 Figure 2a shows the trajectories of our selected knots- extrapolated back to A.D. 1600. somewhat before the estimated explosion date.," Figure 2a shows the trajectories of our selected knots extrapolated back to A.D. 1600, somewhat before the estimated explosion date."
 The dots are the individual kuot measurements with the width of cach line indicating its statistical weight., The dots are the individual knot measurements with the width of each line indicating its statistical weight.
 Because the knots may lave decelerated by varying amounts. we estimated the center usimg oulv the knots lines of position. and did not apply any constraints arising from the tine dependence (i.c. forcing the knots to start at the same epoch).," Because the knots may have decelerated by varying amounts, we estimated the center using only the knots' lines of position, and did not apply any constraints arising from the time dependence (i.e, forcing the knots to start at the same epoch)."
 We constiucted a trajectory for cach knot and conrputed its positional uncertainty oy near the time of the explosion by propagating the estimated position aud proper motion errors., We constructed a trajectory for each knot and computed its positional uncertainty $\sigma_{i0}$ near the time of the explosion by propagating the estimated position and proper motion errors.
 Because of the long tine lever. the proper motion uncertaiutv dominated the errors in alb cases.," Because of the long time lever, the proper motion uncertainty dominated the errors in all cases."
" With this information we could compute. for auv .Y and Y. a likelihood fuuctiou of the form where dj), is the perpendicular distance between CX.Y) and the knot’s liue of position."," With this information we could compute, for any $X$ and $Y$, a likelihood function of the form where $d_{i \perp}$ is the perpendicular distance between $(X,Y)$ and the knot's line of position."
 The CV.) which iashuizes this is our estimate of the expansion center.," The $(X,Y)$ which maximizes this is our estimate of the expansion center."
 This procedure eave No—191 mas and Y—|2812 mas. referred to the IdD76 ceuter.," This procedure gave $X = +91$ mas and $Y = +2812$ mas, referred to the KvdB76 center."
" This translates iuto a(J2000) = 23h 236 27777 (ΕΠ, A(J2000) = 58"" Is! 1907E £074L."," This translates into $\alpha$ (J2000) = $^{\rm h}$ $^{\rm m}$ $27 \fs 77$ $\pm 0 \fs 05$, $\delta$ (J2000) = $^{\rm o}$ $48'$ $49 \farcs 4$ $\pm 0 \farcs 4$."
 The center derived using onlv the outer knots nearly coiucided with that derived from the selected shell knots., The center derived using only the outer knots nearly coincided with that derived from the selected shell knots.
 Table to lists our main shell aud outer knot centroids separately along with our final values for the whole suuple., Table 4 lists our main shell and outer knot centroids separately along with our final values for the whole sample.
 The errors given are purely statistical. based on the Monte Carlo calibration of the," The errors given are purely statistical, based on the Monte Carlo calibration of the"
ihe protoplanetary disks.,the protoplanetary disks.
 As an example. Sehlanfimanetal.(2009) focused on the surface density transition that can be produced at the location of tlie ice-line. where a local pressure maxinmun can acl as an accumulation point for planetesimals (Ixretke&Lin2007).," As an example, \citet{sli09} focused on the surface density transition that can be produced at the location of the ice-line, where a local pressure maximum can act as an accumulation point for planetesimals \citep{kl07}."
. If il is assumed (hat (wpe I migration is much slower (han predicted in locally isothermal disk models. this feature could account for planets with orbital radii 0.1 - 2 AU.," If it is assumed that type I migration is much slower than predicted in locally isothermal disk models, this feature could account for planets with orbital radii 0.1 - 2 AU."
 Obviously. a physical explanation for slower migration is needed.," Obviously, a physical explanation for slower migration is needed."
 In this Letter. we present a new slowing mechanism of rapid (wpe I migration -which may occur for planets with masses (hal are too low to open up a gap in their disks (massive planets can οαν form a gap and undergo tvpe II migration).," In this Letter, we present a new slowing mechanism of rapid type I migration -which may occur for planets with masses that are too low to open up a gap in their disks (massive planets can tidally form a gap and undergo type II migration)."
 We show. by means of Monte Carlo radiative transler simulations. that dead zones - the dense inner disk region wherein turbulence cannot be readily excited (Gammniue1996). - support a thermal barrier to migration.," We show, by means of Monte Carlo radiative transfer simulations, that dead zones - the dense inner disk region wherein turbulence cannot be readily excited \citep{g96} - support a thermal barrier to migration."
 One of the most important consequences is that the thermal barrier could account for planets al larger orbital radii., One of the most important consequences is that the thermal barrier could account for planets at larger orbital radii.
 In Ὁ 2. we outline our disk model and discuss tidal torques.," In $\S$ 2, we outline our disk model and discuss tidal torques."
 In Ὁ 3. we analvze how the presence of a thermal barrier impacts the migration rates of low-mass planets.," In $\S$ 3, we analyze how the presence of a thermal barrier impacts the migration rates of low-mass planets."
 In. § 4. we discuss potential issues for the AI-P relation by comparing our stopping mechanism wilh others.," In $\S$ 4, we discuss potential issues for the M-P relation by comparing our stopping mechanism with others."
 Protoplanetary disks are known to be heated by radiation [from the central star (Chiangetal.1993:Hasegawa&Pucdritz2010a.hereafter. ILP10)..," Protoplanetary disks are known to be heated by radiation from the central star \citep[hereafter, HP10]{cg97,dccl98,hp09b}."
 This radiation mainlv determines (he thermal structure of disks (Xenvon&IIartmann1957)., This radiation mainly determines the thermal structure of disks \citep{kh87}.
. This is because viscous heating dominates stellar irradiation heating only within about 1 AU [or the classical T Tauri star svstems (CTTSs:D'Alessioetal.1998). and only within about 0.1 AU for lower mass stars such as M stars (HID10)., This is because viscous heating dominates stellar irradiation heating only within about 1 AU for the classical T Tauri star systems \citep[CTTSs;][]{dccl98} and only within about 0.1 AU for lower mass stars such as M stars (HP10).
direct comparison between the clean light curve and filtered light curve. we have to record the phase information of the initial data as the input of the algorithm. instead. of using random phases.,"direct comparison between the clean light curve and filtered light curve, we have to record the phase information of the initial data as the input of the algorithm instead of using random phases."
" We do this rere because our aim is simply to check the οσοι of ?""oisson noise filtering for the svnthetic algorithm.", We do this here because our aim is simply to check the effect of Poisson noise filtering for the synthetic algorithm.
 The results are shown in Fig. 11.., The results are shown in Fig. \ref{fig_filter}.
 We can see how the Poisson noise is removed in the filtered light. curve., We can see how the Poisson noise is removed in the filtered light curve.
 A cquantitive measurement is the standard deviation. whieh is 20. 420 and 340 for the clean. dirty and filtered light curves respectively.," A quantitive measurement is the standard deviation, which is 320, 420 and 340 for the clean, dirty and filtered light curves respectively."
 Tje excess variation of the filtered light. curve at high frequencies is very probably caused by the distortion introduced. by the exponential transform. which tends to exageerate the positive variation. e.g.In the amplitudes: of the Lares.," The excess variation of the filtered light curve at high frequencies is very probably caused by the distortion introduced by the exponential transform, which tends to exaggerate the positive variation, e.g. the amplitudes of the flares."
 The conclusion is that the svnthetic light curve created by our algorithm can be considered. essentially. free of Poisson noise., The conclusion is that the synthetic light curve created by our algorithm can be considered essentially free of Poisson noise.
 Lt is worthy to point out that if the phases were known. we could: reconstruct the time series strictly by. inverse Fourier transform. because this time-to-frequencey. transition is completely reversible.," It is worthy to point out that if the phases were known, we could reconstruct the time series strictly by inverse Fourier transform, because this time-to-frequency transition is completely reversible."
 Phe exponential transform would be not be necessary., The exponential transform would be not be necessary.
 We therefore face an interesting problem: if the phase is known. the exponential is redundant. for reconstructing the initial time series. which is completely defined by the fourier spectrum: however if we know nothing about the phases and assume them to be random. in order to reproduce a time series satisfactorily we have to apply the exponential transformation.," We therefore face an interesting problem: if the phase is known, the exponential is redundant for reconstructing the initial time series, which is completely defined by the fourier spectrum; however if we know nothing about the phases and assume them to be random, in order to reproduce a time series satisfactorily we have to apply the exponential transformation."
 We will discuss this problem in section ?7?.., We will discuss this problem in section \ref{sec_posnois}.
 The above process of subtracting the Poisson noise is similar to Wiener filtering., The above process of subtracting the Poisson noise is similar to Wiener filtering.
 The Wiener filter is the optimal filter in the least-square sense for the removal of noise from a time domain signal., The Wiener filter is the optimal filter in the least-square sense for the removal of noise from a time domain signal.
 Ehe Wiener filter is designed in the Fouricr domain and can be expressed as (Pressetal.1992) in which :*S and NV are the Fourier transforms of the intrinsic signal and the noise. res»eetivelv.," The Wiener filter is designed in the Fourier domain and can be expressed as \citep{Pre92}: : in which $S$ and $N$ are the Fourier transforms of the intrinsic signal and the noise, respectively."
 The denominator [SCpNCAP is proportional to the PDS of the measurec light curve Cunder the assumption that signal and noise are statistically independent., The denominator $|S(f)|^2+|N(f)|^2$ is proportional to the PDS of the measured light curve (under the assumption that signal and noise are statistically independent).
 Phe ilter can be constructed if the true. form of the intrinsic) over [SCP is known or can be estimated well., The filter can be constructed if the true form of the intrinsic power $|S(f)|^2$ is known or can be estimated well.
 Our algorithm and the Wiener filter share some conimon ideas ic» separate noise and. signa in the frequeney domain. which can not be done in the time domain.," Our algorithm and the Wiener filter share some common ideas — to separate noise and signal in the frequency domain, which can not be done in the time domain."
 We fixed the noise power to 2 ancl applie a Wiener filter to the same data in Fig. 11, We fixed the noise power to 2 and applied a Wiener filter to the same data in Fig. \ref{fig_filter}.
 The dillerence between the Wiener filtering solution and ours is shown in Fig. 12, The difference between the Wiener filtering solution and ours is shown in Fig. \ref{fig_wnr}.
 ~The filtering elfect are ecnerally similar for the two methocds., The filtering effect are generally similar for the two methods.
 1t the PDS used in the Wiener filtering and our algorithm are those averaged over many segments (panelb and din Fig.e 12)).," If the PDS used in the Wiener filtering and our algorithm are those averaged over many segments (panel and in Fig. \ref{fig_wnr}) ),"
 our algorithmo> appears to preserve more short time-scale [Luctuations. which makes it more simular to the original one.," our algorithm appears to preserve more short time-scale fluctuations, which makes it more similar to the original one."
 I£ the PDS of the single segment shown in the figure is used in designing the Wiener filter (panele in Fie. 120)J," If the PDS of the single segment shown in the figure is used in designing the Wiener filter (panel in Fig. \ref{fig_wnr}) ),"
 its solution would be much more noisy than the original light curve., its solution would be much more noisy than the original light curve.
 From this perspective. our algorithm seems to providea more stable filter as it is able to subtract," From this perspective, our algorithm seems to providea more stable filter as it is able to subtract"
5 a also find significantly lower mass-to-light ratios for SDSS J1420--602 and SDSS JI1250+052 than they do for the other SLACS members.,", they also find significantly lower mass-to-light ratios for SDSS J1420+602 and SDSS J1250+052 than they do for the other SLACS members."
 One possible solution is that (he lens masses are significantly mis-estimated due to contamination [rom a group or cluster halo. but only [1115484535 has a neighboring. bright galaxy. and it is sufficiently distant to only modestly perturb the estimated mass.," One possible solution is that the lens masses are significantly mis-estimated due to contamination from a group or cluster halo, but only H1543+535 has a neighboring, bright galaxy and it is sufficiently distant to only modestly perturb the estimated mass."
 The broad uncertainties and occasional outliers mean (hat it is important to have a quantitative approach to determining the homogeneity of the sample aud to appropriately weieht each object when determining mean properties., The broad uncertainties and occasional outliers mean that it is important to have a quantitative approach to determining the homogeneity of the sample and to appropriately weight each object when determining mean properties.
 This is why we introduced (he Bavesian osol relsec:methoc.., This is why we introduced the Bayesian frameworks of \\ref{sec:method}. .
 Fie., Fig.
 s10. shows our estimates of the lractional svstematic errors Irom our first analvsis method 6))., \ref{fig:figure6} shows our estimates of the fractional systematic errors from our first analysis method (Eqn. \ref{eqn:e1e2}) ).
 The best fit estimates for the fractional svstematic errors in the velocily dispersion and huninositv are ος70.1 and ej~0.18., The best fit estimates for the fractional systematic errors in the velocity dispersion and luminosity are $e_\sigma \simeq 0.1$ and $e_L\simeq 0.18$.
 The reported measurement errors lie well outside the likelihood region., The reported measurement errors lie well outside the likelihood region.
 For the dynamical errors. the best [it svstematic errors are quite consistent with our prior estimates based on simple considerations about the dynamical data.," For the dynamical errors, the best fit systematic errors are quite consistent with our prior estimates based on simple considerations about the dynamical data."
 Fie., Fig.
 ll shows that the results lor the homogeneity of the sample are very sensitive to the assumed uncertainties., \ref{fig:figure5} shows that the results for the homogeneity of the sample are very sensitive to the assumed uncertainties.
" If we simply used the stated measurement errors. (hen the probability that (he sample is homogeneous in its dwnamical properties (i.e. (hat the ""good"" uncertainty estimates are correct and the scatter is due only to measurement error) is p,<24% and (hat it is homogeneous in mass-to-light ratio evolution is pp<14%."," If we simply used the stated measurement errors, then the probability that the sample is homogeneous in its dynamical properties (i.e. that the “good” uncertainty estimates are correct and the scatter is due only to measurement error) is $p_\sigma \le{24\%}$ and that it is homogeneous in mass-to-light ratio evolution is $p_L \le{14\%}$."
" Many objects a low probabilities of belonging to either a homogeneous dynamical subset (SDSS J16210053 wilh p,=0.005. SDSS J1250+0523 with p,=0.010. SDSS JO0T31—321 with p,=0.010. PGI1154-080 with p,= 0.029. and SDSS J142002 with p,— 0.042) or a homogeneous evolutionary subset (SDSS J1250+0523 p,s0. n1113 pp&O0. SDSS J0912--002 p,=0.001. SDSS J1420+602 p,=0.001 and ""15494-305« Mp,= 0.001)."," Many objects have low probabilities of belonging to either a homogeneous dynamical subset (SDSS J1627–0053 with $p_\sigma = 0.005$, SDSS J1250+0523 with $p_\sigma = 0.010$, SDSS J0737+321 with $p_\sigma = 0.010$, PG1115+080 with $p_\sigma = 0.029$ , and SDSS J1420+602 with $p_\sigma = 0.042$ ) or a homogeneous evolutionary subset (SDSS J1250+0523 $p_L \approx 0$, H1543+535 $p_L \approx 0$, SDSS J0912+002 $p_L = 0.001$, SDSS J1420+602 $p_L = 0.001$ and MG1549+305 $p_L = 0.001$ )."
 Not surprisingly. these objects are also outliers in the individual fits from previous section.," Not surprisingly, these objects are also outliers in the individual fits from the previous section."
" If. we include our estimates of the svsteniatic errors in interpreting the dvnanmical measurements. then the probability that the sample is homogeneous in its dvnamical properties rises to p,>40%. but the probability of a homogeneous evolutionary population remains small at pp<14%."," If we include our estimates of the systematic errors in interpreting the dynamical measurements, then the probability that the sample is homogeneous in its dynamical properties rises to $p_\sigma \ge 40\%$, but the probability of a homogeneous evolutionary population remains small at $p_L\le{14\%}$."
" With the inclusion of the svstematic error estimates. the objects with the lowest. probabilities ol belonging to the homogeneous dvnamical are PGIIIS»sO (withp,=0. 48). SDSS J1250+0523 (with p,= 0.49). SDSS J1627un0053 (withp,= 0.52). SDSS JOT37+321"," With the inclusion of the systematic error estimates, the objects with the lowest probabilities of belonging to the homogeneous dynamical subset are PG1115+080 (with$p_\sigma = 0.48$ ), SDSS J1250+0523 (with $p_\sigma = 0.49$ ), SDSS J1627–0053 (with$p_\sigma = 0.52$ ), SDSS J0737+321"
We thank the anonymous referee for verv useful suggestions and Y.W. Yu for useful discussion.,We thank the anonymous referee for very useful suggestions and Y.W. Yu for useful discussion.
 KSC! is supported by a grant under INU 7011/10p., KSC is supported by a grant under HKU 7011/10p.
 VAD and DOC are partly supported by the NSC-REDR Joint Research Project RPOONO4 and 09-02-92000-LLELIC-a.. CXII is supported in part by the National Science Council. Taiwan. under grants NSC 98-2923-M-008-001-MY3 and NSC 99-2112-M-008-015-MY3.," VAD and DOC are partly supported by the NSC-RFBR Joint Research Project RP09N04 and 09-02-92000-HHC-a. CMK is supported in part by the National Science Council, Taiwan, under grants NSC 98-2923-M-008-001-MY3 and NSC 99-2112-M-008-015-MY3."
The dilferential number counts for EROs on the CDES are given in Table 1 and plotted on Figure 5.,The differential number counts for EROs on the CDFS are given in Table 1 and plotted on Figure 5.
 Firstly. the three ERO counts plotted. here are consistent within the error bars.," Firstly, the three ERO counts plotted here are consistent within the error bars."
 Our CDES counts are closer to the uncorrected count of Paper L. suggesting the incompleteness corrections may have been overestimated.," Our CDFS counts are closer to the uncorrected count of Paper I, suggesting the incompleteness corrections may have been overestimated."
 For this paper. rather than attempting to correct for incompleteness. we have assume completeness to fv.=21.5. and clisregarded the final poin in fitting slopes and models (incompleteness will appear more suddenly for this cata due to its more uniform depth).," For this paper, rather than attempting to correct for incompleteness, we have assumed completeness to $K_s=21.5$, and disregarded the final point in fitting slopes and models (incompleteness will appear more suddenly for this data due to its more uniform depth)."
 The most obvious feature on the plot is a markec Uattening of the count slope. seen in all three sets. of observations but most apparent with the CDES.," The most obvious feature on the plot is a marked flattening of the count slope, seen in all three sets of observations but most apparent with the CDFS."
" The coun slope best-litting the the ELAIS:N2 and CDES counts a 17.0xAN.€19.5 i» ?=OFO+O11. and Uattens to ~—0.16€0.05 at 19.0—A,«Xb (fit to CDES counts only)."," The count slope best-fitting the the ELAIS:N2 and CDFS counts at $17.0\leq K_s\leq 19.5$ is $\gamma=0.59\pm 0.11$, and flattens to $\gamma=0.16\pm 0.05$ at $19.0\leq
K_s\leq 21.5$ (fit to CDFS counts only)."
 In Paper I we presented simple models of the number counts of EROs. based on the assumption that both plltOs and dsfEROs are. progenitors of the present-cay 2/80. ealaxies. and hence that their luminosity function (LE) at any redshift can be linked to the LE. of local E/SO0s by means of a particular evolutionary model.," In Paper I we presented simple models of the number counts of EROs, based on the assumption that both pEROs and dsfEROs are progenitors of the present-day E/S0 galaxies, and hence that their luminosity function (LF) at any redshift can be linked to the LF of local E/S0s by means of a particular evolutionary model."
 We adopted the local Eso LE derived by IXochanek et al. (, We adopted the local E/S0 LF derived by Kochanek et al. (
"2001) in the A-band. from the survey. a Schechter function with Mj,=24.31. a=0.92 and ó*—0.0015435 Mpe5 for 5=0.7.","2001) in the $K$ -band, from the survey, a Schechter function with $M^*_K=-24.31$, $\alpha=-0.92$ and $\phi^*=0.0015435$ $\rm Mpc^{-3}$ for $h=0.7$."
 The ERO counts were modelled. by evolving this LE with the galaxies split 50:50 between our. elliptical. and SO models of passive L evolution (see Section. 4.2). and including only the galaxies within the redshift ranges in which their respective models give ERO colours (i.c. approx.," The ERO counts were modelled by evolving this LF with the galaxies split 50:50 between our elliptical and S0 models of passive $L^*$ evolution (see Section 4.2), and including only the galaxies within the redshift ranges in which their respective models give ERO colours (i.e. approx."
 2oc l), $z>1$ ).
 dn the Pure Luminosity Evolution (PLE) mocel only L* is evolved. while ó* and à remain constant from the formation redshift onwards.," In the Pure Luminosity Evolution (PLE) model only $L^*$ is evolved, while $\phi^*$ and $\alpha$ remain constant from the formation redshift onwards."
 The post-starburst. fading of dsfEROs is assumed to be similar in degree to the passive evolution of the pEROs., The post-starburst fading of dsfEROs is assumed to be similar in degree to the passive evolution of the pEROs.
 In Paper L the ELAIS:N2 ERO counts were significantLy lower than expected. if all present-day [ος evolved: by this PLE mocel. ancl much closer to a non-evolving moclel.," In Paper I, the ELAIS:N2 ERO counts were significantly lower than expected if all present-day E/S0s evolved by this PLE model, and much closer to a non-evolving model."
 Llowever. the compact angular sizes of most EROs impliced significant evolution in their surface brightness.," However, the compact angular sizes of most EROs implied significant evolution in their surface brightness."
 A merging model was also considered. which combinedthe PLE models evolution of luminosity (per unit. mass)," A merging model was also considered, which combinedthe PLE model's evolution of luminosity (per unit mass)"
(from HETE-2)) 050802. 050803. ancl 0550820a (from Swiff)).,"(from ), 050802, 050803, and 050820a (from )."
 Their peak luminosities are calculaed in exactly he same way as in ROL and €105., Their peak luminosities are calculated in exactly the same way as in R01 and G05.
 For GRDs detected by we used the spectral fit. provided. by Sakamoto(2005) and theZLETE website.," For GRBs detected by, we used the spectral fit provided by \citet{sak04} and the website."
 For GRBs detected wο]. peak spectra are extracted. from tος event Liles. hen fitted with a power law which is sullicient for all cases (in the enerev rouge 15-350 keV)," For GRBs detected by, peak spectra are extracted from their event files, then fitted with a power law which is sufficient for all cases (in the energy range 15-350 keV)."
" Although Golenetskiietal. (2005)... Pal'shinοal. (2005). and Cummingsetal.(2005) have reported the detectionl of a second. larger episode of emission from CRB )5082"" (bx bothHind ancl το). onlv the data the first episode from aare available tous."," Although \citet{gol05}, , \citet{pal05}, and \citet{cum05} have reported the detection of a second, larger episode of emission from GRB 050820a (by both and ), only the data for the first episode from are available to us."
 Thus. for GLBa¢ds20a. the variability ancl peak luminosity listed in Table 1 to its first episode (of duration 30 sec).," Thus, for GRB 050820a, the variability and peak luminosity listed in Table 1 refer to its first episode (of duration $\sim 30$ sec)."
 The time bin of cach GARB lighteurve is as follow., The time bin of each GRB lightcurve is as follow.
 lor GRBs detected by BATSE. except 000131. the time bin is Gms.," For GRBs detected by BATSE, except 000131, the time bin is 64-ms."
 GRB 000131 does not have a G4-ms lighteurve. so we use its 1.024-sec. lighteurve.," GRB 000131 does not have a 64-ms lightcurve, so we use its 1.024-sec lightcurve."
 Although a bin of. 1.024-sec ds somewhat large. the duration. of Q00131. is about 100-sec which is much larger than its time bin.," Although a bin of 1.024-sec is somewhat large, the duration of 000131 is about 100-sec which is much larger than its time bin."
 For GRBs detected: by the time bin is 164-ms.," For GRBs detected by, the time bin is 164-ms."
 While Or CRBs detected bySuwiff.. weextrac G4-ms lightcurves [rom their event files available/ in the publie data archive.," While for GRBs detected by, we extract 64-ms lightcurves from their event files available in the public data archive."
" As we analyze the GRB lighteurves we use the toal counts int1e energy range as LolOw: 25-I0 keV for GRBs detectec by - PSE."":0 PMnikeV for those detected by and 25-350 vkkeV detected bySuwiff."," As we analyze the GRB lightcurves we use the total counts in the energy range specified as follow: 25-300 keV for GRBs detected by BATSE, 30-400 keV for those detected by, and 25-350 keV for those detected by."
. We have viec| to the range of energy for GRBs detected by cliferent instruments have largest overlap., We have tried to make the range of energy for GRBs detected by different instruments have largest overlap.
 Finally. we remark that [or the GRBs detected: by BATSE. t1ο ightcurve data in the pre- and: post-burst sections were cividecd equallyinto 64-ms time bins from their," Finally, we remark that for the GRBs detected by BATSE, the lightcurve data in the pre- and post-burst sections were divided equallyinto 64-ms time bins from their"
From (he Spitzer archive we downloaded DBCD files reduced with the 55C pipeline version 16.0 or 16.1.,From the Spitzer archive we downloaded BCD files reduced with the SSC pipeline version 16.0 or 16.1.
 At 70 jm. we used GeRT (version 514.0 v1.1 [060415]) to do column mean subtraction and time filtering on the BCD files.," At 70 $\mu$ m, we used GeRT (version S14.0 v1.1 [060415]) to do column mean subtraction and time filtering on the BCD files."
 We used Mopex (version 13.1.5) to create mosaics for 24 and jas images and obtained aperture photometry using IDL.," We used Mopex (version 18.1.5) to create mosaics for 24 and $\,\mu$ m images and obtained aperture photometry using IDL."
" At jan. we used an aperture radius of 7"". skv annulus between 40"" and 50"". and aperture correction of 1.61: at yan. we used an aperture radius of 8"". skv annulus between 39"" and 65"". and aperture correction of 3.70. appropriate for a KIN blackbody."," At $\,\mu$ m, we used an aperture radius of $''$ , sky annulus between $''$ and $''$, and aperture correction of 1.61; at $\,\mu$ m, we used an aperture radius of $''$, sky annulus between $''$ and $''$, and aperture correction of 3.70, appropriate for a K blackbody."
 After identifving stars with jm excess. we recaleulated their fluxes with an aperture correction of 3.83. appropriate for a GOIN blackbody.," After identifying stars with $\,\mu$ m excess, we recalculated their fluxes with an aperture correction of 3.83, appropriate for a K blackbody."
 Appropriate color corrections were also performed., Appropriate color corrections were also performed.
 Thanks to the small aperture. nearby sources had no effect on our photometry.," Thanks to the small aperture, nearby sources had no effect on our photometry."
 At jan. the aperture was placed around the centroid of each star. while at jam. the aperture was placed at the same position as for the 24jm image.," At $\,\mu$ m, the aperture was placed around the centroid of each star, while at $\,\mu$ m, the aperture was placed at the same position as for the $\,\mu$ m image."
 Ifa 244an position was nol available. we used fixed coordinates.," If a $\,\mu$ m position was not available, we used fixed coordinates."
 For sources brighter than. άν and having signal-to-noise ratio of 211. we checked their spatial extent. by comparing the images to a stellar point-spread hunction (PSF).," For sources brighter than mJy and having signal-to-noise ratio of $\geq$ 11, we checked their spatial extent by comparing the images to a stellar point-spread function (PSF)."
 For extended objects 110647. 338858. 2207129. 445682. and 1115617) photometry was extracted bv fitting a PSF broadened by an appropriate (wo-climensional Gaussian.," For extended objects 10647, 38858, 207129, 48682, and 115617) photometry was extracted by fitting a PSF broadened by an appropriate two-dimensional Gaussian."
 The Iluxes of € Eri were taken [rom Backmanetal.(2009)., The fluxes of $\epsilon$ Eri were taken from \citet{backman}.
. We collected near-infrawed. photometry from the 241ASS Al-Skv Catalog of Point Sources (Skrutskieetal.2006).. Morel&Magnenat (1978)... and Ducati(2002)... jm fluxes from the MSX Infrared Point-Source Catalog 2003).. and jm fluxes fromthe IRAS catalog of point sources (with appropriate color correction).," We collected near-infrared photometry from the 2MASS All-Sky Catalog of Point Sources \citep{2mass}, \citet{morel}, and \citet{ducati}, $\,\mu$ m fluxes from the MSX Infrared Point-Source Catalog \citep{msx}, and $\,\mu$ m fluxes fromthe IRAS catalog of point sources (with appropriate color correction)."
 Spectral tvpes. effective temperatures. ancl metallicities came from the NASA," Spectral types, effective temperatures, and metallicities came from the NASA"
Clearly. systematic evolution of one or more of the cquantities appearing in g during the outburst could have a similar effect in making £2441911) oscillate around the actual orbital period 2.,"Clearly, systematic evolution of one or more of the quantities appearing in $g$ during the outburst could have a similar effect in making $P_{\rm crit}({\rm BH})$ oscillate around the actual orbital period $P$."
 Phe most likely alternative candidate is the disc aspect ratio {111. which would appear explicitly with the power 1.5 if we substitute for g in (6)).," The most likely alternative candidate is the disc aspect ratio $H/R$, which would appear explicitly with the power 1.5 if we substitute for $g$ in \ref{pcrit}) )."
 The aspect ratio could. evolve svstematically on a viscous timescale because the disc may warp under radiative torques (Pringle. 996).," The aspect ratio could evolve systematically on a viscous timescale because the disc may warp under radiative torques (Pringle, 1996)."
 X warp presenting more of the disc surface to the central source would tend to stabilize i against a return to cquiescence even though the central luminosity was below the Eddington limit., A warp presenting more of the disc surface to the central source would tend to stabilize it against a return to quiescence even though the central luminosity was below the Eddington limit.
 Again considerably more work is required to check this possibility., Again considerably more work is required to check this possibility.
 ] have shown that the Eddington limit implies a critical orbital period 244(DII) beyond. which blackhole LAINBs cannot appear as persistent svstems., I have shown that the Eddington limit implies a critical orbital period $P_{\rm crit}({\rm BH})$ beyond which black–hole LMXBs cannot appear as persistent systems.
 The precise. value of Paga(OM) is subject to uncertainties expressed. bv. the quantity g in (3)).," The precise value of $P_{\rm crit}({\rm
BH})$ is subject to uncertainties expressed by the quantity $g$ in \ref{crit2}) )."
 E have argued that g cannot be very απ [rom unity if we are to understand. the cillerence in he stability properties of discs in neutronstar and. blackvole svstems., I have argued that $g$ cannot be very far from unity if we are to understand the difference in the stability properties of discs in neutron–star and black--hole systems.
 In this case GRO 1655-40 lies much closer to Poa(1211) than any other blackhole svstem., In this case GRO J1655-40 lies much closer to $P_{\rm crit}({\rm BH})$ than any other black–hole system.
 The unusual behaviour of CARO J1655-40 may result rom) its location very close to. Pay(DIDI): evolution of he disc size or possible radiative warping may move he svstem across the boundary. where a subEddington uminosity can keep the disc stably in the high state., The unusual behaviour of GRO J1655-40 may result from its location very close to $P_{\rm crit}({\rm BH})$; evolution of the disc size or possible radiative warping may move the system across the boundary where a sub–Eddington luminosity can keep the disc stably in the high state.
 “Phis system. and those at longer orbital periods. probably have central aceretion rates which are highly superEdedington during outbursts.," This system, and those at longer orbital periods, probably have central accretion rates which are highly super–Eddington during outbursts."
 Since observed radiative luminosities are mildly sub.Lclelington. most of this mass must be expolled.," Since observed radiative luminosities are mildly sub–Eddington, most of this mass must be expelled."
 Strong support for this comes from the observation of P Cvent profiles in GIRO 165540 (IIvnes et al.," Strong support for this comes from the observation of P Cygni profiles in GRO J1655–40 (Hynes et al.,"
 1998)., 1998).
 The superluminal jets observed (Lijellming ltupen. 1995) in an outburst of this svsteni may therefore simply. represent the most dramatic part of this outllow.," The superluminal jets observed (Hjellming Rupen, 1995) in an outburst of this system may therefore simply represent the most dramatic part of this outflow."
 ] gratefully acknowledge the support of a PPARC Senior Fellowship., I gratefully acknowledge the support of a PPARC Senior Fellowship.
Sometimes. as is the case here. the wavelength of mode 1 is much longer than that of mode 2 or 3.,"Sometimes, as is the case here, the wavelength of mode 1 is much longer than that of mode 2 or 3."
 In the absence of dissipation. three-mocde couplings are most easily calculated from an action principle. Llere ὃς indicates a first-order variation with respect to the displacements £. which are regarded as functions of the spatial coordinates ài and time /.," In the absence of dissipation, three-mode couplings are most easily calculated from an action principle, Here $\delta_\xi$ indicates a first-order variation with respect to the displacements $\vxi$, which are regarded as functions of the spatial coordinates $\bx$ and time $t$."
 Phus a=#| £(x./)isthe actual position of a [uid element whose equilibrium position is ®.," Thus $\vx=\bx+\vxi(\bx,t)$ is the actual position of a fluid element whose equilibrium position is $\bx$."
 For clarity. we sometimes indicate the basic state with an overbar: e.e.. o(x) is the mass density in the basic state.," For clarity, we sometimes indicate the basic state with an overbar: e.g., $\bar\rho(\bx)$ is the mass density in the basic state."
 In the case of axisvmmetric motions of the shearing sheet. the Lagrangian density to be used in equation (33)) is The frequencies £2 and # are constants.," In the case of axisymmetric motions of the shearing sheet, the Lagrangian density to be used in equation \ref{action}) ) is The frequencies $\Omega$ and $\kappa$ are constants."
" For simplicity. we assume that C. the internal energy. per unit mass. has the form appropriate to an isothermal gas of uniform sound speed c, The density p dillers from. p. because. of changes in volume: Therefore. the internal encrey (35)) contains terms of all orders in £."," For simplicity, we assume that $U$, the internal energy per unit mass, has the form appropriate to an isothermal gas of uniform sound speed $c_{\rm s}$: The density $\rho$ differs from $\bar\rho$ because of changes in volume: Therefore, the internal energy \ref{polytrope}) ) contains terms of all orders in $\vxi$."
 Phe quadratic and cubic terms are If the spatial derivatives of £ are small. higher-order terms can be neglected.," The quadratic and cubic terms are If the spatial derivatives of $\vxi$ are small, higher-order terms can be neglected."
 Phen C» and the other quadratic parts of £ determine the linear equations of motion. while ( provides the dominant non-linear interactions.," Then $U_2$ and the other quadratic parts of $\cal L$ determine the linear equations of motion, while $U_3$ provides the dominant non-linear interactions."
" A 5general disturbance can be expanded in terms of the spatial eigenfunctions [δι} of the linear normal Absent non-linear interactions. the coellicients. (8,(01 evolve independently according to where w, is the natural frequency of the a! normal mode."," A general disturbance can be expanded in terms of the spatial eigenfunctions $\{\hxi_\alpha\}$ of the linear normal Absent non-linear interactions, the coefficients $\{q_\alpha(t)\}$ evolve independently according to where $\omega_\alpha$ is the natural frequency of the $\alpha^{\rm
 th}$ normal mode."
" Non-linear equations of motion for the qs result from The spatial eigenfunctions have the normalization (12)): therefore £, has units of length ancl 4 is dimensionless.", Non-linear equations of motion for the $q$ s result from with The spatial eigenfunctions have the normalization \ref{massnorm}) ); therefore $\hxi_\alpha$ has units of length and $q_\alpha$ is dimensionless.
 Consider a situation. in which only three. mocdes [αιqo.da] are significantly excited.," Consider a situation in which only three modes $\{q_1,q_2,q_3\}$ are significantly excited."
 Then the Lagrangian reduces to where we have divided out an overall factor of ΑΗ”. and The behaviour of a svstem of three oscillators inearly coupled as in (42)) is well known (Sagdeev&CGaleev1969:Ixumar&Goodman 1996): 1.," Then the Lagrangian reduces to where we have divided out an overall factor of $MH^2$, and The behaviour of a system of three oscillators non-linearly coupled as in \ref{threeL}) ) is well known \cite{sg69,kg96}: 1."
 The Hamiltonian corresponding to (42)) has a local rut not a global minimum at the origin. because the highest erms are odd in d.," The Hamiltonian corresponding to \ref{threeL}) ) has a local but not a global minimum at the origin, because the highest terms are odd in $q$."
 When. as here. (42)) results from. runcation of a physical system with a positive-definite Hamiltonian. then quartic and perhaps higher terms must » retained if the amplitude or coupling is sulliciently large.," When, as here, \ref{threeL}) ) results from truncation of a physical system with a positive-definite Hamiltonian, then quartic and perhaps higher terms must be retained if the amplitude or coupling is sufficiently large."
 2., 2.
 In the opposite limit of small zimplitudes or weakcoupling. where the cubic term is small comparec to he quadratic ones. non-linearity is important only if approximate resonance exists among the natural frequencies of the three linearized oscillators.," In the opposite limit of small amplitudes or weakcoupling, where the cubic term is small compared to the quadratic ones, non-linearity is important only if approximate resonance exists among the natural frequencies of the three linearized oscillators."
 Without loss of edet wy@weDαλ.," Without loss of , let $\omega_1\ge\omega_2\ge\omega_3$."
 Resonance exists if wy&we|wy. and the accuracy of the resonance is characterized by the smallness of On the other hand. the strength of the coupling can be characterized by a dimensionless parameter such as where { is the total energy of the svstem (42)).," Resonance exists if $\omega_1\approx\omega_2+\omega_3$, and the accuracy of the resonance is characterized by the smallness of On the other hand, the strength of the coupling can be characterized by a dimensionless parameter such as where $E$ is the total energy of the system \ref{threeL}) )."
 3., 3.
 For « l. slowexchange of energy among the three oscillators can occur on time-scales ~(ew).1 provided," For $\epsilon\ll 1$ , slowexchange of energy among the three oscillators can occur on time-scales $\sim(\epsilon\omega)^{-1}$ provided"
"surfaces behave for small and large silicate erains. aud showed that the Ty, surface moves closer to the star for iucreasing erain size until a critical value. which for silicates is about 1.2μπα.","surfaces behave for small and large silicate grains, and showed that the $T_{eff}$ surface moves closer to the star for increasing grain size until a critical value, which for silicates is about 1.2."
" Larger graius produce rims with T,gg surfaces practically independent of o.", Larger grains produce rims with $T_{eff}$ surfaces practically independent of $a$.
 Therefore. for a fixed stellar huninosity. silicates with ο~1.2;1n eeive the nium value of the distance of the ria from the star.," Therefore, for a fixed stellar luminosity, silicates with $a\sim 1.2$ give the minimum value of the distance of the rim from the star."
 Conversely. if the measured rin distance is equal to this αι value. one can derive frou it only a lower limit (~ 1.2;12)) to the grain size.," Conversely, if the measured rim distance is equal to this minimum value, one can derive from it only a lower limit $\sim 1.2$ ) to the grain size."
 The rim euidssion peaks at neariufrared wavelengths., The rim emission peaks at near-infrared wavelengths.
 At ASSμια. one can assume that the observed flux is he stun of the stellar. | xin emission. with oulv uceligible contribution from the outer disk (sec. e.g. DDNOI).," At $\lambda
\simless 5-7$, one can assume that the observed flux is the sum of the stellar + rim emission, with only negligible contribution from the outer disk (see, e.g., DDN01)."
 We uodel the stellar plotospheric flux using standard Iuucz nocdel atinosplieres., We model the stellar photospheric flux using standard Kurucz model atmospheres.
 Due to the limited coverage of the &/—e plane of the existing near-intrared interferometers. it is not possible at preseut to recover full images from the available data. aud one lias to resort to the analvsis of the visibilities ou given interferometric basclines.," Due to the limited coverage of the $u-v$ plane of the existing near-infrared interferometers, it is not possible at present to recover full images from the available data, and one has to resort to the analysis of the visibilities on given interferometric baselines."
alignment of voids in the sample.,alignment of voids in the sample.
 Phe possible origins for the void alignment are discussed in section 5. and in section 6 we locus on the role of tidal fields in determining the evolutionary history of voids.," The possible origins for the void alignment are discussed in section 5, and in section 6 we focus on the role of tidal fields in determining the evolutionary history of voids."
 Finally. section 7 concludes with a short cliscussion anc prospects.," Finally, section 7 concludes with a short discussion and prospects."
 ]t is essential to have a statistically representative void sample for our study of the shapes of voids and their relative alignment., It is essential to have a statistically representative void sample for our study of the shapes of voids and their relative alignment.
 We also need a sullicientIy large spatial coverage in order to evaluate tidal field contributions over a large range of scales., We also need a sufficiently large spatial coverage in order to evaluate tidal field contributions over a large range of scales.
 Thus it is necessary to have a simulation with a large box size., Thus it is necessary to have a simulation with a large box size.
" We used the VES simulation from the Virgo SuperconputingConsortium... a simulation of cosmic structure formation in a CDM cosmology with Ου= 0.3. Qi,=03. dy=τὸkms*\Ipe and ox=0.9."," We used the VLS simulation from the Virgo Supercomputing, a simulation of cosmic structure formation in a $\Lambda$ CDM cosmology with $\Omega_{m,0}=0.3$ , $\Omega_{\Lambda,0}=0.7$, $H_0=70 \: \mathrm{km \:
s}^{-1} \mathrm{Mpc}^{-1}$ and $\sigma_8=0.9$."
 The simulation contains 512% N-body particles. each. with a mass of 6.86LohlulM. in. à comparatively. large box of EAside 479h+Alpe.," The simulation contains $512^3$ N-body particles, each with a mass of $6.86 \times
10^{10}h^{-1} M_{\odot}$ in a comparatively large box of side $479
h^{-1} \mathrm{Mpc}$."
 We used the particle distribution at the final timestep. corresponding to the current cosmic epoch @=1.," We used the particle distribution at the final timestep, corresponding to the current cosmic epoch $a=1$."
 The particle distribution of the simulation is converted into a grid-based. density field by means of Delaunay Triangle Field Estimator (ΕΤΕ) (vandeWevgacrt&Schaap2007)., The particle distribution of the simulation is converted into a grid-based density field by means of Delaunay Triangle Field Estimator (DTFE) \citep{weyschaap2007}.
. The kev feature of LYPEFE is that it is a reconstruction method that does not involve any user-delined. paranicters., The key feature of DTFE is that it is a reconstruction method that does not involve any user-defined parameters.
 Moreover. its natural ancl intrinsic filtering ancl interpolation procedure vields a density. field. that remains faithful. to both the density anc shape structure of the original particle distribution.," Moreover, its natural and intrinsic filtering and interpolation procedure yields a density field that remains faithful to both the density and shape structure of the original particle distribution."
 DTEE guarantees an optimal representation of the geometry and topology. of the weblike patterns in the mass distribution., DTFE guarantees an optimal representation of the geometry and topology of the weblike patterns in the mass distribution.
 A slice through the D'TEI resanipled density. field is shown in the first panel of figure 1.., A slice through the DTFE resampled density field is shown in the first panel of figure \ref{fig:slices}.
 After resampling the point density distribution. with D'EFIZ. we applied the Watershed. Void. Finder (VE) (Platen.vandeWevgaert&Jones2007) in order to identify the voids in the simulation.," After resampling the point density distribution with DTFE, we applied the Watershed Void Finder (WVF) \citep{platen2007} in order to identify the voids in the simulation."
 The WWE procedure traces the basin and its encompassing boundary for cach minimum in the spatial mass distribution., The WVF procedure traces the basin and its encompassing boundary for each minimum in the spatial mass distribution.
 Because WVE is free of any a priori shape criterion it is ideally suited to analyzing the morphology of underdense regions in the cosmic web., Because WVF is free of any a priori shape criterion it is ideally suited to analyzing the morphology of underdense regions in the cosmic web.
 The WVE procedure works as follows (seePlaten.vanWeveacrt&Jones2007.foràdetailed: description).," The WVF procedure works as follows \citep[see][for a detailed
description]{platen2007}."
 First we remove shot noise elfects in the raw D'TELE density Ποιά by smoothing at the Nyquist scale (zz1.07‘\Ipe): this is done using a Butterworth ο=2 filter.," First we remove shot noise effects in the raw DTFE density field by smoothing at the Nyquist scale $\approx 1.0
h^{-1}\mathrm{Mpc}$ ); this is done using a Butterworth $n=2$ filter."
 Then we identify the minima in the resulting density Geld ancl tag each minimum with a unique identification number., Then we identify the minima in the resulting density field and tag each minimum with a unique identification number.
 We can visualize the density field as a landscape with basins around cach minimum., We can visualize the density field as a landscape with basins around each minimum.
 Starting from the minima we [lood. this landscape., Starting from the minima we flood this landscape.
 As the flood level rises the basins surrounding each miminum start to fill up., As the flood level rises the basins surrounding each miminum start to fill up.
 Walls gradually emerge along the crest lines of the density Ποιά at the interstices between distinct regions., Walls gradually emerge along the crest lines of the density field at the interstices between distinct regions.
 The final product of the procedure will be a division of the density field into individual void cells., The final product of the procedure will be a division of the density field into individual void cells.
 In the first panel of figure 1. cach void identified by N'VE is indicated by the solid. black line marking the surrounding void boundary., In the first panel of figure \ref{fig:slices} each void identified by WVF is indicated by the solid black line marking the surrounding void boundary.
 Phe image shows that we indeed have a large number of voids in our sample., The image shows that we indeed have a large number of voids in our sample.
 In the upper right-hand. panel we zoom in on a region of the simulation box (the white box in first panel) which we use for the purpose of illustrating the subsequent steps (the analysis is done on the entire box)., In the upper right-hand panel we zoom in on a region of the simulation box (the white box in first panel) which we use for the purpose of illustrating the subsequent steps (the analysis is done on the entire box).
 The upper right panel also has lines indicating the (projected) magnitude and direction of the major axis of each void., The upper right panel also has lines indicating the (projected) magnitude and direction of the major axis of each void.
 Visual inspection of the void regions in this panelmanifestly suggests some degree of alignment., Visual inspection of the void regions in this panelmanifestly suggests some degree of alignment.
 Quantitative analvsis will establish the significance of that alignment., Quantitative analysis will establish the significance of that alignment.
"sources, Which cannot be very old. without the need for iuvoking enormous space velocitics frou. the nearest supernova renmnauts.","sources, which cannot be very old, without the need for invoking enormous space velocities from the nearest supernova remnants."
 Iu this paper we present evidence for a similar compact cluster of high-mass stars which las heretofore beeu hidden in the glare of its brightest colponcuts. the pair of M5 supergiaut stars.," In this paper we present evidence for a similar compact cluster of high-mass stars which has heretofore been hidden in the glare of its brightest components, the pair of M5 supergiant stars."
 The 1998 outburst season of SCR L900]LL preseuted an opportunity to search for optical and near-infrared variability of the double M stars. or other sources within the ROSAT URI error circle. which might be correlated to the SCR outbursts via sole process such as dass transfer to a compact object.," The 1998 outburst season of SGR 1900+14 presented an opportunity to search for optical and near-infrared variability of the double M stars, or other sources within the ROSAT HRI error circle, which might be correlated to the SGR outbursts via some process such as mass transfer to a compact object."
 Beetuning in carly May. aud continuing through midJuly 1998 we carried out an I aud Jbaud monitoring campaign at the U.S. Naval Observatory. Flagstaff Station (NOFS) which eveutiwilly comprised 2025 short exposure frames of «ata with 51.160 seconds of opcu shutter time during 16 nights. intended to sample variability tinescales down to a few seconds.," Beginning in early May and continuing through mid–July 1998 we carried out an I– and J–band monitoring campaign at the U.S. Naval Observatory, Flagstaff Station (NOFS) which eventually comprised 2025 short exposure frames of data with 54,460 seconds of open shutter time during 16 nights, intended to sample variability timescales down to a few seconds."
 The results of this work found no variablity for any object witlii the ROSAT URI eror circle aud are presentcc Linore fully in Vrbaetal.(2000)., The results of this work found no variablity for any object within the ROSAT HRI error circle and are presented more fully in \citet{vrb20}.
. Ilowever. it was recognized that the numerous short Ibane exposures constituted several hours of total exposure time. which could be stacked to form a deep Ibaud image to search for a counterpart at the position of the Frail.EKulka-rui.&Bloom(1999) variable radio source.," However, it was recognized that the numerous short I–band exposures constituted several hours of total exposure time, which could be stacked to form a deep I–band image to search for a counterpart at the position of the \citet{fra99} variable radio source."
 To the 1998 data were added additional short exposure framesi from 1995 and 1999., To the 1998 data were added additional short exposure frames from 1995 and 1999.
 In all. 217 frames of individual exposure time between 1 and 10 nunutes were coadded to form a net image of about 6.5 hours total exposure.," In all, 217 frames of individual exposure time between 1 and 10 minutes were coadded to form a net image of about 6.5 hours total exposure."
 All frames were obtained with oue of two Tektronix οἱ CCDs ou the 1.55am Strand Astrometric Telescope a the USNOFS., All frames were obtained with one of two Tektronix 2K CCDs on the 1.55–m Strand Astrometric Telescope at the USNOFS.
 I was additionally recognized that. since the exposures used were short cuough uot to saturate the three bright M stars (A. Beand C of V96). their helt could largely be removed bx PSF subtraction.," It was additionally recognized that, since the exposures used were short enough not to saturate the three bright M stars (A, B,and C of V96), their light could largely be removed by PSF subtraction."
 Figure l is an approximately 15 x 145 aresec portion of the uedianfiltered composite Ibaud inage centered ou the V96 M stars; with a limiting detection magnitude of I z 26.5.," Figure 1 is an approximately 45 x 45 arcsec portion of the median–filtered composite I–band image centered on the V96 M stars, with a limiting detection magnitude of I $\approx$ 26.5."
 In this nuage the M stars ABC have been removed. although heir positions are still apparent due to imperfect subtraction.," In this image the M stars ABC have been removed, although their positions are still apparent due to imperfect subtraction."
 The position of the variable radio source is shown. but no counterpart is visible ο I 5 26.5. which is cousistent with the detections in the near infrared of Eikeuberrv&Dror (1999).," The position of the variable radio source is shown, but no counterpart is visible to I $\approx$ 26.5, which is consistent with the non-detections in the near infrared of \citet{eik99}."
. Unfortunately. lione of the rearly 9060 frames frou 1995 were obtained siauultaneouslv with a eunray burst from SCR 1900|LI.," Unfortunately, none of the nearly 200 frames from 1998 were obtained simultaneously with a gamma–ray burst from SGR 1900+14."
 Of ereater interest is that the subtracted Ixud miaege shows what appears to be a cluster of stars. and possibly uchulosity. ceutered ou the xosition of the AMI stars.," Of greater interest is that the subtracted I--band image shows what appears to be a cluster of stars, and possibly nebulosity, centered on the position of the M stars."
 The IRAS source found at this location bv vanParadijsetal.(1996) shows a steeply rising cherey spectrum that can )o iuterpreted as warm dust iu the cluster region., The IRAS source found at this location by \citet{van96} shows a steeply rising energy spectrum that can be interpreted as warm dust in the cluster region.
 Figure 1. also shows identification uunibers of the possible cluster stars., Figure 1 also shows identification numbers of the possible cluster stars.
" Ou UT 1999 οctober 28 we used the ASTROCAAL IR imager. wuch cuplovs an SBRC 1021? TuSh detector. at the 1.55a clescope to obtain a 1600 secoud net exposure Jband image of this region,"," On UT 1999 October 28 we used the ASTROCAM IR imager, which employs an SBRC $^2$ InSb detector, at the 1.55–m telescope to obtain a 1600 second net exposure J–band image of this region."
 An approximately 15 x 15 arcsec region of this nuage is shown iu Figure 2. where again the M stars were somewhat successfully PSEsubtracted.," An approximately 45 x 45 arcsec region of this image is shown in Figure 2, where again the M stars were somewhat successfully PSF–subtracted."
 We obtained photometry for the cluster stars roni the I and Jxul frames. calibrated with several 1 and Jband local standards which iad previously beeu set up for our variability nouitorine program.," We obtained photometry for the cluster stars from the I– and J–band frames, calibrated with several I– and J–band local standards which had previously been set up for our variability monitoring program."
 The photometric results are xesented in Table 1 where the results for starspA 5Γ and 6 are presented together as they could not (0 separated in the Jband observations., The photometric results are presented in Table 1 where the results for stars 5 and 6 are presented together as they could not be separated in the J–band observations.
 The observed (PJ) z 7 colors are far larger than for any unreddened star aud indicate that they suffer extremely high extinction., The observed (I–J) $\approx$ 7 colors are far larger than for any unreddened star and indicate that they suffer extremely high extinction.
 Asstuning that the cluster stars are at tle same distance and suffer the same extinction as the ΑΙ supergiaut stars (12-15 kpe: Ay = 10.241.0: V96) we placed all stars iu au Mj vs. (IJ) CAL diagram (Figure 3). assunüug normal interstellar extinction (Bessel&Brett1955). and where the error bars include the ranges im distance aud Ay values given above.," Assuming that the cluster stars are at the same distance and suffer the same extinction as the M supergiant stars (12-15 kpc; $_V$ = $\pm$ 1.0; V96) we placed all stars in an $M_I$ vs. (I–J) CM diagram (Figure 3), assuming normal interstellar extinction \citep{bes88}, and where the error bars include the ranges in distance and $_V$ values given above."
 The solid curves show the approximate loci for supergiauts and charts later than AQ and for eiauts later than GO while the dashed lines show the MO (IJ) colors. for," The solid curves show the approximate loci for supergiants and dwarfs later than A0 and for giants later than G0 while the dashed lines show the M0 (I–J) colors, for"
would be expected if the blue light is coming from a voung population of stars.,would be expected if the blue light is coming from a young population of stars.
 Their true nature can of course only be assessed by. spectroscopy., Their true nature can of course only be assessed by spectroscopy.
 The similarities of the broac-band colours of FCCOLG to those of star-forming or amorphous cdwarfs. its relatively strong core and the presence of emission. clouds support the conclusion. that PCCOLG is actively forming. stars. albeit at a very. leasurely pace when compared to BC'Ds and amorphous cdwarls who are about a factor 1000 more [luminous in Ilo.," The similarities of the broad-band colours of FCC046 to those of star-forming or amorphous dwarfs, its relatively strong core and the presence of emission clouds support the conclusion that FCC046 is actively forming stars, albeit at a very leasurely pace when compared to BCDs and amorphous dwarfs who are about a factor 1000 more luminous in $\alpha$."
 The nuclear emission of PCCOLG and LCOC207 can be adequately. accounted for by photo-ionisation by post-AGB stars although a contribution of llo emission from star-formation cannot be excluded., The nuclear emission of FCC046 and FCC207 can be adequately accounted for by photo-ionisation by post-AGB stars although a contribution of $\alpha$ emission from star-formation cannot be excluded.
 Only the emission. from the six clouds. observed in. EC'XC046 (supernova remants. Wolf-Itavet nebulae) can be interpreted as unambiguous evidence for recent or ongoing star-formation.," Only the emission from the six clouds observed in FCC046 (supernova remants, Wolf-Rayet nebulae) can be interpreted as unambiguous evidence for recent or ongoing star-formation."
 The presence of physically different) emission regions makes the interpretation of this emission in terms of a star-formation rate cumbersome., The presence of physically different emission regions makes the interpretation of this emission in terms of a star-formation rate cumbersome.
 High-resolution spectroscopy of a broad: wavelength region. is required. to measure the strengths of Ho. L2 and of telltale O. N and 5 emission lines in the visible part of the spectrum.," High-resolution spectroscopy of a broad wavelength region is required to measure the strengths of $\alpha$, $\beta$ and of telltale O, N and S emission lines in the visible part of the spectrum."
 These can be used as diagnosties to probe the physical nature of the cillerent emission clouds., These can be used as diagnostics to probe the physical nature of the different emission clouds.
 Drinkwatera£ (2001). find no distinct class of star-forming BCD galaxies but. instead. observe Hào emission in dwarf galaxies of all sizes ancl types., Drinkwater \cite{dri} find no distinct class of star-forming BCD galaxies but instead observe $\alpha$ emission in dwarf galaxies of all sizes and types.
 Amone these. starforming cles like FCCOLG may prove to. be the descendents of more fiercely. star-forming ναί like DCDs which are not (or no longer) present in Fornax.," Among these, starforming dEs like FCC046 may prove to be the descendents of more fiercely star-forming dwarfs like BCDs which are not (or no longer) present in Fornax."
 As a check. we fitted. exponentials to the surface. brightness profiles of ECC'046 and ECC207 and compared. the extrapolated D-band central surface. brightnesses and the scale-Iengths with those of the Virgo dis. DCDs. and dlrrs. presented in Drinkwater Hardy (1991)..," As a check, we fitted exponentials to the surface brightness profiles of FCC046 and FCC207 and compared the extrapolated B-band central surface brightnesses and the scale-lengths with those of the Virgo dEs, BCDs, and dIrrs presented in Drinkwater Hardy \cite{dha}."
 )oth galaxies have scale-lengths in between those of BCDs and dls. and quite high D-band central surface brightnesses compared to the cles in the Drinkwater Hardy sample.," Both galaxies have scale-lengths in between those of BCDs and dEs, and quite high B-band central surface brightnesses compared to the dEs in the Drinkwater Hardy sample."
 These results support our conjecture that cles that contain ionisecl gas ancl possibly ongoing low-powered star-formation can be considered. as amissing link between BC'Ds and traditional dls., These results support our conjecture that dEs that contain ionised gas and possibly ongoing low-powered star-formation can be considered as amissing link between BCDs and traditional dEs.
 This research has made use of the NASA/IDAC Extragalactic Database (NIZD) which is operated by the Je Propulsion Laboratory. California Institute of Technology. under contract with the National Acronautics ancl Space Administration.," 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 the anonymous referee for helpfu comments., We thank the anonymous referee for helpful comments.
 SDR. wishes to thank Dr. Victor. Debattista [or useful comments on the causes of lopsidedness., SDR wishes to thank Dr. Victor Debattista for useful comments on the causes of lopsidedness.
 WAZ acknowledges the support of the Austrian Science. Fui (project P14783) and of the )jundesmünisterium [tire Jilclune. Wissenschaft und. Ixultur.," WWZ acknowledges the support of the Austrian Science Fund (project P14783) and of the Bundesministerium fürr Bildung, Wissenschaft und Kultur."
disks to reach the ceuter is (from equation 38]) where y=R/10 kpe aud Vann=Vus/200 kan |. and the eas mass is (from equation 35)) The ratio of barvoulc to ανασα. mass within the disk region Ais To the extent that these quautities have been observed. hey are in good agreement with the results of our model.,"disks to reach the center is (from equation \ref{tvisc}) ) where $R_{10} = R/10$ kpc and $V_{200} = V_{\rm max}/200$ km $^{-1}$, and the gas mass is (from equation \ref{coldeneq}) ) The ratio of baryonic to dynamical mass within the disk region $R$ is To the extent that these quantities have been observed, they are in good agreement with the results of our model."
 It is also useful to verity that our approximation that 0.~G ]s valid for these ealaxies., It is also useful to verify that our approximation that $\sigma_* \approx \sigma$ is valid for these galaxies.
 Once stars fori. ransicut spiral structures will dwuamically heat them uutil the stellar disk becomes stable against further spiral patterus (?7)..," Once stars form, transient spiral structures will dynamically heat them until the stellar disk becomes stable against further spiral patterns \citep{sellwood84a, carlberg85a}. ."
" The characteristic timescale for his heating is ώςτων. where Qu,-2 is the limiting value at which the diskbecomes stable against spiral perturbations. Q. is the current Tooumse Q xwanmeter for the stars. and nunuerical experiments show hat rὉ for f,4, evaluated at one disk scale leneth."," The characteristic timescale for this heating is $[(Q_{\rm lim} - Q_*)/\tau] t_{\rm orb}$, where $Q_{\rm lim}\approx 2$ is the limiting value at which the disk becomes stable against spiral perturbations, $Q_*$ is the current Toomre $Q$ parameter for the stars, and numerical experiments show that $\tau\sim 4-5$ for $t_{\rm orb}$ evaluated at one disk scale length."
 If we asstune that the stars are born at Q.=1. then the characteristic timescale over which the heat is where we have taken the radial scale length to be halt of R.," If we assume that the stars are born at $Q_* = 1$, then the characteristic timescale over which the heat is where we have taken the radial scale length to be half of $R$."
 Iu coutrast. the time required to double the stellar Lass Is Thus we see that the time required for stars to increase their velocity dispersion via spiral structure is ecuerally comparable to or longer than the tine required for a new generation of stars to form with the same velocity dispersion as the eas.," In contrast, the time required to double the stellar mass is Thus we see that the time required for stars to increase their velocity dispersion via spiral structure is generally comparable to or longer than the time required for a new generation of stars to form with the same velocity dispersion as the gas."
 Our approximation that the stellar population has the same velocity dispersion as the gas iu these galaxies is therefore reasonable., Our approximation that the stellar population has the same velocity dispersion as the gas in these galaxies is therefore reasonable.
 Iu our idealized models. we have ncelected the influence of stellar feedback by setting G=0.," In our idealized models, we have neglected the influence of stellar feedback by setting $\calG = 0$."
 This is obviously reasonable if we are concerned with the outer parts of a galactic disk where there is no star formation. or a protostellar disk where at most a few stars will fori.," This is obviously reasonable if we are concerned with the outer parts of a galactic disk where there is no star formation, or a protostellar disk where at most a few stars will form."
 It is not reasonable for the centers of prescut-day ealactic disks. where superuovae are clearly miportaut.," It is not reasonable for the centers of present-day galactic disks, where supernovae are clearly important."
 It is questionable whether stellar feedback is importaut in ULIRGs or the high surface deusity ealaxics found iu the carly universe., It is questionable whether stellar feedback is important in ULIRGs or the high surface density galaxies found in the early universe.
 Superuovae are not effective iu such «ΝΟΗΜΑ (27).. but stellar racliation pressure lay be.," Supernovae are not effective in such environments \citep{thompson05, joung09a}, but stellar radiation pressure may be."
 Whether it can actually drive the observed. velocity dispersions in lieh redshift ealaxies is a matter of debate (?7)..," Whether it can actually drive the observed velocity dispersions in high redshift galaxies is a matter of debate \citep{murray09a, krumholz09d}."
 Iu those situatious where feedback is significant. we can qualitatively see low it would change our results by noting that adding a non-zero G to our equatious would have roughly the same effect as loweriug g.," In those situations where feedback is significant, we can qualitatively see how it would change our results by noting that adding a non-zero $\calG$ to our equations would have roughly the same effect as lowering $\eta$."
 Plivsically. if star formation injects turbulence ito the ISM at au appreciable rate. this is equivalent to reduciug the rate at which turbulence decavs we effectively iucrease the “cooling time” of the disk.," Physically, if star formation injects turbulence into the ISM at an appreciable rate, this is equivalent to reducing the rate at which turbulence decays – we effectively increase the “cooling time"" of the disk."
 Consulting equations (31)) (37)). we see that the effect of this is to increase the velocity dispersion aud surface deusitv iu the equilibria state. while reducing the radial velocity aud the rate of aneular momentum transport.," Consulting equations \ref{sigmaeq}) ) – \ref{alphaeq}) ), we see that the effect of this is to increase the velocity dispersion and surface density in the equilibrium state, while reducing the radial velocity and the rate of angular momentum transport."
 We caution that this analysis is only valid as long as the feedback is not too strong., We caution that this analysis is only valid as long as the feedback is not too strong.
 Iu particular. we require that £ remains lurger than G for à Q=1 disk. aud that the turbulent stresses created by the feedback mechanisin are significantly weaker than the stresses induced by eravitational iustabilitv-diiven turbulence.," In particular, we require that $\calL$ remains larger than $\calG$ for a $Q=1$ disk, and that the turbulent stresses created by the feedback mechanism are significantly weaker than the stresses induced by gravitational instability-driven turbulence."
 If the first requirement is not met. then feedback. will drive the velocity dispersion up to the point where Q l. and the gravitational instability will slut off.," If the first requirement is not met, then feedback will drive the velocity dispersion up to the point where $Q>1$, and the gravitational instability will shut off."
 If the latter condition. fails. then exavitatioual instability will continue. but our calculation of the transport rate will not be correct because we have not iucluded stresses Induced by feedback.," If the latter condition fails, then gravitational instability will continue, but our calculation of the transport rate will not be correct because we have not included stresses induced by feedback."
 Even if both requirements are iuet. our analvsis of feedback effects should be regarded as qualitative rather than quantitative.," Even if both requirements are met, our analysis of feedback effects should be regarded as qualitative rather than quantitative."
 Euergv injection G appears on the zieht haud side of the torque equation with the opposite sien as £. but their functional dependence on other disk parameters (surface deusity. velocity dispersion. etc.)," Energy injection $\calG$ appears on the right hand side of the torque equation with the opposite sign as $\calL$, but their functional dependence on other disk parameters (surface density, velocity dispersion, etc.)"
 are almost certainly different., are almost certainly different.
 The exact effects of feedback will depeud ou how euergv injection varies with these quantities. which will iu turi depend onu the type of feedback aud the plysics of the ISML.," The exact effects of feedback will depend on how energy injection varies with these quantities, which will in turn depend on the type of feedback and the physics of the ISM."
 Although we have focused our discussion thus far ou ealactic disks. our model applies for arbitrary rotation curves. gas fractions. aud iufall rates. so we can apply it equally well to protostellar disks.," Although we have focused our discussion thus far on galactic disks, our model applies for arbitrary rotation curves, gas fractions, and infall rates, so we can apply it equally well to protostellar disks."
" To uuderstaud the expected levels of turbulence in protostellar disks. we use the parameterization of infall due to ??.. who introduce the dimensionless uuuboers: where e24 is the sound speed in the disk. Any is the total mass of the disk aud star aud ©;4, is the Keplerian orbital periodof the iufallius material."," To understand the expected levels of turbulence in protostellar disks, we use the parameterization of infall due to \citet{kratter08a, kratter10a}, who introduce the dimensionless numbers: where $c_{s,d}$ is the sound speed in the disk, $M_{*d}$ is the total mass of the disk and star and $\Omega_{k,\rm in}$ is the Keplerian orbital periodof the infalling material."
" Plivsically. & represents the ratio of the external accretion rate to the mnaxinuun rate (~ 62,4/0) at which a stable disk cau process material. while P represeuts (up to a factor of 27) the fraction by which the disk star mass changes per outer disk orbit."," Physically, $\xi$ represents the ratio of the external accretion rate to the maximum rate $\sim c_{s,d}^3/G$ ) at which a stable disk can process material, while $\Gamma$ represents (up to a factor of $2\pi$ ) the fraction by which the disk plus star mass changes per outer disk orbit."
" Tudecd. since pise,C8)=ROνοdf BR. with a little aleebra it is easy to show that. in the case of a WNeplerian disk consisting eutirely of eas. our x smiply reduces to 2s P paramicter."," Indeed, since $v_{\phi}(R) = R\Omega_{k,\rm in} = \sqrt{G M_{*d}/R}$ , with a little algebra it is easy to show that, in the case of a Keplerian disk consisting entirely of gas, our $\chi$ simply reduces to \citeauthor{kratter10a}' 's $\Gamma$ parameter."
 With this understanding. we can explain the observation bv ? that. in their simulations. the typical velocity dispersion of disks that do not fragmentis comparable to the disk thermal sound speed (see their Figure 8).," With this understanding, we can explain the observation by \citet{kratter10a} that, in their simulations, the typical velocity dispersion of disks that do not fragmentis comparable to the disk thermal sound speed (see their Figure 8)."
 For a purely gaseous IXeplerian disk. our model eives s=[ByfCpf.52 and ? show that the disk sound speed is related to the IXepleriau0 velocity at the," For a purely gaseous Keplerian disk, our model gives $s = [3\chi/(4\eta)]^{1/3}$ , and \citeauthor{kratter10a} show that the disk sound speed is related to the Keplerian velocity at the"
Galaxy characteristics. like morphology. and star-formation rate (SER). are observed to change with environment where high density regions like clusters are characterized bv a larger fraction of elliptical galaxies and a lower star-formation rate than seen in the field. (Dressler1980:Gotoetal.2003:Gomez 2003)...,"Galaxy characteristics, like morphology and star-formation rate (SFR), are observed to change with environment where high density regions like clusters are characterized by a larger fraction of elliptical galaxies and a lower star-formation rate than seen in the field \citep{1980ApJ...236..351D,2003MNRAS.346..601G,2003ApJ...584..210G}."
 These observations ave known as the morphologv-density ancl SER-density relations. although Whitmore et al. (," These observations are known as the morphology-density and SFR-density relations, although Whitmore et al. ("
1991.1993) argue that these rellect a tighter ancl more fundamental morphology-radius relation where the distance from the cluster centre is the independent parameter.,"1991,1993) argue that these reflect a tighter and more fundamental morphology-radius relation where the distance from the cluster centre is the independent parameter."
" The. morphologv-density relation shows distinct behavior over three separate reginies which can be characterized in terms of the projected galaxy densitv or the radial distance from the cluster centre. (in terms of the virial radius. £?,.;,. defined by the Girardietal.(L998) as Lea,c0.0020,hu Alpe)."," The morphology-density relation shows distinct behavior over three separate regimes which can be characterized in terms of the projected galaxy density or the radial distance from the cluster centre (in terms of the virial radius, $R_{vir}$ , defined by the \citet{1998ApJ...505...74G} as $R_{vir}\simeq 0.002\sigma_{r}\ h^{-1}_{100}$ Mpc)."
 In the lowest density regions farthest [rom cluster centres (with projected densities <1Alpe7 or radius l Rea) the relation is Hat. suggesting that the physical mechanisms responsible for changes in morphology. are not effective in this regime.," In the lowest density regions farthest from cluster centres (with projected densities $< 1\ \mathrm{Mpc}^{-2}$ or radius $> 1\ R_{vir}$ ) the relation is flat, suggesting that the physical mechanisms responsible for changes in morphology are not effective in this regime."
 Ata characteristic radius of ~1Rea. (projected densities of 16Mpe 7) the fraction of intermediate tvpe (SO) galaxies begins to increase while the late-tvpe. disk (Se) galaxy fraction decreases and the SER. decreases sharply (Gomezetal. 2003)., At a characteristic radius of $\sim 1\ R_{vir}$ (projected densities of $1-6\ \mathrm{Mpc}^{-2}$ ) the fraction of intermediate type (S0) galaxies begins to increase while the late-type disk (Sc) galaxy fraction decreases and the SFR decreases sharply \citep{2003ApJ...584..210G}.
. These trends continue till ~0.3Rea (projected density ον6Alpe 2) where the fraction of intermediate types decreases and the elliptical fraction dramatically increases (Gotoetal.2003).., These trends continue till $\sim 0.3\ R_{vir}$ (projected density $> 6\ \mathrm{Mpc}^{-2}$ ) where the fraction of intermediate types decreases and the elliptical fraction dramatically increases \citep{2003MNRAS.346..601G}.
 The behavior of these relations over the separate reginies indicates a change in the dominant physical mechanisms inlluencing the evolution of galaxies across these environments., The behavior of these relations over the separate regimes indicates a change in the dominant physical mechanisms influencing the evolution of galaxies across these environments.
 There are a variety. of physical mechanisms that could be responsible for altering galaxy morphology in dense environments. including ram pressure stripping. tidal interactions. galaxy harassment. strangulation. and major and minor mergers.," There are a variety of physical mechanisms that could be responsible for altering galaxy morphology in dense environments, including ram pressure stripping, tidal interactions, galaxy harassment, strangulation, and major and minor mergers."
 The vast majority of galaxies in the universe reside in eroups which are small dynamical systems typically containing a handful of large. (~ L.) galaxies and a large number of smaller galaxies (Cicller&Lluchra 2008)..," The vast majority of galaxies in the universe reside in groups which are small dynamical systems typically containing a handful of large $\sim L_*$ ) galaxies and a large number of smaller galaxies \citep{1983ApJS...52...61G, 1987ApJ...321..280T,2004MNRAS.348..866E,2007ApJ...671..153Y,2008A&A...479..927T}."
" These systems have velocity dispersions between ~30500kimsn and intragroup. medium. (IM)"" densitiesNN thatare not well constrained.", These systems have velocity dispersions between $\sim 30-500 \kms$ and intragroup medium (IGM) densities thatare not well constrained.
 Fhus. it has been thought that tidal interactions are likelv to dominate in this environment," Thus, it has been thought that tidal interactions are likely to dominate in this environment"
A132 is a compact elliptical galaxy of around 109AL. southeast of he nucleus of the Andromeda ealaxy.,M32 is a compact elliptical galaxy of around $10^9 M_\sun$ southeast of the nucleus of the Andromeda galaxy.
 It shares the cistinetion of being the nearest elliptical galaxy with NGC 205. Ancromecla’s other elliptical companion.," It shares the distinction of being the nearest elliptical galaxy with NGC 205, Andromeda's other elliptical companion."
 Structtwally. N32 lies near au extrapolation ol elliptical galaxy properties. whereas NGC 205. with its 1uch lower surface brightuess. has more in common with disk galaxies (IyormencdyLOS9).," Structurally, M32 lies near an extrapolation of elliptical galaxy properties, whereas NGC 205, with its much lower surface brightness, has more in common with disk galaxies \citep{kor89}."
. It is ustaly M32. therefore. that attracts attention from those interested in the properties. histories. and stear populations of elliptical galaxies.," It is usually M32, therefore, that attracts attention from those interested in the properties, histories, and stellar populations of elliptical galaxies."
 Euhusiasimn shoulcl be tempered by some caution since M32 is so dense that analogues are rare. aud sOil may represent a stibelass ol elliptical galaxies rather tau elliptical galaxies in geuert.," Enthusiasm should be tempered by some caution since M32 is so dense that analogues are rare, and so it may represent a subclass of elliptical galaxies rather than elliptical galaxies in general."
" It probably coMalus a centra black hole of mass 3xLO"" ML. (Beideretal.1996).", It probably contains a central black hole of mass $3 \times 10^6$ $_\sun$ \citep{ben96}.
. A comprehensive undersandiug of N32's history. wot connect its structure ancl kinematics with its stellar population proyerties., A comprehensive understanding of M32's history would connect its structure and kinematics with its stellar population properties.
 There is some dispute i the literature. bit nost investigations agree that the nuclear regious of M32 are best fit with asllar population of approximately solar composition and an age of. very roughly. | Gyr.," There is some dispute in the literature, but most investigations agree that the nuclear regions of M32 are best fit with a stellar population of approximately solar composition and an age of, very roughly, 4 Gyr."
 Published ig-3lit spectroscopy of N32 (Conzallez 1993. hereafter. G93) does not each as far as 1/3 [1.8 RAPA): of light enclosed] [rom the uucleus where (AST) photometry oL resolved red giants was obtained by Cuillmairetal.(1996).," Published long-slit spectroscopy of M32 (Gonzállez 1993, hereafter G93) does not reach as far as $1\farcm 3$ [1.8 $R_e$ (PA); of light enclosed] from the nucleus where (HST) photometry of resolved red giants was obtained by \citet{grill96}."
. Uuclertle assumption of constant :we the colors of the giants map uniquely to abundance. aud the abuudauce spread found is very suniar to that of the solar neighborhood.," Under the assumption of constant age the colors of the giants map uniquely to abundance, and the abundance spread found is very similar to that of the solar neighborhood."
 The best cousisteucy withextrapolated (93 spectroscopy was obtained with old ages of δ Gyr or older., The best consistency with G93 spectroscopy was obtained with old ages of 8 Gyr or older.
 It should be emphasized that the models simultaneously matehed both the distribution of eiant temperatures aud all spectroscopic iudices., It should be emphasized that the models simultaneously matched both the distribution of giant temperatures and all spectroscopic indices.
 Only. Go:) elves a sultable comparable data set for optical feattuwe-streueth gradieuts ou the Lick/ID5 system [system definition in Wortheyetal.(1901):&Ottavia," Only G93 gives a suitable comparable data set for optical feature-strength gradients on the Lick/IDS system [system definition in \citet{wor94,wor97}] ]."
ni (1997)]]. elal.(1991) gave long-slit data for M32 but did not trausloru completely to the Lick/ID5 systet1., \citet{hardy94} gave long-slit data for M32 but did not transform completely to the Lick/IDS system.
 Davidge(1991) ujeasured eight high-quality indices. but his spectra apparently had a spectral resolution somewhat coarser thau Lick/ID5. as evidenced by the fact that the iarrower iudices we| weaker in comparison stars.," \citet{dav91}
 measured eight high-quality indices, but his spectra apparently had a spectral resolution somewhat coarser than Lick/IDS, as evidenced by the fact that the narrower indices were weaker in comparison stars."
 This data could. in principle. |je linearly trauslormed to the Lick/IDS system. but this has not been attempted here.," This data could, in principle, be linearly transformed to the Lick/IDS system, but this has not been attempted here."
" The Davidge(1991) results do make a very usefi uear-differeutial comparison set. aud we agree with lis conclusion that most spectral indices slow eradients in the central20""."," The \citet{dav91} results do make a very useful near-differential comparison set, and we agree with his conclusion that most spectral indices show gradients in the central."
 Jones&Rose(1991) report that no index gradients are observed iu the central," \citet{jones94}
 report that no index gradients are observed in the central"
feedback efficiencies.,feedback efficiencies.
" With this aim, we looked for the time t at which the mass of the BH is equal to the value 105A-!Mc, independently of the initial BH mass."," With this aim, we looked for the time $t$ at which the mass of the BH is equal to the value $10^{8} h^{-1} M_{\odot}$, independently of the initial BH mass."
 We then plotted in Fig 5 the ellipticity as a function of the time £ needed for the BH to reach such a mass value., We then plotted in Fig 5 the ellipticity as a function of the time $t$ needed for the BH to reach such a mass value.
" We can disentangle the effect of the bar evolution by comparing the bar ellipticities measured in the same disk, at the same times, in a simulation without a central BH (dotted line in Fig.5)."," We can disentangle the effect of the bar evolution by comparing the bar ellipticities measured in the same disk, at the same times, in a simulation without a central BH (dotted line in Fig.5)."
 'This comparison shows that a too fast or too slow growth of the BH results in a small effect on the bar ellipticity., This comparison shows that a too fast or too slow growth of the BH results in a small effect on the bar ellipticity.
" A significant change of ellipticity, with respect to the simulation without the BH, only happens if the BH takes from 2 to 5 Gyrs to reach a mass of 10° Mo."," A significant change of ellipticity, with respect to the simulation without the BH, only happens if the BH takes from 2 to 5 Gyrs to reach a mass of $10^8$ $_\odot$."
" Of course, the subsequent evolution of the bardoes depend on the mass of the BH; a BH which quickly reaches our reference mass and then continues to grow, will have a larger effect on the bar ellipticity at the final time, as shown in Figure 2."," Of course, the subsequent evolution of the bar depend on the mass of the BH; a BH which quickly reaches our reference mass and then continues to grow, will have a larger effect on the bar ellipticity at the final time, as shown in Figure 2."
" In Fig.6 and 7 we provide the profiles of thedifferences of the ellipticities with and without the BH, for the old (Fig."," In Fig.6 and 7 we provide the profiles of the of the ellipticities with and without the BH, for the old (Fig."
 6) and the new (Fig.7) stars at the same times as in Fig., 6) and the new (Fig.7) stars at the same times as in Fig.
" 5.,"," 5.,"
 i.e. when the BH mass reaches the value 10° Mo., i.e. when the BH mass reaches the value $10^8$ $_\odot$.
" These differences are always negatives, for the new stars except for t=2.05 (case i2 in Tab."," These differences are always negatives, for the new stars except for t=2.05 (case i2 in Tab."
" 1), meaning that for all the other times, the bar is stronger at all radii if the BH is not present."," 1), meaning that for all the other times, the bar is stronger at all radii if the BH is not present."
 For the old stars profiles the trend is less evident: at some times we have radii in the disk where the ellipticities of the bar containing the BH is slightly higher., For the old stars profiles the trend is less evident: at some times we have radii in the disk where the ellipticities of the bar containing the BH is slightly higher.
 But it is evident that the differences are always negative at all times as far as the internal radii is concerned., But it is evident that the differences are always negative at all times as far as the internal radii is concerned.
 We interpret this as the confirm that the effect of the BH is to decrease the strength of the inner bars., We interpret this as the confirm that the effect of the BH is to decrease the strength of the inner bars.
 This is consistent with the findings of ? which however only considered the stellar component in a triaxial system and used an adiabatically growing potential to simulate the presence and growth of the central BH.," This is consistent with the findings of \citet{Holley}
 which however only considered the stellar component in a triaxial system and used an adiabatically growing potential to simulate the presence and growth of the central BH."
 They noticed that the major impact of the BH on the triaxiality of the galaxy involves at maximum the 1096 inner mass of the galaxy., They noticed that the major impact of the BH on the triaxiality of the galaxy involves at maximum the $10\% $ inner mass of the galaxy.
" We estimated indeed that the major impact on the variation of the ellipticity is on theinner iso-density contour, containing z1096 of the mass, when the BH is present with respect to our control case."," We estimated indeed that the major impact on the variation of the ellipticity is on the iso-density contour, containing $\approx 10 \%$ of the mass, when the BH is present with respect to our control case."
 'These results are qualitatively confirmed even if we evaluate the ellipticity using the inertial tensor inside our stellar system., These results are qualitatively confirmed even if we evaluate the ellipticity using the inertial tensor inside our stellar system.
"Hux density of 2705s at 6.3 em and a brightness temperature ol⋅ about 15000 Ix.⊳⊳∖ They argue lor⋅ a spectrum fi,.x9""?( vielding the signal of a cillractive lensing event on a like star at 10 611 of assuming that the distance to Rigel is 237 pe (?)..",flux density of $\mu$ Jy at 6.3 cm and a brightness temperature of about 15000 K. They argue for a spectrum $f_\nu \propto \nu^{0.6}$ yielding the signal of a diffractive lensing event on a Rigel-like star at 10 GHz of assuming that the distance to Rigel is 237 pc \citep{1997A&A...323L..49P}.
 Even bluer stars vield even higher variable τις densities., Even bluer stars yield even higher variable flux densities.
 Using the Od-supergiant LID 190429 as an exemplar vields so a nearby clillractive lensing event would be detectable against an carly supereiant in the Large. Magellanie Cloud (LMC) or Small Magellanic Cloud (SAIC)., Using the O4-supergiant HD 190429 as an exemplar yields so a nearby diffractive lensing event would be detectable against an early supergiant in the Large Magellanic Cloud (LMC) or Small Magellanic Cloud (SMC).
 For all of these estimates the only source of noise included is at the receiver., For all of these estimates the only source of noise included is at the receiver.
 The radio emission of giants and supergiants mav be sullicienth noisy to increase the detection. limits outlined in 3.3.., The radio emission of giants and supergiants may be sufficiently noisy to increase the detection limits outlined in \ref{sec:detection}.
 Nearby racio-louc quasars typically have brightness temperatures of about 1035 IN and flux densities of about 1 Jy. much brighter than typical stars: however. they. of course. are much rarer and it is less likely that nearby substellar objects will cause lensing events.," Nearby radio-loud quasars typically have brightness temperatures of about $10^{11}$ K and flux densities of about 1 Jy, much brighter than typical stars; however, they, of course, are much rarer and it is less likely that nearby substellar objects will cause lensing events."
 Phe assumption that the quasar Ies at a distance of about 1 Cpe and the lens lies in the solar neighbourhood Any quasar with fi.< would exhibit large oscillations in its Bux during a cillractive microlensing event: whereas brighter sources would exhibit variations of Although lensing events with quasars are likely to be rare. with the SKA it may be possible to monitor a sample of bright quasars continually ancl provide constraints on the number of freely Doating planets.," The assumption that the quasar lies at a distance of about 1 Gpc and the lens lies in the solar neighbourhood Any quasar with $f_\nu < f_{\nu,d}$ would exhibit large oscillations in its flux during a diffractive microlensing event; whereas brighter sources would exhibit variations of Although lensing events with quasars are likely to be rare, with the SKA it may be possible to monitor a sample of bright quasars continually and provide constraints on the number of freely floating planets."
 On the other hand radio emission. of quasars is inherently noisy., On the other hand radio emission of quasars is inherently noisy.
 This might make detecting the dillractive lensing events clillieult or produce false detections., This might make detecting the diffractive lensing events difficult or produce false detections.
 Either of these possibilities merit further studs., Either of these possibilities merit further study.
 ‘To estimate the number of sources that could be detected in the radio with the SKA and whose oscillatory lux could be detected. a detection threshold of 10 nJv is chosen.," To estimate the number of sources that could be detected in the radio with the SKA and whose oscillatory flux could be detected, a detection threshold of 10 nJy is chosen."
 The radio lux density from each of the OGLE-IL sources also has to be modelled., The radio flux density from each of the OGLE-II sources also has to be modelled.
 Phe relationship between bolometric Correction. V f-eolour ancl effective temperature given in? provides a estimate of the angular size of the stellar photosphere as a function of Vf and V.," The relationship between bolometric correction, $V-I$ -colour and effective temperature given in \citet{2007gitu.book.....S} provides a estimate of the angular size of the stellar photosphere as a function of $V-I$ and $V$."
 This relationship depends only weakly on the luminosity class of the stars., This relationship depends only weakly on the luminosity class of the stars.
 Phe radio [lux is assumed. to be proportional to the angular size of the photosphere and normalised to the values for Arcturus in Eq., The radio flux is assumed to be proportional to the angular size of the photosphere and normalised to the values for Arcturus in Eq.
 19 at 10 Cllz., \ref{eq:28} at 10 GHz.
 These curves are shown in red in Fig., These curves are shown in red in Fig.
" 5 and the corresponding values of Af, are shown in blue.", \ref{fig:ogle} and the corresponding values of $\Delta f_\nu$ are shown in blue.
 The normalisation to Arcturus is given in purple and the value of foot in evan.," The normalisation to Arcturus is given in purple and the value of $f_{\nu,d}$ in cyan."
 The reddening in the OGLI-LE fields is extensive. (?).., The reddening in the OGLE-II fields is extensive \citep{2004MNRAS.349..193S}.
 The minimum and maximum mean reddenings are given by the blue arrows. and they are nearly. parallel with the curves of constant racio Hux. so the individual stars do not. nec to be dereddened to get a rough estimate of their. racio Iluxes.," The minimum and maximum mean reddenings are given by the blue arrows, and they are nearly parallel with the curves of constant radio flux, so the individual stars do not need to be dereddened to get a rough estimate of their radio fluxes."
" The OCGLE-LL photometry database. (2?) contains about 21000 OGLE-LL bulge sources with ASc10 nJv a 10 Gilz and 85000 OCGLE-LL bulge sources with f,z10 nJv at 10 Cllz."," The OGLE-II photometry database \citep{2005AcA....55...43S,
 1997AcA....47..319U} contains about 21000 OGLE-II bulge sources with $\Delta f_\nu > 10$ nJy at 10 GHz and 85000 OGLE-II bulge sources with $f_\nu > 10$ nJy at 10 GHz."
 This should be compared. with the number of red chump. red. giants and. red. supergiants that ? used. to detect. microlensing events (1.084.267 stars): therefore. abou eight. percent of microlensing events may be detectable in the racio.," This should be compared with the number of red clump, red giants and red supergiants that \citet{2006ApJ...636..240S} used to detect microlensing events (1,084,267 stars); therefore, about eight percent of microlensing events may be detectable in the radio."
 Furthermore. if the lens is about an Earth mass within a few parsecs about two percent of the sources would vield a detectable oscillatory signal.," Furthermore, if the lens is about an Earth mass within a few parsecs about two percent of the sources would yield a detectable oscillatory signal."
 Only a handful of stars in the OGLE-IEL LAIC and SAIC fields are sullicicntly bright to vield a detectable radio source., Only a handful of stars in the OGLE-II LMC and SMC fields are sufficiently bright to yield a detectable radio source.
 Of course all of these estimates assume that the sources only emit essentially thermal radiation from near their optical photospheres., Of course all of these estimates assume that the sources only emit essentially thermal radiation from near their optical photospheres.
 In fact some fraction of the stars in the bulge and Magellanic Clouds. will be radio loud. but it will take an instrument with a sensitivity rivalling that of the SKA to determine their number: therefore. these estimates provide a moderately conservative lower limit on the number of expected radio sources in the bulge at this [lux density.," In fact some fraction of the stars in the bulge and Magellanic Clouds will be radio loud, but it will take an instrument with a sensitivity rivalling that of the SKA to determine their number; therefore, these estimates provide a moderately conservative lower limit on the number of expected radio sources in the bulge at this flux density."
 The optical lepth of a particular set. of. objects to nmücrolensing is proportional to their mass fraction: the area. subtended by the Einstein. radius of a particular lens 1s proportional to its mass. so the total area (and therefore optical depth) of a particular group of the lenses is proportional to their total mass.," The optical depth of a particular set of objects to microlensing is proportional to their mass fraction; the area subtended by the Einstein radius of a particular lens is proportional to its mass, so the total area (and therefore optical depth) of a particular group of the lenses is proportional to their total mass."
 A simple model is to assume that the density of lenses is constant oul to some maximal distance. vielding (2). (?)..," A simple model is to assume that the density of lenses is constant out to some maximal distance, yielding \citep{1998A&A...329..920C} \citep{2002ApJ...567..304C}."
Consider first the situation in which there are no systematic uncertainties and the inferred blackbody normalization from every spectrum reflects the apparent surface area of the entire neutron star.,Consider first the situation in which there are no systematic uncertainties and the inferred blackbody normalization from every spectrum reflects the apparent surface area of the entire neutron star.
" If this were the case, the intrinsic distribution of blackbody normalizations would be a delta function, while the observed distribution would be broader, with a width equal to the average formal uncertainties of the measurements."," If this were the case, the intrinsic distribution of blackbody normalizations would be a delta function, while the observed distribution would be broader, with a width equal to the average formal uncertainties of the measurements."
" In a more realistic situation, there is an intrinsic range of the inferred blackbody normalizations, caused by a combination of the various effects discussed earlier."," In a more realistic situation, there is an intrinsic range of the inferred blackbody normalizations, caused by a combination of the various effects discussed earlier."
" We assume that, in each flux bin, the intrinsic distribution of normalization values is the Gaussian where A; is its mean and oy is its standard deviation."," We assume that, in each flux bin, the intrinsic distribution of normalization values is the Gaussian where $A_{\rm int}$ is its mean and $\sigma_{\rm int}$ is its standard deviation."
 The observed distribution of blackbody normalizations will be again broader than the intrinsic distribution because of the formal uncertainties in each measurement., The observed distribution of blackbody normalizations will be again broader than the intrinsic distribution because of the formal uncertainties in each measurement.
" Moreover, at low flux levels, a small number of outliers exists, which skews and introduces tails to the observed distribution."," Moreover, at low flux levels, a small number of outliers exists, which skews and introduces tails to the observed distribution."
" Our goal here is to quantify the most probable value of the blackbody normalization, i.e., the parameter A; in the distribution (4)), as well as the intrinsic range of values in each flux bin, i.e., the parameter σε, while excluding the outliers."," Our goal here is to quantify the most probable value of the blackbody normalization, i.e., the parameter $A_{\rm int}$ in the distribution \ref{eq:int_dist}) ), as well as the intrinsic range of values in each flux bin, i.e., the parameter $\sigma_{\rm int}$, while excluding the outliers."
" When the inspection of an observed distribution requires an outlier detection scheme (as, e.g., in the lower right panels of Fig. 3)),"," When the inspection of an observed distribution requires an outlier detection scheme (as, e.g., in the lower right panels of Fig. \ref{fig:kt_flux_detail}) ),"
" we model the distribution of outliers by a similar Gaussian, i.e., with a mean Ag, and a standard deviation ooyz."," we model the distribution of outliers by a similar Gaussian, i.e., with a mean $A_{\rm out}$ and a standard deviation $\sigma_{\rm out}$."
" Our model distribution function is, therefore, in general the Gaussian mixture where 7 measures the relative fraction of outliers in our sample."," Our model distribution function is, therefore, in general the Gaussian mixture where $\eta$ measures the relative fraction of outliers in our sample."
 We are looking for the parameters in these distributions that maximize the posterior probability P(Aint;int;Aout; which measures the likelihood that a particular set of parameters is consistent with the data.," We are looking for the parameters in these distributions that maximize the posterior probability $P(A_{\rm int}, \sigma_{\rm int}, A_{\rm
out}, \sigma_{\rm out}\vert{\rm data})$, which measures the likelihood that a particular set of parameters is consistent with the data."
" Using Bayes' Couc|data),theorem, this probability distribution is where P(data|Aint,Cint,Aout;Tout,η) is the posterior probability that the particular set of normalization data have been measured for a given set of parameters and the last five terms are the prior probabilities for the model parameters; the constant C ensures that the probability density is normalized."," Using Bayes' theorem, this probability distribution is where $P({\rm data}\vert A_{\rm int}, \sigma_{\rm int}, A_{\rm out},
\sigma_{\rm out},\eta)$ is the posterior probability that the particular set of normalization data have been measured for a given set of parameters and the last five terms are the prior probabilities for the model parameters; the constant $C$ ensures that the probability density is normalized."
 We consider flat prior probability distribution for the central value of each Gaussian in an interval that extends beyond the observeda range of normalization values for each source., We consider a flat prior probability distribution for the central value of each Gaussian in an interval that extends beyond the observed range of normalization values for each source.
 We also consider flat prior probability distribution for the standard deviation for each Gaussian from 107? is practicallya to a value equal to the width of the range of normalizations., We also consider a flat prior probability distribution for the standard deviation for each Gaussian from $10^{-3}$ (km/10 $^2$ (which is practically zero) to a value equal to the width of the range of normalizations.
" Finally, we take a flat (km/10prior kpc)?distribution(which of 7 between zero)zero and one."," Finally, we take a flat prior distribution of $\eta$ between zero and one."
 Our results are extremely weakly dependent on the ranges of parameter values we considered., Our results are extremely weakly dependent on the ranges of parameter values we considered.
In addition. (he isotopomer fractionation of CCII might propagate to CCS through the following reactions (Yamada et al.,"In addition, the isotopomer fractionation of CCH might propagate to CCS through the following reactions (Yamada et al."
 2002): and In the reaction (7). the sulfur atom will attack (he end carbon atom of CCIL which has the unpaired electron. to form (he CCS structure (Yamada οἱ al.," 2002): and In the reaction (7), the sulfur atom will attack the end carbon atom of CCH, which has the unpaired electron, to form the CCS structure (Yamada et al."
 2002)., 2002).
 In the case of the sulfur ion. the reaction may occur in a similar way.," In the case of the sulfur ion, the reaction may occur in a similar way."
" So CCS is made [rom ΕΟΟ. and ""CCS OCSis made from[rom CPC CMCILwoughthrough tthese processes."," So $^{13}$ CS is made from $^{13}$ CCH, and $^{13}$ CCS is made from $^{13}$ CH through these processes."
 If tlthese processes are efficient.[I(LU the CCS ratio should be less than unity. given the CÉCIT/PCCLI ratio is greater than unity.," If these processes are efficient, the $^{13}$ $^{13}$ CCS ratio should be less than unity, given the $^{13}$ $^{13}$ CCH ratio is greater than unity."
 This is inconsistent with the observation: both the isotopomer ratios of CCIE and CCS are greater than unity., This is inconsistent with the observation: both the isotopomer ratios of CCH and CCS are greater than unity.
 Fractionation by isotoponier-exchange reactions is also possible: where AZ. the zero-point vibrational energy. difference of MCCIL and C4 CLL is 8.1 Ix (R. Tarroni. private communication; Tarroni Carter 2003).," Fractionation by isotopomer-exchange reactions is also possible: where $\Delta E$ , the zero-point vibrational energy difference of $^{13}$ CCH and $^{13}$ CH, is 8.1 K (R. Tarroni, private communication; Tarroni Carter 2003)."
 As a candidate of the, As a candidate of the
omceipal axis. and we defned the S-coordinate to e the projected angular position of the ealaxy along the assumed principal axis.,"principal axis, and we defined the -coordinate to be the projected angular position of the galaxy along the assumed principal axis."
 Furthermore. he Scoordinate was defined to run negative to ositive from West to East.," Furthermore, the -coordinate was defined to run negative to positive from West to East."
 A linear regression analysis was carried out between the redshitt ane he S-coordinate. which vields both the correlation cocfiicicnt.A. and the likelihood. that the nul ivpothesis correlation between redshift iux xojectedS position) is correct (Bevinetou 1969).," A linear regression analysis was carried out between the redshift and the -coordinate, which yields both the correlation coefficient, and the likelihood that the null hypothesis correlation between redshift and projected position) is correct (Bevington 1969)."
 We repeated the correlation analysis at increments in position angle (PA) of the assume omneipal axis over the full range., We repeated the correlation analysis at increments in position angle (PA) of the assumed principal axis over the full range.
 When the assumed principal axis ds running from SE to NW. positive values are in the NW.," When the assumed principal axis is running from SE to NW, positive values are in the NW."
 In the same wav. when the assumed principal axis is running from SW to NE. positiveS values in the NE.," In the same way, when the assumed principal axis is running from SW to NE, positive values in the NE."
 The correlation analysis was completed both for the 263 GdFE inter-chister ealaxies with redshifts between 17.000 and 22.500 and for the 21 clusters with mean redshifts over he same interval.," The correlation analysis was completed both for the 263 6dF inter-cluster galaxies with redshifts between 17,000 and 22,500 and for the 21 clusters with mean redshifts over the same interval."
 For both clusters and iuter-cluster galaxies. we find that the null hypothesis is rejected at xobabilitv (D) levels of P1%.," For both clusters and inter-cluster galaxies, we find that the null hypothesis is rejected at probability (P) levels of $<1\%$."
 At certain PAs. he plots of R versus PA show a broad peak over zu interval of 20L107.," At certain PAs, the plots of $R$ versus PA show a broad peak over an interval of 20."
". GAP ealaxies show the highest correlation coefficient (R= 0:3) aud lowest probability for the mull hypothesis (P710 "") ata PAS ({as measured East frou North).", 6dF galaxies show the highest correlation coefficient = 0.3) and lowest probability for the null hypothesis $<$ $^{-6}$ ) at a PA $\approx$ $-$ (as measured East from North).
 The clusters also show a significant correlation. with a peak at a PA ot 50°.," The clusters also show a significant correlation, with a peak at a PA of $-$."
 In Figure Ἐν we show the projected5 position plotted versus redshift for all iuter-cluster ealaxies aud clnstcas with redshift between 17.000 : uost22.5 a PA of SO.," In Figure \ref{f7}, we show the projected position plotted versus redshift for all inter-cluster galaxies and clusters with redshift between 17,000 and 22,500 at a PA of $-$."
. The expected cluster peculiar systematic velocities are suppressed for clarity of the inter-cluster galaxy distribution., The expected cluster peculiar velocities are suppressed for clarity of the inter-cluster galaxy distribution.
" The linear regression Bt for the inter-chuster galaxies is plotted as a sold Tine,", The linear regression fit for the inter-cluster galaxies is plotted as a solid line.
 Note that the best ft Tine actually yasses through a zone of low galaxy density: this is examined further in 8233.1., Note that the best fit line actually passes through a zone of low galaxy density; this is examined further in 3.4.
" Wo are now iu a to positionrevisit the substantial »pulatiou of salaxies from, 16.000. to 17.000L."," We are now in a position to revisit the substantial population of galaxies from 16,000 to 17,000."
 To determine whether or not these ealaxies are associated witli the larec-scale redshift rend. we repeat the correlation analysis as a ‘unction of PA now expanding the redshift range to 16.000 22.500f|.," To determine whether or not these galaxies are associated with the large-scale redshift trend, we repeat the correlation analysis as a function of PA now expanding the redshift range to 16,000 $-$ 22,500."
 When the galaxies between 16.000 and 17.000 aare included. the correlation coefficieut is weakened(R= 0.2). aud the probability of no correlation increases to PX LO.7.," When the galaxies between 16,000 and 17,000 are included, the correlation coefficient is weakened = 0.2), and the probability of no correlation increases to $\sim$ $^{-3}$."
 The deviation of the 16.000 17.000 eealaxies from the redshift trend is evident in their spatial segregatiou (especially in 6).," The deviation of the 16,000 $-$ 17,000 galaxies from the redshift trend is evident in their spatial segregation (especially in $\delta$ )."
 We display he spatial location of these galaxies on the sky iu Figure 8.. where the galaxies from 10.000 18.000 aare separated into 1000 sslices;," We display the spatial location of these galaxies on the sky in Figure \ref{f8}, where the galaxies from 16,000 18,000 are separated into 1000 slices."
" Although the galaxies from 16.000.— 17.000 oonlv represeut ~5% of the total population. the spatial segregation of this clump doces not follow he overall trend of the higher redshift ealaxies iu he TRS and provides a significant lever aru, by which the best fit correlation axis is altered."," Although the galaxies from 16,000 17,000 only represent $\sim$ of the total population, the spatial segregation of this clump does not follow the overall trend of the higher redshift galaxies in the HRS and provides a significant lever arm by which the best fit correlation axis is altered."
 Iu short. while the spatiallv-localized. galaxies from 16.000 117.000 nuuav reside within the TRS. they do not appear to follow the large-scale redshift treud established by the clusters aud iuter-cluster galaxies over the range 17.000 222.500*.," In short, while the spatially-localized galaxies from 16,000 17,000 may reside within the HRS, they do not appear to follow the large-scale redshift trend established by the clusters and inter-cluster galaxies over the range 17,000 22,500."
. As noted above. the bestlinear ft between projectedS coordinate aud redshift actually uus through a zoue of low galaxy deusity (Figure 7)).," As noted above, the bestlinear fit between projected coordinate and redshift actually runs through a zone of low galaxy density (Figure \ref{f7}) )."
 The implication is that the ITRS has a bi-modal redshift distribution. ie. the IIRS kinematic extent cousists of two major components in redshift.," The implication is that the HRS has a bi-modal redshift distribution, i.e., the HRS kinematic extent consists of two major components in redshift."
 The redshift bicmodality of the IRS is clearly observed by fitting aud⋅ removing the⋞⋯↸↧−−⋅⋅↗∩↸∏∖⋯↴∖ aat spatiabredshift treud at PA = 80 hen plotting the listogram of residual redshifts. as shown in Fieure 9..," The redshift bi-modality of the HRS is most clearly observed by fitting and removing the systematic spatial-redshift trend at PA $=-$, then plotting the histogram of residual redshifts, as shown in Figure \ref{f9}."
 Fitting cach componcut of he histogram with a Canssiau reveals that the overall umber of galaxies is roughly equal in the wo components. which are separated by ~2500 ((35 Mpc).," Fitting each component of the histogram with a Gaussian reveals that the overall number of galaxies is roughly equal in the two components, which are separated by $\sim$ 2500 (35 Mpc)."
" However. the FWIIM. of the hieher-redshift component (ie. corresponding to the galaxies with original redshift centered at ~21.000 j) is approximately twice as large as for the lower redshift compoucnt. 2200 aud 1100 respectively,"," However, the FWHM of the higher-redshift component (i.e., corresponding to the galaxies with original redshift centered at $\sim$ 21,000 ) is approximately twice as large as for the lower redshift component, 2200 and 1100 , respectively."
 Furthermore. the two components," Furthermore, the two components"
are spatially separated. with the ion emission associated with longer loops.,"are spatially separated, with the ion emission associated with longer loops."
 Miller.IEnislie.Brown(2004) concluded that these observations are consistent with the gvroresonance model of ion acceleration: as the loops grow longer. protons are more likely to reach speeds. and thus can be accelerated. by the magnetosonic waves.," \citet{Miller04} concluded that these observations are consistent with the gyroresonance model of ion acceleration; as the loops grow longer, protons are more likely to reach super-Alfv\'ennic speeds, and thus can be accelerated by the magnetosonic waves."
 This second phase of acceleration need not be gvroresonant., This second phase of acceleration need not be gyroresonant.
 While it appears promising. further study is required to determine if STFA models can accomodate these results.," While it appears promising, further study is required to determine if STFA models can accomodate these results."
 The strong dependence of the post-acceleration electron spectrum on the pitch angle scaltering agent is both a positive and negative feature., The strong dependence of the post-acceleration electron spectrum on the pitch angle scattering agent is both a positive and negative feature.
 It leaves STFA considerable flexibility in matching various characteristics of solar flare N-ravs. which [all outside of the simple scenario studied in this paper., It leaves STFA considerable flexibility in matching various characteristics of solar flare X-rays which fall outside of the simple scenario studied in this paper.
 For example. Linet.al.(1981). first. observed a superhot component in a solar flare. which has since been supported by RITESSI observations (2003).," For example, \citet{Lin81} first observed a superhot component in a solar flare, which has since been supported by RHESSI observations \citet{Krucker03}."
. This thermal. or nearly thermal. spectral component is seen at energies of up io 35keV. Within our STFA framework. the superhot emission can easily be explained bv an enhancement of pileh angle scattering at lower energies. either bv increased whistler wave turbulence. or some other scattering agent.," This thermal, or nearly thermal, spectral component is seen at energies of up to $35$ keV. Within our STFA framework, the superhot emission can easily be explained by an enhancement of pitch angle scattering at lower energies, either by increased whistler wave turbulence, or some other scattering agent."
 While this flexibility naturally allows [or the wide range of flare characteristics observed. it does not vel definitivelv solve the flare acceleration problem.," While this flexibility naturally allows for the wide range of flare characteristics observed, it does not yet definitively solve the flare acceleration problem."
 Instead. it shifts (he focus exclusively (o a well constrained. but largely unspecified. array of pilch angle scattering mechanisms.," Instead, it shifts the focus exclusively to a well constrained, but largely unspecified, array of pitch angle scattering mechanisms."
 This is the single greatest obstacle io STFA models of acceleration., This is the single greatest obstacle to STFA models of acceleration.
" In short. STFA can naturally account lor the thermal spectrum below 10keV. and somewhat less naturally for (he non-thermal spectrum between LOkeV and 100keV. There we have shown that A, must depend inversely on particle energy. in contrast to that of pitch angle scattering by whisUler waves below + LOkev. which is proportional to the particle energv."," In short, STFA can naturally account for the thermal spectrum below $10$ keV, and somewhat less naturally for the non-thermal spectrum between $10$ keV and $100$ keV. There we have shown that $\lambda_p$ must depend inversely on particle energy, in contrast to that of pitch angle scattering by whistler waves below $\backsim 10$ kev, which is proportional to the particle energy."
 Above LOOkeV. shock acceleration is a natural possibilitv: the needed injection of super-thermal electrons may be provided by STFA operating al energies below ££.," Above $100$ keV, shock acceleration is a natural possibility; the needed injection of super-thermal electrons may be provided by STFA operating at energies below $E_{br}$."
 The knee at LOOkeV remains the most difficult spectral feature to accommodate. and we have explained the difficult requirements to pitch angle scattering that this demands.," The knee at $100$ keV remains the most difficult spectral feature to accommodate, and we have explained the difficult requirements to pitch angle scattering that this demands."
 E.B. thanks B. Chandran for discussions., E.B. thanks B. Chandran for discussions.
 We thank J. Maron for sharing (he results of his simulations and acknowledge support from DOE grant DE-EGO02-00EBR54600 and the Laboratory for Laser Enereetics at (he University of Rochester., We thank J. Maron for sharing the results of his simulations and acknowledge support from DOE grant DE-FG02-00ER54600 and the Laboratory for Laser Energetics at the University of Rochester.
 RS acknowledges support from the DOE Lorton Fellowship., RS acknowldges support from the DOE Horton Fellowship.
 We also acknowledge the insighthu critique and comments of ihe reviewer., We also acknowledge the insightful critique and comments of the reviewer.
where Py denotesdissipation.. QzzOy a meau orbital. angular frequencyJ and 7=ÀA7fz79oe? denotes the torque ou the outer [ace of the torus.,"where $P_{d}$ denotesdissipation, $\Omega\approx\Omega_K$ a mean orbital angular frequency and $\tau_-=A^2f_w^2\Omega_-$ denotes the torque on the outer face of the torus."
 The net magnetic flux 274 supported by the torus will partially connect to the black bole and to infinity. respectively. with fractions fj; and fie.," The net magnetic flux $2\pi A$ supported by the torus will partially connect to the black hole and to infinity, respectively, with fractions $f_H$ and $f_w$."
 Thus. Axab<By> in terms of the average poloidal component By in the torus.," Thus, $A\approx ab <B_\theta>$ in terms of the average poloidal component $B_\theta$ in the torus."
 Generally. futfe=1/2— Lwith fux(May [or a slender torus.," Generally, $f_H+f_w={1}/{2}~-~1$ with $f_H\propto (M/a)^2$ for a slender torus."
 A remainder 1—fy;fy. is inactive in losed field-lines (with Dirichlet-Dirichlet bouudary coucditious) between the iuuer light surface aud the outer Leht cylinder. attached to each face as toroidal “bags.”," A remainder $1-f_H-f_w$ is inactive in closed field-lines (with Dirichlet-Dirichlet boundary conditions) between the inner light surface and the outer light cylinder, attached to each face as toroidal “bags."""
 Note that for small dillerential tation. we have (Onitug+Pa/OQntrad5(OQ7-ὉOne—)&2. in which limit tlT elliciency of the radiation is 50%.," Note that for small differential rotation, we have $(\Omega_K\tau_{rad}+P_{d})/{\Omega_K\tau_{rad}}
\approx({\Omega_+\tau_+-\Omega_-\tau_-})/\Omega_K({\tau_+-\tau_-})
\approx 2,$ in which limit the efficiency of the radiation is $50\%$."
" We shall assume that the coupling between the two [aces is dominated by maguetobycdrodyuamical stresses. cue to radial components B, of the maguetic Held."," We shall assume that the coupling between the two faces is dominated by magnetohydrodynamical stresses, due to radial components $B_r$ of the magnetic field."
 These stresses are dissipative. by Olunic heating aud magnuetic reconnection.," These stresses are dissipative, by Ohmic heating and magnetic reconnection."
 This will heat the torus. which brings about thermal and. possibly. ueutrino emission.," This will heat the torus, which brings about thermal and, possibly, neutrino emission."
" By clitmeusioual analysis where the second equation denotes the root-mean-square of the radial [lux averaged over the ---uerlace between the two [aces with contact area πα, ", By dimensional analysis where the second equation denotes the root-mean-square of the radial flux averaged over the interface between the two faces with contact area $2\pi a h$.
While the angular momeutuni transport ---1 the shear layer about this. interface.+ is. mediated. by <5;>>? (he angular momentum transport from the black hole to the torus is meciatec by the average <By>.," While the angular momentum transport in the shear layer about this interface is mediated by $<B_r^2>^{1/2}$, the angular momentum transport from the black hole to the torus is mediated by the average $<B_\theta>$."
 The first comprises the spectral ensity average over all azimuthal quantum uumbers 75. whereas the second ouly involves ni=0.," The first comprises the spectral density average over all azimuthal quantum numbers $m$, whereas the second only involves $m=0$."
" Iudeed. the net flux through the black hole is generated by the corotiug horizou charge q2z«B,>J iu magnetostatic equilibrium with the meau external poloidal magnetic field (Wald1971:DokuchaeyLOST:vanPutten20JOb:Leeetal. 2001)."," Indeed, the net flux through the black hole is generated by the coroting horizon charge $q\approx <B_n>J$ in magnetostatic equilibrium with the mean external poloidal magnetic field \citep{wal74,dok87,mvp00b,lee01}."
. This averaging process is due to the no-hiair theorem., This averaging process is due to the no-hair theorem.
 While the exact ratio depends on the details of the magnetohydrodyuamuic turbulence in the torus. a conservative estimate is that αρ is about the square root of the number of azimuthal modes iu the approximately uniform iufrared spectrum. which should reach up to the first geometrical break atm—fafb. ies. Ap/A/zm(afb)> 7.," While the exact ratio depends on the details of the magnetohydrodynamic turbulence in the torus, a conservative estimate is that $A_r/A$ is about the square root of the number of azimuthal modes in the approximately uniform infrared spectrum, which should reach up to the first geometrical break at $m=a/b$, i.e.: $A_r/A\approx (a/b)^{1/2}$ ."
" Thus. substitution. ofJ the first. into. the second ofJ the stationary"" couditious (3)) gives rise to a positive luminosity iu view oL OQ.z2 OO.-Qzz(9/2)(6/0) aud f<1."," Thus, substitution of the first into the second of the stationary conditions \ref{EQN_B}) ) gives rise to a positive luminosity in view of $\Omega_-\approx \Omega$, $\Omega_+-\Omega_-\approx (3/2)(b/a)\Omega$ and $f_w<1$."
 The first equation of (3)) now reduces to οΟμzi[5/3. With Q=ML2qp? and fux∣∕(M/ay. (his⋅ shows that exΑΟ. −⊳⊋⇁⊳↗⋅Le. the racius of the torus decreases as the black hole spius-dowu.," The first equation of \ref{EQN_B}) ) now reduces to $\Omega/\Omega_H\approx f_H^2/3.$ With $\Omega\approx M^{1/2}/R^{3/2}$ and $f_H\propto (M/a)^2$, this shows that $R\propto M^{7/5}\Omega_H^{2/5}$, i.e., the radius of the torus decreases as the black hole spins-down."
 This defines a horizontal brauch of the frequency dynamics in the f(P)-diagram (vaiPuttenandSarkar2000)., This defines a horizontal branch of the frequency dynamics in the $\dot{f}(f)-$ diagram \citep{mvp00d}.
.. At twice the Wepleriat frequency of the torus. this produces ai observed gravitational wave-frequency of about for canonical CRB values for a black hole-torus system at redshift z.," At twice the Keplerian frequency of the torus, this produces an observed gravitational wave-frequency of about for canonical GRB values for a black hole-torus system at redshift $z$ ."
 If the torus is unstable against breaking up in clumps. or if the torus shows violent expansions in its mean radius. the gravitationa waveswill be episodical. and will correlate with sub-bursts in long GRBs.," If the torus is unstable against breaking up in clumps, or if the torus shows violent expansions in its mean radius, the gravitational waveswill be episodical, and will correlate with sub-bursts in long GRBs."
"in the cluster core, the lifetime of these streams is short and they mix away to continually build M87's extended envelope and Virgo’s intracluster light.","in the cluster core, the lifetime of these streams is short and they mix away to continually build M87's extended envelope and Virgo's intracluster light."
" The combination of M86’s high velocity and its passage through the cluster core makes it difficult to develop or retain very extended streams; instead, it possesses a system of small tidal streams much closer to the galaxy than seen in M87."," The combination of M86's high velocity and its passage through the cluster core makes it difficult to develop or retain very extended streams; instead, it possesses a system of small tidal streams much closer to the galaxy than seen in M87."
" The lack of tidal structures around M84 may be due toa possible recent passage through the cluster core, or M84 may simply have not experienced much recent accretion."," The lack of tidal structures around M84 may be due to a possible recent passage through the cluster core, or M84 may simply have not experienced much recent accretion."
" In contrast, both M49 and M89 display extended (r~50—100 shell systems, arguing that they have not experienced kpc)the strong tidal forces of the Virgo cluster core in the past Gyr or so."," In contrast, both M49 and M89 display extended $r \sim 50-100$ kpc) shell systems, arguing that they have not experienced the strong tidal forces of the Virgo cluster core in the past Gyr or so."
" As the most luminous galaxy in the Virgo Southern Extension, it may be the dominant galaxy of group falling into the Virgo cluster for the first time, and its shell system reflects its own accretion of a smaller satellite on a radial orbit."," As the most luminous galaxy in the Virgo Southern Extension, it may be the dominant galaxy of group falling into the Virgo cluster for the first time, and its shell system reflects its own accretion of a smaller satellite on a radial orbit."
" As M49 falls into Virgo, its shell system will be disrupted and incorporated into the general ICL of the cluster."," As M49 falls into Virgo, its shell system will be disrupted and incorporated into the general ICL of the cluster."
" The complexity of M89’s shell system argues not for an individual accretion event, but rather for multiple satellite accretions or a major merger in its past."," The complexity of M89's shell system argues not for an individual accretion event, but rather for multiple satellite accretions or a major merger in its past."
" Its system of tails, plumes, and shells will likely also be dispersed into Virgo’s extended ICL as the galaxy orbits within the cluster environment."," Its system of tails, plumes, and shells will likely also be dispersed into Virgo's extended ICL as the galaxy orbits within the cluster environment."
" Ultimately, however, morphology alone contains only limited information."," Ultimately, however, morphology alone contains only limited information."
 A better understanding of these features and how they relate to the dynamical history of Virgo and its galaxies would come through studies of their kinematics and stellar populations., A better understanding of these features and how they relate to the dynamical history of Virgo and its galaxies would come through studies of their kinematics and stellar populations.
" Kinematic information can come from identification and follow-up spectroscopy of planetary nebulae Arnaboldi 2004, Doherty 2009) and globular clusters Cotté 2003; Hwang 2008; Lee 2010) associated with the streams, while stellar populations can be studied using deep multiband surface photometry (Rudick 2010) orTelescope imaging of resolved stars in the streams Williams 2007)."," Kinematic information can come from identification and follow-up spectroscopy of planetary nebulae Arnaboldi 2004, Doherty 2009) and globular clusters Côtté 2003; Hwang 2008; Lee 2010) associated with the streams, while stellar populations can be studied using deep multiband surface photometry (Rudick 2010) or imaging of resolved stars in the streams Williams 2007)."
 Such studies would give an integrated picture of the accretion and stripping processes at work in the Virgo Cluster., Such studies would give an integrated picture of the accretion and stripping processes at work in the Virgo Cluster.
" We thank Charley Knox for his tireless work on the mechanical, optical, and electronic support of the Burrell Schmidt."," We thank Charley Knox for his tireless work on the mechanical, optical, and electronic support of the Burrell Schmidt."
" Over the course of this project, JCM has been supported by the NSF through grants AST-9876143, ASTR-0607526, and AST-0707793, as well as by Research Corporation through a Cottrell Scholarship."," Over the course of this project, JCM has been supported by the NSF through grants AST-9876143, ASTR-0607526, and AST-0707793, as well as by Research Corporation through a Cottrell Scholarship."
 CR was supported for part of this work by the Jason J. Nassau Graduate Fellowship fund., CR was supported for part of this work by the Jason J. Nassau Graduate Fellowship fund.
ECGs are showing that local and. early. EPCs populations differ not only for the racial colour variations. but that the whole picture is more complex than the homogeneous one hypothesized from studies of local {οας.,"ETGs are showing that local and early ETGs populations differ not only for the radial colour variations, but that the whole picture is more complex than the homogeneous one hypothesized from studies of local ETGs."
 Reeent observations (77) have shown that at 2 (l<z «2) when the Universe was only 3-4 Cr old. IZICs (hereafter we sav compact) with elfective radius 2-3 times smaller than that ofa typical present-day EIC. coexist with a majority of early-type galaxies whose dimensions are similar to those of local ETGs (we sav normal).," Recent observations \citep{saracco09,mancini10} have shown that at $z$ $<z<$ 2), when the Universe was only 3-4 Gyr old, ETGs (hereafter we say compact) with effective radius 2-3 times smaller than that of a typical present-day ETG coexist with a majority of early-type galaxies whose dimensions are similar to those of local ETGs (we say normal)."
 The only attempt to measure the velocity dispersion of a high-z (2:—2.186) compact IZE€: (7) has resulted. in a σ value of L6557' suggesting. in. these galaxies. a denser distribution. of stellar mass than in normal EPCs.," The only attempt to measure the velocity dispersion of a $z$ $z$ =2.186) compact ETG \citep{vandokkum09}
 has resulted in a $\sigma$ value of $^{+165}_{-95}$ suggesting in these galaxies a denser distribution of stellar mass than in normal ETGs."
 At the same time. the few estimates of velocity clispersions recovered for normal high-z ECGs confirmed their similarity with local populations even or stellar mass density (222)..," At the same time, the few estimates of velocity dispersions recovered for normal $z$ ETGs confirmed their similarity with local populations even for stellar mass density \citep{cenarro09,cappellari09,onodera10}."
 Phese findings point out that he wav in which the stellar mass was accreted on ETCGs in he first 3-4 Gwe. is not univocal for the whole population. rut on the contrary. the differences both in dimension and in structure of compact and normal high-z Γι» suggest hat they underwent dillerent scenarios of formation and/or early evolution (?)..," These findings point out that the way in which the stellar mass was accreted on ETGs in the first 3-4 Gyr, is not univocal for the whole population, but on the contrary, the differences both in dimension and in structure of compact and normal $z$ ETGs suggest that they underwent different scenarios of formation and/or early evolution \citep{saracco10}."
 Aloreover. the compact. EPCs. at first sight. seemed to » very rare in the local Universe (??) and this evidence corroborates the idea that compact ancl normal galaxies should have cilferent mass assembly histories even in the ollowing 9-10 Cover.," Moreover, the compact ETGs, at first sight, seemed to be very rare in the local Universe \citep{shen03,trujillo09} and this evidence corroborates the idea that compact and normal galaxies should have different mass assembly histories even in the following 9-10 Gyr."
 Indeed. dillerentIy from normal galaxies. compact ERGs should undergo a size evolution to reconcile hem with the local dimension of a typical local ECs.," Indeed, differently from normal galaxies, compact ETGs should undergo a size evolution to reconcile them with the local dimension of a typical local ETGs."
" Alany scenarios were proposed to match the size/densitv of igh-z and local EVGs e.g. non dissipativo ""drv merger. aciabatic expansion. age/colour gradient. (22??7).."," Many scenarios were proposed to match the size/density of $z$ and local ETGs e.g. non dissipative “dry” merger, adiabatic expansion, age/colour gradient \citep{boylan06,naab09,fan08,damjanov09,labarbera09}."
 Amone hese. wide credit is given to the merger hypothesis (77) even if no result is still conclusive. (?)..," Among these, wide credit is given to the merger hypothesis \citep{naab09,hopkins10}
 even if no result is still conclusive \citep{nipoti09}."
 Additionally. in the last vear. a new hypothesis is rising beside these scenarios.," Additionally, in the last year, a new hypothesis is rising beside these scenarios."
 Indeed. compact galaxies with masses ancl radii comparable with thosefound at. high-z are now detected x»h in local and intermediate galaxy. clusters (22). as well as in the field. (?) and the number density. of compact ealaxies in local clusters turns out to be consistent with he one measured at high-z (2)..," Indeed, compact galaxies with masses and radii comparable with thosefound at $z$ are now detected both in local and intermediate galaxy clusters \citep{valentinuzzi10,valentinuzzi10b} as well as in the field \citep{stockton10} and the number density of compact galaxies in local clusters turns out to be consistent with the one measured at $z$ \citep{saracco10}."
 This unexpected results rave shaken the previous belief. whereby. compact galaxies were physical systems. confined to the early. Universe. and hat they must subsequently undergo an apparent or real size evolution., This unexpected results have shaken the previous belief whereby compact galaxies were physical systems confined to the early Universe and that they must subsequently undergo an apparent or real size evolution.
 Indeed. the recent observations have shown hat even the local population of IZICis is composed. as in the early Universe. by normal galaxies which obey the well studied scaling relation and by a fraction of compact ealaxies that. with their small radius. and enhanced stellar mass density fall out of any correlations.," Indeed, the recent observations have shown that even the local population of ETGs is composed, as in the early Universe, by normal galaxies which obey the well studied scaling relation and by a fraction of compact galaxies that, with their small radius, and enhanced stellar mass density fall out of any correlations."
 From these observations. it is clear that to gain insight in the complex picture of EECis formation and evolution. it is necessary to individually define the mass assembly. paths ollowed by both normal and compact LLCs.," From these observations, it is clear that to gain insight in the complex picture of ETGs formation and evolution, it is necessary to individually define the mass assembly paths followed by both normal and compact ETGs."
 Fo address this opic it turns out to be fruitful to studs the evolution of the stellar content of both compact and normal galaxies from he carly Universe until the present day. ancl investigate if any dillerence occurs.," To address this topic it turns out to be fruitful to study the evolution of the stellar content of both compact and normal galaxies from the early Universe until the present day, and investigate if any difference occurs."
 To this aim. in this paper we present he study of colour gradients for a composite sample of both compact and normal high-z. ERGs.," To this aim, in this paper we present the study of colour gradients for a composite sample of both compact and normal $z$ ETGs."
 This work ascertains he feasibility of this analysis even for high-z ΙΓ... and provides us the first direct information on the distribution of the stellar content in the first stages of their life.," This work ascertains the feasibility of this analysis even for $z$ ETGs, and provides us the first direct information on the distribution of the stellar content in the first stages of their life."
 In Section 2. we present our sample. and in Section 3 we describe the methods used to derive colour gradients for high-z EPCs.," In Section 2, we present our sample, and in Section 3 we describe the methods used to derive colour gradients for $z$ ETGs."
 In Section 4 we show our results and in Section 5 we present our conclusions., In Section 4 we show our results and in Section 5 we present our conclusions.
" Throughout this paper we adopt a standard cosmology with Ln 3 [0 0,2200.3 and fy—— 00.7."," Throughout this paper we adopt a standard cosmology with $_{0}$ $^{-1}$ $^{-1}$, $\Omega_{m}$ 0.3 and $\Omega_{\Lambda}$ 0.7."
 All the magnitudes are in AB system., All the magnitudes are in AB system.
 An exhaustive study of the colour gradients in high-z IZICis until now has been severely. [limited by many factors such as the lack of spectroscopic redshifts. of a morphological classification. ancl of images with high resolution and signal to noise.," An exhaustive study of the colour gradients in $z$ ETGs until now has been severely limited by many factors such as the lack of spectroscopic redshifts, of a morphological classification, and of images with high resolution and signal to noise."
 Indeed. in the redshift range we are interested. in (1«z«2). the redshift estimates are strictly. compromised by the lack of prominent features in the optical spectra. and as pointed out by νι à reduced S/N can alfect the estimate of the effective radius due to the lack of possible peripheral structures with low surface brightness such as wings or halos.," Indeed, in the redshift range we are interested in $<z<$ 2), the redshift estimates are strictly compromised by the lack of prominent features in the optical spectra, and as pointed out by \citet{mancini10}, a reduced S/N can affect the estimate of the effective radius due to the lack of possible peripheral structures with low surface brightness such as wings or halos."
 In fact. the minimum spatial resolution and the signal-to-noise ratio necessary to properly model the light profiles roni at least the first central kpe to regions beyond. the effective radius. is achievable only with deep space-based imaging.," In fact, the minimum spatial resolution and the signal-to-noise ratio necessary to properly model the light profiles from at least the first central kpc to regions beyond the effective radius, is achievable only with deep space-based imaging."
 Vill now. these constrains have stronely limited he collection of a representative sample able το acdress his topic from the already meagre observations. available or high-z ETCs.," Till now, these constrains have strongly limited the collection of a representative sample able to address this topic from the already meagre observations available for $z$ ETGs."
 We collected a sample o£ 20 EPCs at 0:9zi«1.92 st suited for our purpose (see below). extracted from the complete sample of 34 ETCGs selected from the southern field of the Great Observatories Origins Deep Survey South v2: Ciavalisco et al. 2))," We collected a sample of 20 ETGs at $<z_{spec}<$ 1.92 best suited for our purpose (see below), extracted from the complete sample of 34 ETGs selected from the southern field of the Great Observatories Origins Deep Survey (GOODS-South v2; Giavalisco et al. \citeyear{giavalisco04}) )"
 by 2.., by \citet{saracco10}. .
 Phe survey provides each galaxy both with deep. LIST-ACS imaging in four bands. (P435\W. P606. FT75W and. FSSOLP) and with spectroscopic redshift (Vanzella et al.," The survey provides each galaxy both with deep HST-ACS imaging in four bands (F435W, F606W, F775W and F850LP) and with spectroscopic redshift (Vanzella et al."
 2? and. references therein)., \citeyear{vanzella08} and references therein).
" In addition. surface brightness parameters in the FS50LP band. age and stellar mass AI, derived. in an homogeneous wax for the whole sample are available."," In addition, surface brightness parameters in the F850LP band, age and stellar mass $_{\star}$ derived in an homogeneous way for the whole sample are available."
 For more details on the selection criteria. morphological classification. stellar mass and age estimations of the original complete sample. see ?. and references therein.," For more details on the selection criteria, morphological classification, stellar mass and age estimations of the original complete sample, see \citet{saracco10} and references therein."
 Among the four bands at our disposal. we opted to measure the IF606W-FS50LP colour variations corresponding approximatively to UV-U.— colour in the rest-frame in order to obtain a compromise between. the wavelength baseline covered and the S/N achieved.," Among the four bands at our disposal, we opted to measure the F606W-F850LP colour variations corresponding approximatively to UV-U colour in the rest-frame in order to obtain a compromise between the wavelength baseline covered and the S/N achieved."
 Actually. the E453W. images have à S/N ~ 2 times lower than that of FGOGW images. and this would have prevented us from a reliable analysis of the surface brightness parameters for most of the sample.," Actually, the F453W images have a S/N $\sim$ 2 times lower than that of F606W images, and this would have prevented us from a reliable analysis of the surface brightness parameters for most of the sample."
 Erom the original sample of 34 EPCs. we removed 3 galaxies showing X-ray emission and 11 ealaxies showing anomalies in the analysis of the FGOGW-band images.," From the original sample of 34 ETGs, we removed 3 galaxies showing X-ray emission and 11 galaxies showing anomalies in the analysis of the F606W-band images."
 In particular. these comprise 6 galaxies whose fitting light profile does not reproduce the observed. ones. that is showing significant residuals in the residual maps. and 5 galaxies whose S/N wastoo low to derive their surface brightness profile out to It.," In particular, these comprise 6 galaxies whose fitting light profile does not reproduce the observed ones, that is showing significant residuals in the residual maps, and 5 galaxies whose S/N wastoo low to derive their surface brightness profile out to $_e$ ."
 For the remaining 20 galaxies. the EWIIM. of ~ 0.17 of both F606W- and," For the remaining 20 galaxies, the FWHM of $\sim$ 0.1"" of both F606W- and"
models described in 522.3.,"models described in 2,3."
 The «quantities required for the burst caleulations are the ones shown in Figs., The quantities required for the burst calculations are the ones shown in Figs.
" 2. 3. namely the radius of the gas sphere Πρ. the surface gravity. g. the redshift z(£2,). and the accretion efficiency η,"," 2, 3, namely the radius of the gas sphere $R_g$, the surface gravity $g$, the redshift $z(R_g)$, and the accretion efficiency $\eta$."
 With this information. it is straightforward (0 take any. given model of a fermion-fermion or boson-fermion star. assume a local surface mass accretion rate X (barvonic mass added per unil area per unit lime as measured in the local frame at the surface of (he gas sphere). and compute the (hermonuclear stability of (he accretion laver.," With this information, it is straightforward to take any given model of a fermion-fermion or boson-fermion star, assume a local surface mass accretion rate $\dot \Sigma$ (baryonic mass added per unit area per unit time as measured in the local frame at the surface of the gas sphere), and compute the thermonuclear stability of the accretion layer."
 The (wo top panels in Fig., The two top panels in Fig.
 6 show the results for the fermion-lernion star models described in 822 and the two bottom panels correspond to the boson-fermion models described in 833., 6 show the results for the fermion-fermion star models described in 2 and the two bottom panels correspond to the boson-fermion models described in 3.
 In each panel. (he horizontal axis gives (he accretion huminosity in Eddington units. where μμ is defined at infinity for the total mass of the star: wilh. &=0.4engL71 (correspondingn to electron scattering. in. fullyB ionized. hydrogen).," In each panel, the horizontal axis gives the accretion luminosity in Eddington units, where $L_{\rm Edd}$ is defined at infinity for the total mass of the star: with $\kappa =0.4 ~{\rm cm^2g^{-1}}$ (corresponding to electron scattering in fully ionized hydrogen)."
x The vertical axis extends over the [ull range of gas mass (hat we have considered in the hybrid models., The vertical axis extends over the full range of gas mass that we have considered in the hybrid models.
 The symbols (filled and open circles) in the panels correspond to mo«clels (hat are predicted (o exhibit bursts and the empty spaces to models that are. predicted not to have bursts., The symbols (filled and open circles) in the panels correspond to models that are predicted to exhibit bursts and the empty spaces to models that are predicted not to have bursts.
 We see that there is a considerable range of accretion rate for which the svstems will produce bursts., We see that there is a considerable range of accretion rate for which the systems will produce bursts.
 Therefore. (he absence of bursts in DIICs argues against such a bybricl model for DIICs.," Therefore, the absence of bursts in BHCs argues against such a hybrid model for BHCs."
 A comparison of Figs., A comparison of Figs.
 4 and 6 shows that bursts occur in. fermion-fermion and boson-fermion mocdels for lower accretion rates compared to DIIC: models with hard surfaces., 4 and 6 shows that bursts occur in fermion-fermion and boson-fermion models for lower accretion rates compared to BHC models with hard surfaces.
 This dillerence has an interesting explanation., This difference has an interesting explanation.
 Recall that the Eddineton luminosity was defined with respect to the total mass of the hybrid star. which is the obvious choice for an observer at infinity.," Recall that the Eddington luminosity was defined with respect to the total mass of the hybrid star, which is the obvious choice for an observer at infinity."
 However. (he accretion and burst physics occur on the surface of the gas sphere which lies well within the dark matter sphere.," However, the accretion and burst physics occur on the surface of the gas sphere which lies well within the dark matter sphere."
 Here. the local Eddington Iuminosity is given by Lictdeas=AxRicg/n. which is different [rom the L4 defined earlier.," Here, the local Eddington luminosity is given by $L_{\rm Edd,gas}=4\pi R_g^2 cg/\kappa$, which is different from the $L_{\rm Edd}$ defined earlier."
 Redshilting {his Iuminositv {ο the observer al infinity gives which is (he physically correct luminosity (0 use as the scale when analvsing bursts from these objects., Redshifting this luminosity to the observer at infinity gives which is the physically correct luminosity to use as the scale when analysing bursts from these objects.
 We find that all the models we have analysed are unstable for all accretion rates up to the local Edclington limit., We find that all the models we have analysed are unstable for all accretion rates up to the local Eddington limit.
 Such models are shown by (he solid circles in Fig., Such models are shown by the solid circles in Fig.
 6., 6.
 In fact. the models are generally unstable even for slightly super-Eddineton local accretion rates. as shown by (he open circles.," In fact, the models are generally unstable even for slightly super-Eddington local accretion rates, as shown by the open circles."
he CETL frames consist of 1024 024 pixels. with a pixel size of 0.0909 arc seconds.,"the UFTI frames consist of 1024 $\times$ 1024 pixels, with a pixel size of 0.0909 arc seconds."
 The Drs. narrow filter is centred on the wavelength of the Bes line (2.166 micron: of the ight was obtained in the wavelength range 2.1512.171 jun in case of HCAMA. observations. and in the range 2.1552.177 pm in case of ΕΙΤΙ observations).," The $\gamma$ narrow filter is centred on the wavelength of the $\gamma$ line (2.166 micron; of the light was obtained in the wavelength range 2.151–2.171 $\mu$ m in case of IRCAM3 observations, and in the range 2.155--2.177 $\mu$ m in case of UFTI observations)."
 Phe night was xhotometric only during the 1999. May 23 observations.," The night was photometric only during the 1999, May 23 observations."
 The exposure time used in the Bre filter was 100 seconds. and in the HE and Ex filter band a LO second exposure was used.," The exposure time used in the $\gamma$ filter was 100 seconds, and in the H and K filter band a 10 second exposure was used."
 On 1999. October 13 an observation time of LOO seconds was used in the Ix. band.," On 1999, October 13 an observation time of 100 seconds was used in the K band."
 All images were dark subtracted., All images were dark subtracted.
 Five (or three in case of the 1999. October 13 observations) citheree Li frames were used. to calculate a sky. image.," Five (or three in case of the 1999, October 13 observations) dithered IR frames were used to calculate a sky image."
 This. dark. subtracted sky image was subtracted from the dark subtracted image after scaling it to the object image level., This dark subtracted sky image was subtracted from the dark subtracted image after scaling it to the object image level.
 The resulting images were IHatfielded. where the Datfield image was obtained by normalizing the combined five (or three) dithered images.," The resulting images were flatfielded, where the flatfield image was obtained by normalizing the combined five (or three) dithered images."
 The reduced images were aligned and combined., The reduced images were aligned and combined.
 In Fig. 1..," In Fig. \ref{finding_chart},"
 we show the observed field in both the Ix and L filter bands., we show the observed field in both the K and H filter bands.
 Clearly visible is that objects 502 and 513. which were blended in the images of Navlor et al. (," Clearly visible is that objects 502 and 513, which were blended in the images of Naylor et al. ("
1991). are resolved into two separate stars.,"1991), are resolved into two separate stars."
 We used three reference stars in the field (503. 507. 512 in the images of Navlor et al.," We used three reference stars in the field (503, 507, 512 in the images of Naylor et al."
 1991. see Fig. 1))," 1991, see Fig. \ref{finding_chart}) )"
 to obtain differential magnitudes of the counterpart., to obtain differential magnitudes of the counterpart.
 These stars were calibrated. by observing the standard star LID 161903 on 1999. May 23.," These stars were calibrated by observing the standard star HD 161903 on 1999, May 23."
 To obtain the dillerential magnitudes. we used the point spreacl fitting (psf) routine to both the reference and object stars using the DoPLLOT package (Schechter. Alateo. Saha 1993).," To obtain the differential magnitudes, we used the point spread fitting (psf) routine to both the reference and object stars using the DoPHOT package (Schechter, Mateo, Saha 1993)."
 The magnitudes derived in this way did not cilfer significantly from the magnitudes: derived using aperture photometry., The magnitudes derived in this way did not differ significantly from the magnitudes derived using aperture photometry.
 We corrected the magnituces or the airmass dependent atmospheric extinction in the LL and Ix band., We corrected the magnitudes for the airmass dependent atmospheric extinction in the H and K band.
 The magnitudes we derived in the HL and [x mands are listed in Table 2.., The magnitudes we derived in the H and K bands are listed in Table \ref{mags}.
 We seached for variability on imescales of £;10 minutes and in between the observations. rut no significant variability was observed. in any of the stars listed in Table 2..," We seached for variability on timescales of $\la10$ minutes and in between the observations, but no significant variability was observed in any of the stars listed in Table \ref{mags}."
 We determined an upper limit on photometric variability on timescales of <10 minutes of 0.6 =magnitudes in the LE and Ix. band., We determined an upper limit on photometric variability on timescales of $\la10$ minutes of 0.6 magnitudes in the H and K band.
 In Table 2) we also List 1ο flux densities obtained in the Ll ancl [x filter bands. as well as the Bre Ix instrumental magnitude cillerence.," In Table \ref{mags} we also list the flux densities obtained in the H and K filter bands, as well as the $\gamma$ –K instrumental magnitude difference."
 No μαancard magnitude in the Bre filter is known for the star LID 161903. therefore we could only caleulate instrumental magnitudes in this band.," No standard magnitude in the $\gamma$ filter is known for the star HD 161903, therefore we could only calculate instrumental magnitudes in this band."
 Accretion disks are known to sometimes produce M emission lines (eg., Accretion disks are known to sometimes produce $\gamma$ emission lines (eg.
 Bandyopadhyay et al., Bandyopadhyay et al.
 1997:1999)., 1997;1999).
 Therefore. if à strong Bre emission line is present in the accretion disk of GX 51 the counterpart could. appear brighter in this filter.," Therefore, if a strong $\gamma$ emission line is present in the accretion disk of GX 5–1 the counterpart could appear brighter in this filter."
 We compared the instrumental Bro Ix colour of the stars 502. 513. ancl our reference stars (503. 507. and 512): these are also listect in Table 2.," We compared the instrumental $\gamma$ --K colour of the stars 502, 513, and our reference stars (503, 507, and 512); these are also listed in Table 2."
 Star 513 seems to have a smaller instrumental Bree Ix. colour. although the clleet is only marginally detected.," Star 513 seems to have a smaller instrumental $\gamma$ –K colour, although the effect is only marginally detected."
 We also checked for variability in the Bre band. but no significant variability was found on timescales of minutes with an upper limit of 0.435 magnitude.," We also checked for variability in the $\gamma$ band, but no significant variability was found on timescales of minutes with an upper limit of 0.45 magnitude."
 We used the higher. resolution ΕΤ images. obtained on 1999. October S for our astrometry.," We used the higher resolution UFTI images obtained on 1999, October 8 for our astrometry."
 ‘Vo define astrometric solutions for the It frames we used. secondary astrometric standards derived from: United. Ixingdom Schmidt photographic5 plate material measured. using5 the precision microdensitometer SuperCOSMOS (eg., To define astrometric solutions for the IR frames we used secondary astrometric standards derived from United Kingdom Schmidt photographic plate material measured using the precision microdensitometer SuperCOSMOS (eg.
 Hambly et, Hambly et
(1983)... we determine the core temperature ως via Che equation We then compare Zour to 1 and iterate until thev match.,", we determine the core temperature $T_{\mathrm{core}}$ via the equation We then compare $T_{\mathrm{core}}$ to $T$ and iterate until they match."
 Note that we do not modily (he Formulae to account for the volume of the core., Note that we do not modify the formulae to account for the volume of the core.
 Since we do not know the equation of state of the core. we cannot solve for the cores proper volume.," Since we do not know the equation of state of the core, we cannot solve for the core's proper volume."
" However. since (he formulae are estimates. and since the luminosity is a very strong function of the temperature and L7x T""). this approximation is innocuous."," However, since the formulae are estimates, and since the luminosity is a very strong function of the temperature $L_{\nu}^{\mathrm{mURCA}} \propto T^{8}$ and $L_{\nu}^{\mathrm{\pi}} \propto T^{6}$ ), this approximation is innocuous."
" In our second method. we simply assign a value for the core temperature Z.,4 and iterate until =T4; αἱ the erust-core interlace."," In our second method, we simply assign a value for the core temperature $T_{\mathrm{core}}$ and iterate until $T = T_{\mathrm{core}}$ at the crust-core interface."
 We assume photons. electrons. ions. aud free neutrons supply the pressure.," We assume photons, electrons, ions, and free neutrons supply the pressure."
 To calculate the photon and electron contributions to the pressure. we follow the same procedure as in Paper L while for the ious and free neutrons. we follow the prescriptions of Brown(2000).," To calculate the photon and electron contributions to the pressure, we follow the same procedure as in Paper I, while for the ions and free neutrons, we follow the prescriptions of \citet{B00}."
. The phase of the ions. whether solid or liquid. is determined by the dimensionless coupling parameter ∖∖↽↥∐↲↕⋅≼↲∣∣∣↕⊳∖⇁⊔∐↲↕∪∐∐∏∐↓∣↽≻≼↲↕⋅≺⇂≼↲∐⋝," The phase of the ions, whether solid or liquid, is determined by the dimensionless coupling parameter where $n_{I}$ is the ion number density."
∖⊽∐⋡∖↽⋅↕∐⊔∐↲∪∏∩↲↕⋅∐↓∪⊳∖⇁↥↥≀↧∶∖↽≼↲↕⋅⊳∖⊽∪↓⋟⊔∐↲≺∢↕⋅∏⊳∖⊽↥⋅∖∖⊽↥∐↲↕⋅≼↲↕⇁↙∖∕∖⋊⊥⋅ we use (he lree energy fits of Chabrier&Potekhin(1998) for the ion equation of state.," In the outermost layers of the crust, where $\Gamma < 1$, we use the free energy fits of \citet{CP98} for the ion equation of state."
 For o>1 we use the analvtical fits of Farouki&Hamaguchi(1993) [ον the Helmholtz free enerev to caleulate the ion pressure., For $\Gamma > 1$ we use the analytical fits of \citet{FH93} for the Helmholtz free energy to calculate the ion pressure.
 We assume the ions are in the liquid phase when ]«DL<173 and the solid phase when [>173., We assume the ions are in the liquid phase when $1 < \Gamma < 173$ and the solid phase when $\Gamma > 173$.
 The analvlical fits are valid for a plasma., The analytical fits are valid for a one-component plasma.
 Llowever. in the accreted laver more (han one species is usually present al a given densitv.," However, in the accreted layer more than one species is usually present at a given density."
" In (his case we approximate the multi-component mixture as a plasma by making the substitutions Z—(Z) and n,—n/t,,"". where t, 15 (he mean molecular weight per nucleus."," In this case we approximate the multi-component mixture as a one-component plasma by making the substitutions $Z \rightarrow \langle Z \rangle$ and $n_{I} \rightarrow n / \mu_{nuc}$, where $\mu_{nuc}$ is the mean molecular weight per nucleus."
 Below (he accreted laver. we assume only one species is present al a given density.," Below the accreted layer, we assume only one species is present at a given density."
 We calculate the [ree neutron pressure from (he compressible liquid-drop nuclear model of Mackie&Bavin(1977)., We calculate the free neutron pressure from the compressible liquid-drop nuclear model of \citet{MB77}.
. For py>1.3xLOM gem.7. we use the equation of state from Negele&Vautherin(1973)...The photon entropy formula is the same as (hat in Paper I. We calculate the Coulomb portion of the ion entropy [rom the [ree energy fits of Chabrier(1993) and (hie ideal portion from the fits of Farouki&Hamaeuchi (1993).," For $\rho_{0} > 1.3 \times 10^{13}$ $\mathrm{g\,cm}^{-3}$, we use the equation of state from \citet{NV73}.The photon entropy formula is the same as that in Paper I. We calculate the Coulomb portion of the ion entropy from the free energy fits of \citet{C93} and the ideal portion from the fits of \citet{FH93}."
. The Weatment of the electron aud [ree, The treatment of the electron and free
beam is ~50” (corresponding to a spatial scale of ~280 kpe at :=6.56). implying that all eemission from the LAEs (and any nearby galaxies at similar redshifts) would lie within the telescope beam.,"beam is $\sim 50''$ (corresponding to a spatial scale of $\sim 280$ kpc at $z = 6.56$ ), implying that all emission from the LAEs (and any nearby galaxies at similar redshifts) would lie within the telescope beam."
 The data were analyzed using the data analysis package. following standard procedures.," The data were analyzed using the data analysis package, following standard procedures."
" A second-order baseline was fit to cach scan during the initial calibration, after which the data were examined on a scan-by-scan basis for residual baseline structure: this was done independently for both polarizations."," A second-order baseline was fit to each scan during the initial calibration, after which the data were examined on a scan-by-scan basis for residual baseline structure; this was done independently for both polarizations."
" Conservatively, all scans showing baseline structure on scales of a few tens of MHz (that might mimic a putative spectral linc) were edited out and not included in the final analysis: this resulted in the excision of ~25% of data for cach target."," Conservatively, all scans showing baseline structure on scales of a few tens of MHz (that might mimic a putative spectral line) were edited out and not included in the final analysis; this resulted in the excision of $\sim 25$ of data for each target."
 The final on-source integration times were ~12 hours for HCM 6A and ~11 hours for IOK-I., The final on-source integration times were $\sim 12$ hours for HCM 6A and $\sim 11$ hours for IOK-1.
" For each source, data from the two polarizations were combined together with appropriate weights, based on their root-mean-square (RMS) noise values to produce the final spectra."," For each source, data from the two polarizations were combined together with appropriate weights, based on their root-mean-square (RMS) noise values to produce the final spectra."
 The spectra were then smoothed to coarser resolutions (50. 150 and 300 1») to search for lline emission.," The spectra were then smoothed to coarser resolutions (50, 150 and 300 ) to search for line emission."
 The final spectra obtained towards HCM 6A and IOK-1 are shown in the four panels of Fig. I..," The final spectra obtained towards HCM 6A and IOK-1 are shown in the four panels of Fig. \ref{fig:spectra},"
 at velocity resolutions of ~50 aand ~1501., at velocity resolutions of $\sim 50$ and $\sim 150$.
. The final RMS noise values per 50 echannel are 52 μὴν (HCM 6A) and 51 μὴν (IOK-1). and per 150 cchannel are 31;y (HCM 6A) and 30;Jy (IOK-1).," The final RMS noise values per $50$ channel are 52 $\mu$ Jy (HCM 6A) and $51$ $\mu$ Jy (IOK-1), and per $150$ channel are $31 \mu$ Jy (HCM 6A) and $30 \mu$ Jy (IOK-1)."
 No evidence for line emission was seen in the spectra at these (or other) velocity resolutions., No evidence for line emission was seen in the spectra at these (or other) velocity resolutions.
While the high. timing precision of MSPs has allowed the precise measurement. of many parameters and. effects. pulsar timing sulfers from the inherent fact that the noise sources that contribute to the timing resicuals are not well understood.,"While the high timing precision of MSPs has allowed the precise measurement of many parameters and effects, pulsar timing suffers from the inherent fact that the noise sources that contribute to the timing residuals are not well understood."
 “To first order. our timing resicuals are composed of noise that follows Gaussian statisties and that as à white power spectrum.," To first order, our timing residuals are composed of noise that follows Gaussian statistics and that has a white power spectrum."
 For each time-of-arrival (LOA). he amount of receiver noise is estimated. by the TOA uncertainty. as determined. from a least-squares fit to a ligh signal-to-noise ratio template profile.," For each time-of-arrival (TOA), the amount of receiver noise is estimated by the TOA uncertainty, as determined from a least-squares fit to a high signal-to-noise ratio template profile."
 Ht is. however. common for these uncertainties to be underestimated or or additional sources of white noise to contribute to the imine residuals.," It is, however, common for these uncertainties to be underestimated or for additional sources of white noise to contribute to the timing residuals."
 One reason might be self-standarding: in 16 process of deriving an average TO for an observation. 1e integrated: pulse. profile is correlated with a template xofile.," One reason might be self-standarding: in the process of deriving an average TOA for an observation, the integrated pulse profile is correlated with a template profile."
 I£ the template profile is generated [rom. addition X many observations. then at some low level the noise from 16 observation can correlate with the noise in the standard. cacing to an underestimation of the POA uncertainty.," If the template profile is generated from addition of many observations, then at some low level the noise from the observation can correlate with the noise in the standard, leading to an underestimation of the TOA uncertainty."
 Also. 16 Cross-correlation method typically used has been shown o underestimate PO uncertainties in the high-noise regime (?)..," Also, the cross-correlation method typically used has been shown to underestimate TOA uncertainties in the high-noise regime \citep{hbo05}."
 Poor selection of standard. profiles can underestimate w TOA uncertainty as well., Poor selection of standard profiles can underestimate the TOA uncertainty as well.
 All of these ellects cause the »ulsar timing parameters to be consequently more uncertain ian initially expected., All of these effects cause the pulsar timing parameters to be consequently more uncertain than initially expected.
 Assuming these effects scale with the uncertainties they allect. one can attempt. to mitigate this underestimation bv multiplication of the TOA uncertainties » the square root of the reduced. X7.2 value of the timing resicluals. as is commonly done in other fields.," Assuming these effects scale with the uncertainties they affect, one can attempt to mitigate this underestimation by multiplication of the TOA uncertainties by the square root of the reduced $\chi^2$ value of the timing residuals, as is commonly done in other fields."
 Underestimation of the white noise contribution is not he only challenge in assessing pulsar timing parameters and heir true uncertainties. though.," Underestimation of the white noise contribution is not the only challenge in assessing pulsar timing parameters and their true uncertainties, though."
 The presence of non-white noise in pulsar timing residuals is very common for voung »ulsars and. as timing baselines increase. starts to become important in timing of some AISPs as well (222)...," The presence of non-white noise in pulsar timing residuals is very common for young pulsars and, as timing baselines increase, starts to become important in timing of some MSPs as well \citep{sc10,vbs+08,sns+05}."
 While he spectral properties and. origins of non-white noise in AMISPs are as vet not understood. because the white noise is still too prominent to allow detailed: analvsis. it. has already been shown that the least-squares fitting performed in pulsar timing reports underestimated uncertainties for he parameters in the timing fit and may even corrupt the xwameter values themselves (2)...," While the spectral properties and origins of non-white noise in MSPs are as yet not understood because the white noise is still too prominent to allow detailed analysis, it has already been shown that the least-squares fitting performed in pulsar timing reports underestimated uncertainties for the parameters in the timing fit and may even corrupt the parameter values themselves \citep{vbs+08}."
 X technique to improve he least-squares fitting process to mitigate such elfects has recently been proposed. (?).., A technique to improve the least-squares fitting process to mitigate such effects has recently been proposed \citep{chc+10}.
 A (third. problem may be present in the form. of signals hat are part of a non-white spectrum such as GWs., A third problem may be present in the form of signals that are part of a non-white spectrum – such as GWs.
 ot only does this type of signal allect the fitting. process as described: above. through introduction of power at à very specific frequency. it has the potential to be fully absorbed in the timing signature of periodic parameters in he pulsar timing model. such as pulsar position. proper motion. parallax or many binary parameters.," Not only does this type of signal affect the fitting process as described above, through introduction of power at a very specific frequency it has the potential to be fully absorbed in the timing signature of periodic parameters in the pulsar timing model, such as pulsar position, proper motion, parallax or many binary parameters."
 On the one iand this can prove useful since independent. measurement of parameters such as parallax (by. e.g... VLBI) can be combined with the pulsar timing measurement {ο place rounds on the amount of corrupting noise present (sec. e.g. 7)). but on the other hand it is worthwhile to assess he amount of influence such noise (especially predicted noise sources such as the GAVB) can have on pulsar timing parameters.," On the one hand this can prove useful since independent measurement of parameters such as parallax (by, e.g., VLBI) can be combined with the pulsar timing measurement to place bounds on the amount of corrupting noise present (see, e.g. \citealt{dvt+08}) ), but on the other hand it is worthwhile to assess the amount of influence such noise (especially predicted noise sources such as the GWB) can have on pulsar timing parameters."
 Low frequency (100 10' Uz) CWs are expected: fron supermassive black hole binary systems (SMDBILDs). cosmic strings. and GW's from the big bang and inflationary cra of the early universe.," Low frequency $10^{-9}$ $10^{-7}$ Hz) GWs are expected from supermassive black hole binary systems (SMBHBs), cosmic strings, and GWs from the big bang and inflationary era of the early universe."
 GWs from these sources can manifest themselves in different ways., GWs from these sources can manifest themselves in different ways.
 Single nearby SAIBIIBs can produce resolvable waves with periods on the order of vears (?).., Single nearby SMBHBs can produce resolvable waves with periods on the order of years \citep{wl03}.
 SMBIIDs and cosmic strings can also produce. CAV bursts (2277). in which the duration of the GW signal is much less than the observation time.," SMBHBs and cosmic strings can also produce GW bursts \citep{dv01,smc07,lss09} in which the duration of the GW signal is much less than the observation time."
 We also expect. pulsar timine arravs to be sensitive to a stochastic background of unresolvable sources., We also expect pulsar timing arrays to be sensitive to a stochastic background of unresolvable sources.
 This stochastic background can be described by a characteristic strain spectrum (f) delined as a frequency:dependent. power law (7?) Llere cL ds the climensionless amplitude ancl à is the spectral index.," This stochastic background can be described by a characteristic strain spectrum $h_c(f)$ defined as a frequency–dependent power law \citep{jhs+06}
 Here $A$ is the dimensionless amplitude and $\alpha$ is the spectral index."
 The power in the GWD can then subsequently be written as In accordance with many cosmological theories. one can also write QueCf). the energy density per unit logarithmic frequeney interval. in. terms of the characteristic strain spectrum as where Ly is the Hubble constant.," The power in the GWB can then subsequently be written as In accordance with many cosmological theories, one can also write $\Omega_{{\rm gw}}(f)$, the energy density per unit logarithmic frequency interval, in terms of the characteristic strain spectrum as where $H_0$ is the Hubble constant."
 This paper will focus primarily on a stochastic background of SMDLIID. sources with a spectral index of a=——2/3 (???7)..," This paper will focus primarily on a stochastic background of SMBHB sources with a spectral index of $\alpha = -2/3$ \citep{wl03,jb03,ein+04}."
 Reeent work has shown that this simple power law does not hold. true at higher frequencies (f210. 7) due to the discrete number of sources., Recent work has shown that this simple power law does not hold true at higher frequencies $f> 10^{-8}$ ) due to the discrete number of sources.
 At these frequencies the characteristic strain is written as (?) where fo. fo. and 5 are mocdeldepencent parameters vascd on specific SAIBIB merger scenarios.," At these frequencies the characteristic strain is written as \citep{svc08}
 where $h_0$, $f_0$, and $\gamma$ are model-dependent parameters based on specific SMBHB merger scenarios."
 “Phe implications that this result will have on our simulations will be discussed. in Section 4.3. where we test. whether his broken power law will make a significant dillerence to methocs that use periodic pulsar parameters with relatively ueh-frequencey fitting functions., The implications that this result will have on our simulations will be discussed in Section \ref{upper} where we test whether this broken power law will make a significant difference to methods that use periodic pulsar parameters with relatively high-frequency fitting functions.
 Although a direct. detection of the CWD has not been made to date. methods using pulsar timing residuals have oen used. to clisprove proposed SMDBIID systems (7). and o put limits on SMDIID coalescence rates (72). and on the dimensionless strain amplitude (???)..," Although a direct detection of the GWB has not been made to date, methods using pulsar timing residuals have been used to disprove proposed SMBHB systems \citep{jll+04} and to put limits on SMBHB coalescence rates \citep{wjy+11} and on the dimensionless strain amplitude \citep{srt+90,jhs+06,hlj+11}."
 Phe most stringent xiblished: upper limit to date is Ax1.110+ (?).., The most stringent published upper limit to date is $A\le 1.1\times 10^{-14}$ \citep{jhs+06}.
 They use a statistic sensitive to a red spectrum., They use a statistic sensitive to a red spectrum.
 In this paper. we present a method. which relies on the derived. timing (?) and VLBI (7) parameters for individual pulsars.," In this paper, we present a method which relies on the derived timing \citep{vbc+09} and VLBI \citep{dvt+08} parameters for individual pulsars."
 It involves adding simulated Cs to pulsar timing parameters and refitting for the pulsar timing parameters to determine, It involves adding simulated GWs to pulsar timing parameters and refitting for the pulsar timing parameters to determine
Additional evidence for morphological transformation is provided bv the high dispersion (¢>250 +)) SOfa-Sa members at 2=0.83 (Fie. ??)).,Additional evidence for morphological transformation is provided by the high dispersion $\sigma>250$ ) S0/a-Sa members at $z=0.83$ (Fig. \ref{BVz_sigma}) ).
 Theonly 2=0.33 counterparts to these systems are E-SO menibers., The $z=0.33$ counterparts to these systems are E-S0 members.
 Although red early-type spirals have been observed iu lower redshift clusters. c.g. ? and I&00b. none have dispersions as lieh as those in MS1051.," Although red early-type spirals have been observed in lower redshift clusters, e.g. \citet{bower:92} and K00b, none have dispersions as high as those in MS1054."
 Iu our cluster E|A sample. we find a trend of decreasing huninosity aud internal velocity dispersion with decreasing redshift.," In our cluster E+A sample, we find a trend of decreasing luminosity and internal velocity dispersion with decreasing redshift."
" This evolution issimilar to the observed decrease since zo Loin the maximaunn huuiuositv of field galaxies uudergoing rapid star formation (""dowu-siziusο).", This evolution issimilar to the observed decrease since $z\sim1$ in the maximum luminosity of field galaxies undergoing rapid star formation \citep[``down-sizing'';][]{cowie:96}.
 While a similar trend has also been suggested for clusters: (27?).. here we find compelling evidence that down-sizing applies directlv to cluster E|A galaxies.," While a similar trend has also been suggested for clusters \citep{poggianti:01,kodama:01,poggianti:03}, here we find compelling evidence that down-sizing applies directly to cluster E+A galaxies."
 The E|A’s in our most distant cluster (2= 0.83) can be Iuninous (£ up to 2.5 L) aud cau have high internal velocity dispersious (o>200 1)., The E+A's in our most distant cluster $z=0.83$ ) can be luminous $L$ up to $2.5L^{\ast}$ ) and can have high internal velocity dispersions $\sigma>200$ ).
 In contrast. the E|Às in our lowest redshift cluster (2= 0.33) are LoSL aud have low dispersions (0<150 i3," In contrast, the E+A's in our lowest redshift cluster $z=0.33$ ) are $L\lesssim L^{\ast}$ and have low dispersions $\sigma<150$ )."
j The data are such that if anv bright. hieh dispersion E|A’s existed in our lower redshift clusters. we would have detected them.," The data are such that if any bright, high dispersion E+A's existed in our lower redshift clusters, we would have detected them."
 One possible concern is that we may be observing au evolution in the E|A rather than a real evolution i mass (as traced by X a7)., One possible concern is that we may be observing an evolution in the E+A rather than a real evolution in mass (as traced by $\propto r_e\sigma^2$ ).
 If the E|A fraction increases with redshift. the likchhood of observing a luminous. high dispersion E|A also increases.," If the E+A fraction increases with redshift, the likelihood of observing a luminous, high dispersion E+A also increases."
 With only three clusters. we cannot determine with certainty if the cluster E|A fraction continues to increase at z20.3. but we do note the E|A fraction is highest (~13% )) in the 2=0.85 cluster.," With only three clusters, we cannot determine with certainty if the cluster E+A fraction continues to increase at $z>0.3$, but we do note the E+A fraction is highest $\sim13$ ) in the $z=0.83$ cluster."
 We attempt to break the degeneracy between evolution in nuniber fraction and in mass by comparing the E|A uaenitude. velocity dispersion. and nass distributious o those of the spectroscopically confirmed cluster x»»ulation.," We attempt to break the degeneracy between evolution in number fraction and in mass by comparing the E+A magnitude, velocity dispersion, and mass distributions to those of the spectroscopically confirmed cluster population."
 If E|A’s are distributed like these other cluster imenibers. we expect to find no difference in he EJA Luuunositv. velocity dispersion. aud miss distributious when compared to the rest of the cluster nelbers.," If E+A's are distributed like these other cluster members, we expect to find no difference in the E+A luminosity, velocity dispersion, and mass distributions when compared to the rest of the cluster members."
 Even if the E1A fraction evolves. this should )o true at all redshifts.," Even if the E+A fraction evolves, this should be true at all redshifts."
 IHTowever. if we cau establish that E|Αν are distiibuted differently from the other cluster ucnibers. this would support evolution in mass.," However, if we can establish that E+A's are distributed differently from the other cluster members, this would support evolution in mass."
 Iu Fig. ?7.. ," In Fig. \ref{KS_test}, ,"
"we compare the bhuuinositw. internal velocity. dispersiou. and adnass (X 7,07) distribution of spectroscopically confirmed cluster members to the E|AS (Fig. ??.."," we compare the luminosity, internal velocity dispersion, and mass $\propto r_e\sigma^2$ ) distribution of spectroscopically confirmed cluster members to the E+A's (Fig. \ref{KS_test},"
 left panels)., left panels).
 Tere we combine all hnree clusters to improve the statistics and use the uou-xuwanetre Rohnuosorov-Smurnov (7) and Wilcoxon ests (7).. and consider ouly aemubers brighter than Mp.=19.15log/.," Here we combine all three clusters to improve the statistics and use the non-parametric Kolmogorov-Smirnov \citep{press:92} and Wilcoxon tests \citep{siegel:88}, and consider only members brighter than $M_{Be}=-19.1$."
. Both tests find the E|A magnitude distribution to be indistinguishable frou that of the nembers., Both tests find the E+A magnitude distribution to be indistinguishable from that of the members.
 Conversely. the same tests find the 6 aud nass distributions to be different with ~90% confidence.," Conversely, the same tests find the $\sigma$ and mass distributions to be different with $\sim90$ confidence."
 Although they can be as bright as the dominant earlv-vpes. the E|A in this sample tend to have lower velocity dispersious and masses when compared to the rest of the cluster population.," Although they can be as bright as the dominant early-types, the E+A's in this sample tend to have lower velocity dispersions and masses when compared to the rest of the cluster population."
" Civen we know galaxies are brightened during the E|A pliase by as uch as AASp,~1.25 mae refhrieht}). we note cluster E|A’s would automatically be expected to have lower dispersions in a magnitude Ignaited sample."," Given we know galaxies are brightened during the E+A phase by as much as $\Delta M_{Be}\sim1.25$ mag \\ref{bright}) ), we note cluster E+A's would automatically be expected to have lower dispersions in a magnitude limited sample."
 To remove this possible bias. we now apply a velocity dispersion limit of o>150 in addition to our magnitude lit (Fie. ??..," To remove this possible bias, we now apply a velocity dispersion limit of $\sigma>150$ in addition to our magnitude limit (Fig. \ref{KS_test},"
 right pauels)., right panels).
 Again. we find the luminosity distributions of E|As aud cluster 1ienibers to be indistinguishable while their dispersion and mass distributions are different (>95% CL for both).," Again, we find the luminosity distributions of E+A's and cluster members to be indistinguishable while their dispersion and mass distributions are different $>95$ CL for both)."
 These results indicate the iucrease in cluster E]A Duuinositv and velocity dispersion with redshift reflects evolution iu the E|A iass distribution rather than evolution in their uuuuber fraction., These results indicate the increase in cluster E+A luminosity and velocity dispersion with redshift reflects evolution in the E+A mass distribution rather than evolution in their number fraction.
 To remove any possible bias introduced by spectroscopicicopleteness!.. we now estimate a complete cluster suuple bv weighting cach member by the inverse of the clusters maguitude selection function (27)..," To remove any possible bias introduced by spectroscopic, we now estimate a complete cluster sample by weighting each member by the inverse of the cluster's magnitude selection function \citep{vandokkum:00,tran:02}."
 Tere we assune the worst case scenario where the cluster sample is incomplete but the E|A sample is complete: in this case. woe would expect the miuimuiuu difference between the two populations.," Here we assume the worst case scenario where the cluster sample is incomplete but the E+A sample is complete; in this case, we would expect the minimum difference between the two populations."
 As before. we consider only galaxies with Wp.19.1 anda >150!.," As before, we consider only galaxies with $M_{Be}\leq-19.1$ and $\sigma>150$."
. We find again a lareec difference between the two distributions of the velocity dispersions aud masses (Fie. ??))., We find again a large difference between the two distributions of the velocity dispersions and masses (Fig. \ref{ksfull}) ).
" We establish the significance of the difference by deriving the probability distribution of the D,,,, statistic tooi this modified I&-S test from simulations.", We establish the significance of the difference by deriving the probability distribution of the $D_{max}$ statistic in this modified K-S test from simulations.
 We assume iat the parent populations are the same. but that the spectroscopically confirmed cluster sample suffers frou incompleteness for which the counts are corrected.," We assume that the parent populations are the same, but that the spectroscopically confirmed cluster sample suffers from incompleteness for which the counts are corrected."
 Frou l3100 realizations. we fud that the probability of finding Ding>Diyalobserved) is lower than for both the velocity dispersion aud mass distributions.," From 5000 realizations, we find that the probability of finding $D_{max} >
D_{max}(observed)$ is lower than for both the velocity dispersion and mass distributions."
" Thus. it is very uulikely that the E|A’s are drawn frou the same parcut population as the rest of the cluster ΠΟΙΟΣ,"," Thus, it is very unlikely that the E+A's are drawn from the same parent population as the rest of the cluster members."
 We find additional evidence of mass dowmn-siziug ly combining our ΤΑ. sample with results from the literature (Fie. ??))., We find additional evidence of mass down-sizing by combining our E+A sample with results from the literature (Fig. \ref{sigma_z}) ).
 While high σ ΕΙA’s are found in clusters up to ~1.3 (T). it seems only low σ ones exist in nearby clusters. e.g. Coma.," While high $\sigma$ E+A's are found in clusters up to $z\sim1.3$ \citep{vandokkum:03}, it seems only low $\sigma$ ones exist in nearby clusters, e.g. Coma."
 We also find a treud of inercasing σ with redshift in the range 0.02<2 1.27., We also find a trend of increasing $\sigma$ with redshift in the range $0.02<z<1.27$ .
 This increase in the characteristic E|A mass with redshift is cousisteut with the trend of increasing age with increasing velocity dispersion found in Coma carly-typcs bv 2. , This increase in the characteristic E+A mass with redshift is consistent with the trend of increasing age with increasing velocity dispersion found in Coma early-types by \citet{caldwell:03}. .
Note these results do not exclude lower σ E|A’s at higher redshift. rather. lower o E|A’s simply fall below our strict selection criteria.," Note these results do not exclude lower $\sigma$ E+A's at higher redshift, rather, lower $\sigma$ E+A's simply fall below our strict selection criteria."
 Excellent examples of this point are E]Avs 1358313. 1358tel. and20532081 (Table ??)).," Excellent examples of this point are E+A's 1358–343, 1358–481, and2053–2081 (Table \ref{ea_sample}) )."
 Although fainter than our magnitude limit. all three have hieh S/N spectra aud pecestered velocity dispersious <110 |.," Although fainter than our magnitude limit, all three have high $S/N$ spectra and velocity dispersions $<110$ ."
Similarly it is easy to show that Ay=(1|1/:24)/(1AIF) giving Ay=0.125 and 0.33 for R5 and R8.,Similarly it is easy to show that $k_1=(1+1/\beta_3)/(1+M^2)$ giving $k_1=0.125$ and $0.33$ for R5 and R8.
 According to this equation the photoevaporation flow should shock for simulations RI. R2. RS and R8 at og.=20.21.25.67cm.7 respectively.," According to this equation the photoevaporation flow should shock for simulations R1, R2, R5 and R8 at $n_{\mathrm{H}}=20,\ 21,\ 25,\ 67\,\mathrm{cm}^{-3}$ respectively."
 In the simulations at /=150 kyr the actual densities are 7. whereas at /=200kyr they are ngcls.19.30.I100cnm . in both cases comparable to the values oredieted.," In the simulations at $t=150\,$ kyr the actual densities are $n_{\mathrm{H}}\simeq25,\ 22,\ 31,\ 75\,\mathrm{cm}^{-3}$ , whereas at $t=200\,$ kyr they are $n_{\mathrm{H}}\simeq18,\ 19,\ 30,\ 100\,\mathrm{cm}^{-3}$ , in both cases comparable to the values predicted."
 This simple model has obvious limitations. in particular we lave not specified the form of the boundary between regions II and III — it is not a shock. but if the magnetic field strength changes significantly then a contact discontinuity forms to equalise the total oressure.," This simple model has obvious limitations, in particular we have not specified the form of the boundary between regions II and III – it is not a shock, but if the magnetic field strength changes significantly then a contact discontinuity forms to equalise the total pressure."
 Also we have not considered any parallel field component which. if present. would alter the pressure balance.," Also we have not considered any parallel field component which, if present, would alter the pressure balance."
 Despite this he model quantitatively captures the properties of the over-dense ridge., Despite this the model quantitatively captures the properties of the over-dense ridge.
 Addition of an opposing ram pressure in the ambient medium can clearly have a similar effect to a downstream magnetic field in that it increases the density at which the photoevaporation flow termination shock forms (and hence also the post-shock density f2 Y., Addition of an opposing ram pressure in the ambient medium can clearly have a similar effect to a downstream magnetic field in that it increases the density at which the photoevaporation flow termination shock forms (and hence also the post-shock density $\rho_2$ ).
 The differences between R8 and R3a reftig:Emission250-—8 show that even an inflow of 0;23kms can have an observable effect.," The differences between R8 and R8a \\ref{fig:Emission250}- \ref{fig:EmissionR88a_I} show that even an inflow of $v_3\simeq3\,\mathrm{km}\,\mathrm{s}^{-1}$ can have an observable effect."
 Further work will be required to investigate observational differences (possibly in the shape and velocity of gas within the ridge and/or whether it is sheet- or bar-like) which could be used to distinguish between a magnetically confined bright ridge and one which is ram-pressure confined., Further work will be required to investigate observational differences (possibly in the shape and velocity of gas within the ridge and/or whether it is sheet-like or bar-like) which could be used to distinguish between a magnetically confined bright ridge and one which is ram-pressure confined.
 This work contirms the suggestion by ?. that their observations can in principle constrain the field strength in M16 when combined with detailed simulations., This work confirms the suggestion by \citet{SugWatTamEA07} that their observations can in principle constrain the field strength in M16 when combined with detailed simulations.
 On the evidence of these simulations (and those of 2) it appears that the magnetic field in the region around the pillars in M16 cannot be as large as the 160 //G field in model RS/R8a. and is likely |B]5550 μα. This can be deduced by comparing observations of the field orientation in the H region and IIa emission around the pillars with the emission maps presented here and in ?..," On the evidence of these simulations (and those of \citealt{HenArtDeCEA09}) ) it appears that the magnetic field in the region around the pillars in M16 cannot be as large as the $160\,\mu$ G field in model R8/R8a, and is likely $\vert\mathbf{B}\vert\lesssim50\,\mu$ G. This can be deduced by comparing observations of the field orientation in the H region and $\mathrm{H}\alpha$ emission around the pillars with the emission maps presented here and in \citet{HenArtDeCEA09}."
 The recombination line intensity in the images from ?. clearly decreases with distance from the ionisation front and was shown to be consistent with a spherically expanding photoevaporation flow. which matches only our weak and medium field strength models.," The recombination line intensity in the images from \citet{HesScoSanEA96}
 clearly decreases with distance from the ionisation front and was shown to be consistent with a spherically expanding photoevaporation flow, which matches only our weak and medium field strength models."
 Additionally no prominent ribbon/ridge or sheet-like features are present near the pillars., Additionally no prominent ribbon/ridge or sheet-like features are present near the pillars.
 Interpreting the the polarisation. measurements. within the pillars in MI6 as further evidence for a weak field implicitly assumes the pillars formed via a mechanism similar to the one considered here., Interpreting the the polarisation measurements within the pillars in M16 as further evidence for a weak field implicitly assumes the pillars formed via a mechanism similar to the one considered here.
 Because the rocket effect always accelerates gas away from the radiation source and into the shadowed region. we believe that this alignment of weak fields with the pillar axis is a generic feature of all such models. but the initial conditions for pillar formation are not static (ef.2). and it is uncertain how well correlated the initial magnetic field orientation would be between dense and raretied gus.," Because the rocket effect always accelerates gas away from the radiation source and into the shadowed region, we believe that this alignment of weak fields with the pillar axis is a generic feature of all such models, but the initial conditions for pillar formation are not static \citep[cf.][]{GriBurNaaEA10} and it is uncertain how well correlated the initial magnetic field orientation would be between dense and rarefied gas."
 Compared to the simulations of ?.. the RDI of clumps in our models is weaker leading to less flattened structures.," Compared to the simulations of \citet{HenArtDeCEA09}, the RDI of clumps in our models is weaker leading to less flattened structures."
 The main reason is that here the clumps are considerably more centrally concentrated with higher initial densities. making them less susceptible to compression.," The main reason is that here the clumps are considerably more centrally concentrated with higher initial densities, making them less susceptible to compression."
 Additionally the clump in their model is much closer to the ionising source and subject to higher incident radiation flux (only partially offset by the higher source luminosity in our model). increasing the effect of RDI.," Additionally the clump in their model is much closer to the ionising source and subject to higher incident radiation flux (only partially offset by the higher source luminosity in our model), increasing the effect of RDI."
 Thermal physics models and differing geometric effects due to source proximity may also have an effect., Thermal physics models and differing geometric effects due to source proximity may also have an effect.
 The weak field model WSOL in ? should be roughly comparable to our model RS., The weak field model W80L in \citet{HenArtDeCEA09} should be roughly comparable to our model R5.
 Fig., Fig.
 4 shows that the ratio μονονυπ|BF) in dense neutral gas remains at ~0.3 for 300 kyr in R5. similar to the ratio in neutral gas shown in for WSOL. The subsequent increase in this ratio in RS may represent a later evolutionary phase but. because of the simulation differences already mentioned. it is difficult to quantify this.," \ref{fig:R258_Bevo} shows that the ratio $\langle\vert
B_x\vert\rangle/\langle\sqrt{B_y^2+B_z^2}\rangle$ in dense neutral gas remains at $\sim0.3$ for 300 kyr in R5, similar to the ratio in neutral gas shown in \citet[][fig.~12]{HenArtDeCEA09} for W80L. The subsequent increase in this ratio in R5 may represent a later evolutionary phase but, because of the simulation differences already mentioned, it is difficult to quantify this."
 Our results are otherwise in good agreement with those of ? considering the differences in the simulation initial conditions., Our results are otherwise in good agreement with those of \citet{HenArtDeCEA09} considering the differences in the simulation initial conditions.
 We also find that that the photoionisation of dense clumps is very different in strongly magnetised media than in the non-magnetised case. with the dynamics becoming more planar than axisymmetric.," We also find that that the photoionisation of dense clumps is very different in strongly magnetised media than in the non-magnetised case, with the dynamics becoming more planar than axisymmetric."
 Photoevaporated ionised gas tends to form ribbon-like structures which can (transiently) have significant optical depths and lead to recombination behind them., Photoevaporated ionised gas tends to form ribbon-like structures which can (transiently) have significant optical depths and lead to recombination behind them.
 Clump compression along tield lines creates flattened sheet-like structures and an ionisation front which is far from axisymmetric., Clump compression along field lines creates flattened sheet-like structures and an ionisation front which is far from axisymmetric.
 Despite the simplistic initial conditions used here and in TLIO. qualified support for these models comes from the 3D R-HD simulations of ?..," Despite the simplistic initial conditions used here and in ML10, qualified support for these models comes from the 3D R-HD simulations of \citet{GriBurNaaEA10}."
 They used an isothermal self-gravitating decaying turbulence model as the initial conditions. varying the urbulent Mach number at which the radiation source is switched on.," They used an isothermal self-gravitating decaying turbulence model as the initial conditions, varying the turbulent Mach number at which the radiation source is switched on."
 In agreement with the trends we reported they also found hat to form pillars the density field was required to include both arge low-density regions and reasonably massive dense regions of sufficient overdensity to trap the ionisation front., In agreement with the trends we reported they also found that to form pillars the density field was required to include both large low-density regions and reasonably massive dense regions of sufficient overdensity to trap the ionisation front.
 Because of the dynamic initial conditions in their simulations they were also able o show the dependence on initial gas motions. finding that high Tach number turbulence did not produce pillar-like structures as successfully as models with Mach number Al~4-10 because structures formed and dispersed too rapidly.," Because of the dynamic initial conditions in their simulations they were also able to show the dependence on initial gas motions, finding that high Mach number turbulence did not produce pillar-like structures as successfully as models with Mach number $M\sim4$ –10 because structures formed and dispersed too rapidly."
 When the Mach number was too low a sufficient density contrast to form pillars was not obtained., When the Mach number was too low a sufficient density contrast to form pillars was not obtained.
 ? also found that ionised gas pressure is the dominant driver of the dynamics and gravity appears to play a smaller role. an explicit assumption in our work based on previous calculations by ?..," \citet{GriBurNaaEA10} also found that ionised gas pressure is the dominant driver of the dynamics and gravity appears to play a smaller role, an explicit assumption in our work based on previous calculations by \citet{EsqRag07}."
 In our opinion ? overstate the differences between our results and theirs — in both models a combination of RDI and the rocket effect reinforces pre-existing inhomogeneities in the ISM and generates elongated structure along the radiation propagation direction., In our opinion \citet{GriBurNaaEA10} overstate the differences between our results and theirs – in both models a combination of RDI and the rocket effect reinforces pre-existing inhomogeneities in the ISM and generates elongated structure along the radiation propagation direction.
 We do not see our results as being in conflict with those of ?z rather that they have confirmed many of our conclusions and also extended our work by studying pillar formation in a more realistic initial density field., We do not see our results as being in conflict with those of \citet{GriBurNaaEA10}; rather that they have confirmed many of our conclusions and also extended our work by studying pillar formation in a more realistic initial density field.
 These results suggest that the initially static models considered in MLIO and in this work can capture the essential physics of the pillar formation and evolution. once the initial conditions of dense regions surrounded by a less dense ambient medium have been set up.," These results suggest that the initially static models considered in ML10 and in this work can capture the essential physics of the pillar formation and evolution, once the initial conditions of dense regions surrounded by a less dense ambient medium have been set up."
 As noted in MLIO. our models ean also explain the LOS velocities seen in the pillars in M16 (??).. although we do not see the helical morphology and apparent rotation found in some elephant trunks (2)..," As noted in ML10, our models can also explain the LOS velocities seen in the pillars in M16 \citep{Pou98,WhiNelHolEA99}, although we do not see the helical morphology and apparent rotation found in some elephant trunks \citep{GahCarJohEA06}."
 This may require an initially dynamic density field since such structures seem to occur quite readily in the simulations of ο., This may require an initially dynamic density field since such structures seem to occur quite readily in the simulations of \citet{GriBurNaaEA10}.
 Our simulations (and. those of 23) suggest that ionisation fronts with a strong perpendicular magnetic field should have clear observational consequences in both the morphology of the recombination emission and of the dense gas., Our simulations (and those of \citealt{HenArtDeCEA09}) ) suggest that ionisation fronts with a strong perpendicular magnetic field should have clear observational consequences in both the morphology of the recombination emission and of the dense gas.
 ? note that while the Orion Bar has a similar linear shape to the ribbon-like structures seen here. it is associated with the main ionisation/dissociation," \citet{HenArtDeCEA09}
 note that while the Orion Bar has a similar linear shape to the ribbon-like structures seen here, it is associated with the main ionisation/dissociation"
The aim of this simulation was to compare the performance of the present algorithm to others. which have mostly been tested on white-noise only light curves.,"The aim of this simulation was to compare the performance of the present algorithm to others, which have mostly been tested on white-noise only light curves."
 Ifthe present method is to improve on the performance of the Bayesian approach it is derived. from. it should. be able to detect reliably a 1.02) planet orbiting a G2 star with photon noise to V—13. given. three transits in the light curve.," If the present method is to improve on the performance of the Bayesian approach it is derived from, it should be able to detect reliably a $1.0~R_{\oplus}$ planet orbiting a G2V star with photon noise to $V=13$, given three transits in the light curve."
 In 2.. simulations showed that such a planet should. be easily. detected: around. a smaller (WOW) but fainter (V= 14) star with the older algorithm and no filtering.," In \citet{af02}, simulations showed that such a planet should be easily detected around a smaller (K5V) but fainter $V=14$ ) star with the older algorithm and no filtering."
 The V—13. G2 case corresponds to a S/V that is larger by a factor of 1.07. and should therefore. be detected easily if the new method is as ellicient as the old.," The $V=13$, G2 case corresponds to a $S/N$ that is larger by a factor of 1.07, and should therefore be detected easily if the new method is as efficient as the old."
 After a set of simulations was run for such a configuration. the maximum cetection statistic from. the noise only light curves was S/N=5.79. while the minimum value from the light curves with transits was S/N=741 (sce Fig.," After a set of simulations was run for such a configuration, the maximum detection statistic from the noise only light curves was $S/N=5.79$, while the minimum value from the light curves with transits was $S/N=7.41$ (see Fig."
 15aa)., \ref{fig:hdist}a a).
 Any threshold in between would therefore allow the detection of all the transits where present. with no false alarms.," Any threshold in between would therefore allow the detection of all the transits where present, with no false alarms."
 Note that the S/N limit of 6. quoted by 2? for their BLS method. which is statistically close to ours. falls as expected in the range of thresholds that would be suitable in the present case.," Note that the $S/N$ limit of 6, quoted by \citet{kzm02} for their BLS method, which is statistically close to ours, falls as expected in the range of thresholds that would be suitable in the present case."
 e This configuration is identical to that in Sect. 4.2.1...," $\bullet$ This configuration is identical to that in Sect. \ref{sec:photonly},"
 but with stellar variability added., but with stellar variability added.
 Lt is also similar to the case illustrated in Figs., It is also similar to the case illustrated in Figs.
 to LE. but with a smaller. planet.," \ref{fig:lc} to \ref{fig:trres}, but with a smaller planet."
 The results are shown 39.in Fig., The results are shown in Fig.
 15bb. The distributions of the detection statistics from the light curves with and without transits overlap almost. entirely. tthe performance is poor.," \ref{fig:hdist}b b. The distributions of the detection statistics from the light curves with and without transits overlap almost entirely, the performance is poor."
 The threshold that minimises the sum of false alarnis and. missed. detection leads to 56 of the first and 26 of the second., The threshold that minimises the sum of false alarms and missed detection leads to 56 of the first and 26 of the second.
 Assuming that the sampling rate. light curve duration. and stellar apparent magnitude are fixed. there are three [actors which should. lead to better performance: a larger planet. a shorter orbital period. mmore transits) or a smaller star.," Assuming that the sampling rate, light curve duration, and stellar apparent magnitude are fixed, there are three factors which should lead to better performance: a larger planet, a shorter orbital period more transits) or a smaller star."
 Each of these options in turn is investigated below., Each of these options in turn is investigated below.
 e1.5 The histograms are relatively well separated (see Fig., $\bullet$ The histograms are relatively well separated (see Fig.
 Lee). with only a small overlap. so that the optimal threshold. of SYN=7.85 lead to one missed detection and no false alarms.," \ref{fig:hdist}c c), with only a small overlap, so that the optimal threshold of $S/N=7.85$ lead to one missed detection and no false alarms."
 lt djs interesting to note the similarity between the results of this simulation and the requirements used for the design of the mission. which was to detect. planets eiven a signal-to-noise ratio totalling at least 8 for at least three," It is interesting to note the similarity between the results of this simulation and the requirements used for the design of the mission, which was to detect planets given a signal-to-noise ratio totalling at least 8 for at least three."
s. e The aim of this set. of simulations was to investigate the ellect of increasing the number of transits in the light curve by a factor of two by reducing the orbital period to 182 d. This is equivalent to increasing the overall curation of the observations., $\bullet$ The aim of this set of simulations was to investigate the effect of increasing the number of transits in the light curve by a factor of two by reducing the orbital period to 182 d. This is equivalent to increasing the overall duration of the observations.
 As expected. this leads to higher S/N. values and hence better performance. with only 13 false alarms aud 16 missed detections (see Fig.," As expected, this leads to higher $S/N$ values and hence better performance, with only 13 false alarms and 16 missed detections (see Fig."
 1544)., \ref{fig:hdist}d d).
 e A lS star is smaller than a G2 star. leading to deeper transits. but also more active. leading to more stellar variability.," $\bullet$ A K5 star is smaller than a G2 star, leading to deeper transits, but also more active, leading to more stellar variability."
 Reeent studies(?)| suggested that the former clleet prevailect over the latter. and that Ix or even AL type stars might make better targets for space missions seeking to detect habitable planets than €i stars. but these were based only on results from a few individual light. curves. rather than Monte Carlo simulations.," Recent \citep{afg04} suggested that the former effect prevailed over the latter, and that K or even M type stars might make better targets for space missions seeking to detect habitable planets than G stars, but these were based only on results from a few individual light curves, rather than Monte Carlo simulations."
 The present tests confirm this trend: the separation between the with- and without transit. distributions is wider (see Fig., The present tests confirm this trend: the separation between the with- and without transit distributions is wider (see Fig.
 Tec) than in the previous case. though the best-threshold false alarm: ancl missed. detection rates remain high at 13 and Note the higher S/N. values for the transit-less light curves compared to the G2 case. which suggests the presence of more residual stellar variability after filtering. as would be expected.," \ref{fig:hdist}e e) than in the previous case, though the best-threshold false alarm and missed detection rates remain high at 13 and Note the higher $S/N$ values for the transit-less light curves compared to the G2 case, which suggests the presence of more residual stellar variability after filtering, as would be expected."
 Starting [rom ao general purpose maxiniuun likelihood approach we have demonstrated the the links between a variety of period and transit finding methods ancl have shown that matched. filters. cross-correlation. least-squares fitting ancl maximum likelihood methods are all facets of the same underlving principle.," Starting from a general purpose maximum likelihood approach we have demonstrated the the links between a variety of period and transit finding methods and have shown that matched filters, cross-correlation, least-squares fitting and maximum likelihood methods are all facets of the same underlying principle."
 In the simple approximation of rectangular-shaped transits embedded on a Hat continuum and in white noise. all of these approaches can be tuned to eive similar detection results.," In the simple approximation of rectangular-shaped transits embedded on a flat continuum and in white noise, all of these approaches can be tuned to give similar detection results."
 The transit detection algorithm presented here provides a unified approach linking all these methods., The transit detection algorithm presented here provides a unified approach linking all these methods.
 Computational ellicieney is of particular importance in the context of large. long duration. high sampling missions such as anclAcpler.. and the present method would allow a search for transits by habitable planets to be performed on 20.000 3 vr long light curves with LO min sampling in less than a," Computational efficiency is of particular importance in the context of large, long duration, high sampling missions such as and, and the present method would allow a search for transits by habitable planets to be performed on 20,000 3 yr long light curves with 10 min sampling in less than a"
with NAIM over COSMOS (e...Drusaetal.2010.2007:Salvatoetal. 2009).. which allowed us to svstematically exclude the X-ray. detected ACNs from our final sample down to a flux limited ουσene:=5«1016 cre 2 1 (less than DO).,"with XMM over COSMOS \citep[e.g.,][]{Brusa:10,Brusa:07,Salvato:09}, which allowed us to systematically exclude the X-ray detected AGNs from our final sample down to a flux limited $S_{0.5-2 keV} = 5\times10^{-16}$ erg $^{-2}$ $^{-1}$ (less than )."
 Basedou deep photometry obtained with D baud. : band and dy laud filters. Daddietal.(2001) proposed a criterion to sclect star-forming galaxies iu the redshift range of κτιςὃς BDN—(0K)ap(Bojan 0.2.," Basedon deep photometry obtained with $B$ –band, $z$ --band and $K$ –band filters, \citet{Daddi:2004} proposed a criterion to select star-forming galaxies in the redshift range of $1.4<z<2.5$: $BzK \equiv (z-K)_{AB} - (B-z)_{AB} > -0.2$ ."
" In the plane defiue ID[A as a function of DB (hereafter the BA diagram). the extinction vector obtained for the attenuation law of Calzettietal.(2000) is parallel to the line characterized by D:AN=0.2 at lb«i-ϱ2.5,Therefore this criterion preseuts the streneth of beiug mostly independent of dust obscuration."," In the plane defined by $z-K$ as a function of $B-z$ (hereafter the $BzK$ diagram), the extinction vector obtained for the attenuation law of \citet{Cal:00} is parallel to the line characterized by $BzK = -0.2$ at $1.5<z<2.5$.Therefore this criterion presents the strength of being mostly independent of dust obscuration."
" The B baud. : baud aud A baud photometry used w Daddictal.(2001) was based on the 2 aud dy, filters available at the VET as well as on the FS50LP > baud filter of UST."," The $B$ –band, $z$ –band and $K$ –band photometry used by \citet{Daddi:2004} was based on the $B$ and $K_{s}$ filters available at the VLT as well as on the F850LP $z$ –band filter of HST."
 Ou the other haud. our COSMOS shotometry was determined throush By aud +! baud observations obtained at the Subaru Telescope aud. A uad data taken at CEITT (Capalsetab.2007:MeCrackeuetal.. 2010).," On the other hand, our COSMOS photometry was determined through $B_{J}$ and $z^{+}$ –band observations obtained at the Subaru Telescope and $K_{s}$ --band data taken at CFHT \citep{Capak:07,McCra:10}."
". In order to adapt the original BA criterion o the COSMOS data. we thus determined the evolution of the BA variable throueh the COSMOS filters as a Anctiou of redshift and with a set of star-forming galaxy cluplates similar to the library of SEDs used by bertetal.(2009). for their catalog of photometric redshifts in COSMOS. aud we compared this BA variable to re BLA, color iitially defined by Daddietal.(2001)."," In order to adapt the original $BzK$ criterion to the COSMOS data, we thus determined the evolution of the $BzK$ variable through the COSMOS filters as a function of redshift and with a set of star-forming galaxy templates similar to the library of SEDs used by \citet{Ilbert:09} for their catalog of photometric redshifts in COSMOS, and we compared this $BzK$ variable to the $BzK_o$ color initially defined by \citet{Daddi:2004}."
 The star-forming SEDs used by Ibertetal.(2009) Were generated with the stellar population svuthesis model of Bruzual&Charlot(2003) asstuine exponenutiallv-declining star formation histories aud starburst ages between 0.03 aud 3 Car., The star-forming SEDs used by \citet{Ilbert:09} were generated with the stellar population synthesis model of \citet{Bruzual:2003} assuming exponentially-declining star formation histories and starburst ages between 0.03 and 3 Gyr.
" Tu the redshift range of 1.1<2κ2.5 we found BA DB.N,-—0lnmmnmas with a very sunall cispersion dieu by the choice of SED template.", In the redshift range of $1.4<z<2.5$ we found $BzK - BzK_o = 0.1$ mag with a very small dispersion driven by the choice of SED template.
 To apply the BK selection technique to the COSMOS survey we thus added a svstematic offsetof .lnuunasg to the initial criterion proposed bv Daddietal.(2001).. leading to the identification of star-forming DA ealaxies with the following color: Another widely-used) selection of distant star-forming sources was proposed bv Steidelotal.(2001) andl Adelberecretal.(2001) ming UV/optical broad-banud color selection techniques.," To apply the $BzK$ selection technique to the COSMOS survey we thus added a systematic offsetof mag to the initial criterion proposed by \citet{Daddi:2004}, leading to the identification of star-forming $BzK$ galaxies with the following color: Another widely-used selection of distant star-forming sources was proposed by \citet{Steidel:04} and \citet{Adel:04} using UV/optical broad-band color selection techniques."
" Based on photometry obtained iu the C,. G and R bands aud using the associated C,—C and GR colors. they defined two criteria refered as the “BAD aud ""DX selectious to identify galaxies at 1.1 < z <2. aud 1.9 <2 x 2.7 respectively."," Based on photometry obtained in the $U_{n}$, $G$ and $R$ bands and using the associated $U_n-G$ and $G-R$ colors, they defined two criteria refered as the “BM” and “BX” selections to identify galaxies at 1.4 $\le$ z $\le$ 2.1 and 1.9 $\le$ z $\le$ 2.7 respectively."
 At the wavelenetls where these two selection techniques can be applied. the COSMOS observations were carried out at the CEITT aud at the Subaru Telescope with the «4. g! aud r! filters (Capaketal.2007).. which differ substautiallv from the filters used by Steideletal.(2001).," At the wavelengths where these two selection techniques can be applied, the COSMOS observations were carried out at the CFHT and at the Subaru Telescope with the $u^{*}$, $g^{+}$ and $r^{+}$ filters \citep{Capak:07}, which differ substantially from the filters used by \citet{Steidel:04}."
.. As a result we were not able to adapt the initial BAL/BN selection to the COSMOS photometry woapplving simple terms of color corrections and/or systematic offsets to our data., As a result we were not able to adapt the initial $BM/BX$ selection to the COSMOS photometry by applying simple terms of color corrections and/or systematic offsets to our data.
 Following the approach xoposed by Crazianetal.(2007) we considered a slightly mocified version of the BAL/BN criterion using he «Vy and Vji! colors iustead of thle colors initially used by Adelbergeretal.(200)., Following the approach proposed by \citet{Grazian:07} we considered a slightly modified version of the $BM/BX$ criterion using the $u^{*}-V_{J}$ and $V_{J}-i^{+}$ colors instead of the colors initially used by \citet{Adel:04}.
. To determine he most appropriate color cuts for our VWyi!* diagraiu. we computed the evolution of color tracks followed by star-ornüueg galaxies as a function of redshift. i a wav very simular to that eiuploved by Adelbergeretal.(2001). so as to eusure a selection of star-formune sources as close as oossible to the original criterion.," To determine the most appropriate color cuts for our $u^{*}V_{J}i^{+}$ ' diagram, we computed the evolution of color tracks followed by star-forming galaxies as a function of redshift, in a way very similar to that employed by \citet{Adel:04} so as to ensure a selection of star-forming sources as close as possible to the original criterion."
 We used the spectral energv distributions of two starburst ealaxies along he list of galaxy templates considered by Hbertetal. for their analysis of the COSOS photometric redshifts., We used the spectral energy distributions of two starburst galaxies among the list of galaxy templates considered by \citet{Ilbert:09} for their analysis of the COSMOS photometric redshifts.
 These two SEDs were chosen as being the uost representativo templates of galaxies bevoud according to the SED fitting infered by Hbertetal. (2009)., These two SEDs were chosen as being the most representative templates of galaxies beyond $z~\sim1$ according to the SED fitting infered by \citet{Ilbert:09}.
.. These two templates correspond tfo starburst uodels taken from (Druzual&Charlot2003.. hereafter πα to which cussion lines has been added to have a better understanding of the COSMOS colors (for more details see Hbertetal. 2009)).," These two templates correspond to starburst models taken from \citealt{Bruzual:2003}, hereafter BC03) to which emission lines has been added to have a better understanding of the COSMOS colors (for more details see \citealt{Ilbert:09}) )."
 Following Adclherecretal.(200 1).. we also took iuto account the effect of extinction by reddening each template up to £(BVj=02 assuniue the attenuation curve of Calzettietal.(2000).," Following \citet{Adel:04}, we also took into account the effect of extinction by reddening each template up to $E(B-V)=0.2$ assuming the attenuation curve of \citet{Cal:00}."
. The exact determination of our new selection is illustrated on Fig 1.., The exact determination of our new selection is illustrated on Fig \ref{fig:BM_track_opt}. .
 First we defined he lower aud upper Duits of our criterion on the «Vy color using the location of the galaxy tracks at respectively +=1.5 aud 2= δι Second. we used a lower luit of 0.25 for the Vyi! color.," First we defined the lower and upper limits of our criterion on the $u^{*}-V_{J}$ color using the location of the galaxy tracks at respectively $z=1.5$ and $z=2.8$ : Second, we used a lower limit of $-0.25$ for the $V_{J}-i^{+}$ color."
 It is similar to the cut chosen by Crazianetal. ).. although we note that its effect is negligible since very few sources are bluer than this linit.," It is similar to the cut chosen by \citet{Grazian:07}, , although we note that its effect is negligible since very few sources are bluer than this limit."
 Finally. we iuposed an upper lait on this second color so as to allow the selection of sources corresponding to the reddest teiiplates of our diagram (E(BVj0.2 nuuag:," Finally, we imposed an upper limit on this second color so as to allow the selection of sources corresponding to the reddest templates of our diagram $E(B-V)$ mag):"
this effect. we write For standard candles. which can be identified independent of distance. ο=0.,"this effect, we write For standard candles, which can be identified independent of distance, $\gamma=0$."
 We are most directly interested in comparing to optical depth measurements using clump giants. which are approximately standard candles.," We are most directly interested in comparing to optical depth measurements using clump giants, which are approximately standard candles."
 We therefore adopt +=0 as the default., We therefore adopt $\gamma=0$ as the default.
 For bulee sources and for. respectively. disk aud bulge lenses. we find In fact. (7).(disk) does not significantly depend on 5. but ἐτ).(bulge) does.," For bulge sources and for, respectively, disk and bulge lenses, we find In fact, $\langle \tau\rangle_\gamma({\rm disk})$ does not significantly depend on $\gamma$, but $\langle \tau\rangle_\gamma({\rm bulge})$ does."
" For example (7)(bulge)=0.86x10 The total optical depth due to stars Chat is predicted by this mass profile for observations toward DW. (r)u(total)=1.63x10"". agrees reasonably well with the two measurements made using clump giants."," For example $\langle \tau\rangle_1({\rm bulge})=0.86\times 10^{-6}$ The total optical depth due to stars that is predicted by this mass profile for observations toward BW, $\langle \tau\rangle_0({\rm total}) = 
1.63\times 10^{-6}$, agrees reasonably well with the two measurements made using clump giants."
" When these are adjusted to a common mean direction al DW (Afonsoetal.2003).. they vield 7=2.132:0.40xLO"" (Popowskietal.2001) and 1.082:0.30xLO9 (Afonsoetal.2003)."," When these are adjusted to a common mean direction at BW \citep{eros}, they yield $\tau=2.13\pm 0.40\times 10^{-6}$ \citep{macho3} and $\tau=1.08\pm 0.30\times 10^{-6}$ \citep{eros}."
. While the agreement between the observations ancl the model predictions is comforting. 1 is important (ο recognize that the model has some uncertainties.," While the agreement between the observations and the model predictions is comforting, it is important to recognize that the model has some uncertainties."
 These are most easily discussed by wiitüng the predicted optical depth as This equation serves to define D.. which may be thought of roughly as the characteristic source-lens separation.," These are most easily discussed by writing the predicted optical depth as This equation serves to define $\overline{D_\gamma}$, which may be thought of roughly as the characteristic source-lens separation."
 This characteristic separation depends only on the mass profile ancl (through 5) on the observational strategy., This characteristic separation depends only on the mass profile and (through $\gamma$ ) on the observational strategy.
 It can be evaluated trivially for any mass model., It can be evaluated trivially for any mass model.
" For the Dwekοἱal.(1995). bulge model used here. On (he other haud. X,depends only on (he surface density of stars."," For the \citet{dwek} bulge model used here, 	On the other hand, $\Sigma_*$depends only on the surface density of stars."
 For Iuminous stars. (his is practically an observed quantity (Holtzmanetal.1993:Zoccali 2000).. and the," For luminous stars, this is practically an observed quantity \citep{holtzman,zoccali}, , and the"
and 2 )).,and - )+ _1 )+ _2 ^2 - 4 _2 ).
 To first order. there is no effect of collisions on the growth rate of the MEI: the results above are (hen exactly same as equations (20) ancl (21) in QDII (who neglected collisions entirely).," To first order, there is no effect of collisions on the growth rate of the MRI; the results above are then exactly same as equations (20) and (21) in QDH (who neglected collisions entirely)."
 Collisional effects modily the closure only at order C. though one has to go to this order to lind the first order dependence of vw on » in the dispersion relation.," Collisional effects modify the closure only at order $\zeta^2$, though one has to go to this order to find the first order dependence of $\omega$ on $\nu$ in the dispersion relation."
" The results from the last section provide useful expressions lor ὁρ aud op, in the low and high collisionality regimes. |C|«1 and 6>1. but it would be convevient to have a single set of equations (hat can provide a robust transition between (hese two regimes."," The results from the last section provide useful expressions for $\delta
p_\Perp$ and $\delta p_\Par$ in the low and high collisionality regimes, $|\zeta| \ll 1$ and $|\zeta| \gg 1$, but it would be convenient to have a single set of equations that can provide a robust transition between these two regimes."
 The snyderetal.(1997) closure approximations. which we discuss in (his sectio1. can do this.," The \citet{ref:Snyder} closure approximations, which we discuss in this section, can do this."
 The second moments of the drift kinetic equation (eq. 10} , The second moments of the drift kinetic equation (eq. \ref{eq:DKE}] ])
vield evolution equations [or dp_ and dp) (see. e.g.. eqs. [," yield evolution equations for $\delta p_\Perp$ and $\delta p_\Par$ (see, e.g., eqs. ["
16]-[17] of Snyder et 11997).,16]-[17] of Snyder et 1997).
 The linearized versions of these equations. including a BCLs collision operator. are given by," The linearized versions of these equations, including a BGK collision operator, are given by"
in the field ancl in the higher metallicity clusters.,in the field and in the higher metallicity clusters.
 Ivansetal.(1999) found overabundances of s-process elements like Da and La in Ald., \citet{Ivans1999} found overabundances of $s$ -process elements like Ba and La in M4.
 s Cen also shows evidence of s-process enhancement in its more metal-rich stars (Cunhlaetal.2002)., $\omega$ Cen also shows evidence of $s$ -process enhancement in its more metal-rich stars \citep{Cunha2002}.
. It would be tempting to attribute M4's increased Cu abundance (and therefore also that of the field) to enhanced s-processing as well., It would be tempting to attribute M4's increased Cu abundance (and therefore also that of the field) to enhanced $s$ -processing as well.
 ILowever. the bulk of solar system Cu is made from the weak. not main. s-process. unlike Da and La. Oulv about of the solar svstem Cu can be attributed to the main s-process (Ixappeleretal.1989).," However, the bulk of solar system Cu is made from the weak, not main, $s$ -process, unlike Ba and La. Only about of the solar system Cu can be attributed to the main $s$ -process \citep{Kappeler1989}."
. Daralfe&Takahashi(1993) find (hat (he massive star (weak s-process) contribution is an order of magnitude too small (for all |Fe/1]) to reproduce the field star abundance. and increasing (he main s-process contribution to M4 should not make much difference in (he Cu abundance.," \cite{Baraffe1993} find that the massive star (weak $s$ -process) contribution is an order of magnitude too small (for all [Fe/H]) to reproduce the field star abundance, and increasing the main $s$ -process contribution to M4 should not make much difference in the Cu abundance."
 Ii any. case. even s-process enhanced stars in w Cen still show a low [Cu/Fe] (though there is some Cu enhancement of giants at the highest metallicities: see Pancinoetal. 2002)).," In any case, even $s$ -process enhanced stars in $\omega$ Cen still show a low [Cu/Fe] (though there is some Cu enhancement of giants at the highest metallicities; see \citealt{Pancino2002}) )."
 Cunhaetal.(2002) attribute the low [Cu/Fe) in w Cen to enhanced SNe Type II (and litle SNe Type Ia) enrichment., \citet{Cunha2002} attribute the low [Cu/Fe] in $\omega$ Cen to enhanced SNe Type II (and little SNe Type Ia) enrichment.
 If so. then the enhancement in MA's Cu cannot be due to Type II SNe. either.," If so, then the enhancement in M4's Cu cannot be due to Type II SNe, either."
 This conclusion is reinforced by the Lact that the Cu abundances in M15 stars do not correlate with the Eu abundances., This conclusion is reinforced by the fact that the Cu abundances in M15 stars do not correlate with the Eu abundances.
 Eu. an r-process element. is commonly. associated wilh Tvpe II SNe.," Eu, an $r$ -process element, is commonly associated with Type II SNe."
 If Cu owed its production to (he same process. Chen it ought to show the same star-to-star. variation seen in (he MIS Eu abundances.," If Cu owed its production to the same process, then it ought to show the same star-to-star variation seen in the M15 Eu abundances."
 An inspection of the Eu abundances in Snedenetal.(1997). for MI5 stars shows that the highest and lowest [Eu/Fe] stars in our sample. IN462 and 583. have virtually identical [Cu/Fe].," An inspection of the Eu abundances in \citet{Sneden1997} for M15 stars shows that the highest and lowest [Eu/Fe] stars in our sample, K462 and K583, have virtually identical [Cu/Fe]."
 The highest and lowest |Cu/Fe] stars. IN634 and IN853. have essentially the same [Eu/Fe).," The highest and lowest [Cu/Fe] stars, K634 and K853, have essentially the same [Eu/Fe]."
 There is therefore no indication that [Cu/Fe] is in any. way related to the SNe ‘Type I tracer [Eu/Fe]| in M15., There is therefore no indication that [Cu/Fe] is in any way related to the SNe Type II tracer [Eu/Fe] in M15.
 Taken together. the Cu abundances in globular clusters ancl halo field stars suggest a third possibility. that at hieher metallicity stellar Ci abundances receive a significant," 	 Taken together, the Cu abundances in globular clusters and halo field stars suggest a third possibility, that at higher metallicity stellar Cu abundances receive a significant"
issue of the relevance of the distance measured here for the enure Serpens complex.,issue of the relevance of the distance measured here for the entire Serpens complex.
" In this respect, it 1s important to point out that EC 95 is not just any star located in the direction of Serpens."," In this respect, it is important to point out that EC 95 is not just any star located in the direction of Serpens."
" As we have seen earlier, itis a very young Herbig AeBe star."," As we have seen earlier, it is a very young Herbig AeBe star."
" Such intermediate-mass stars are not born in isolation, but as part of small clusters."," Such intermediate-mass stars are not born in isolation, but as part of small clusters."
" Since EC 95 is one of at least 11 pre-main sequence stars in the compact SVS 4 region, there 1s no doubt that it is physically associated with that small cluster (see also Eiroa Casali 1989), and that the distance measured here is also the distance to SVS 4."," Since EC 95 is one of at least 11 pre-main sequence stars in the compact SVS 4 region, there is no doubt that it is physically associated with that small cluster (see also Eiroa Casali 1989), and that the distance measured here is also the distance to SVS 4."
" In addition, SVS 4 is universally acknowledged to be part of the Serpens core region EEiroa Casali 1992), and its members (including EC 95) have always been considered part of the Serpens young stellar cluster (Eiroa Casali 1992)."," In addition, SVS 4 is universally acknowledged to be part of the Serpens core region Eiroa Casali 1992), and its members (including EC 95) have always been considered part of the Serpens young stellar cluster (Eiroa Casali 1992)."
" Thus, we argue that the distance to EC 95 measured here also provides an accurate estimate of the distance to the Serpens core."," Thus, we argue that the distance to EC 95 measured here also provides an accurate estimate of the distance to the Serpens core."
 We note further that the Serpens core is only about 5’ across on the plane of the sky (0.6 pe at a distance of 415 pe)., We note further that the Serpens core is only about $'$ across on the plane of the sky (0.6 pc at a distance of 415 pc).
" Thus, depth ellects are not expected to add significantly to the error budget on the determination of the distance to the core."," Thus, depth effects are not expected to add significantly to the error budget on the determination of the distance to the core."
" As a consequence, we argue that the distance to the Serpens core should henceforth be assumed to be 415 +5 Un pc."," As a consequence, we argue that the distance to the Serpens core should henceforth be assumed to be 415 $\pm$ 5 pc."
" With an angular diameter of about 3°, the Serpens cloud is much larger than the Serpens core."," With an angular diameter of about $^\circ$, the Serpens cloud is much larger than the Serpens core."
" At a distance of 415 pe, this would correspond to a physical diameter of about 20 pc."," At a distance of 415 pc, this would correspond to a physical diameter of about 20 pc."
" The depth of the Serpens complex is also likely to be of that order, and depending on the location of the core relative to the rest of the complex, the mean distance appropriate for the Serpens cloud might be up to 20 pe less or 20 pe more than the distance to the core."," The depth of the Serpens complex is also likely to be of that order, and depending on the location of the core relative to the rest of the complex, the mean distance appropriate for the Serpens cloud might be up to 20 pc less or 20 pc more than the distance to the core."
" Thus, we argue that a conservative estimate of the mean distance to the Serpens cloud would be 415 + 25 pc."," Thus, we argue that a conservative estimate of the mean distance to the Serpens cloud would be 415 $\pm$ 25 pc."
 This value is significantly larger than the figure reported by Straizyys et ((1996) for the Serpens molecular cloud (d = 259 + 37 pc)., This value is significantly larger than the figure reported by Straižyys et (1996) for the Serpens molecular cloud $d$ = 259 $\pm$ 37 pc).
 Since the total extent of the Serpens cloud on the plane of the sky is only about 20 pc. itis extremely unlikely to be 150 pc deep.," Since the total extent of the Serpens cloud on the plane of the sky is only about 20 pc, it is extremely unlikely to be 150 pc deep."
" Instead, we argue that several unrelated regions are likely to coexist along the line of sight."," Instead, we argue that several unrelated regions are likely to coexist along the line of sight."
" As mentioned above, Serpens is one of the many dust clouds forming the large structure known as the Aquila Rift."," As mentioned above, Serpens is one of the many dust clouds forming the large structure known as the Aquila Rift."
" Straizyys et (2003) have shown that the front edge of that structure is at about 230 pe, and that its depth is about 80 pe."," Straižyys et (2003) have shown that the front edge of that structure is at about 230 pc, and that its depth is about 80 pc."
" The discrepancy between our result and that of of StraiZyvs et ((1996) could be readily explained if the Serpens molecular cloud were not physically associated with the Aquila Rift, but instead located behind it."," The discrepancy between our result and that of of Straižyys et (1996) could be readily explained if the Serpens molecular cloud were not physically associated with the Aquila Rift, but instead located behind it."
" In this situation, since the method used by Straizyys et ((1996) is sensitive lo the position of the first obscuring material located along the line of sight, it would have naturally picked out the foreground Aquila Rift clouds, rather that the more distance Serpens region."," In this situation, since the method used by Straižyys et (1996) is sensitive to the position of the first obscuring material located along the line of sight, it would have naturally picked out the foreground Aquila Rift clouds, rather that the more distance Serpens region."
" Indeed, in their concluding remarks, Straizyys et (2003) state thatRiff."," Indeed, in their concluding remarks, Straižyys et (2003) state that."
" Such a superposition along the same line of sight of different clouds at different distances is not enurely surprising since that line of sight passes only slightly above the Galactic plane, but certainly warrants caution when considering individual regions in that direction."," Such a superposition along the same line of sight of different clouds at different distances is not entirely surprising since that line of sight passes only slightly above the Galactic plane, but certainly warrants caution when considering individual regions in that direction."
" For instance, it is quite plausible that some of the patchy structures seen in the direction of Serpens on optical plates are in fact associated with l'oreground material in the Aquila Rift."," For instance, it is quite plausible that some of the patchy structures seen in the direction of Serpens on optical plates are in fact associated with foreground material in the Aquila Rift."
PPARC stucentship anc PIU acknowlecdexss support from the European Union through the ναΙΤ]:ο and. Mobility Research Network €ant ERBEAIRA/ΤΟΝ0195.,PPARC studentship and PR acknowledges support from the European Union through the Training and Mobility Research Network Grant ERBFMRX/CT98/0195.
 1n addition. we gratefully acknowledge helpful contributions from the referee. Dr. L. lxaper.," In addition, we gratefully acknowledge helpful contributions from the referee, Dr. L. Kaper."
proceeds as follows.,proceeds as follows.
 First. the star is allowed. to. evolve for some period of time.," First, the star is allowed to evolve for some period of time."
 To lose mass. the evolution is halted and. mass is lost as described above.," To lose mass, the evolution is halted and mass is lost as described above."
 Once the star has returned to an equilibrium configuration. the evolution is restarted. and continues until the next mass loss step.," Once the star has returned to an equilibrium configuration, the evolution is restarted, and continues until the next mass loss step."
 This process is repeated. until the star reaches the desired evolutionary stage., This process is repeated until the star reaches the desired evolutionary stage.
 In this paper. however. we will consider only zero-age main sequence (ZAXMS) models.," In this paper, however, we will consider only zero-age main sequence (ZAMS) models."
 The effects of 2D mass loss on stellar evolution will be discussed in a future paper., The effects of 2D mass loss on stellar evolution will be discussed in a future paper.
 The ellects. of rotation on mass loss rates can be seen in Figure 1. for the two considered. mass loss rates., The effects of rotation on mass loss rates can be seen in Figure \ref{fig:vrates} for the two considered mass loss rates.
 The VOI rates are always higher than the WSO rates. but the cilference decreases as the mass of the model increases.," The V01 rates are always higher than the K89 rates, but the difference decreases as the mass of the model increases."
 This is consistent with the results of Vinketal(2000).. who found that their theoretical rates resolved the discrepancy between theoretical and observed mass loss rates for normal O stars.," This is consistent with the results of \citet{vink00}, who found that their theoretical rates resolved the discrepancy between theoretical and observed mass loss rates for normal O stars."
 The observed rates are typically a factor of two higher than those predicted. by racliation-driven wind theory. but the Vinkctal(2000). ancl VOL rates are in good agreement with observations for these stars.," The observed rates are typically a factor of two higher than those predicted by radiation-driven wind theory, but the \citet{vink00} and V01 rates are in good agreement with observations for these stars."
 1n general. the mass loss rates decrease as the rotation rate increases.," In general, the mass loss rates decrease as the rotation rate increases."
 Phe exception is the WSO rate in the 30 nmimodels. which increase slightly. with increasing rotation rate.," The exception is the K89 rate in the 30 models, which increase slightly with increasing rotation rate."
 In this model. the elective. temperature is. close to 400000 Ix. where our parametrization of & has a discontinuitv clue to lines from €NO elements.," In this model, the effective temperature is close to 000 K, where our parametrization of $k$ has a discontinuity due to lines from CNO elements."
 Above 400000 Ix. &À increases sharply. and the resulting mass loss rates are higher than at temperatures below 400000 Ix. In the 30 nunoclels. the effective temperatures are around: 390000 Ix. just below this gap.," Above 000 K, $k$ increases sharply, and the resulting mass loss rates are higher than at temperatures below 000 K. In the 30 models, the effective temperatures are around 000 K, just below this gap."
 However. as the rotation rate increases. the pole becomes hotter. and. temperatures in this region are above 400000 Ik. This local increase in the mass loss rate at the pole increases the overall mass loss rate for the star.," However, as the rotation rate increases, the pole becomes hotter, and temperatures in this region are above 000 K. This local increase in the mass loss rate at the pole increases the overall mass loss rate for the star."
 “Phe οσο becomes more pronounced. as the rotation rate increases. and the mass loss rate increases with rotation.," The effect becomes more pronounced as the rotation rate increases, and the mass loss rate increases with rotation."
 The 20 and 40 nunocels are sulliciently far from this jump that the mass loss rates are not alfected., The 20 and 40 models are sufficiently far from this jump that the mass loss rates are not affected.
 The VOL models do not depend on our parameterization of the force multiplier parameters. ancl so this ellect is not seen in these rates.," The V01 models do not depend on our parameterization of the force multiplier parameters, and so this effect is not seen in these rates."
 Using our 2D models. we can also compare the anisotropy of the mass loss rates to that predicted using our pseudo-1D models.," Using our 2D models, we can also compare the anisotropy of the mass loss rates to that predicted using our pseudo-1D models."
 The dillerence between 2D. and. pseucdo-1D calculations is shown for the INNO rates in Figure 2. and for the VOL rates in Figure 3..., The difference between 2D and pseudo-1D calculations is shown for the K89 rates in Figure \ref{fig:kudrates} and for the V01 rates in Figure \ref{fig:vinkrates}.
 As expected. our 2D models lose more mass at the pole and less mass from the equator than the pseudo-1D models.," As expected, our 2D models lose more mass at the pole and less mass from the equator than the pseudo-1D models."
" The effects can be significant (nearly 0.1 dex at the pole) even for relatively slowly rotating models (0.3 ,).", The effects can be significant (nearly 0.1 dex at the pole) even for relatively slowly rotating models (0.3 $\Omega_c$ ).
 In Figure 2.. the ellect of the jump in & near 0000 can be seen in the sharp decrease in mass loss rate near the equator of the 40 numodel.," In Figure \ref{fig:kudrates}, the effect of the jump in $k$ near 000 can be seen in the sharp decrease in mass loss rate near the equator of the 40 model."
 Compare this with the 20 numodel. where the temperature is always well below the jump. and the mass loss rate varies smoothlv with co-[atitcle.," Compare this with the 20 model, where the temperature is always well below the jump, and the mass loss rate varies smoothly with co-latitude."
 Despite the dilferences. in distribution of mass loss. the total integrated: mass lost in the 2D) and. pseudo-1D calculations is nearly identical.," Despite the differences in distribution of mass loss, the total integrated mass lost in the 2D and pseudo-1D calculations is nearly identical."
 The total mass lost in cach case is shown in Table 2.., The total mass lost in each case is shown in Table \ref{tab:massloss}.
 The dilference in integrated mass lost is largest [or models where the range of surface temperatures covers the jump in mass loss rates caused. by, The difference in integrated mass lost is largest for models where the range of surface temperatures covers the jump in mass loss rates caused by
reproduce this behaviour.,reproduce this behaviour.
 In particular for face-on galaxies. he optical depth will always be underestimated. by such approximations. as illustrated. in Figure2.," In particular for face-on galaxies, the optical depth will always be underestimated by such approximations, as illustrated in Figure."
 If. we compare he attenuation curves corresponding to isotropic and anisotropic scattering however. we see that the dillerence oetween them are only of the order of a hudredth of a magnitude.," If we compare the attenuation curves corresponding to isotropic and anisotropic scattering however, we see that the difference between them are only of the order of a hudredth of a magnitude."
 Anisotropy elfects are essentially washed out., Anisotropy effects are essentially washed out.
 Inversely it will be impossible to determine an AREF from yhotometry., Inversely it will be impossible to determine an ARF from photometry.
 The ellects of scattering are also important if we investigate the influence of the star-dust geometry on the attenuation in cise galaxies., The effects of scattering are also important if we investigate the influence of the star-dust geometry on the attenuation in disc galaxies.
 If scattering is not taken into account. as in Disnev et ((1989).. we Line that je attenuation is more cllective if the dust. distribution is extended.," If scattering is not taken into account, as in Disney et (1989), we find that the attenuation is more effective if the dust distribution is extended."
 For a same amount of dust. the larecr the lavering parameter. the larger the attenuation.," For a same amount of dust, the larger the layering parameter, the larger the attenuation."
 In particular ls means that the overlying screen geometry is the most cllicient obscuring geometry. whereas galaxies with a dust scaleheight smaller than the stelar scaleheight. are less ellicienIv obsceured.," In particular this means that the overlying screen geometry is the most efficient obscuring geometry, whereas galaxies with a dust scaleheight smaller than the stellar scaleheight, are less efficiently obscured."
 However. wher1 scattering is taken into accotunt. this picture does not hod anvmore.," However, when scattering is taken into account, this picture does not hold anymore."
 We find the remarkable effect of scattering that in the face-on direction. galaxies with a moderate optical depth. (75.« 2) are most ellicicntly: obscured by a centrally concentrated. dust distribution.," We find the remarkable effect of scattering that in the face-on direction, galaxies with a moderate optical depth $\tau_0<2$ ) are most efficiently obscured by a centrally concentrated dust distribution."
 This is very interesting because the optical depth of spiral galaxies is thought to be of the order unity in optical bands., This is very interesting because the optical depth of spiral galaxies is thought to be of the order unity in optical bands.
 The clleets of scattering and geometry not only need to be investigated in a qualitative way. it is important to know them quantitatively.," The effects of scattering and geometry not only need to be investigated in a qualitative way, it is important to know them quantitatively."
 Εις allows us to answer questions as how large our error is when we approximate anisotropic scattering by assuming it is forward. or when we assume a dust secalehcight equal to that of the stars. where in reality it is only half of it.," This allows us to answer questions as how large our error is when we approximate anisotropic scattering by assuming it is forward, or when we assume a dust scaleheight equal to that of the stars, where in reality it is only half of it."
 The magnitude of these errors. depends on the inclination., The magnitude of these errors depends on the inclination.
 In the face-on direction. the errors induced. by not properly taking scattering into account are largest.," In the face-on direction, the errors induced by not properly taking scattering into account are largest."
 In the»s approximation. the induced. errors rise up to nearly half a magnitude. for forward scattering they are of the order of 0.15 mag at optical wavelengths (Figure 2b).," In the approximation, the induced errors rise up to nearly half a magnitude, for forward scattering they are of the order of 0.15 mag at optical wavelengths (Figure b)."
 Phe errors introduced. by uncertainty about the stardust geometry are only of the order of a lew Πιοοας of a magnitude (Figure Tb). and thus significantly smaller.," The errors introduced by uncertainty about the star-dust geometry are only of the order of a few hundredths of a magnitude (Figure ), and thus significantly smaller."
 For inclined directions. the optical depth along lines-of-sight towards the observer is much larger.," For inclined directions, the optical depth along lines-of-sight towards the observer is much larger."
 Phe attenuation curve then becomes less dependent on the angular redistribution function. in agreement with Di Bartolomeo et ((1995).," The attenuation curve then becomes less dependent on the angular redistribution function, in agreement with Di Bartolomeo et (1995)."
 Phe dillerences between the attenuation curves corresponding to cilferent star-clust ecometries grows significantly., The differences between the attenuation curves corresponding to different star-dust geometries grows significantly.
 For example. for a galaxy with an inclination of 75° (Geo= 0.25). the differences between the true. isotropic. forward. ancl two-stream attenuation curves become about 0.1 mag at optical wavelengths. and only a few hundredth of a magnitude in the UV (Figure 2aa)," For example, for a galaxy with an inclination of $^\circ$ $\mu=0.25$ ), the differences between the true, isotropic, forward and two-stream attenuation curves become about 0.1 mag at optical wavelengths, and only a few hundredth of a magnitude in the UV (Figure \ref{scatimpo.ps}a a)."
 llowever. assumingὃν a homogeneouso slab mocel instead. of our template model. the induced error on the attenuation curve is about 0.3 magnitudes at optical anc more than half a magnitude at UV wavelengths.," However, assuming a homogeneous slab model instead of our template model, the induced error on the attenuation curve is about 0.3 magnitudes at optical and more than half a magnitude at UV wavelengths."
 For face-on ealaxies it is thus important to include scattering in a proper wav in the modelling. for inclined. galaxies it is important to have a fairly good idea of the star-dust. gcometry of the ealaxy.," For face-on galaxies it is thus important to include scattering in a proper way in the modelling, for inclined galaxies it is important to have a fairly good idea of the star-dust geometry of the galaxy."
 1n the light5 of the adopted: models. two remarks are appropriate. (," In the light of the adopted models, two remarks are appropriate. ("
1) By working in plane-parallel goometry. we have the advantage that we could use four independent methods to solve the IPIE. such that the accuracy of the obtained results can be checked carefullv.,"1) By working in plane-parallel geometry we have the advantage that we could use four independent methods to solve the RTE, such that the accuracy of the obtained results can be checked carefully."
 We are well aware of the fact that plane-parallel galaxy models co not represent very realistic ealactic disces., We are well aware of the fact that plane-parallel galaxy models do not represent very realistic galactic discs.
 More. detailed modelling requires an exponential fallolf in the racial direction (Freeman 1970). a distinction in attenuation between arm and interarm regions WWhite ct 22000). and an inclusion of the elfects of clumping of both stars and dust (Witt Gordon 1996. 2000: Bianchi ct 22000).," More detailed modelling requires an exponential fall-off in the radial direction (Freeman 1970), a distinction in attenuation between arm and interarm regions White et 2000), and an inclusion of the effects of clumping of both stars and dust (Witt Gordon 1996, 2000; Bianchi et 2000)."
 Nevertheless we are convinced that our mocelling can contribute to the understanding of the mechanism of radiative transfer. ancl we have all reasons to believe that our results would hold qualitatively in more complex mocdols. (," Nevertheless we are convinced that our modelling can contribute to the understanding of the mechanism of radiative transfer, and we have all reasons to believe that our results would hold qualitatively in more complex models. ("
2) We know that scattering and goometry are not the only two elements that introduce uncertainties to the attenuation of cdisc galaxies.,2) We know that scattering and geometry are not the only two elements that introduce uncertainties to the attenuation of disc galaxies.
 In Article E we solved the RPE for identica galaxy models. but with two different sets of optical dus parameters found in the literature.," In Article I we solved the RTE for identical galaxy models, but with two different sets of optical dust parameters found in the literature."
 We obtained cillerences between the attenuation curves olf the order ofa few tenths of a magnitude., We obtained differences between the attenuation curves of the order of a few tenths of a magnitude.
 Uncertainty about the optical properties of the dust hence also introduces errors to the attenuation curve., Uncertainty about the optical properties of the dust hence also introduces errors to the attenuation curve.
 Llowever. these errors are independent of those introduce » an inaccurate treatment of scattering or geometry. au hey hence do not alfect the conclusion of this work.," However, these errors are independent of those introduced by an inaccurate treatment of scattering or geometry, and they hence do not affect the conclusion of this work."
 As a final remark. we re-iterate a warning that has also been issued by others: do not use too simplistic models o determine the opacity in cise galaxies.," As a final remark, we re-iterate a warning that has also been issued by others: do not use too simplistic models to determine the opacity in disc galaxies."
 There are many wavs to investigate the amount of attenuation or the optical hickness of dise galaxies., There are many ways to investigate the amount of attenuation or the optical thickness of disc galaxies.
 Following Nilouris ct (1997). we can divide them into two categories. the small ΑΝ approach and the large N approach.," Following Xilouris et (1997), we can divide them into two categories, the small $N$ approach and the large $N$ approach."
 The small No approach ries to determine the opacity of individual nearby disc ealaxies by constructing detailed radiative transfer mocoels., The small $N$ approach tries to determine the opacity of individual nearby disc galaxies by constructing detailed radiative transfer models.
 Obviously. these methods would. reveal wrong results if scattering is neglected.," Obviously, these methods would reveal wrong results if scattering is neglected."
 Ehe large No approach aims at determining a mean value for the optical depth in disc ealaxies. by statistically studying a large sample of galaxies.," The large $N$ approach aims at determining a mean value for the optical depth in disc galaxies, by statistically studying a large sample of galaxies."
 Of such a sample of galaxies a certain observable is then compared to a galaxy model. in order to derive the optical depth.," Of such a sample of galaxies a certain observable is then compared to a galaxy model, in order to derive the optical depth."
 However. these methods. are οΠου to. interpret because of selection elfects (Davies et 11993). and there are often. mocdel-dependent.," However, these methods are difficult to interpret because of selection effects (Davies et 1993), and there are often model-dependent."
 For example. Saunders ct ((1990) estimate an average effective optical depth of disc galaxies bv fitting a screen model to the optical and. far-infrared luminosity Functions.," For example, Saunders et (1990) estimate an average effective optical depth of disc galaxies by fitting a screen model to the optical and far-infrared luminosity functions."
 Trewhella et ((1997) recdid these calculations with a sandwich model. and found a very dillerent. conclusion.," Trewhella et (1997) redid these calculations with a sandwich model, and found a very different conclusion."
 We want to stress that also in such studies the cllects of scattering. need to be taken into account. because they are. except for very inclined galaxies. at least as important as the elfects of geometry.," We want to stress that also in such studies the effects of scattering need to be taken into account, because they are, except for very inclined galaxies, at least as important as the effects of geometry."
likely contributor.,likely contributor.
 Indeed. if: as widely believed. radio galaxy hosts are giant ellipticals or their progenitors at all redshifts. then one can estimate the amount of UV light expected from star formation if radio galaxies form all their zz3«10444. of stars in a single burst starting at 2=ox and finishing at 2=ld.," Indeed, if, as widely believed, radio galaxy hosts are giant ellipticals or their progenitors at all redshifts, then one can estimate the amount of UV light expected from star formation if radio galaxies form all their $\approx 3\times 10^{11} M_{\odot}$ of stars in a single burst starting at $z=\infty$ and finishing at $z=1$."
 This is plotted on 55 as the lone-casher line. assuming a Sealo (1986) initial mass function.," This is plotted on 5 as the long-dashed line, assuming a Scalo (1986) initial mass function."
 The average star formation rate. 65A.vr. * is high enough thaunobsceured star formation at or above this rate should. be easily detected in our z2 objects.," The average star formation rate, $65 M_{\odot}$ $^{-1}$ is high enough that star formation at or above this rate should be easily detected in our $z\sim 2$ objects."
 The fact that they al lie close to or fainter than this line could be attributed to several causes: (1) obscuration by dust may be extinguishing the UV light. (2) the star-forming episodes are of. shor duration. (3) the star-forming episodes occur mostly at very high redshift. (4) the star formation occurs in small sub-units before the radio galaxy host assembles. or (5)r the cosmology is significantly dillerent [rom Einstein cle Sitter.," The fact that they all lie close to or fainter than this line could be attributed to several causes: (1) obscuration by dust may be extinguishing the UV light, (2) the star-forming episodes are of short duration, (3) the star-forming episodes occur mostly at very high redshift, (4) the star formation occurs in small sub-units before the radio galaxy host assembles, or (5) the cosmology is significantly different from Einstein – de Sitter."
 Llughes and collaborators are. performing a SCUBA-based. subnim survey of high redshift. radio galaxies. [ron the 3€ ancl 6€ (Eales 1985) surveys which should help to acidress point (1) HIIughes Dunlop 1998: Hughes et 11998)., Hughes and collaborators are performing a SCUBA-based submm survey of high redshift radio galaxies from the 3C and 6C (Eales 1985) surveys which should help to address point (1) Hughes Dunlop 1998; Hughes et 1998).
 Current limits on star formation rates are about an order of magnitude higher than 6542. 1., Current limits on star formation rates are about an order of magnitude higher than $65 M_{\odot}$ $^{-1}$.
 Nevertheless. several detections of 2οzX4.3 galaxies have already been mace at this level.," Nevertheless, several detections of $2 \stackrel{<}{_{\sim}} z \stackrel{<}{_{\sim}}4.3$ galaxies have already been made at this level."
 In addition Best et (1998) have reported a probable detection of the z1.2 radio galaxy 3€C324., In addition Best et (1998) have reported a probable detection of the $z=1.2$ radio galaxy 3C324.
 These detections. however. may only be upper limits too. in the sense that much of the PLR. emission could be coming from dust heated. by the ACN rather than from a starburst.," These detections, however, may only be upper limits too, in the sense that much of the FIR emission could be coming from dust heated by the AGN rather than from a starburst."
 The laree dust masses. involved. though. suggest at the very least that a large amount of star formation must have taken place in these objects by the time they are observed.," The large dust masses involved, though, suggest at the very least that a large amount of star formation must have taken place in these objects by the time they are observed."
 Possibility. (2) can probably be ruled: out unless the starbursts occur systematically before the formation of the radio source., Possibility (2) can probably be ruled out unless the starbursts occur systematically before the formation of the radio source.
 Even so. such very bright starbursts should be easily detected in the IV/submm (if they are dustv) or in optical narrow-band searches if not.," Even so, such very bright starbursts should be easily detected in the IR/submm (if they are dusty) or in optical narrow-band searches if not."
 Support for (3) or (4). very high redshift star formation either coherently or in small subunits which subsequently merge. comes from the studies of the old stellar populations in the radio galaxies 3€65 (2=L2: Lacy et 11995b: Stockton et 1995) and S3WOOL (2=1.55. Dunlop et 11996).," Support for (3) or (4), very high redshift star formation either coherently or in small subunits which subsequently merge, comes from the studies of the old stellar populations in the radio galaxies 3C65 $z=1.2$; Lacy et 1995b; Stockton et 1995) and 53W091 $z=1.55$, Dunlop et 1996)."
 Phe old stellar populations seen in some radio galaxies contrast with the studies of Zepf (1997) ancl Barger et ((1999) who find relatively low numbers of very red. galaxies in opticalfintrared studies of the Hubble Deep Field. (IDE) ancl its Hlanking fields., The old stellar populations seen in some radio galaxies contrast with the studies of Zepf (1997) and Barger et (1999) who find relatively low numbers of very red galaxies in optical/infrared studies of the Hubble Deep Field (HDF) and its flanking fields.
 These show that only ~50 per cent of field. ellipticals are in place by 2=1. and that the remainder probably formed. at zο3.," These show that only $\sim 50$ per cent of field ellipticals are in place by $z=1$, and that the remainder probably formed at $z\stackrel{<}{_{\sim}}3$."
M The relatively high UV. luminosity density. produced by 2.~4 Lyman-dropout galaxies found by Steidel et ((1998). however. points to he possibility that at least some galaxies formed at. higher redshifts. ," The relatively high UV luminosity density produced by $z\sim 4$ Lyman-dropout galaxies found by Steidel et (1998), however, points to the possibility that at least some galaxies formed at higher redshifts. ["
Dust-obsceurecd starbursts may allect this picture if they are important contributors to the star. formation srocess in ellipticals. but currently this is uncertain TV'Erentham. Blain Goldader 1998).],"Dust-obscured starbursts may affect this picture if they are important contributors to the star formation process in ellipticals, but currently this is uncertain Trentham, Blain Goldader 1998).]"
" A possible explanation for the apparent. discrepancy oween the ages of some radio galaxies ancl the. field ellipticals is that giant elliptical galaxies formed earlier than normal ~L, elliptical galaxies.", A possible explanation for the apparent discrepancy between the ages of some radio galaxies and the field ellipticals is that giant elliptical galaxies formed earlier than normal $\sim L_*$ elliptical galaxies.
 This would. be broacly consistent with an extrapolation of a trend. deduced: by Cowie et al. (, This would be broadly consistent with an extrapolation of a trend deduced by Cowie et al. (
1996) for more massive galaxies to have their major episodes of star formation at earlier epochs.,1996) for more massive galaxies to have their major episodes of star formation at earlier epochs.
 Lf the oldest. galaxies are the super-L. population. they will be rare in the relatively small area field surveys mace to date.," If the oldest galaxies are the $L_*$ population, they will be rare in the relatively small area field surveys made to date."
 Explanation (5). an incorrect cosmology. remains possible.," Explanation (5), an incorrect cosmology, remains possible."
 For example an O3;=0.5.040.5 cosmology with the same value of ffy only requires a minimum star formation rate of zz50M.vr.+ toform all the stars by z— I. and the emission will also appear fainter at à given recdshif due to the higher luminosity distance.," For example an $\Omega_{\rm M}=0.5, 
\Omega_{\Lambda}=0.5$ cosmology with the same value of $H_0$ only requires a minimum star formation rate of $\approx 50 M_{\odot} {\rm yr^{-1}}$ to form all the stars by $z=1$ , and the emission will also appear fainter at a given redshift due to the higher luminosity distance."
 These combine to make the magnitude for à z=2 galaxy forming stars a he minimum rate 0.8 mag fainter. for example.," These combine to make the $R$ -magnitude for a $z=2$ galaxy forming stars at the minimum rate 0.8 mag fainter, for example."
 The lack of UM. emission also argues somewhat agains jet-inclucecl star formation being an important contributor o the star formation process of the galaxy as a whole. a cast at zZ3.," The lack of UV emission also argues somewhat against jet-induced star formation being an important contributor to the star formation process of the galaxy as a whole, at least at $z\stackrel{<}{_{\sim}}3$."
 Wit were. one would expect all radio galaxies o show large amounts of UN. and/or submini emission.," If it were, one would expect all radio galaxies to show large amounts of UV and/or submm emission."
 Lt remains possible though that an initial episode of star ormation activity could be triggered by an carly outburst of radio jet activity at high. redshift. and that. subsequent episodes of radio jet activity would. produce more mocoest starbursts. consistent with the relatively low limits on the unobscured star formation rates we inferfor the δς radio ealaxies.," It remains possible though that an initial episode of star formation activity could be triggered by an early outburst of radio jet activity at high redshift, and that subsequent episodes of radio jet activity would produce more modest starbursts, consistent with the relatively low limits on the unobscured star formation rates we inferfor the 8C radio galaxies."
 , 
πι=—uno.,$u_{z+}=-u_{z-}$.
 Because of these relations. we can restrict ourselves to solving the equations for the positively charged fluid. and will henceforth drop the plus subscript for simplicity.," Because of these relations, we can restrict ourselves to solving the equations for the positively charged fluid, and will henceforth drop the plus subscript for simplicity."
 The simplest solution of these equations is Cae case of a circularly polarized wave., The simplest solution of these equations is the case of a circularly polarized wave.
 Then D—0. and we have: and the magnitude of the perpendicular component of the four-momentunm equals the oy parameter à. defined using the electric field amplitude as parallel component of the four-velocityv is a constant.," Then $B=0$, and we have: The frequency coincides with the (proper) plasma frequency: and the magnitude of the perpendicular component of the four-momentum equals the or parameter $\strength$, defined using the electric field amplitude as The parallel component of the four-velocity is a constant."
" In the laboratory frame. which moves al speed —e/0, as seen from the I-frame. the frequency of the wave is where L4 is the Lorentz factor of the transformation between the II-frame andthe [Iraae."," In the laboratory frame, which moves at speed $-c/v_{\phi}$ as seen from the H-frame, the frequency of the wave is where $\Gamma_>$ is the Lorentz factor of the transformation between the H-frame andthe frame."
From the derived My and fos. values. the mass of the progenitor (My. can be determined using an initial-final mass relationship(?).,"From the derived $M_{\rm WD}$ and $t_{\rm cool}$ values, the mass of the progenitor $M_{\rm prog}$ ) can be determined using an initial-final mass relationship."
. From) the calculated μου. we used the stellar tracks of to derive the progenitor's lifetime (poo).," From the calculated $M_{\rm prog}$, we used the stellar tracks of to derive the progenitor's lifetime $t_{\rm prog}$ )."
 The total age of the WDs. and consequently that of the low-mass companion. follows directly by adding fp. and £4.," The total age of the WDs, and consequently that of the low-mass companion, follows directly by adding $t_{\rm prog}$ and $t_{\rm cool}$."
 The final age value is provided in Table 7.., The final age value is provided in Table \ref{results1}.
 In this Table we compiled the final atmospheric parameters. the mass of the WD. the Nass of the progenitor star. the cooling time of the WD. the main-sequence time of the progenitor star. the total age. the ratio between the cooling time and the total age. and the colour of the low-mass companions.," In this Table we compiled the final atmospheric parameters, the mass of the WD, the mass of the progenitor star, the cooling time of the WD, the main-sequence time of the progenitor star, the total age, the ratio between the cooling time and the total age, and the colour of the low-mass companions."
 The first 18 WDs in the Table have atmospheric parameters determined from the Balmer line profile fitting., The first 18 WDs in the Table have atmospheric parameters determined from the Balmer line profile fitting.
 The three objects in the middle were analysed spectroscopically. but the derived loge are outside of the valid parameter range of our procedure.," The three objects in the middle were analysed spectroscopically, but the derived $\log g$ are outside of the valid parameter range of our procedure."
 The nine WDs at the end of the table have temperatures determined by VJK photometry and the mear logg value for our sample estimated from the spectroscopic determinations., The nine WDs at the end of the table have temperatures determined by $VJHK$ photometry and the mean $\log g$ value for our sample estimated from the spectroscopic determinations.
" Some of the WDs in our sample have atmospheric parameters and. in some cases. masses. cooling times. and ages estimated from previous investigations. such as?..2., ?.. and?."," Some of the WDs in our sample have atmospheric parameters and, in some cases, masses, cooling times, and ages estimated from previous investigations, such as, , and."
. We can compare our results to the previous determination., We can compare our results to the previous determination.
 Our Το[u and logg values are compared to those in the literature and are shown in Fig. 6..," Our $T_{\rm eff}$ and $\log
g$ values are compared to those in the literature and are shown in Fig. \ref{t_log_comp}."
 In general the agreement between the Τη determinations is good within the uncertainties. but there are some discrepant results for some of the targets. such as NLTT26379and G56-BIB. In the case of," In general the agreement between the $T_{\rm eff}$ determinations is good within the uncertainties, but there are some discrepant results for some of the targets, such as NLTT26379and G86-B1B. In the case of"
"diamond in the figure) resides well away from this plane at a distance of 83 kpc, 3.4 times the thickness of the PoS. There is increasing evidence that NGC 2419 is an accreted object.","diamond in the figure) resides well away from this plane at a distance of 83 kpc, 3.4 times the thickness of the PoS. There is increasing evidence that NGC 2419 is an accreted object."
" Specifically, Cohenetal.(2010),, argue that due to its internal [Fe/H] spread this cluster is the former nucleus (or nuclear star cluster) of a disrupted dwarf."," Specifically, \citet{Cohen10}, argue that due to its internal [Fe/H] spread this cluster is the former nucleus (or nuclear star cluster) of a disrupted dwarf."
 Potentially therefore NGC 2419 had been accreted away from the plane apparently preferred by the vast majority of the MW's accreted objects., Potentially therefore NGC 2419 had been accreted away from the plane apparently preferred by the vast majority of the MW's accreted objects.
 Our findings reinforce those of Yoon&Lee(2002) from a sample of GCs restricted to Πας<20 kpc., Our findings reinforce those of \citet{Yoon02} from a sample of GCs restricted to $R_{GC} < 20$ kpc.
" In that study, these authors isolated a set of young halo clusters based on metallicity and RR Lyrae pulsation period (as discussed in refSection:partitionGCs))."," In that study, these authors isolated a set of young halo clusters based on metallicity and RR Lyrae pulsation period (as discussed in \\ref{Section:partitionGCs}) )."
" Their set of seven young GCs (their ‘group II-b' ) describe a plane orientated towards (=183°+15°, b=—3°+9° (at significance compared to an isotropic distribution), which is consistent with the PoS derived here."," Their set of seven young GCs (their `group II-b' ) describe a plane orientated towards $\ell =183^{\circ} \pm 15^{\circ}$, $\textit{b} =-3^{\circ} \pm 9^{\circ}$ (at significance compared to an isotropic distribution), which is consistent with the PoS derived here."
" The PoS is therefore, persistent in the spatial distribution of the MW’s YH GCs to the inner galaxy."," The PoS is therefore, persistent in the spatial distribution of the MW's YH GCs to the inner galaxy."
" Although we here use YH GCs as a tracer of accreted systems, it is expected that accreted systems will deposit both YH and OH clusters."," Although we here use YH GCs as a tracer of accreted systems, it is expected that accreted systems will deposit both YH and OH clusters."
 As pointed out by Da the Sgr dwarf is contributing to both groups., As pointed out by \citet{DaCostaArmandroff95} the Sgr dwarf is contributing to both groups.
" Furthermore, Mackey propose that of the OH GCs were contributed via accretions."," Furthermore, \citet{Mackey04} propose that of the OH GCs were contributed via accretions."
 The fact that our analysis had not shown any radial anisotropy in the distribution of OH GCs is perhaps a consequence of the smaller fraction of accreted systems in this grouping compared to the YH GCs., The fact that our analysis had not shown any radial anisotropy in the distribution of OH GCs is perhaps a consequence of the smaller fraction of accreted systems in this grouping compared to the YH GCs.
 We have shown that the YH GC population at galactocentric distances exceeding 10 kpc exhibits thesame orientation (within uncertainties) as that defined by the MW satellites., We have shown that the YH GC population at galactocentric distances exceeding 10 kpc exhibits the orientation (within uncertainties) as that defined by the MW satellites.
 This argues for a strong causal link between the origins of the outer halo GCs and the MW satellites., This argues for a strong causal link between the origins of the outer halo GCs and the MW satellites.
" In the next section we discuss the origins of the planar arrangements of dwarf galaxies around the MW and M31, and by direct association, the origin of the outer halo globular clusters."," In the next section we discuss the origins of the planar arrangements of dwarf galaxies around the MW and M31, and by direct association, the origin of the outer halo globular clusters."
 Three scenarios are presented in the literature regarding the development of the spatial distribution of satellites: that the satellites are in-situ tracers of a prolate dark matter halo; that they are remnants from the break up of a large progenitor at early times tthe satellites are tidally disrupted galaxies - TDGs); or they are tracers of collapse along filaments of large scale structure (LSS)., Three scenarios are presented in the literature regarding the development of the spatial distribution of satellites: that the satellites are in-situ tracers of a prolate dark matter halo; that they are remnants from the break up of a large progenitor at early times the satellites are tidally disrupted galaxies – TDGs); or they are tracers of collapse along filaments of large scale structure (LSS).
 Cosmological simulations of dark matter halos shows that under ACDM cosmology halos are predominantly prolate, Cosmological simulations of dark matter halos shows that under $\Lambda$ CDM cosmology halos are predominantly prolate
the models will approach those of numerical heat conduction for clouds at rest in a static HIM (presented by us in Paper D).,the models will approach those of numerical heat conduction for clouds at rest in a static HIM (presented by us in \cite{vh05}) ).
 The cloud masses were chosen to cover a range between 10? - 10? M:., The cloud masses were chosen to cover a range between $10^{1}$ - $10^{5}$ $_{\sun}$.
 Because the initial model has to fulfill Eqs. (12) , Because the initial model has to fulfill Eqs. \ref{gl10}) )
and (13)). mass and radius are fixed by the initial central cloud density and external pressure and temperature.," and \ref{gl11}) ), mass and radius are fixed by the initial central cloud density and external pressure and temperature."
 The saturation parameter oy (Table 2) indicates à moderately saturated heat conduction for model U and E while model K lies nearly in the suprathermal regime (Balbus McKee. 1982)).," The saturation parameter $\sigma_0$ (Table 2) indicates a moderately saturated heat conduction for model U and E while model K lies nearly in the suprathermal regime (Balbus McKee, \cite{bm82}) )."
" The importance of heat conductior in these simulations is also indicated by the fact that the Field length A, is much larger than the cloud radius δὲ which means that evaporation of the clouds is expected and that the temperature structure of the gas Is dominated by conduction (Begelman McKee 1990)).", The importance of heat conduction in these simulations is also indicated by the fact that the Field length $\lambda_{\mbox{\tiny F}}$ is much larger than the cloud radius $R_{\mbox{\tiny cl}}$ which means that evaporation of the clouds is expected and that the temperature structure of the gas is dominated by conduction (Begelman McKee \cite{bm90}) ).
" The different dynamical timescales 7,, defined as the sound travel time over one cloud radius. the timescales 754; for the growth of KH instability (see Appendix B) and for evaporation are listed in Table 3.."," The different dynamical timescales $\tau_{\mbox{\tiny dyn}}$ defined as the sound travel time over one cloud radius, the timescales $\tau_{\mbox{\tiny KH}}$ for the growth of KH instability (see Appendix B) and for evaporation are listed in Table \ref{t3}."
 Because of the huge density contrast and the large gravitational acceleration of the models U and E. KH instability should be suppressed. at least at the beginning.," Because of the huge density contrast and the large gravitational acceleration of the models U and E, KH instability should be suppressed, at least at the beginning."
 Because of the stability reasons mentioned in Appendix B and because the cloud mass of model E is close to the lower stability limit. this cloud is expected to be disrupted during the calculation.," Because of the stability reasons mentioned in Appendix B and because the cloud mass of model E is close to the lower stability limit, this cloud is expected to be disrupted during the calculation."
 Model U is further inside the mass limit than Model E and will therefore survive longer than the less massive cloud., Model U is further inside the mass limit than Model E and will therefore survive longer than the less massive cloud.
" Model K on the other hand should develop KH instability after 7,=0.15 Myr."," Model K on the other hand should develop KH instability after $\tau_{\mbox{\tiny KH}} = 0.45\,$ Myr."
 Although the evaporation time of Model U and E is too large to be reached during the simulation. we should be able to follow the disintegration process due to evaporation of Model K. In all calculations of πι the effect of saturation is considered.," Although the evaporation time of Model U and E is too large to be reached during the simulation, we should be able to follow the disintegration process due to evaporation of Model K. In all calculations of $\tau_{\mbox{\tiny eva}}$ the effect of saturation is considered."
 The inclusion of heat conduction tends to stabilize massive and large clouds as illustrated by comparing the density contours at the same times (25 Myr. 50 Myr and 75 Myr after the beginning of the calculations) for the model U without (Fig. 2))," The inclusion of heat conduction tends to stabilize massive and large clouds as illustrated by comparing the density contours at the same times (25 Myr, 50 Myr and 75 Myr after the beginning of the calculations) for the model U without (Fig. \ref{f2}) )"
 and with heat conduction (Fig. 3))., and with heat conduction (Fig. \ref{f3}) ).
 Without heat conduction the edge of the cloud is torn by KH instability shortly after the beginning as mentioned in Appendix B. A very complex velocity structure with many vortices behind the cloud forms., Without heat conduction the edge of the cloud is torn by KH instability shortly after the beginning as mentioned in Appendix B. A very complex velocity structure with many vortices behind the cloud forms.
 The increase in the maximum velocity during the calculation is due to acceleration of the gas by Bernoulli's effect when it streams around the formed cloudlets., The increase in the maximum velocity during the calculation is due to acceleration of the gas by Bernoulli's effect when it streams around the formed cloudlets.
 It is therefore only a local effect which does not affect the large cloud as a whole., It is therefore only a local effect which does not affect the large cloud as a whole.
 In the presence of cooling stripped-off cloud material becomes thermally unstable and forms cloudlets that hit the cloud from the rear., In the presence of cooling stripped-off cloud material becomes thermally unstable and forms cloudlets that hit the cloud from the rear.
 As mentioned by Dinge (1997)) these cloudlets produce soundwaves which propagate through the cloud., As mentioned by Dinge \cite{d97}) ) these cloudlets produce soundwaves which propagate through the cloud.
 On the front side these waves produce distortions that can act as seeds for RT instability that lead to an elongation of the cloud perpendicular to the stream direction., On the front side these waves produce distortions that can act as seeds for RT instability that lead to an elongation of the cloud perpendicular to the stream direction.
 This effect is artifically intensified by the applied numerical symmetry., This effect is artifically intensified by the applied numerical symmetry.
 Material once collected on the z-axis sticks there and cannot be removed because the velocity in the radial direction is set to zero at the axis., Material once collected on the z-axis sticks there and cannot be removed because the velocity in the radial direction is set to zero at the axis.
 A detailed analysis of this artefact and the influence of this axis effect is given in Appendix A. The cloud develops a compound envelope. with a radially decreasing density in the core region and a diluted outer part of material that is only slightly gravitationally bound.," A detailed analysis of this artefact and the influence of this axis effect is given in Appendix A. The cloud develops a compound envelope, with a radially decreasing density in the core region and a diluted outer part of material that is only slightly gravitationally bound."
 The loss of gas by stripping and the recapture from the rear leads to a complex mass-loss function with unsteady losses and gains., The loss of gas by stripping and the recapture from the rear leads to a complex mass-loss function with unsteady losses and gains.
"allowing us to write the background density as. with 2, being the critical density required for spherical collapse. extrapolated using linear theory to the present time (=1.686. ignoring the weak cosmological dependence). à στ 0.71. p — 0.3. and A = 0.322.","allowing us to write the background density as, with $\delta_{sc}$ being the critical density required for spherical collapse, extrapolated using linear theory to the present time $=1.686$, ignoring the weak cosmological dependence), a $\approx$ 0.71, p $=$ 0.3, and A $\approx$ 0.322."
 ση.z) is the rms value of the initial Huctuation field when smoothed with a top hat filter and extrapolated to the present time using linear theory.," $\sigma(m,z)$ is the rms value of the initial fluctuation field when smoothed with a top hat filter and extrapolated to the present time using linear theory."
" where ές is the growth factor from Carroll. Press ""Turner (1992)."," where $G$ is the growth factor from Carroll, Press Turner (1992)."
 We will consider two similar HOD mocels., We will consider two similar HOD models.
 The first one is based on the model used in Zehavi et al. (, The first one is based on the model used in Zehavi et al. (
2005) (hereafter Z mocel) to compare to the SDSS data. and is motivated by Ixravtsoy et al. (,"2005) (hereafter Z model) to compare to the SDSS data, and is motivated by Kravtsov et al. ("
2004).,2004).
 The second model was proposed by Tinker ct al. (, The second model was proposed by Tinker et al. (
"2005) (hereafter PWZZ model) and is given by. where M,,;, is the minimum mass for a halo to host one central galaxy. ancl AZ; is the mass of a halo hosting on average one satellite galaxy.","2005) (hereafter TWZZ model) and is given by, where $M_{min}$ is the minimum mass for a halo to host one central galaxy, and $M_1$ is the mass of a halo hosting on average one satellite galaxy."
 Phe 1 represents one central galaxy placed at the center of mass of the parent. halo. and the satellite galaxies follow the underlving dark matter distribution.," The '1' represents one central galaxy placed at the center of mass of the parent halo, and the satellite galaxies follow the underlying dark matter distribution."
 PWZZ model has been used to study the ΠΟ for a range of redshifts and number densities anc found to eive results for the correlation function in good agreement with various redshift surveys in the range z=05] (Conroyetal. 2006)., TWZZ model has been used to study the HOD for a range of redshifts and number densities and found to give results for the correlation function in good agreement with various redshift surveys in the range $z=[0-5]$ \citep{con06}.
. Our purpose here will be to obtain the best-fit LLOD parameters for the two models. and compare the nuniber-weighted halo masses and number of galaxies.," Our purpose here will be to obtain the best-fit HOD parameters for the two models, and compare the number-weighted halo masses and number of galaxies."
 We have decided to use these models in order to keep things simple and easy to interpret., We have decided to use these models in order to keep things simple and easy to interpret.
 Dased on the statisties of the sample and the number of data points used. it is best to use HOD models with a minimal number of [ree parameters adapted to the science case at hand. ie. for this paper. the average halo masses and number galaxies mentioned below.," Based on the statistics of the sample and the number of data points used, it is best to use HOD models with a minimal number of free parameters adapted to the science case at hand, i.e. for this paper, the average halo masses and number galaxies mentioned below."
 The main results that are obtained should remain essentially the same irrespective of the HOD model chosen., The main results that are obtained should remain essentially the same irrespective of the HOD model chosen.
 A complementary approach would be to use modeling based on conditional luminosity functions (CLE) or conditional occupation numbers (CON) (e.g. van den Bosch et al., A complementary approach would be to use modeling based on conditional luminosity functions (CLF) or conditional occupation numbers (CON) (e.g. van den Bosch et al.
 2003. Yang et al.," 2003, Yang et al."
 2003. Cooray 2006).," 2003, Cooray 2006)."
 The present altempt is a first at using a large number of ealaxy spectra at high redshift to study the evolutionary behaviour of a few properties pertaining to the galaxy ancl dark matter distribution., The present attempt is a first at using a large number of galaxy spectra at high redshift to study the evolutionary behaviour of a few properties pertaining to the galaxy and dark matter distribution.
 These few! properties are certainly not comprehensive. and this work can be seen as a starting point for more studies using the sample.," These 'few' properties are certainly not comprehensive, and this work can be seen as a starting point for more studies using the sample."
 Moreover. larger data samples from. ongoing and upcoming redshift surveys," Moreover, larger data samples from ongoing and upcoming redshift surveys"
Vy=Ahad.,$Y_X\equiv M_{\rm gas}T$.
 This quautitv has been suggested by munerical simulations to exhibit low iutrinsic scatter regardless of the cluster dynamical state. in particular sjuce deviatious of temperature and σας inass from the normalization of the mass scaling relations partly auti-correlate during cluster mergers.," This quantity has been suggested by numerical simulations to exhibit low intrinsic scatter regardless of the cluster dynamical state, in particular since deviations of temperature and gas mass from the normalization of the mass scaling relations partly anti-correlate during cluster mergers."
 The cluster mass. Mog. has been estimated using the Vy proxy in DII. assumnidue the Msg). Vy scaling relation to be calibrated from lydrostatic nass estimates in a nearby cluster suuple observed with (Arnaudctal. POLO).," The cluster mass, $M_{500}$, has been estimated using the $Y_X$ proxy in B11, assuming the $M_{500}$ $Y_X$ scaling relation to be calibrated from hydrostatic mass estimates in a nearby cluster sample observed with \citep{arn10}."
" This amass estimate. Ag)=13.091702NLoar i, vields a 20 % exeess with respect to our weal-lensineglh iass."," This mass estimate, $M_{500}=13.09^{+1.40}_{-1.68}\times10^{14}\Msun h^{-1}$ , yields a 20 $\%$ excess with respect to our weak-lensing mass."
 While imareinally significant (l.lo significance level). this mass discrepancy slightly exceeds the ~6% scatter of the Vy proxy. suggested bv nuuercal simulations in Kravtsovotal.(2006).," While marginally significant $\sigma$ significance level), this mass discrepancy slightly exceeds the $\sim6\%$ scatter of the $Y_X$ proxy suggested by numerical simulations in \cite{kra06}."
. Okabeetal.(20106) have investigated clynatical dependence on πας» observable scaling relations. based on X-ray observables (Zhangctal.2008) and weak- lensing masses (Okabeetal.2010b).," \cite{oka10c} have investigated a dynamical dependence on mass observable scaling relations, based on X-ray observables \citep{zha08} and weak- lensing masses \citep{oka10b}."
. This study found the normalization of the Afsyy Vy scaling relation to be lower for disturbed chisters than for undisturbed clusters. contradicting the prediction of normalization independence in cluster dynamical states.," This study found the normalization of the $M_{500}$ $Y_X$ scaling relation to be lower for disturbed clusters than for undisturbed clusters, contradicting the prediction of normalization independence in cluster dynamical states."
 Mass estimates of A2163 relving on the unudisturbed and disturbed cluster scaling relation calibrated ey Okabeetal(20100) yield ALERTmq453!22&103.5| and MASSια... respectively.," Mass estimates of A2163 relying on the undisturbed and disturbed cluster scaling relation calibrated by \cite{oka10c} yield $M_{500}^{\rm (undist)}\simeq14.53^{+2.5}_{-2.1}\times10^{14}\Msun h^{-1}$ and $M_{500}^{\rm (dist)}\simeq11.4^{+1.8}_{-1.5}\times10^{14}\Msun h^{-1}$, respectively."
 Iuterestiusbv. the mass estimate with the scaling relation for disturbed clusters fully agrees with weak-lensing mass. while the uudisturbed cluster estimate vields a higher value. consistent with the Voy estimate of Bll.," Interestingly, the mass estimate with the scaling relation for disturbed clusters fully agrees with weak-lensing mass, while the undisturbed cluster estimate yields a higher value, consistent with the $Y_X$ estimate of B11."
 Since A2163 is an ongoing imerecr. the normalization for disturbed clusters gives a better result.," Since A2163 is an ongoing merger, the normalization for disturbed clusters gives a better result."
 In order to constrain the cosinological parameters (e.c.constructVilkhlininetal.2009a.b).. it is of prime iniportauce to and calibrate a low-scatter mass proxy.," In order to constrain the cosmological parameters \citep[e.g,][]{vik09,vik09b}, it is of prime importance to construct and calibrate a low-scatter mass proxy."
 Receutlv.. Milleuniuu Cas Simulations (Staneketal.2010) predicted. that the temperature anclcontradictsgas-niass deviations are positively correlated. which Iravtsovetal.(2006).," Recently, Millennium Gas Simulations \citep{sta10} predicted that the temperature and gas-mass deviations are positively correlated, which contradicts \citet{kra06}."
. It is also important to construct a low-scatter iuass proxy usine solely observational data. based ou intrinsic covariance measurement| and principal conrponent analvsis (Okabeetal.20106).," It is also important to construct a low-scatter mass proxy using solely observational data, based on intrinsic covariance measurement and principal component analysis \citep{oka10c}."
 Further svstematic studies. includiug both uunucerical sinulation and observational study. are required for this.," Further systematic studies, including both numerical simulation and observational study, are required for this."
 From the iuversion of background salaxv shear xtternu. we revealed a bimodal mass distribution in the central region of A2?163 aud various anisotropies at larger radii the most significant of which correspoudine to the rorthern subcluster A2163-B. Modeling the mucderlving τος dimensional distribution of the cluster mass with hree compoucuts further allowed us to coustrain the nass ratio between the two ceutral components to 1:5. and attribute comparable mass values to the central aud rorthern subclusters.," From the inversion of a background galaxy shear pattern, we revealed a bimodal mass distribution in the central region of A2163 and various anisotropies at larger radii, the most significant of which corresponding to the northern subcluster A2163-B. Modeling the underlying three dimensional distribution of the cluster mass with three components further allowed us to constrain the mass ratio between the two central components to 1:8, and attribute comparable mass values to the central and northern subclusters."
 The spatial coincidence between XN-rav peak. ass and member galaxy distribution in A2163-B sugeests hat A2163-B did not vet interact with A2163-A. While coinciding with the bimodal galaxy distribution revealed in ALOs. the ceutral mass distribution appears mstead as spatially segregated from the brightest N-rav oittiug eas region.," The spatial coincidence between X-ray peak, mass and member galaxy distribution in A2163-B suggests that A2163-B did not yet interact with A2163-A. While coinciding with the bimodal galaxy distribution revealed in M08, the central mass distribution appears instead as spatially segregated from the brightest X-ray emitting gas region."
 Iu particular. the gas bullet sueeested to cross the cluster atmosphere from the evidence of a cold front. in BLL. appears as preceded by the secondary mass peak to a projected distance of ~2!2sohkpe aloug its westward direction of motion.," In particular, the gas bullet suggested to cross the cluster atmosphere from the evidence of a cold front, in B11, appears as preceded by the secondary mass peak to a projected distance of $\sim2\farcm\sim280h^{-1}~{\rm kpc}$ along its westward direction of motion."
 Asstuing an infalline subcluster has experienced a transient separation of its eas and dark matter components as a result of ran pressure stripping. this configuration would require the eas core to have survived tidal distortions exerted by the main cluster. and the core temperature to be consistent with the subcluster mass.," Assuming an infalling subcluster has experienced a transient separation of its gas and dark matter components as a result of ram pressure stripping, this configuration would require the gas core to have survived tidal distortions exerted by the main cluster, and the core temperature to be consistent with the subcluster mass."
 In the following. we discuss how these conditions allow us to put some additional constraints ou the kinematics of the ongoing subcluster accretion.," In the following, we discuss how these conditions allow us to put some additional constraints on the kinematics of the ongoing subcluster accretion."
 Oue possibility for explaining the offset between mass and eas distributions is the ram-pressure stripping: ifthe ranu-pressure force on the X-ray core is stronger than the evavity around the core region. the gas is stripped from its eravitational potential.," One possibility for explaining the offset between mass and gas distributions is the ram-pressure stripping: ifthe ram-pressure force on the X-ray core is stronger than the gravity around the core region, the gas is stripped from its gravitational potential."
 This condition is expressed as (Takizawa 2006).., This condition is expressed as \citep{tak06}. .
" Tore. ri is the radius ofthe Nav core. ALCSrego) is the spherical mass of the subcluster within the radius Fees Peres we the density of the core and its surrounding gas. respectively, aud ο is the velocity of the core in the ceuter-ofimass frame."," Here, $r_{\rm core}$ is the radius of the X-ray core, $M(<
 r_{\rm core})$ is the spherical mass of the subcluster within the radius $r_{\rm
core}$, $\rho_{\rm core,sur}$ are the density of the core and its surrounding gas, respectively, and $v$ is the velocity of the core in the center-of-mass frame."
 <1 is fudee factor at an order of unitv., $A$ is a fudge factor at an order of unity.
 This is why the ranu-pressure stripping is not effective due to a Ikelvin-IIehuholtz instability. magnetic fields. and shock heating.," This is why the ram-pressure stripping is not effective due to a Kelvin-Helmholtz instability, magnetic fields, and shock heating."
 D11 shows a lower Iit of the density jump. Pecro/Pau 1.28. at the west edge of the core (red-curved ne iu Figure 18)).," B11 shows a lower limit of the density jump, $\rho_{\rm core}/\rho_{\rm sur}=1.28$ , at the west edge of the core (red-curved line in Figure \ref{fig:chan+kappa}) )."
 We cousider the ranur-pressure stripping coudition on the sub cluster., We consider the ram-pressure stripping condition on the sub cluster.
 The substructure mass inside μα ds calculated from the TSIS model obtained by the weak-lensing analysis., The substructure mass inside $r_{\rm core}$ is calculated from the TSIS model obtained by the weak-lensing analysis.
 Since AMTXs. the condition. (11)) is feefrom the core size.," Since $M_{\rm TSIS} \propto
r$, the condition \ref{eq:Pram}) ) is freefrom the core size."
 Although we cousider the internal structure of eas. the resultant condition does not senificautlv chanec.," Although we consider the internal structure of gas, the resultant condition does not significantly change."
 Figure 21 plots the ranipressure stripping condition {παμεPeay las a function of iufall velocity c. where Pa/Panay cives the ratio of the right-hand side to the left-hand side of Equation (11)).," Figure \ref{fig:Pram} plots the ram-pressure stripping condition $P_{\rm
ram}/P_{\rm grav}-1$ as a function of infall velocity $v$, where $P_{\rm ram}/P_{\rm grav}$ gives the ratio of the right-hand side to the left-hand side of Equation \ref{eq:Pram}) )."
 We adopt A=0.5aud0.9., We adopt $A=0.5~{\rm and}~0.9$.
 MOS found the eradicut of line-ofsieht velocity cj.~1250kins1. giving the lower-limit of πα velocity.," M08 found the gradient of line-of-sight velocity $v_{\rm
los}\sim1250~{\rm km~s^{-1}}$, giving the lower-limit of infall velocity."
 The iufall velocity is expected from the lasses to have an order of (Ricker&Sarazin2001).. where M aud rare the virial nass and radius. respectively.," The infall velocity is expected from the masses to have an order of \citep{ric01}, where $M$ and $r$ are the virial mass and radius, respectively."
 We here used observed runcated mass and radius for the sub cluster., We here used observed truncated mass and radius for the sub cluster.
 The case of A—0.9 satisfies the rau-pressure stripping condition or allvelocities above 05., The case of $A=0.9$ satisfies the ram-pressure stripping condition for allvelocities above $\delta v_{\rm los}$ .
 The case of A=0.5also satisfies the condition around 2100kis ," The case of $A=0.5$also satisfies the condition around $2100~{\rm
km~s^{-1}}$ ."
"""Therefore. he N-ray core iitially associated with the sub cluster is casily stripped away from its central region."," Therefore, the X-ray core initially associated with the sub cluster is easily stripped away from its central region."
 However. we ust keep in munud that the estimated density jumpmight eive the lower limit. due to the deprojection method we," However, we must keep in mind that the estimated density jumpmight give the lower limit, due to the deprojection method we"
Let us return to the analvsis of the full. inhomogeneous equation (51).,"Let us return to the analysis of the full, inhomogeneous equation (51)."
 When the condition of the adiabatie evolution du(7)/dz««?(7) holds. then the approximate solution of Eq. (," When the condition of the adiabatic evolution ${\rm
d}\omega(\tau)/{\rm d} \tau \ll \omega^2(\tau)$ holds, then the approximate solution of Eq. ("
51) has the following Form (Chagelishvili.Rogava&Segal1994): where the non-periodie solution bj(7) is given bv: and can be readily identified as (he shear-modilied (EM) perturbation.,51) has the following form \citep{c94}: where the non-periodic solution $b_E(\tau)$ is given by: and can be readily identified as the shear-modified (EM) perturbation.
 It (urns out Chat another physically important phenomenon (hat Cakes place in the svslem under consideration for moderate and high shearing rates. is the generation of the GAW by the EM perturbations.," It turns out that another physically important phenomenon that takes place in the system under consideration for moderate and high shearing rates, is the generation of the GAW by the EM perturbations."
 An illustrative example is given by the Fig., An illustrative example is given by the Fig.
 2. where the nunmerical solution of Eq. (," 2, where the numerical solution of Eq. ("
51) for the case when NV=1 and HR=0.7 lor the variable b(7) is shown.,51) for the case when $N = 1$ and $R=0.7$ for the variable $b(\tau)$ is shown.
 The initial conditions were chosen in such away that at the beginning (al A.(0)=35) (here exists only the EX perturbation., The initial conditions were chosen in such a way that at the beginning (at $K_z(0) = 35$ ) there exists only the EM perturbation.
 Namely. the initial conditions were found by means of Eqs. (," Namely, the initial conditions were found by means of Eqs. ("
60) and (61) with AL—0 and Z= 1).,60) and (61) with $A_\pm=0$ and ${\cal I}=1$ ).
 The figure clearly demonstrates the generation ol the GAW while the EM passes through the interval of non-adiabatie evolution. situated in the vicinity of the point A(7*)=0.," The figure clearly demonstrates the generation of the GAW while the EM passes through the interval of non-adiabatic evolution, situated in the vicinity of the point ${\cal K}_z(\tau^\ast)=0$."
 For the quantitative description of the wave generation process. analogously to the reflection ancl (iransmission coefficients defined in the previous section. we deline the Ge in the following wav: With this definition. G is proportional to the ratio of the generated wave energy {ο ihe οποιον of incident entropy mode perturbation.," For the quantitative description of the wave generation process, analogously to the reflection and transmission coefficients defined in the previous section, we define the $G_\pm$ in the following way: With this definition, $G_\pm$ is proportional to the ratio of the generated wave energy to the energy of incident entropy mode perturbation."
 From the svnumetry of the problem. it is obvious that G—G=G.," From the symmetry of the problem, it is obvious that $G_+ = G_- \equiv G$."
 In Figuree 3. the dependence of the egeneration coefficient (£2) on the normalized shear parameter J? for different values of the Brunt-Vaiisalla [requencey: No=1 (solid line). .N—2 (dashed line) and NV=3 (dash-dotted line) is presented.," In Figure 3, the dependence of the generation coefficient $G(R)$ on the normalized shear parameter $R$ for different values of the Brunt-Väiisällä frequency: $N = 1$ (solid line), $N = 2$ (dashed line) and $N = 3$ (dash-dotted line) is presented."
attempted a more physically-constrained generating process to model all the spectral-timing properties simultaneously.,attempted a more physically-constrained generating process to model all the spectral-timing properties simultaneously.
 The usual course of action is to extract information in the frequeney domain. such as a PDS. from the time series.," The usual course of action is to extract information in the frequency domain, such as a PDS, from the time series."
 However. sometimes we need to do the opposite: to reconstruct the time series from the PDS.," However, sometimes we need to do the opposite: to reconstruct the time series from the PDS."
 The simulation of random time series with arbitrary PDS has a long and established history (seees.Davisetal.1981:Liu&Mun-son1982) in the field. of digital signal processing.," The simulation of random time series with arbitrary PDS has a long and established history \citep[see e.g.][]{Dav81,LM82} in the field of digital signal processing."
 There are also papers on simulating time series. with specific marginal distribution. e.g. lognormal (Johnson1994).," There are also papers on simulating time series with specific marginal distribution, e.g. lognormal \citep{Joh94}."
. In astrophysical research the reasons and. benefits to perform such a reconstruction are various., In astrophysical research the reasons and benefits to perform such a reconstruction are various.
 Sometimes it. provides a more direct tool to judge the models or simulation methods (foranexample.seeTimmoer&Ixónig1995).," Sometimes it provides a more direct tool to judge the models or simulation methods \citep[for an example, see][]{TK95}."
. Also it can be used to estimate the error bars by Monte Carlo simulation (c.g.Doneetal.1992)., Also it can be used to estimate the error bars by Monte Carlo simulation \citep[e.g.][]{Don92}.
. Since the PDS does not contain the hase information. in order to do so one must assign values o the phases as the reconstruction based on the PDS alone is not unique.," Since the PDS does not contain the phase information, in order to do so one must assign values to the phases as the reconstruction based on the PDS alone is not unique."
 One easy way to generatedata that reproduce a given PDS is to choose the Fourier amplitude according to he PDS and assign random phases between 0.23] (Doneetal. 1992).," One easy way to generate data that reproduce a given PDS is to choose the Fourier amplitude according to the PDS and assign random phases between $[0,2\pi]$ \citep{Don92}."
. Based on the theory of linear stochastic oocess and the faet that the PDS itself follows a chi-square distribution. Timmoer&Ixónig(1995). proposed a algorithm actically identical to Davies&Harte(LOST)- το produce he whole variety of possible non-deterministic linear time series from the PDS by randomizing both the phases and amplitudes.," Based on the theory of linear stochastic process and the fact that the PDS itself follows a chi-square distribution, \citet{TK95} proposed a algorithm practically identical to \citet{DH87}- —to produce the whole variety of possible non-deterministic linear time series from the PDS by randomizing both the phases and amplitudes."
 Some authors use the cnerev-resolvecl PSDs instead of the total PSD in the method of Timmer& (1995).. and shift the phase to vield light curves with desired lag function between them (e.g.Zoghbiοἱal.2010).," Some authors use the energy-resolved PSDs instead of the total PSD in the method of \citet{TK95}, and shift the phase to yield light curves with desired lag function between them \citep[e.g., ][]{Zog10}."
. Recently. the non-linear behavior of observed. light. curves was studied by Uttleyctal.(2005).," Recently, the non-linear behavior of observed light curves was studied by \citet{Utt05}."
. They suggested. that an additional exponential transform needs to be applied to the time series created with the method of immer&Konig (1005)., They suggested that an additional exponential transform needs to be applied to the time series created with the method of \citet{TK95}.
. BILBs are known to exhibit X-ray spectral evolution on short time-scales., BHBs are known to exhibit X-ray spectral evolution on short time-scales.
 This evolution is reflected in the presence of lags between the light curves at different energy ranges and asyvmmetries of the cross-correlation function. between them. as well as fast variations of the corresponding hardness ratio.," This evolution is reflected in the presence of lags between the light curves at different energy ranges and asymmetries of the cross-correlation function between them, as well as fast variations of the corresponding hardness ratio."
 However. the conventional spectral models. applied to these systems are designed to fit the energy. spectrum averaged over. usually. several thousand seconds.," However, the conventional spectral models applied to these systems are designed to fit the energy spectrum averaged over, usually, several thousand seconds."
 Because of limited. statistics. it is not. possible to follow the energy spectrum over the short time-scales corresponding to the observed fast. variability.," Because of limited statistics, it is not possible to follow the energy spectrum over the short time-scales corresponding to the observed fast variability."
 ln this work we propose a new technique that simulates a time series starting from the actual intensity measurements., In this work we propose a new technique that simulates a time series starting from the actual intensity measurements.
 Specifically. we simulate the light. curves in dillerent energy bins reproducing all the properties observed. in thereal data: the average energy spectrum. the PDS as a function of energy. ancl the the frequencydependent lag spectra between clilferent energy. bands.," Specifically, we simulate the light curves in different energy bins reproducing all the properties observed in thereal data: the average energy spectrum, the PDS as a function of energy and the the frequency-dependent lag spectra between different energy bands."
 In the simulation. no Poisson noise is of course introduced.," In the simulation, no Poisson noise is of course introduced."
 With the simulated. “clean” light curves in cillerent energy bins. we can study the variations of the energy. spectrum on short time-scales.," With the simulated “clean"" light curves in different energy bins, we can study the variations of the energy spectrum on short time-scales."
 Our work is improved. (or dillerent) in three aspects when compared. with the papers mentioned above., Our work is improved (or different) in three aspects when compared with the papers mentioned above.
 For the first. besides the PDS. we make use of other measurements. including energy spectra and [ag spectra as input to the simulation.," For the first, besides the PDS, we make use of other measurements, including energy spectra and lag spectra as input to the simulation."
 Secondly. we require that. the simulated time series should reproduce almost all the timing ancl spectral properties.," Secondly, we require that the simulated time series should reproduce almost all the timing and spectral properties."
 t last we explore the possible application of the method. including filtering Poisson noise ancl data extrapolation.," At last we explore the possible application of the method, including filtering Poisson noise and data extrapolation."
 Our work. based. on those by Timmer&Wonie(1995) and Uttlovetal.(2005).. can be seen as a continuation of them.," Our work, based on those by \citet{TK95} and \citet{Utt05}, can be seen as a continuation of them."
 In contrast to Arévalo&Uttley(2006)... our work is mocdoel-independent ancl aims at developing an algorithm that recovers the time series preserving the information and filtering the noise.," In contrast to \citet{AU06}, our work is model-independent and aims at developing an algorithm that recovers the time series preserving the information and filtering the noise."
 The article is organized as follows: the preparatory works of data analysis and parameter estimation are introduced in section ??.. including the non-linearity study (section ??)). energy. dependence of PDS (section ??)) agm spectra (section ??)). coherence function (section 77)) and distribution of the phases (section. ??)).," The article is organized as follows: the preparatory works of data analysis and parameter estimation are introduced in section \ref{sec_pre}, including the non-linearity study (section \ref{sec_nl}) ), energy dependence of PDS (section \ref{sec_pdsen}) ), lag spectra (section \ref{sec_lagen}) ), coherence function (section \ref{sec_coh}) ) and distribution of the phases (section \ref{sec_phas}) )."
 The important results are presented in section ?77.., The important results are presented in section \ref{sec_result}.
 In. section ?? 1e algorithm: is defined by steps., In section \ref{sec_alg} the algorithm is defined by steps.
 The simulated. light. curve is compared. with the observed. onc (section ??)) and the issue of Poisson noise subtraction is cliscussed (section 7? , The simulated light curve is compared with the observed one (section \ref{sec_test}) ) and the issue of Poisson noise subtraction is discussed (section \ref{sec_subnoise}) ).
As one important application. the energye spectra on short time-scales (dynamic energy spectra) are derived. and. the variation of spectral shape is investigated. in section ?77..," As one important application, the energy spectra on short time-scales (dynamic energy spectra) are derived and the variation of spectral shape is investigated in section \ref{sec_des}."
 Another possible application. the simulation of data with better time and energy. resolution than observations can be measured. directly from the observations. is discussed in section 2?..," Another possible application, the simulation of data with better time and energy resolution than observations can be measured directly from the observations, is discussed in section \ref{sec_extint}."
 Phe issues associated with phase ancl noise are discussed in section. 2?.., The issues associated with phase and noise are discussed in section \ref{sec_posnois}.
 Phe conclusions are presented. in section ??.., The conclusions are presented in section \ref{sec_con}.
 The recentral idea of the algorithm is to synthesize light curves that reproduce all observed. properties both in the time and frequency domain., The central idea of the algorithm is to synthesize light curves that reproduce all observed properties both in the time and frequency domain.
 Phese are: Once these properties are extracted. from. the data. svnthetie data curve can be constructed to reproduce the same results.," These are: Once these properties are extracted from the data, synthetic data curve can be constructed to reproduce the same results."
 A preliminary step is to obtain the above quantities with good accuracy lor a black-hole binary., A preliminary step is to obtain the above quantities with good accuracy for a black-hole binary.
 We used a sinele observation. of Cygnus. N-1 from the Proportional Counter Array (PCA) on board the Rossi X-ray Timing Explorer TE) (ObsLD 10238-01-05-000)., We used a single observation of Cygnus X-1 from the Proportional Counter Array (PCA) on board the Rossi X-ray Timing Explorer ) (ObsID 10238-01-05-000).
 Cre X-1 is the first-cliscovered black hole binary ancl has been studied. for several decades., Cyg X-1 is the first-discovered black hole binary and has been studied for several decades.
 I8 brightness and. persistence make it a perfect target. for N-ray timing research., Its brightness and persistence make it a perfect target for X-ray timing research.
 “Phe observation was carried out in March. 1996. when (νο N-1 was in its hard spectral state. the most common for the source (e.g. 2006)..," The observation was carried out in March, 1996, when Cyg X-1 was in its hard spectral state, the most common for the source \citep[e.g.][]{Wil06}. ."
 The data configuration used here is the eoneric PCA binned mode 00.2249. which," The data configuration used here is the generic PCA binned mode 249, which"
lt has long been acknowledged that neutron stars (NSs) have strong magnetic fields. which max play a variety of roles in the physics of these objects.,"It has long been acknowledged that neutron stars (NSs) have strong magnetic fields, which may play a variety of roles in the physics of these objects."
 Magnetic fields can change the stability of a NS. allect its evolution and cooling properties. induce precession ancl provide the restoring force for a class of oscillation moces (Harding&Lai2006:\ereghetti2008).," Magnetic fields can change the stability of a NS, affect its evolution and cooling properties, induce precession and provide the restoring force for a class of oscillation modes \citep{harding_lai,mereghetti}."
. They may also produce crust-core coupling and alfect the post-eliteh spin behaviour of NSs (IZasson1979:LJib.IXaspi&CGavriil2008).," They may also produce crust-core coupling and affect the post-glitch spin behaviour of NSs \citep{easson,dib_kg}."
. All of these elfects are likely to be sensitive to the details of the magnetic-fied configuration in the stellar interior. whereas we are only able to observe the exterior. dominantly divolar. field.," All of these effects are likely to be sensitive to the details of the magnetic-field configuration in the stellar interior, whereas we are only able to observe the exterior, dominantly dipolar, field."
 For this reason considerable οἱort has gone into moclelling the interior magnetic fields of neutron stars: we give an overview of this in seclion 2., For this reason considerable effort has gone into modelling the interior magnetic fields of neutron stars; we give an overview of this in section 2.
 Despite considerable progress. the vast tnajority of stucies on magnetisec neutron stars trea hem as barotropic bodies.," Despite considerable progress, the vast majority of studies on magnetised neutron stars treat them as barotropic single-fluid bodies."
 Whilst this is a sensible way to begin producinοIn simplified moces. more realistic sttidies need to confront. some of the detailed interior physics of NSs.," Whilst this is a sensible way to begin producing simplified models, more realistic studies need to confront some of the detailed interior physics of NSs."
 For example. over for vovears since the irst predictions tha neutron star matter would 'ontain superfluid neutrons and superconducting proons (see. e.g... Bavnn.Chick&Pines(1Of 39)). there have been no tempts to construct multilluid magnetic equiibria along these lines.," For example, over forty years since the first predictions that neutron star matter would contain superfluid neutrons and superconducting protons (see, e.g., \citet{baym_pp}) ), there have been no attempts to construct multifluid magnetic equilibria along these lines."
 Phe issue is highly. topical. οο recent observations ofH the cooling of the voung NS in Cassiopeia AX are well CXDIained by a mode with superlluid. neirons and superconducting protons (Shterninetal.2011:Page2011|.," The issue is highly topical, too — recent observations of the cooling of the young NS in Cassiopeia A are well explained by a model with superfluid neutrons and superconducting protons \citep{casA_sht,casA_page}."
 1n the caseo “ho magnetic Lele there has been more progress. including studies of the equilibria and oscillation modes of superluicl NSs (c.g.UO» Prix&Rieutorel(202):Prix.NovakComoer(2005):Yoshida&Eviguchi(2004):Passamonti.HaskellAndersson (2009))).," In the case of no magnetic field there has been more progress, including studies of the equilibria and oscillation modes of superfluid NSs (e.g. \citet{prix_r,prix_nc,yosh_eri,passa_sf}) )."
 The closest. relatec work on Magneised stars is probablythe 5ucl. of barotropic NSs with superconductivitv. by Aketin&Wasserman(2008).," The closest related work on magnetised stars is probablythe study of barotropic NSs with superconductivity, by \citet{akgun_wass}."
". A simpler problem than a NS with superluicitv/superconductivity is a stratified (i.e. non-barotropic). magnetised star composed of normal Πα,"," A simpler problem than a NS with superfluidity/superconductivity is a stratified (i.e. non-barotropic), magnetised star composed of normal fluid."
 Stratification is expected to exist in NSs (Iteisenegger&Goldreich 1992).. where it can allow for," Stratification is expected to exist in NSs \citep{reis_gold}, , where it can allow for"
"'The effect of increasing the torus opening angle O7 is similar to the increasing of the effective tilt angle Άγιοι, which both result in a more randomized viewing angles of the disks of AGN hosts.","The effect of increasing the torus opening angle $\Theta_T$ is similar to the increasing of the effective tilt angle $\Delta_{TS,m}$, which both result in a more randomized viewing angles of the disks of AGN hosts."
" Therefore, an independent measurement of Or from the type 2 AGN fraction is crucial to constrain the tilt angle Arg in our model."," Therefore, an independent measurement of $\Theta_T$ from the type 2 AGN fraction is crucial to constrain the tilt angle $\Delta_{TS}$ in our model."
" In this section, we test the scenario that the over-density of the edge-on galaxies of type 2 AGNs is caused by an extra dust layer aligned with the stellar disk."," In this section, we test the scenario that the over-density of the edge-on galaxies of type 2 AGNs is caused by an extra dust layer aligned with the stellar disk."
" Therefore, we no more assume that the nuclear obscurer is aligned with the stellar disk as that in the aligned torus model(Section ??)), but consider it being randomly oriented."," Therefore, we no more assume that the nuclear obscurer is aligned with the stellar disk as that in the aligned torus model(Section \ref{torus}) ), but consider it being randomly oriented."
" Besides the random orientated torus, the dust aligned with the stellar disk will obscure the nucleus when it is viewed as edge-on."," Besides the random orientated torus, the dust aligned with the stellar disk will obscure the nucleus when it is viewed as edge-on."
" Using the denotations as in aligned torus model, a randomly oriented nuclear torus means that the orientations of the stellar disk and torus plane are independent of each other, i.e. cos(Arg) follows a random distribution between 0 and 1."," Using the denotations as in aligned torus model, a randomly oriented nuclear torus means that the orientations of the stellar disk and torus plane are independent of each other, i.e. $cos(\Delta_{TS})$ follows a random distribution between 0 and 1."
" For its opening angle, we set Op=45°, the lower limit of the aligned torus model, since we have an extra component of type 2 AGNs obscured by the host-aligned dust layer."," For its opening angle, we set $\Theta_T=45^\circ$, the lower limit of the aligned torus model, since we have an extra component of type 2 AGNs obscured by the host-aligned dust layer."
" For host-aligned obscurer, we assume its height is the same as the stellar disk."," For host-aligned obscurer, we assume its height is the same as the stellar disk."
" Thus, for a stellar disk with height y, its nucleus will be obscured when its viewing angles satisfies tan(ig)«7."," Thus, for a stellar disk with height $\gamma$, its nucleus will be obscured when its viewing angles satisfies $i_S$ $<\gamma$."
 We then combine these two types of obscurers and get the final type 2 AGN sample., We then combine these two types of obscurers and get the final type 2 AGN sample.
 The other model settings and procedures are the same as in aligned tours model., The other model settings and procedures are the same as in aligned tours model.
 We show the model prediction as the dashed line in Fig. 3.., We show the model prediction as the dashed line in Fig. \ref{model}.
" As we can see, this extra stellar obscurer model indeed predicts over-density of the low axis ratio galaxies for the AGN sample."," As we can see, this extra stellar obscurer model indeed predicts over-density of the low axis ratio galaxies for the AGN sample."
" However, this over-density mostly takes place at b/a<0.4."," However, this over-density mostly takes place at $b/a<0.4$."
" For the others with b/a>0.4, the predicted Nagn/Neax is almost a constant, whereas the observations show continuous decreasing of type 2 AGNs in more round galaxies."," For the others with $b/a>0.4$ , the predicted $N_{AGN}/N_{GAL}$ is almost a constant, whereas the observations show continuous decreasing of type 2 AGNs in more round galaxies."
 This is because that most of the stellar disks having y<0.4(see Fig. 1))., This is because that most of the stellar disks having $\gamma<0.4$ (see Fig. \ref{btoa}) ).
" Therefore, this model prediction shows significantly poorer ~36, outside the confidence interval fitting(y?of the y? distribution with 8 freedoms) than the aligned torus model."," Therefore, this model prediction shows significantly poorer $\chi^2\approx 36$, outside the confidence interval of the $\chi^2$ distribution with 8 freedoms) than the aligned torus model."
" However, we would mention that there is no tuneable parameter in this stellar dust model, whereas the aligned torus model has two free parameters."," However, we would mention that there is no tuneable parameter in this stellar dust model, whereas the aligned torus model has two free parameters."
" Setting Or to be a free parameter in the stellar dust model does not help, because the torus was assumed to be orientated randomly."," Setting $\Theta_T$ to be a free parameter in the stellar dust model does not help, because the torus was assumed to be orientated randomly."
" However, assuming that the stellar dust layer following the same shape of the stars might be too simplistic."," However, assuming that the stellar dust layer following the same shape of the stars might be too simplistic."
" A more sophisticated treatment of the distribution of the stellar dust might improve the fit(e.g. Maiolino&Rieke (1995))),"," A more sophisticated treatment of the distribution of the stellar dust might improve the fit(e.g. \cite{Maiolino95}) ),"
 but is out of the range of this study., but is out of the range of this study.
" In this study, we select a sample of type 2 AGNs hosted by spiral galaxies from the DR7 of the SDSS."," In this study, we select a sample of type 2 AGNs hosted by spiral galaxies from the DR7 of the SDSS."
 We build a control sample of non-active galaxies to the AGN sample by matching their observational and physical properties in detail., We build a control sample of non-active galaxies to the AGN sample by matching their observational and physical properties in detail.
" By comparing with the control sample, we find that the AGN hosts are systematically biased to edge-on views."," By comparing with the control sample, we find that the AGN hosts are systematically biased to edge-on views."
" By modelling the height and ellipticity of the disk galaxies with a non-parametric technic, we further find that this systematical bias can not be quantified by an extra dust layer aligned with stellar disk but can be nicely reproduced by assuming an average tilt angle of ~30 degree between the torus plane and stellar disk."," By modelling the height and ellipticity of the disk galaxies with a non-parametric technic, we further find that this systematical bias can not be quantified by an extra dust layer aligned with stellar disk but can be nicely reproduced by assuming an average tilt angle of $\sim 30$ degree between the torus plane and stellar disk."
" Some of the assumptions in our model are simplified, e.g. the constant type 2 AGN fraction."," Some of the assumptions in our model are simplified, e.g. the constant type 2 AGN fraction."
 There are studies suggesting that the opening angle of the torus is correlated with the central AGN luminosity., There are studies suggesting that the opening angle of the torus is correlated with the central AGN luminosity.
" For high luminosity AGNs, the distance of the torus from the nucleus is further (‘receding torus model’) so that the torus opening angel and the type 2 AGN fraction fo are smaller(Lawrence1991)."," For high luminosity AGNs, the distance of the torus from the nucleus is further (`receding torus model') so that the torus opening angel and the type 2 AGN fraction $f_2$ are \citep{Lawrence91}."
". Most of our AGNs are low luminosity objects(Liony< and the type 2 AGN fraction has been shown to be 105L5),roughly a constant in this luminosity region(Simpson2005;Luetal.2010)."," Most of our AGNs are low luminosity $L_{\rm{[OIII]}}< 10^8L_\odot$ ), and the type 2 AGN fraction has been shown to be roughly a constant in this luminosity \citep{Simpson05,Lu10}."
. A separation of our sample into two sub-samples according to Lion also would not show any significant differences but reduce the goodness of the statistics., A separation of our sample into two sub-samples according to $L_{\rm{[OIII]}}$ also would not show any significant differences but reduce the goodness of the statistics.
" In the unified AGN diagram, the torus lies on the same plane of the accretion disk."," In the unified AGN diagram, the torus lies on the same plane of the accretion disk."
" In this case, the mean tilt angle between the torus plane and the stellar disk constrained from our model could also be understood as the mean tilt between the accretion disk and stellar disk."," In this case, the mean tilt angle between the torus plane and the stellar disk constrained from our model could also be understood as the mean tilt between the accretion disk and stellar disk."
"(2011a) determined a temperature of KK for JJ1929+4447, placing it in the middle of the DBV instability strip and not on the blue edge.","(2011a) determined a temperature of K for J1929+4447, placing it in the middle of the DBV instability strip and not on the blue edge."
" To compute all our models, we used the White Dwarf Evolution Code (WDEC)."," To compute all our models, we used the White Dwarf Evolution Code (WDEC)."
" The WDEC evolves hot polytrope models from temperatures close to 100,000K down to the temperature of our choice."," The WDEC evolves hot polytrope models from temperatures close to 100,000K down to the temperature of our choice."
 Models in the temperature range of interest for the present study are thermally relaxed solutions to the stellar structure equations., Models in the temperature range of interest for the present study are thermally relaxed solutions to the stellar structure equations.
 Each model we compute for our grids is the result of such an evolutionary sequence., Each model we compute for our grids is the result of such an evolutionary sequence.
 The WDEC is described in detail in Lamb van Horn (1975) and Wood (1990)., The WDEC is described in detail in Lamb van Horn (1975) and Wood (1990).
 We used smoother core composition and with the more complex that result profilesfrom stellar experimentedevolution calculations (Salaris et al., We used smoother core composition profiles and experimented with the more complex profiles that result from stellar evolution calculations (Salaris et al.
 profiles1997)., 1997).
 We updated the envelope equation of state tables from those calculated by Fontaine et al. (, We updated the envelope equation of state tables from those calculated by Fontaine et al. (
1977) to those given by Saumon et al. (,1977) to those given by Saumon et al. (
1995).,1995).
 We use OPAL (Iglesias Rogers 1996) and plasmon neutrino rates opacitiespublished by Itoh et al. (, We use OPAL opacities (Iglesias Rogers 1996) and plasmon neutrino rates published by Itoh et al. (
1996).,1996).
 DBVs are younger than their cooler cousins the DAVs., DBVs are younger than their cooler cousins the DAVs.
" Time dependent diffusion calculations (e.g. Dehner Kawaler 1995) show that at KK, a typical temperature for a DBV, the carbon has not fully settled into the core of the star yet."," Time dependent diffusion calculations (e.g. Dehner Kawaler 1995) show that at K, a typical temperature for a DBV, the carbon has not fully settled into the core of the star yet."
" We expect the helium layer to be separated into a mixed He/C layer with a pure He layer on top, as shown in Fig. 1.."," We expect the helium layer to be separated into a mixed He/C layer with a pure He layer on top, as shown in Fig. \ref{f1}."
" Following Metcalfe (2005), we adopted and parameterized this structure in our models."," Following Metcalfe (2005), we adopted and parameterized this structure in our models."
 We calculated of models the WDEC and then ran fitting subroutinegrids to match the usingperiods of the models a (Peaic) with the observed periods and calculated residuals using the usual formula where Nops 1s the number of periods present in the pulsation spectrum., We calculated grids of models using the WDEC and then ran a fitting subroutine to match the periods of the models $\rm P_{calc}$ ) with the observed periods and calculated residuals using the usual formula where $\rm n_{obs}$ is the number of periods present in the pulsation spectrum.
" In our asteroseismic fits, we vary up to 6 parameters; the effective temperature, the mass and 4 structure parameters."," In our asteroseismic fits, we vary up to 6 parameters; the effective temperature, the mass and 4 structure parameters."
 There are two associated with the shapes of the oxygen (and carbon) parameterscore composition profiles: the central oxygen abundance (Χο). and the edge of the homogeneous carbon and oxygen core (αι).," There are two parameters associated with the shapes of the oxygen (and carbon) core composition profiles: the central oxygen abundance $\rm X_o$ ), and the edge of the homogeneous carbon and oxygen core $\rm q_{fm}$ )."
" For envelope structure, Meny marks the location of the base of the helium layer and Mg. the location where the helium abundance rises to 1 (see Fig. 1))."," For envelope structure, $\rm M_{env}$ marks the location of the base of the helium layer and $\rm M_{He}$ the location where the helium abundance rises to $1$ (see Fig. \ref{f1}) )."
" Meny and Mye are mass coordinates, defined as e.g. Meny=—log(1—M(r)/M.), where M(r) is the mass enclosed in radius r and M, is the stellar mass."," $\rm M_{env}$ and $\rm M_{He}$ are mass coordinates, defined as e.g. $\rm M_{env} = -\log(1 - M(r)/M_*)$ , where M(r) is the mass enclosed in radius r and $\rm M_*$ is the stellar mass."
" With only 5 periods, 6 parameter fits are underconstrained."," With only 5 periods, 6 parameter fits are underconstrained."
" While there is much to learn from attempting 6 parameter fits, we settled for 4 parameters (later relaxing a 5°”)."," While there is much to learn from attempting 6 parameter fits, we settled for 4 parameters (later relaxing a $5^{th}$ )."
" There are three logical ways of fixing 2 of the 6 1) fix the mass and effective temperature accordingparameters: to the spectroscopy, 2) fix the core structure parameters, and 3) fix the envelope parameters."," There are three logical ways of fixing 2 of the 6 parameters: 1) fix the mass and effective temperature according to the spectroscopy, 2) fix the core structure parameters, and 3) fix the envelope parameters."
" In light of the basic pulsational properties of the object (see also section 3.3)), option 1) seems the least promising."," In light of the basic pulsational properties of the object (see also section \ref{periodspacing}) ), option 1) seems the least promising."
" Of the other two choices, we decided to first try fixing the envelope structure to that of Dehner Kawaler (1995)."," Of the other two choices, we decided to first try fixing the envelope structure to that of Dehner Kawaler (1995)."
" This meant that M.n, was fixed to -2.80 for all models and Mg. was first fixed to -5.50 for models between KK and KK, -5.90 for models between KK and KK and -6.30 for models between KK and KK, to match the profiles resulting from the diffusive settling computed by Dehner Kawaler (1995)."," This meant that $\rm M_{env}$ was fixed to -2.80 for all models and $\rm M_{He}$ was first fixed to -5.50 for models between K and K, -5.90 for models between K and K and -6.30 for models between K and K, to match the profiles resulting from the diffusive settling computed by Dehner Kawaler (1995)."
 We calculated 2 grids of models; one covering a broad range of parameter space at lower resolution and one zooming in on the promising area of parameter space with resolution., We calculated 2 grids of models; one covering a broad range of parameter space at lower resolution and one zooming in on the promising area of parameter space with higher resolution.
 The range of parameters and step sizes forhigher each are summarized in table 2.., The range of parameters and step sizes for each are summarized in table \ref{t2}.
" The broad grid contains 305,820 models that succesfully converged (out of 315,700 total computed) and the higher resolution grid contains 403,065 converged models, with a similar success rate."," The broad grid contains 305,820 models that succesfully converged (out of 315,700 total computed) and the higher resolution grid contains 403,065 converged models, with a similar success rate."
" Table 2 also shows the parameters for the best fit models, discussed in section 3.4.."," Table \ref{t2} also shows the parameters for the best fit models, discussed in section \ref{fits}."
" The average provides a useful asteroseismic measure of the mass periodand spacingtemperature of the star, independent of the details of internal chemical composition profiles."," The average period spacing provides a useful asteroseismic measure of the mass and temperature of the star, independent of the details of internal chemical composition profiles."
" Higher k modes are not trapped in the core and according to asymptotic theory, they are evenly spaced in period."," Higher $k$ modes are not trapped in the core and according to asymptotic theory, they are evenly spaced in period."
 This spacing is given by (Unno et al., This spacing is given by (Unno et al.
 1989) where Τ1 and ra are turning points of the mode and N is the Brunt-Vàiisállà frequency., 1989) where $r_1$ and $r_2$ are turning points of the mode and N is the Brunt-Väiisällä frequency.
 The asymptotic period spacing is / , The asymptotic period spacing is $\ell$ 
consider only 0<VN/3.,consider only $n \leq \sqrt{N}/3$.
 This means that instead of the yossible 2.N harmonies. we will study ouly ~Αθ.," This means that instead of the possible $2N$ harmonics, we will study only $\simeq N/9$."
 This (together with the avoiding of ο=0 terms) means that we will test ounlv ~(56)% of all allowed independent jurnmioldes., This (together with the avoiding of $m = 0$ terms) means that we will test only $\simeq (5-6)\%$ of all allowed independent harmonics.
" Concerning the ""sigu-test the accuracy secus to be uuch better than for Studeuts f test."," Concerning the ""sign-test"" the accuracy seems to be much better than for Student's $t$ test."
 By this we mean ο sav that there is no problem with the correctness of a conclusion coming from the Bernoulli test., By this we mean to say that there is no problem with the correctness of a conclusion coming from the Bernoulli test.
 Therefore. the “sigu-test™ may be used for the sue harvuionics for which Studeut’s f test was used.," Therefore, the ""sign-test"" may be used for the same harmonics for which Student's $t$ test was used."
 For the used values of » the positional errors (of sizes ~Il degrees. Ελαctal. 1991)) should eive no further complications.," For the used values of $n$ the positional errors (of sizes $\simeq 1-4$ degrees, \cite{fishman94}) ) should give no further complications."
 We will consider only such values of n. When the typical augular size belonging to ann (2mn: Peebles 1980. Chapt.," We will consider only such values of $n$, when the typical angular size belonging to an $n$ $ \simeq \pi/n$; Peebles 1980, Chapt."
 16) will be uch larger than the size of the positional error., 46) will be much larger than the size of the positional error.
 The detailed discussion presented by Teemark et al. (, The detailed discussion presented by Tegmark et al. (
1996) shows that oy such values of η no complications should arise from the positional errors.,1996) shows that for such values of $n$ no complications should arise from the positional errors.
 Iu order to test the isotropy of 2281 CRBs collected in πο DATSE Cióunusc-hRav Durst Catalog (Meegauetal. 1995)) uutil the eud of 1998. we calculated their spherical harmonics up tov=15.," In order to test the isotropy of 2281 GRBs collected in Current BATSE Gamma-Ray Burst Catalog \cite{meegan}) ) until the end of 1998, we calculated their spherical harmonics up to $n=15$."
" This maxima B value was chosen iu accordance with the discussion in Sect.2. where we restrictedk ourselves to xVN3,"," This maximum $n$ value was chosen in accordance with the discussion in Sect.2, where we restricted ourselves to $n \leq
\sqrt{N}/3$."
 Ilo No=2281. aud VN3=15.9.," Here $N=2281$, and $\sqrt{N}/3 = 15.9$."
 In other words. oestead of 2«2281=1562 possible independent spherical inrniondes we tested onlv (16216)—210 both with Studeut’s f test and sign tests.," In other words, instead of $2\times 2281= 4562$ possible independent spherical harmonics we tested only $(16^2 - 16) = 240$ both with Student's $t$ test and sign tests."
 The results are collected in Table 1. in which we preseut all dipole aud quadrupole ers (Gu order to compare them with Dalázzs ct al.," The results are collected in Table 1, in which we present all dipole and quadrupole terms (in order to compare them with Balázzs et al."
 1998). mt for larger harmonics only the termes. for which either f|>1.96 or ων<1093 or kyc1188.," 1998), but for larger harmonics only the terms, for which either $|t| >1.96$ or $k_{\mathrm{obs}} < 1093$ or $k_{\mathrm{obs}} > 1188$."
 For f|>1.96 there is a smaller than 54n probability that here is still an isotropy: for |f|>2.58 this probability is stualler than 1% (Trtmpler&Weaver 1953))., For $|t| > 1.96$ there is a smaller than $\%$ probability that there is still an isotropy; for $|t| > 2.58$ this probability is smaller than $1\%$ \cite{trumpler}) ).
 For the “sien test™ one needs [KosN/2|>VN to have a >95.1 sienificance level for amisotropy. where Άρη is the observed uuuber of CRBs having the eiven harmonic neeative value.," For the ""sign test"" one needs $|k_{\mathrm{obs}obs} - N/2| > \sqrt{N}$ to have a $>95.4\%$ significance level for anisotropy, where $k_{\mathrm{obs}}$ is the observed number of GRBs having the given harmonic negative value."
 We also present the a=0 cases for conmparisou as well. but these values will not be taken as indications of mtrinsie audsotropy.," We also present the $m = 0$ cases for comparison as well, but these values will not be taken as indications of intrinsic anisotropy."
 For jj=0 the “sien test Is applied oulv for odd (b. of course.," For $m=0$ the ""sign test"" is applied only for odd $n$, of course."
 Table 1 shows at there are three a=0 coupoucuts with [£|>1.96 (4= 1.2.12).," Table 1 shows that there are three $m = 0$ components with $|t| >1.96$ $n=1, 2, 12$ )."
 The bigeest value is the m=ιν=0 quadrupole teria with f=1.26.," The biggest value is the $n=2, m=0$ quadrupole term with $t = 4.26$."
 This means that there exists an anisotropy with a certainty: the probability that this quadrupole terii is non-zero due to chance is much smaller than 0.1% probability (t=3.29 corresponds to a 0.15€( probability)., This means that there exists an anisotropy with a certainty; the probability that this quadrupole term is non-zero due to chance is much smaller than $0.1\%$ probability $t=3.29$ corresponds to a $0.1\%$ probability).
 In fact. this is nothing new (Balazsetal. 1998)): it again confiniis that he observed distribution of all CRBs is without doubt audsotropic.," In fact, this is nothing new \cite{balazs98}) ); it again confirms that the observed distribution of all GRBs is without doubt anisotropic."
 We will interpret these three terms as the anisotropy hat follows frou the uou-uniforii sky exposure unction of BATSE instimucut., We will interpret these three terms as the anisotropy that follows from the non-uniform sky exposure function of BATSE instrument.
 There are 1ο further dipole aud quadrupole anisotropics above |f]>1.96: the sign test also gives 10 such anisotropies., There are no further dipole and quadrupole anisotropies above $|t| > 1.96$; the sign test also gives no such anisotropies.
 Ou the other hand. there are 19 m#0 harmonics above the 95% significance level. (," On the other hand, there are 19 $m\neq 0$ harmonics above the $95\%$ significance level. ("
In 12 cases [f|>1.96: in 7 cases the sign test gives anisotropy above the 95‘ sienificance level: for &=9.178 and v=pan=. respectively. both tests give anisotropy.),"In 12 cases $|t| > 1.96$; in 7 cases the sign test gives anisotropy above the $95\%$ significance level; for $n=9, m =8$ and $n=13, m =8$, respectively, both tests give anisotropy.)"
 Iu addition. for five harmonics oue has |f|72.58.," In addition, for five harmonics one has $|t| > 2.58$."
 For two of thei oue has ων1093 as well., For two of them one has $ k_{\mathrm{obs}} < 1093$ as well.
" Concerning the 95% significance level. oue expects that in 2.210/20=21 cases, one can obtain this “by chance”. too."," Concerning the $95\%$ significance level, one expects that in $2\times 240/20 =24$ cases, one can obtain this ""by chance"", too."
 This is more than the 19 cases obtained. and the difference could well be due to chance.," This is more than the 19 cases obtained, and the difference could well be due to chance."
" Coucerning the 99* sienificance level. one expects [8 cases theoretically, aud we obtain 7 ones."," Concerning the $99\%$ significance level, one expects 4.8 cases theoretically, and we obtain 7 ones."
"and we defined as “merger” a particle that had been accreted into the main progenitor of the galaxy and previously belonged to another structure, We defined the accretion fraction as and the merger fraction fmerg such that face+fmerg=1.","and we defined as “merger” a particle that had been accreted into the main progenitor of the galaxy and previously belonged to another structure, We defined the accretion fraction as and the merger fraction $f_\text{merg}$ such that $f_\text{acc} + f_\text{merg} = 1$."
" By definition, we have 0€facesfmerg1."," By definition, we have $0\le
f_\text{acc},f_\text{merg}\le 1$."
" As a consequence of the multi-zoom thechnique, and that galaxies can enter the level 3 box during the simulation, we had to select galaxies to be studied."," As a consequence of the multi-zoom thechnique, and that galaxies can enter the level 3 box during the simulation, we had to select galaxies to be studied."
 We only computed this accretion fraction for galaxies that could be tracked back in time until before t=7 Gyr so that the fraction could be computed for at least 2 Gyr of its lifetime., We only computed this accretion fraction for galaxies that could be tracked back in time until before $t = 7$ Gyr so that the fraction could be computed for at least 2 Gyr of its lifetime.
" We discarded galaxies that could not be tracked earlier than 7 Gyr, which either entered the box later, or were lost when computing the merger tree, possibly after a merger event."," We discarded galaxies that could not be tracked earlier than 7 Gyr, which either entered the box later, or were lost when computing the merger tree, possibly after a merger event."
 This left us with 530 galaxies that had been tracked from fap)«7.0 Gyr to t=9.1 Gyr., This left us with 530 galaxies that had been tracked from $t_\text{app} < 7.0$ Gyr to $t = 9.1$ Gyr.
" Figure 15 shows the accretion fraction as a function of mass for these 530 galaxies, as well as the (number) histogram of the accretion fraction."," Figure \ref{fig:hist_acc} shows the accretion fraction as a function of mass for these 530 galaxies, as well as the (number) histogram of the accretion fraction."
" We found a mean accretion fraction of77%,, and a median value of92%."," We found a mean accretion fraction of, and a median value of."
". In black, we plotted the median accretion fraction in mass bins, where the errorbars are the aand ppercentiles."," In black, we plotted the median accretion fraction in mass bins, where the errorbars are the and percentiles."
 We can see that most galaxies have a very high accretion fraction., We can see that most galaxies have a very high accretion fraction.
 The trend for low-mass galaxies at facc=1 indicates that several galaxies undergo no mergers and are fed only by accretion., The trend for low-mass galaxies at $f_\text{acc}= 1$ indicates that several galaxies undergo no mergers and are fed only by accretion.
" This could be a spurious effect caused by galaxies entering the box at late time, and experiencing no mergers."," This could be a spurious effect caused by galaxies entering the box at late time, and experiencing no mergers."
" However, even when we consider only galaxies that are present in the box between 3 Gyr and 9.1 Gyr, the histogram still shows such a trend with a mean value of and median of82%."," However, even when we consider only galaxies that are present in the box between 3 Gyr and 9.1 Gyr, the histogram still shows such a trend with a mean value of and median of."
. We now study the mean stellar age of galaxies as a function of the galaxy mass., We now study the mean stellar age of galaxies as a function of the galaxy mass.
" For this study, we use both zoom levels two and three because the level three simulation stops before z=0, but has a higher mass resolution."," For this study, we use both zoom levels two and three because the level three simulation stops before $z=0$, but has a higher mass resolution."
 Figure 16 shows the median of the mean stellar age of the galaxies as a function of the galaxy mass at the last output for level 3 (z= 0.46) and 2 (z= 0)., Figure \ref{fig:downsiz} shows the median of the mean stellar age of the galaxies as a function of the galaxy mass at the last output for level 3 $z=0.46$ ) and 2 $z=0$ ).
 The errorbars correspond to the and ppercentiles., The errorbars correspond to the and percentiles.
 The differences between the blue dots in the two panels are then due bowth to our low resolution and the temporal evolution., The differences between the blue dots in the two panels are then due bowth to our low resolution and the temporal evolution.
" It is interesting to see that in the second level of zoom, galaxies outside the R3=8.56 Mpc radius (1.6., red points) formed their stars more recently than the ones within the box (blue points)."," It is interesting to see that in the second level of zoom, galaxies outside the $R_3 = 8.56$ Mpc radius (i.e., red points) formed their stars more recently than the ones within the box (blue points)."
 This is certainly due to the lower average density of the region in the level 2 simulation which is located outside of the level 3 box., This is certainly due to the lower average density of the region in the level 2 simulation which is located outside of the level 3 box.
" We can see that at low masses, the dispersion is large: among the least massive galaxies, some form their stars early, while others form them late."," We can see that at low masses, the dispersion is large: among the least massive galaxies, some form their stars early, while others form them late."
" At each epoch of the universe, there is a large number of dwarfs, whose stars are forming actively."," At each epoch of the universe, there is a large number of dwarfs, whose stars are forming actively."
 This behaviour, This behaviour
One of the most important results from the Infrared Astronomical Satellite (£8.15). all sky surveys was the detection of a new class of galaxy where the bulk of the bolometric emission lies in the infrared wavebanel (Soiferetal.1984:Sanders&Mirabel 1996).,"One of the most important results from the Infrared Astronomical Satellite ) all sky surveys was the detection of a new class of galaxy where the bulk of the bolometric emission lies in the infrared waveband \cite{soi,sa1}."
. Phis population. termed “Luminous Infrared Galaxies. (L1Cs). becomes the dominant extragalactic population at LR luminosities above LOML.;. with a higher space density. tmn all other classes of galaxy of comparable bolometric Iuniinosityv.," This population, termed 'Luminous Infrared Galaxies' (LIGs), becomes the dominant extragalactic population at IR luminosities above $10^{11}L_{\sun}$, with a higher space density than all other classes of galaxy of comparable bolometric luminosity."
 At the brightest. end of the LLG population lie the Ilvperluminous Infrared. Caaxtes (LILIRGs). those with Lin>WPAAL. (Rowan-Hobinson2000)...," At the brightest end of the LIG population lie the Hyperluminous Infrared Galaxies (HLIRGs), those with $L_{IR} > 10^{13.0} h_{65}^{-2} L_{\sun}$ \cite{rr2}."
 The first LILIRG to be found. (P09O04)4109) was identified by WWleinmann et al. (1988)...," The first HLIRG to be found (P09104+4109) was identified by Kleinmann et al. \shortcite{kl},"
 wih a [ar infrared. luminosity of 1.5.LOMhh., with a far infrared luminosity of $1.5\times10^{13}h_{50}^{-2}L_{\sun}$.
 1n 1991. Re»an-IHobinson et al.," In 1991, Rowan-Robinson et al."
 identified L10214]|4724 at 2=2.286. with an apparent far infrared luminosity of 3 ΠΠ”...Later observations of this," identified F10214+4724 at $z=2.286$, with an apparent far infrared luminosity of $3\times10^{14}h^{-2}_{50}L_{\sun}$ .Later observations of this"
This particle distribution leads to à spiral structure in the disk.,This particle distribution leads to a spiral structure in the disk.
 Figure 3. shows the surface density. contrast (smoothed with a Gaussian kernel) for patterns obtained by distributing particles on stacked 1:2 (left) and. 2:1 (right) orbits., Figure \ref{fig:patterns} shows the surface density contrast (smoothed with a Gaussian kernel) for patterns obtained by distributing particles on stacked 1:2 (left) and 2:1 (right) orbits.
 The three rows of Figure 3) show a time-lapse sequence of pattern evolution., The three rows of Figure \ref{fig:patterns} show a time-lapse sequence of pattern evolution.
 The top row shows the initial conditions. and the second and the third rows show patterns at? =Ta and /=20754 correspondinglv.," The top row shows the initial conditions, and the second and the third rows show patterns at $t = T_{2:1}$ and $t = 20\,T_{2:1}$ correspondingly."
 75.4=2z/w»4 denotes a period of rotation of the 2:1 pattern., $T_{2:1} = 2\pi/\omega_{2:1}$ denotes a period of rotation of the 2:1 pattern.
 The frequeney of the 1:2 orbit. precession depends monotonically on the radius. so one expects. differential rotation to destroy the pattern.," The frequency of the 1:2 orbit precession depends monotonically on the radius, so one expects differential rotation to destroy the pattern."
 Indeed. at /=754. the spiral is seen to wind up. and by f=20754. it is wound up so tightly that the smoothing removes all traces of structure.," Indeed, at $t=T_{2:1}$, the spiral is seen to wind up, and by $t=20\,T_{2:1}$, it is wound up so tightly that the smoothing removes all traces of structure."
 The evolution of the 2:1 pattern is markedly cilferent., The evolution of the 2:1 pattern is markedly different.
 Signs of shear are clearly seen after a single rotation., Signs of shear are clearly seen after a single rotation.
" However. even after twenty rotations. there is still a pattern present around rp,z9.6 (which is exactly where the minimum of we occurs)."," However, even after twenty rotations, there is still a pattern present around $r_*\approx9.6$ (which is exactly where the minimum of $\omega_{2:1}$ occurs)."
 As this time span corresponds to almost 50 orbital rotations at £7. the pattern is remarkably persistent.," As this time span corresponds to almost 50 orbital rotations at $r_*$, the pattern is remarkably persistent."
 In the last section. we have shown that an accretion disk around a compact object can support persistent. rotating patterns due to the collective excitations of particles in the disk.," In the last section, we have shown that an accretion disk around a compact object can support persistent rotating patterns due to the collective excitations of particles in the disk."
 “Pheir existence depends on &eneral. relativity effects and is sensitive to the parameters of the central body but not to the accretion rate., Their existence depends on general relativity effects and is sensitive to the parameters of the central body but not to the accretion rate.
 All the frequencies in the problem scale inversely. proportionally to the central body mass., All the frequencies in the problem scale inversely proportionally to the central body mass.
 In addition. persistent pattern frequencies depend on the spin parameter.," In addition, persistent pattern frequencies depend on the spin parameter."
 Figure 4. shows the rotation frequencies of the three lowest-order persistent patterns (2:1. 3:1. ancl 3:2) for a 10ÀZ;-mass black hole as the spin is varied.," Figure \ref{fig:wa:rad} shows the rotation frequencies of the three lowest-order persistent patterns (2:1, 3:1, and 3:2) for a $10M_{\sun}$ -mass black hole as the spin is varied."
 This dependence in principle could be used to measure the mass and spin of the central object. provided that the frequencies of two distinct modes are observed. ancl identified: correctly.," This dependence in principle could be used to measure the mass and spin of the central object, provided that the frequencies of two distinct modes are observed and identified correctly."
 One should note. though. that for multi-armed patterns (for example the 3:2 pattern which has two arms) modulation frequeney could be a multiple of the rotation frequency.," One should note, though, that for multi-armed patterns (for example the 3:2 pattern which has two arms) modulation frequency could be a multiple of the rotation frequency."
 several dilferent. persistent. patterns could coexist in the accretion cisk: however. it is likely that the lowest-order ones are strongly. selected. based on geometrical considerations.," Several different persistent patterns could coexist in the accretion disk; however, it is likely that the lowest-order ones are strongly selected based on geometrical considerations."
 Surface density modulation of the 2:1 pattern. is second-order in particle displacement 2. while the 3:1 and 3:2 xuterns are third-order.," Surface density modulation of the 2:1 pattern is second-order in particle displacement $\varepsilon$, while the 3:1 and 3:2 patterns are third-order."
 The cancellation. of. Ilower-order erms is directly caused. by. the multiple-fold. gcometry of he orbits with »1., The cancellation of lower-order terms is directly caused by the multiple-fold geometry of the orbits with $n>1$.
 Being higher-order. could. explain why these persistent. patterns are not apparent in the linear »erturbation analvsis of Wagonerctal.(2001)..., Being higher-order could explain why these persistent patterns are not apparent in the linear perturbation analysis of \citet{2001ApJ...559L..25W}.
 Despite second-order scaling. the 2:1 pattern in Figure 3 (lower right) shows 1% amplitude of the surface density modulation or moderate displacement values (2/7;8 0.022).," Despite second-order scaling, the 2:1 pattern in Figure \ref{fig:patterns}
 (lower right) shows $1\%$ amplitude of the surface density modulation for moderate displacement values $\varepsilon/r_* \approx 0.022$ )."
 Ehe radial extent of the 2:1 pattern (Ar~ 4) also appears to be wider han that of a fundamental g-modoe (the width of which is ooportional; to ὃς1/2 and is estimated as Ar~1 by (2001)))., The radial extent of the 2:1 pattern $\Delta r \sim 4$ ) also appears to be wider than that of a fundamental $g$ -mode (the width of which is proportional to $c_s^{1/2}$ and is estimated as $\Delta r \sim 1$ by \citet{2001ApJ...559L..25W}) ).
"The magnitude is measured in the r-, i-, and z-bands for the u-, g-, and r-dropout samples, respectively.","The magnitude is measured in the $r$ -, $i$ -, and $z$ -bands for the $u$ -, $g$ -, and $r$ -dropout samples, respectively."
" These bands probe flux at approximately 1600À rest-frame of the sources at the expected mean redshifts, so that only a minor k-correction will be sufficient to compare the results for the different epochs directly, see the upper panel of Fig. 7.."," These bands probe flux at approximately $\rm{\AA}$ rest-frame of the sources at the expected mean redshifts, so that only a minor k-correction will be sufficient to compare the results for the different epochs directly, see the upper panel of Fig. \ref{fig:kcorr}."
" We transform the apparent magnitudes to absolute magnitudes and perform a k-correction to a rest-frame wavelength of 1600À using the mean redshifts for each of the dropout samples, i.e. we assume all sources to be at the same redshift."," We transform the apparent magnitudes to absolute magnitudes and perform a k-correction to a rest-frame wavelength of $\rm{\AA}$ using the mean redshifts for each of the dropout samples, i.e. we assume all sources to be at the same redshift."
" The uncertainties in the mean are expected to be approximately 0.1 for the three dropout samples, as argued in Sect. ??.."," The uncertainties in the mean are expected to be approximately $0.1$ for the three dropout samples, as argued in Sect. \ref{sec:redshiftdist}."
" This leads to uncertainties in both distance modulus and K-correction, resulting in a systematic error in the absolute magnitudes of our estimated LF, see the lower panel of Fig. 7.."," This leads to uncertainties in both distance modulus and k-correction, resulting in a systematic error in the absolute magnitudes of our estimated LF, see the lower panel of Fig. \ref{fig:kcorr}."
" The final uncertainties are about 0.07, 0.05 and 0.04 in the absolute magnitude for the u-, g-, and r-dropout samples, respectively."," The final uncertainties are about 0.07, 0.05 and 0.04 in the absolute magnitude for the $u$ -, $g$ -, and $r$ -dropout samples, respectively."
" After dividing the number counts by Ve, which corrects for incompleteness and Eddington bias, and subtracting the distance modulus and the k-correction from the apparent magnitudes, we obtain the LF in absolute magnitudes at 1600À."," After dividing the number counts by $V_{\rm{eff}}$, which corrects for incompleteness and Eddington bias, and subtracting the distance modulus and the k-correction from the apparent magnitudes, we obtain the LF in absolute magnitudes at $\AA$."
" Results from the four fields are binned to Amag=0.3, combined, and shown in Fig."," Results from the four fields are binned to $\Delta$ mag=0.3, combined, and shown in Fig."
 8 and Table 1.., \ref{fig:newLFme} and Table \ref{tab:datame}.
 Uncertainties in the magnitude direction are due to uncertainties in the redshift distribution of source galaxies., Uncertainties in the magnitude direction are due to uncertainties in the redshift distribution of source galaxies.
 The four independent analyses of the fields allow us to estimate field-to-field variations for each of the data points., The four independent analyses of the fields allow us to estimate field-to-field variations for each of the data points.
" Vertical error bars reflect either this uncertainty, or the Poisson noise term, whichever is largest."," Vertical error bars reflect either this uncertainty, or the Poisson noise term, whichever is largest."
 Usually the field-to-field variance dominates., Usually the field-to-field variance dominates.
" As a consequence of the way these are computed, Poisson noise is always taken into account."," As a consequence of the way these are computed, Poisson noise is always taken into account."
" We fit a Schechter function (?) to the binned datapoints, with M"" being the characteristic magnitude, o being the faint-end slope, and ¢* being the overall normalisation."," We fit a Schechter function \citep{schechter76} to the binned datapoints, with $M^{*}$ being the characteristic magnitude, $\alpha$ being the faint-end slope, and $\phi^{*}$ being the overall normalisation."
" Using x? statistics on a three dimensional grid of 500? different Schechter parameter combinations, we find the minimal value Qu) for each of the dropout samples yielding the best fit values."," Using $\chi^{2}$ statistics on a three dimensional grid of $500^{3}$ different Schechter parameter combinations, we find the minimal value $\chi_{\rm{min}}^{2}$ ) for each of the dropout samples yielding the best fit values."
" To estimate the errors in the fitted parameters, we project the 3-dimensional distribution of y? to 3 planes by taking the minimum X? along the projected dimension."," To estimate the errors in the fitted parameters, we project the 3-dimensional distribution of $\chi^2$ to 3 planes by taking the minimum $\chi^{2}$ along the projected dimension."
 In Fig., In Fig.
" 9 the and confidence levels are shown, which correspond to a Ay?-2.3 and 6.17 with respect to XL "," \ref{fig:ellipsallme} the and confidence levels are shown, which correspond to a $\Delta
 \chi^{2}$ =2.3 and 6.17 with respect to $\chi^2_{\rm min}$ ."
"In Table2 we give the confidence levels on each individual parameter, corresponding to ΔΥΖΞ1.0."," In Table \ref{tab:sparms} we give the confidence levels on each individual parameter, corresponding to $\Delta
 \chi^{2}$ =1.0."
hand. for the maximal mass distribution the probability is Pzz0.6 indicating that for these masses the short GRB sample is fully consistent with the galaxy mass function.,"hand, for the maximal mass distribution the probability is $P\approx 0.6$ indicating that for these masses the short GRB sample is fully consistent with the galaxy mass function."
 Using the intermediate case of SSP masses for the early-type hosts and the young+old masses for the late-type hosts. we find a probability of about 0.3. indicating that this combination 1s also fully consistent with the galaxy mass function.," Using the intermediate case of SSP masses for the early-type hosts and the young+old masses for the late-type hosts, we find a probability of about 0.3, indicating that this combination is also fully consistent with the galaxy mass function."
 Separating the early-type hosts we find that their SSP masses are fully consistent with the IIbertetal.(2010) mass function of quiescent galaxies (P~0.8): their large maximal masses. on the other hand. are inconsistent with the mass function. with Pz0.007.," Separating the early-type hosts we find that their SSP masses are fully consistent with the \citet{isl+10} mass function of quiescent galaxies $P\approx 0.8$ ); their large maximal masses, on the other hand, are inconsistent with the mass function, with $P\approx 0.007$."
 Finally. for the late-type hosts we find a clear inconsistency of the single age SSP masses with the Ibertetal.(2010) mass function of intermediate-activity galaxies. with P~4«107.," Finally, for the late-type hosts we find a clear inconsistency of the single age SSP masses with the \citet{isl+10} mass function of intermediate-activity galaxies, with $P\approx 4\times 10^{-7}$."
 However. the maximal mass distribution is fully consistent with the mass function (P~ 0.3). while the young+old mass distribution is marginally consistent (P= 0.1).," However, the maximal mass distribution is fully consistent with the mass function $P\approx 0.3$ ), while the young+old mass distribution is marginally consistent $P\approx 0.1$ )."
 To summarize. the distribution of short GRB host masses is compatible with the overall mass distribution of galaxies only if their stellar masses are given by the SSP masses for the early-type hosts and the maximal or young+old masses for the late-type hosts.," To summarize, the distribution of short GRB host masses is compatible with the overall mass distribution of galaxies only if their stellar masses are given by the SSP masses for the early-type hosts and the maximal or young+old masses for the late-type hosts."
 Since the opposite scenario (maximal masses for the early-type hosts and SSP masses for the late-type hosts) is unlikely. we conclude that the existing sample of short GRB hosts is consistent with the galaxy mass function.," Since the opposite scenario (maximal masses for the early-type hosts and SSP masses for the late-type hosts) is unlikely, we conclude that the existing sample of short GRB hosts is consistent with the galaxy mass function."
 Equivalently. this means that short GRBs may indeed track stellar mass alone.," Equivalently, this means that short GRBs may indeed track stellar mass alone."
 However. we caution that the host demographics seem to be at odds with the expected equal fractions of total stellar mass in early- and late-type galaxies. unless nearly all of the unidentified hosts are early-type galaxies.," However, we caution that the host demographics seem to be at odds with the expected equal fractions of total stellar mass in early- and late-type galaxies, unless nearly all of the unidentified hosts are early-type galaxies."
 This. along with the somewhat lower than expected masses of the late-type hosts. leaves open the possibility that at least a subset of short GRB progenitors track star formation activity rather than stellar mass.," This, along with the somewhat lower than expected masses of the late-type hosts, leaves open the possibility that at least a subset of short GRB progenitors track star formation activity rather than stellar mass."
 Despite the possibility that some short GRB progenitors may track star formation activity. we find that the inferred stellar masses and population ages of short GRB hosts are generally distinet from those of long GRB hosts in both the single age SSP and maximal models.," Despite the possibility that some short GRB progenitors may track star formation activity, we find that the inferred stellar masses and population ages of short GRB hosts are generally distinct from those of long GRB hosts in both the single age SSP and maximal models."
 Most importantly. this is true for the subset of late-type hosts.," Most importantly, this is true for the subset of late-type hosts."
 In the framework of the single age SSP model we find a K-S probability of only 0.006 that the long and short GRB hosts are drawn from the same mass distribution., In the framework of the single age SSP model we find a K-S probability of only $0.006$ that the long and short GRB hosts are drawn from the same mass distribution.
 The probability is higher for the subset of late-type short GRB hosts. Pz0.1 (Figure 3)).," The probability is higher for the subset of late-type short GRB hosts, $P\approx 0.1$ (Figure \ref{fig:masses_1a}) )."
 However. since the SSP values represent the mass of only the young stellar populations. they are mostly reflective of the star formation activity rather than the total stellar mass.," However, since the SSP values represent the mass of only the young stellar populations, they are mostly reflective of the star formation activity rather than the total stellar mass."
 If we use Instead the maximal masses. the K-S probability that the long GRB hosts and late-type hosts of short GRBs are drawn from the same sample is negligible. P=4«10? (Figure 4)). demonstrating that they are distinct galaxy populations.," If we use instead the maximal masses, the K-S probability that the long GRB hosts and late-type hosts of short GRBs are drawn from the same sample is negligible, $P\approx 4\times
10^{-5}$ (Figure \ref{fig:masses_1b}) ), demonstrating that they are distinct galaxy populations."
 A similar conclusion is apparent from a comparison of the single age SSP population ages., A similar conclusion is apparent from a comparison of the single age SSP population ages.
 The K-S probability that the long GRB hosts and late-type hosts of short GRBs are drawn from the same distribution ts only Pz0.006., The K-S probability that the long GRB hosts and late-type hosts of short GRBs are drawn from the same distribution is only $P\approx 0.006$.
 Thus. the long GRB hosts have significantly lower stellar masses than the subset of late-type short GRB hosts. and their young stellar population are significantly younger.," Thus, the long GRB hosts have significantly lower stellar masses than the subset of late-type short GRB hosts, and their young stellar population are significantly younger."
 Indeed. a comparison of the long GRB host maximal masses to the [bertetal.(2010) mass function of high-activity galaxies at z0.7 (appropriate for the long GRB sample considered here) indicates à K-S probability of only 0.002 that the long GRB hosts are drawn from the galaxy mass function.," Indeed, a comparison of the long GRB host maximal masses to the \citet{isl+10} mass function of high-activity galaxies at $z\sim 0.7$ (appropriate for the long GRB sample considered here) indicates a K-S probability of only $0.002$ that the long GRB hosts are drawn from the galaxy mass function."
 This is consistent with our understanding that their massive star progenitors select galaxies by star formation (and perhaps additional factors such as metallicity)., This is consistent with our understanding that their massive star progenitors select galaxies by star formation (and perhaps additional factors such as metallicity).
 The apparent distinction between long GRB hosts and the late-type hosts of short GRBs in terms of their stellar masses and young population ages strengthens our similar previous conclusion based on their star formation rates. specific star formation rates. luminosities. and metallicities (Berger2009).. as well as physical sizes (Fongetal.2010).," The apparent distinction between long GRB hosts and the late-type hosts of short GRBs in terms of their stellar masses and young population ages strengthens our similar previous conclusion based on their star formation rates, specific star formation rates, luminosities, and metallicities \citep{ber09}, as well as physical sizes \citep{fbf10}."
 In essentially every property the late-type short GRB hosts point to a population of more quiescent. massive. and evolved galaxies than the hosts of long GRBs.," In essentially every property the late-type short GRB hosts point to a population of more quiescent, massive, and evolved galaxies than the hosts of long GRBs."
 We conclude that this rules out the idea that short GRB progenitors in late-type hosts are massive stars identical to long GRB progenitors etal.2009).. A determination of the delay function from the derived stellar population ages is complicated by two primary factors.," We conclude that this rules out the idea that short GRB progenitors in late-type hosts are massive stars identical to long GRB progenitors \citep{vzo+09}, A determination of the delay function from the derived stellar population ages is complicated by two primary factors."
 First. we have to assume that the short GRB progenitors in each host were formed within the inferrec stellar population.," First, we have to assume that the short GRB progenitors in each host were formed within the inferred stellar population."
 This assumption is justified statistically both for an association of the progenitors with stellar mass and with star formation activity. as long as we can appropriately normalize the rates of short GRBs.," This assumption is justified statistically both for an association of the progenitors with stellar mass and with star formation activity, as long as we can appropriately normalize the rates of short GRBs."
 Second. while we can determine single age SSP ages from the broad-band photometry. these data are not sufficient to provide an age breakdown (by mass) for multiple stellar components.," Second, while we can determine single age SSP ages from the broad-band photometry, these data are not sufficient to provide an age breakdown (by mass) for multiple stellar components."
 Indeed. for our hybrid young+old model we had to fix the age of the old population (to the age of the universe. in this case).," Indeed, for our hybrid young+old model we had to fix the age of the old population (to the age of the universe, in this case)."
" Still. we find that in the young+old model. the bulk of the mass (%55—99%: Table 2)) Is contained in the old stellar population. and so the progenitors would have ""old"" ages (7Z resp) If they tracked stellar mass."," Still, we find that in the young+old model, the bulk of the mass $\approx 55-99\%$; Table \ref{tab:short}) ) is contained in the old stellar population, and so the progenitors would have “old” ages $\tau\gtrsim\tau_{\rm SSP}$ ) if they tracked stellar mass."
 As a result of these limitations we can only explore the implications of two main scenarios. namely that short GRBs track mass and/or star formation activity.," As a result of these limitations we can only explore the implications of two main scenarios, namely that short GRBs track mass and/or star formation activity."
 In the context of the former scenario we have shown in refsec:mass that the short GRBs in early-type hosts trace stellar mass., In the context of the former scenario we have shown in \\ref{sec:mass} that the short GRBs in early-type hosts trace stellar mass.
 Therefore. we can use their SSP ages to provide a rough estimate of the progenitor ages. which we find to be 720.8—4.4 Gyr. with a median of about 3 Gyr.," Therefore, we can use their SSP ages to provide a rough estimate of the progenitor ages, which we find to be $\tau\approx 0.8-4.4$ Gyr, with a median of about 3 Gyr."
 On the other hand. for the late-type hosts (for which we can extract no credible information on the mass-weighted stellar population age). we can infer a typical delay relative to the most recent star formation episode under the assumption that these progenitors track star formation activity.," On the other hand, for the late-type hosts (for which we can extract no credible information on the mass-weighted stellar population age), we can infer a typical delay relative to the most recent star formation episode under the assumption that these progenitors track star formation activity."
 We find SSP ages of 7z:0.03—0.5 Gyr. with a median of about 0.25 Gyr. or young+old ages of about 0.01—0.4 Gyr with a median of about 0.1 Gyr.," We find SSP ages of $\tau\approx 0.03-0.5$ Gyr, with a median of about 0.25 Gyr, or young+old ages of about $0.01-0.4$ Gyr with a median of about 0.1 Gyr."
 Thus. if short GRBs follow both stellar mass (in early-type galaxies) and star formation activity (in late-type galaxies). the typical delay times are about 3 and 0.2 Gyr. respectively.," Thus, if short GRBs follow both stellar mass (in early-type galaxies) and star formation activity (in late-type galaxies), the typical delay times are about 3 and 0.2 Gyr, respectively."
 Using multi-band photometry for 19 short GRB host galaxies we extracted stellar masses and ages under the assumption of single age populations. combined young+old populations. and maximal mass populations.," Using multi-band photometry for 19 short GRB host galaxies we extracted stellar masses and ages under the assumption of single age populations, combined young+old populations, and maximal mass populations."
 The resulting values allow us to investigate whether short GRBs track the cosmie stellar mass distribution. to estimate their typical," The resulting values allow us to investigate whether short GRBs track the cosmic stellar mass distribution, to estimate their typical"
attained is high. while in the latter case the observational uncertainty in the central regions is very large.,"attained is high, while in the latter case the observational uncertainty in the central regions is very large."
 In both cases the inner mass distribution is soft. there is no a massive cD galaxy and one can assume that both clusters are dark matter dominated.," In both cases the inner mass distribution is soft, there is no a massive cD galaxy and one can assume that both clusters are dark matter dominated."
" We shall infer from observations the behaviour of the halo core radius {4 and of the central density p, with the halo maximum circular velocity Vo, (he gravitational potential well).", We shall infer from observations the behaviour of the halo core radius $R_c$ and of the central density $\rho_c$ with the halo maximum circular velocity $V_m$ (the gravitational potential well).
 AI the data we use have been taken from the literature but the parameters we adopt have been estimated from our analysis., All the data we use have been taken from the literature but the parameters we adopt have been estimated from our analysis.
" ὃν fitting the observed. rotation curves of the sample ealaxies alter subtraction of the disk contribution to the rotation curve allows us to fit the two parameters of a isothermal model. 2, and e. where ο is the one-dimensional velocity dispersion."," By fitting the observed rotation curves of the sample galaxies after subtraction of the disk contribution to the rotation curve allows us to fit the two parameters of a non-singular isothermal model, $R_c$ and $v$, where $v$ is the one-dimensional velocity dispersion."
 Phe central density is then: pe=9aTfAgGIU., The central density is then: $\rho_c =9 \ v^2 /4 \pi G R_c^2$.
 The properties of the sample objects ave listed in Table 1., The properties of the sample objects are listed in Table 1.
" In the various columns we have: the name. the maximum circular velocity Vi, in kms. the core radius 2. in kpc. the central density p. in M. /pc. and the references used."," In the various columns we have: the name, the maximum circular velocity $V_{m}$ in km/s, the core radius $R_c$ in kpc, the central density $\rho_c$ in $M_{\odot}$ $^3$, and the references used."
 Lt is important to realize that a present. day rotation curve is not only the result of an initial dark halo structure. but is a consequence of the process of disk formation. which as it will be shown. can alter the inner shapes of galactic rotation curves.," It is important to realize that a present day rotation curve is not only the result of an initial dark halo structure, but is a consequence of the process of disk formation, which as it will be shown, can alter the inner shapes of galactic rotation curves."
 Two ellects contribute to changing the density distribution of a clark halo during disk. formation. both relevant only in the central regions. precisely. where the problem of the existence or absence of a soft. core arises.," Two effects contribute to changing the density distribution of a dark halo during disk formation, both relevant only in the central regions, precisely where the problem of the existence or absence of a soft core arises."
 Firstly. as a result of disk formation. the baryonic component Contraction makes the barvons in the central regions approximately as dynamically relevant as the dark matter.," Firstly, as a result of disk formation, the baryonic component contraction makes the baryons in the central regions approximately as dynamically relevant as the dark matter."
 Secondly. the contraction of the barvons alters the total mass distribution in the inner regions. forcing the dark halo to adjust to the now mocified gravitational potential.," Secondly, the contraction of the baryons alters the total mass distribution in the inner regions, forcing the dark halo to adjust to the now modified gravitational potential."
 These two points are essentially well known. and have been treated in standard disk galaxy formation mocdels. e.g. Fall Efstathiou 1980. Flores et al.," These two points are essentially well known, and have been treated in standard disk galaxy formation models, e.g. Fall Efstathiou 1980, Flores et al."
 1993: Dalcanton et al., 1993; Dalcanton et al.
 1997: Firmani Avila-Reese 2000 and Hernandez Gilmore 1998 who show explicitly the relevance of the above cllects even in the central regions of LSB systems., 1997; Firmani Avila-Reese 2000 and Hernandez Gilmore 1998 who show explicitly the relevance of the above effects even in the central regions of LSB systems.
 A. detailed modeling of the sample of five galaxies by. Swaters ct al. (, A detailed modeling of the sample of five galaxies by Swaters et al. (
2000) allows us to quantify this possibility. and. to asses the evidence supporting shallow cores at this region of the LSB galactic distribution.,"2000) allows us to quantify this possibility, and to asses the evidence supporting shallow cores at this region of the LSB galactic distribution."
 With such a modeling we can also estimate the uncertainties of our other data., With such a modeling we can also estimate the uncertainties of our other data.
 For cach of these galaxies we use a simple disk formation model where a fraction £F of the original halo mass is turned into an exponential disk having the clisk scale length of the observed galaxy., For each of these galaxies we use a simple disk formation model where a fraction $F$ of the original halo mass is turned into an exponential disk having the disk scale length of the observed galaxy.
 Phe gravitational pull sullerecl by the inner regions of the initial dark halo is calculated: using an hypothesis of adiabatie invariance for the orbits of the clark particles. and the final rotation curve calculated taking into account the modified halo and the contribution of the exponential disk (Hernánndez & Cilmore 1998).," The gravitational pull suffered by the inner regions of the initial dark halo is calculated using an hypothesis of adiabatic invariance for the orbits of the dark particles, and the final rotation curve calculated taking into account the modified halo and the contribution of the exponential disk (Hernánndez $\&$ Gilmore 1998)."
 Phe parameters of this disk formation model were optimized using the full observed rotation curves. together with an imposed. Tullv-Fisher relation (Firmani & Avila-Reese 2000) and the observed disk scale raclius of the galaxies in question.," The parameters of this disk formation model were optimized using the full observed rotation curves, together with an imposed Tully-Fisher relation (Firmani $\&$ Avila-Reese 2000) and the observed disk scale radius of the galaxies in question."
 In this way we solved for the values of E which best vield a final rotation curve., In this way we solved for the values of F which best yield a final rotation curve.
 We have modeled these galaxies using two cüllerent dark halo structures. namely a NEW profile and a Wing profile.," We have modeled these galaxies using two different dark halo structures, namely a NFW profile and a King profile."
 The analytic NEW profile is p(r)=psdfrs)lppaged) with Ες the scale radius corresponding to the scale at which the ogarithmic slope is -2., The analytic NFW profile is $\rho(r)=\rho_s(r/r_s)^{-1}(1+r/r_s)^{-2}$ with $r_s$ the scale radius corresponding to the scale at which the logarithmic slope is -2.
" Since p, and ry are correlated and hey depend only on the mass. the density. profiles of haloes can be described by a one-parameter family of models. where he parameter is the mass."," Since $\rho_c$ and $r_s$ are correlated and they depend only on the mass, the density profiles of haloes can be described by a one-parameter family of models, where the parameter is the mass."
 The Wine density profile. has he form: p=pof(ríro.D). with po the central. density and ry the core radius (the radius at which the density is roughly po/3).," The King density profile has the form: $\rho=\rho_0 f(r/r_0,P)$ , with $\rho_0$ the central density and $r_0$ the core radius (the radius at which the density is roughly $\rho_0/3$ )."
 The form parameter is P=W(0)0. xing WO) the relative gravitational potential and σ the inear velocity. dispersion in the center.," The form parameter is $P=\Psi(0)/\sigma^2$, being $\Psi(0)$ the relative gravitational potential and $\sigma$ the linear velocity dispersion in the center."
 We adopt the same ormalism of Binney & ‘Tremaine assuming for [ the same unction displaved in their Fig.4-9., We adopt the same formalism of Binney $\&$ Tremaine assuming for f the same function displayed in their Fig.4-9.
 Fig., Fig.
 1l shows the rotation curves of E568-1. E568-3 and 1574-1. in the Ist. 2nd and 3rd. panels. respectively (dots with error bars).," 1 shows the rotation curves of F568-1, F568-3 and F574-1, in the 1st, 2nd and 3rd panels, respectively (dots with error bars)."
 The dashed curves give the unique CDM JW halo which has à maximum velocity matching that of the observations. for cach galaxy.," The dashed curves give the unique CDM NFW halo which has a maximum velocity matching that of the observations, for each galaxy."
 Panel (1) refers to hat galaxy [rom Swaters et al. (, Panel (1) refers to that galaxy from Swaters et al. (
2000) for which the NEW wofile fits best.,2000) for which the NFW profile fits best.
 Panel. (2) gives the opposite case. where he NEW profile fails completely to reproduce the data.," Panel (2) gives the opposite case, where the NFW profile fails completely to reproduce the data."
 For the remaining three galaxies only marginal agreement tween the NEW model and the rotation curves is possible: a representative case of them is given in panel (3)., For the remaining three galaxies only marginal agreement between the NFW model and the rotation curves is possible; a representative case of them is given in panel (3).
 Due to the disk formation processes modifving the initial halo. however. the comparison mace through the dashed. curves is. far from being ai fair one.," Due to the disk formation processes modifying the initial halo, however, the comparison made through the dashed curves is far from being a fair one."
 More representative of a hypothetical reality of NEW. profiles is the comparison shown by the continuous curves and the data points., More representative of a hypothetical reality of NFW profiles is the comparison shown by the continuous curves and the data points.
 In this case we take the unique CDM NEW profile which after disk formation has the required. asymptotic velocity of the observed. galaxies., In this case we take the unique CDM NFW profile which after disk formation has the required asymptotic velocity of the observed galaxies.
 In this case we see that whilst for F568-1 in panel (1) the fit remains good. in the other two cases no aerecment is possible. and the NEW option must be rejected.," In this case we see that whilst for F568-1 in panel (1) the fit remains good, in the other two cases no agreement is possible, and the NFW option must be rejected."
 In Fig., In Fig.
 2 we repeat the analysis of Fig., 2 we repeat the analysis of Fig.
 1. but starting from a non-singular isothermal halo taken as a Ixing sphere with a form parameter that will be determined. by. the best fit to the observations.," 1, but starting from a non-singular isothermal halo taken as a King sphere with a form parameter that will be determined by the best fit to the observations."
 The data points remain as in the previous case., The data points remain as in the previous case.
 The thick continuous curves give the model that after disk formation has the required asymptotic velocity and the proper shape., The thick continuous curves give the model that after disk formation has the required asymptotic velocity and the proper shape.
 As it can be seen. the entire sample in this case is quite accurately fitted by the non-singular dark halo taken.," As it can be seen, the entire sample in this case is quite accurately fitted by the non-singular dark halo taken."
 Phe thin continuous curves give the contribution to the final rotation curve due to the dark halo. after being mocilied bv the disk formation.," The thin continuous curves give the contribution to the final rotation curve due to the dark halo, after being modified by the disk formation."
 This shows that the final dark halo does indeed dominate the resulting rotation curve. with the exponential disk eiving only a minor contribution.," This shows that the final dark halo does indeed dominate the resulting rotation curve, with the exponential disk giving only a minor contribution."
 The dashed lines give the rotation curve of the initial dark halo. before disk formation took place.," The dashed lines give the rotation curve of the initial dark halo, before disk formation took place."
 This Last is given to show the ellects of the gravitational pull sullered by the dark haloesas a result of the concentration of the, This last is given to show the effects of the gravitational pull suffered by the dark haloesas a result of the concentration of the
keeping the inclination and expansion velocity constant.,keeping the inclination and expansion velocity constant.
" As demonstrated in Figure 8,, and Table 4,, the observed spectrum shows the central component has higher velocities at earlier times, implying that some deceleration has occurred in this direction as the ejecta expanded."," As demonstrated in Figure \ref{fig:early}, and Table \ref{tb:gauss}, the observed spectrum shows the central component has higher velocities at earlier times, implying that some deceleration has occurred in this direction as the ejecta expanded."
 We then modelled the earlier epoch data (Figure 8)) so that we keep the polar blobs and prolate structure expanding linearly but the ring width (w) was derived from the values in Table 4 for component 2 (with the ratio of the semi-major to semi-minor axis kept always as 1.15)., We then modelled the earlier epoch data (Figure \ref{fig:early}) ) so that we keep the polar blobs and prolate structure expanding linearly but the ring width $w$ ) was derived from the values in Table \ref{tb:gauss} for component 2 (with the ratio of the semi-major to semi-minor axis kept always as 1.15).
 The results are shown in Figure 8.., The results are shown in Figure \ref{fig:early}.
 The assumption ofa decelerating ring replicates the spectra well (Figure 8))., The assumption ofa decelerating ring replicates the spectra well (Figure \ref{fig:early}) ).
 The fact that the ring shows a smooth flat top structure compared to the observed spectra is because we do not include small scale structure in the model., The fact that the ring shows a smooth flat top structure compared to the observed spectra is because we do not include small scale structure in the model.
 There is also some higher velocity material associated with the wings of the central component that is not reproduced., There is also some higher velocity material associated with the wings of the central component that is not reproduced.
" Furthermore, to better replicate the line profiles it was required that we change the density ratios of the components with time (Table 5))."," Furthermore, to better replicate the line profiles it was required that we change the density ratios of the components with time (Table \ref{tb:density}) )."
 What is evident from the ratio of the densities is that the prolate structure appears to reduce in density compared with the other structures while the blobs initially increase in density compared with the ring then this ratio reduces again at a later time., What is evident from the ratio of the densities is that the prolate structure appears to reduce in density compared with the other structures while the blobs initially increase in density compared with the ring then this ratio reduces again at a later time.
" We have constrained an overall structure, inclination and expansion velocity for the nebular remnant in V2672 Oph from modelling the Ha."," We have constrained an overall structure, inclination and expansion velocity for the nebular remnant in V2672 Oph from modelling the $\alpha$ ."
 The inclination and, The inclination and
We also performed our analysis using PPetrosian maguitudes frou the DR? catalogue. which are derived from the sinele frame nuages. in place of he Stripe 852 catalogue co-add model magnitudes. which are derived from the stacked images.,"We also performed our analysis using Petrosian magnitudes from the DR7 catalogue, which are derived from the single frame images, in place of the Stripe 82 catalogue co-add model magnitudes, which are derived from the stacked images."
 A comparison of sinele-fraine Petrosian magnitudes with co-add model uagenitudes shows the two types of magnitudes agree for 1e niost part. though there is scatter in the difference which increases with magnitude.," A comparison of single-frame Petrosian magnitudes with co-add model magnitudes shows the two types of magnitudes agree for the most part, though there is scatter in the difference which increases with magnitude."
 The «baud difference exhibits the largest scatter auc a slielt bias iucdicating iat the sinele-frame Petrosian ας magnitudes teud ο be brighter., The $u$ -band difference exhibits the largest scatter and a slight bias indicating that the single-frame Petrosian $u$ -band magnitudes tend to be brighter.
 We fund that using sinele-frame photometry can chauge ιο derived ealaxy properties and the uncertainties on jese properties. thus possibly affecting the significance ft trends with IIR.," We find that using single-frame photometry can change the derived galaxy properties and the uncertainties on these properties, thus possibly affecting the significance of trends with HR."
 The photometric errors on the sinele-yale inagnitudes are roughly teu times larecr than ιο photometric errors on the co-add magnitudes., The photometric errors on the single-frame magnitudes are roughly ten times larger than the photometric errors on the co-add magnitudes.
 As a result. using sinelo-frame maenitudes reduces the 4? values of the SED fits aud expauds the rauge of SED nodels that provide reasonable fts. according to our uethod described iu Section 3.3..," As a result, using single-frame magnitudes reduces the $\chi^2$ values of the SED fits and expands the range of SED models that provide reasonable fits, according to our method described in Section \ref{DerGalProps}."
 This then has the effect of potentially shifting the median aud increasing the width of the \?-weighted PDF for the galaxy properties. which changes our derived values for these propertics and increases their uncertainties," This then has the effect of potentially shifting the median and increasing the width of the $\chi^2$ -weighted PDF for the galaxy properties, which changes our derived values for these properties and increases their uncertainties."
 The derived galaxy nass is robust and relatively unaffected by the difference )etween sinegle-frame and co-add photometry. although he uncertainties on the mass are more than twice as aree for the sinele-fraie data.," The derived galaxy mass is robust and relatively unaffected by the difference between single-frame and co-add photometry, although the uncertainties on the mass are more than twice as large for the single-frame data."
 The average age is uch nore seusitive. to this difference., The average age is much more sensitive to this difference.
 Overall. the sinegle-rane Petrosian magnitudes produce vounecr ages aud arecr mucertaintics on the age. but the scatter m both of these quantities is large.," Overall, the single-frame Petrosian magnitudes produce younger ages and larger uncertainties on the age, but the scatter in both of these quantities is large."
 The vounecr ages may be due in part to the «-band maeuitude difference. since nore fux iu bluer bauds cau be interpreted as Helit fron vounger stars.," The younger ages may be due in part to the $u$ -band magnitude difference, since more flux in bluer bands can be interpreted as light from younger stars."
 As a test. we inflated the errors on the co-add magnitudes by a factor of 10 aud found that the results essentially reproduce those obtained frou using the sinele-frame Petrosian magnitudes sugeesting that the size of the photometric errors plays a substantial role in the discrepancy in derived ealaxy properties.," As a test, we inflated the errors on the co-add magnitudes by a factor of 10 and found that the results essentially reproduce those obtained from using the single-frame Petrosian magnitudes suggesting that the size of the photometric errors plays a substantial role in the discrepancy in derived galaxy properties."
 We coufiii with a significance of 3.00 the result ound bv Iwellyetal.(2010)... Sullivanet.al. (2010).. and Lanipeitlctal.(2010). that massive galaxies tend o host overluminousla.," We confirm with a significance of $3.0 \sigma$ the result found by \citet{kel10}, \citet{sul10}, and \citet{lam10} that massive galaxies tend to host overluminous."
 We also find iudication. with a significance of 1.90. that even after light-cirve correction. overhuuinous tend to occur in older stellar populations.," We also find indication, with a significance of $1.9 \sigma$, that even after light-curve correction, overluminous tend to occur in older stellar populations."
 We note hat the Neilletal.(2009) trend of TTR with hos age was based on luninositvaweighted age while iu lis work we calculate massaveielted age. making a direct comparison difficult.," We note that the \citet{nei09} trend of HR with host age was based on luminosity-weighted age while in this work we calculate mass-weighted age, making a direct comparison difficult."
 However. the direction of he age trend we see agrees with the Neilletal.(2009) reud for their low-extinction hosts.," However, the direction of the age trend we see agrees with the \citet{nei09} trend for their low-extinction hosts."
 The IIR. trend with rost Dununositv-weiehted age plotted by Callaghereal.(2008) is in the opposite direction from the trend we find here. though the significance of then trend is weeheible aud their methods different.," The HR trend with host luminosity-weighted age plotted by \citet{gal08} is in the opposite direction from the trend we find here, though the significance of their trend is negligible and their methods different."
 We expect tha nass-welghted age is a more unbiased measure of the age of the ealaxy because it is not as stronglv affected by UV fux from vouug stars as Dhuuimositvwelehted age (seeLeeetal.2007.Table13.," We expect that mass-weighted age is a more unbiased measure of the age of the galaxy because it is not as strongly affected by UV flux from young stars as luminosity-weighted age \citep[see][Table 1]
{lee07}."
 Furthermore. the niass-weiehted age gives iore weight to older stellar populations. to which pprogenitors inmost probably belong. aud is therefore more likely to be correlated with properties than luminosity-weiglted age.," Furthermore, the mass-weighted age gives more weight to older stellar populations, to which progenitors most probably belong, and is therefore more likely to be correlated with properties than luminosity-weighted age."
 The trends we fiud of IIR. with mass and age agree with each other in the seuse that ealaxy mass aud age are correlated. with older galaxies generally being more nassive.," The trends we find of HR with mass and age agree with each other in the sense that galaxy mass and age are correlated, with older galaxies generally being more massive."
 Based on the mass-age distribution in Figure 3.. we split our data iuto two groups: an (Age;«5 Car eroup (which euconipasses nearly the eutire range of masses) aud a logMass 210.2 eroup (which encompasses rearly the cutire rauge of ages).," Based on the mass-age distribution in Figure \ref{figAgevMass}, we split our data into two groups: an $\langle \mathrm{Age} \rangle<5$ Gyr group (which encompasses nearly the entire range of masses) and a logMass $>10.2$ group (which encompasses nearly the entire range of ages)."
" This was done iun au effort to investigate the effect of one of the variables (mss or age] on IIR while attempting to ""control or the other."," This was done in an effort to investigate the effect of one of the variables (mass or age) on HR while attempting to “control"" for the other."
 In Figure 7 we plot IR against age for he logMass >10.2 eroup and IIR against mass for he (Age)«5 Gyr eroup.," In Figure \ref{figControl} we plot HR against age for the logMass $>10.2$ group and HR against mass for the $\langle \mathrm{Age} 
\rangle <5$ Gyr group."
 Within these groups we fud hat the IIR correlation with mass is much weaker tha in the full sample. aud that the IIR. plot with agPO IS consistent with no correlation.," Within these groups we find that the HR correlation with mass is much weaker than in the full sample, and that the HR plot with age is consistent with no correlation."
 Estimates of host ealaxy nass are muore robust and have smaller uucertaiuties han estimates ofaget... and this in part may be why IIBs are more stronely correlated with mass.," Estimates of host galaxy mass are more robust and have smaller uncertainties than estimates of, and this in part may be why HRs are more strongly correlated with mass."
 Thus. the rue uuderlving property influcucing the eexplosiou is still unelear.," Thus, the true underlying property influencing the explosion is still unclear."
 The strength of both correlations av be improved bv having UV and ucar-TR amatches for all hosts and bv calculating galaxy nmaguitudes i a consistent imanner through matched apertures for all survey types (as was done. eg. in Talletal.2011)). casting that UV-optical-NIR. colors are accurate.," The strength of both correlations may be improved by having UV and near-IR matches for all hosts and by calculating galaxy magnitudes in a consistent manner through matched apertures for all survey types (as was done, e.g., in \citealp{hil10}) ), ensuring that UV-optical-NIR colors are accurate."
 It is also possible that the relationship between IIR. auc age Or Inass is not simply linear aud max be more complex., It is also possible that the relationship between HR and age or mass is not simply linear and may be more complex.
 Additionally. in au ideal case of a well-resolved extended host. a local age computed from photometry obtained frou the location of the Hin the ealaxy would be preferable to the elobal galaxy average age that we compute here and would likely correlate more strongly with properties of thela.," Additionally, in an ideal case of a well-resolved extended host, a local age computed from photometry obtained from the location of the in the galaxy would be preferable to the global galaxy average age that we compute here and would likely correlate more strongly with properties of the."
 We find that the IIR. trend. with mass persists if we consider the subsample for which iis complete., We find that the HR trend with mass persists if we consider the subsample for which is complete.
 Therefore. based ou our measurements auc. the completeness of our dataset. it is likely that that are unclerhuninous after light-curve correction do not occur iu massive galaxies.," Therefore, based on our measurements and the completeness of our dataset, it is likely that that are underluminous after light-curve correction do not occur in massive galaxies."
 This view is consisteut with the results of I&asenetal.(2009) who showed using ssnmnulatious and the Tiuuuesetal.(2003) model that motallicity can affect the explosion plysics in such a wav as to cause mnctal-rich progenitors to produce, This view is consistent with the results of \citet{kas09} who showed using simulations and the \citet{tim03} model that metallicity can affect the explosion physics in such a way as to cause metal-rich progenitors to produce
where [is the incomplete gamma function.,where $\Gamma$ is the incomplete gamma function.
" The integral is sensitive to the choice of L,,,;,,. especially for small 3. so we explore a range of F,,,;,,."," The integral is sensitive to the choice of $L_{min}$, especially for small $\beta$, so we explore a range of $L_{min}$."
 The incomplete gamma function was calculated using Mathematica (v. 4.0.1.0)., The incomplete gamma function was calculated using Mathematica (v. 4.0.1.0).
 Strong emission is an indicator of high star—formation rates and starburst activity., Strong emission is an indicator of high star–formation rates and starburst activity.
" Therefore. the lumimosity function of starburst galaxies was assumed to follow an luminosity function,"," Therefore, the luminosity function of starburst galaxies was assumed to follow an luminosity function."
" At.= 1.3. Yan (1999)) find a=—1.35. Q-—17«10Mpe""and —7«10|l"," At $z=1.3$ , Yan \nocite{Yan99}) ) find $\alpha = -1.35$ , $\Phi^* = 1.7 \times 10^{-3}$, and $L^* = 7 \times
10^{42}$."
 In Equation 2. and 3.. the factor£ Cy arises because the cold gas causing the absorption is expected to remain after the outflow has ceased and the galaxy is no longer visible inHo.," In Equation \ref{eq:nsigint} and \ref{eq:nsig}, the factor $C_t$ arises because the cold gas causing the absorption is expected to remain after the outflow has ceased and the galaxy is no longer visible in."
" We parameterize this as C5. where 7 is the time over which one can observe veryτη. strong absorption from the superwind and £j, is the ratio of the lifetime of the symmetric—invertedsystems to the lifetime of the luminosity."," We parameterize this as $C_t = \tau /t_{{\Ha}}$, where $\tau$ is the time over which one can observe very strong absorption from the superwind and $t_{\Ha}$ is the ratio of the lifetime of the symmetric–invertedsystems to the lifetime of the luminosity."
" Plugging Equation 3. into Equation | and using |N(:)0.15 and Cy=1. we obtain a family of C; L,,;,/L curves. which we present in Figure 2."," Plugging Equation \ref{eq:nsig} into Equation \ref{eq:dndz} and using $N(z)=0.15$ and $C_f=1$, we obtain a family of $C_t$ $L_{min}/L^*$ curves, which we present in Figure ."
" We place C; and L,,;, on the axes because they are the most uncertain parameters (see 5)).", We place $C_t$ and $L_{min}$ on the axes because they are the most uncertain parameters (see \ref{sec:dndzlocal}) ).
" Ifvalues are chosen for A. o. and ο. the C; and L,,;,, values necessary to produce ;V(:)=0.15 canbe read from the curves."," Ifvalues are chosen for $R^*$, $\alpha$, and $\beta$, the $C_t$ and $L_{min}$ values necessary to produce $N(z)=0.15$ canbe read from the curves."
 Separate panels are shown for A=2. 5. 10. and 20 kpe and the curves shown are for Ξ0. 0.05. 0.1. and 0.15.," Separate panels are shown for $R^*=2$, $5$, $10$, and $20$ kpc and the curves shown are for $\beta = 0$, $0.05$ , $0.1$, and $0.15$."
 Note that a change in ./ by an amount A> is equivalent to a change in à by an amount 2A3., Note that a change in $\beta$ by an amount $\Delta \beta$ is equivalent to a change in $\alpha$ by an amount $2\Delta \beta$.
 Theoretical models and observations of local superwinds can provide us with reasonable approximations of Jj A. C. and Lyin for comparison to our results in Figure 2..," Theoretical models and observations of local superwinds can provide us with reasonable approximations of $\beta$, $R^*$, $C_t$, and $L_{min}$ for comparison to our results in Figure \ref{fig:dndz}."
 The luminosity will persist as long as there is a steady flow of tonizing photons from the nucleus of the starburst., The luminosity will persist as long as there is a steady flow of ionizing photons from the nucleus of the starburst.
 Therefore. the luminosity should last as long as the O and B stars producing the starburst and driving the superwind (~10° years).," Therefore, the luminosity should last as long as the O and B stars producing the starburst and driving the superwind $\sim 10^7$ years)."
 The timescale for absorption must be at least this long because it is observed in the post-starburst dwarf. NGC1705.," The timescale for absorption must be at least this long because it is observed in the post–starburst dwarf, $1705$."
 The low-tonization gas will certainly persist for longer than this. but diffusion will eventually cause the material to spread out enough that the very strong systems are no longer seen.," The low–ionization gas will certainly persist for longer than this, but diffusion will eventually cause the material to spread out enough that the very strong systems are no longer seen."
 The timescale for this is not known exactly. but it is probably at least a few times the age of the starburst.," The timescale for this is not known exactly, but it is probably at least a few times the age of the starburst."
 The reason that we have used C as the ordinate of Figure 2 is because it is one of the most uncertain parameters., The reason that we have used $C_t$ as the ordinate of Figure \ref{fig:dndz} is because it is one of the most uncertain parameters.
" We can place a constraint on L,,;, by again considering NGC1705. which has an luminosity of los(Lg4/L)= (Marlowetal. 1997))."," We can place a constraint on $L_{min}$ by again considering $1705$, which has an luminosity of $\log (L_{\Ha}/L^*)=-2.7$ \cite{Marlow97}) )."
 Though NGC1705 is à starburst known to produce absorption over a large velocity spread. it has not been observed along a background quasar line of sight and we cannot be certainthat à black-bottomed profile with à central inversion would be produced.," Though $1705$ is a starburst known to produce absorption over a large velocity spread, it has not been observed along a background quasar line of sight and we cannot be certainthat a black–bottomed profile with a central inversion would be produced."
" Therefore. we explore a range of 3.5«logL,,;,—1.5. allowing for uncertainty in either direction."," Therefore, we explore a range of $-3.5 < \log L_{min} <
-1.5$, allowing for uncertainty in either direction."
" In Figure 2.. the curves rise dramatically (and require large C) at high £,,;;. so we expect that. to produce WO.)=0.15. logL,,;, must be less than about 2.5."," In Figure \ref{fig:dndz}, the curves rise dramatically (and require large $C_t$ ) at high $L_{min}$, so we expect that, to produce $N(z)=0.15$, $\log L_{min}$ must be less than about $-2.5$."
 The similarity solution of Mac Low MeCray (1988) predicts RxL? foran expanding superbubble. where £L is the total luminosity of the early-type stars driving the bubble.," The similarity solution of Mac Low McCray \nocite{MM88}) ) predicts $R \propto L^{0.2}$ for an expanding superbubble, where $L$ is the total luminosity of the early–type stars driving the bubble."
 Most of this luminosity will be hydrogen-ionizing. so one would expect RoxLY? as well.," Most of this luminosity will be hydrogen–ionizing, so one would expect $R \propto L_{H{\alpha}}^{ 0.2}$ as well."
 The later stages of the superwind (post-blowout). however. cannot be treated as an expanding superbubble.," The later stages of the superwind (post–blowout), however, cannot be treated as an expanding superbubble."
 At this point in the evolution of the superwind. the outflowing material i$ no longer being accelerated away from the galaxy but is. rather. being decelerated by ram pressure from the intergalactic medium (IGM) and by the galaxy potential well.," At this point in the evolution of the superwind, the outflowing material is no longer being accelerated away from the galaxy but is, rather, being decelerated by ram pressure from the intergalactic medium (IGM) and by the galaxy potential well."
 Post-blowout outflows in more massive (and thereforemore luminous) galaxies will have higher—velocity outflows. resulting in greater ram pressure from the IGM.," Post–blowout outflows in more massive (and thereforemore luminous) galaxies will have higher–velocity outflows, resulting in greater ram pressure from the IGM."
 More massive galaxies would also experience greater gravitational deceleration., More massive galaxies would also experience greater gravitational deceleration.
 Both of these effects act to decrease the lummosity slope to ./«0.2., Both of these effects act to decrease the radius--luminosity slope to $\beta < 0.2$.
 We only plot curves for Q<7x0.15 in Figure 2. because the material will probably disperse before it has been significantly decelerated., We only plot curves for $0 \le \beta \le 0.15$ in Figure \ref{fig:dndz} because the material will probably disperse before it has been significantly decelerated.
 Lower values of ./ produce more absorbers because they imply that the Holmberg relation is flat (J~0) and the total cross section is being dominated by the large numbers of dwarf galaxies at the faint end of the luminosity function., Lower values of $\beta$ produce more absorbers because they imply that the Holmberg relation is flat $\beta \sim 0$ ) and the total cross section is being dominated by the large numbers of dwarf galaxies at the faint end of the luminosity function.
 The absorption radit of far—IR—-bright starburst galaxies can be used to estimate plausible values of R° forΜαι., The absorption radii of far–IR–bright starburst galaxies can be used to estimate plausible values of $R^*$ for.
 Absorption in is known to occur out to radii of 5 kpe with Cy=1 (Heckmanetal. 2000))., Absorption in is known to occur out to radii of $5$ kpc with $C_f=1$ \cite{HeckmanNaD}) ).
 The radii are lower limits because the background starlight becomes too faint beyond this point and because may exist out to a larger radius thanNal., The radii are lower limits because the background starlight becomes too faint beyond this point and because may exist out to a larger radius than.
" If we are conservative and take R°=5 kpe. we require alow Z,,,;,, and/or a high C5."," If we are conservative and take $R^*=5$ kpc, we require a low $L_{min}$ and/or a high $C_t$."
 There is reason to believe. however. that the absorption will be seen at larger radit.," There is reason to believe, however, that the absorption will be seen at larger radii."
 In a low-resolution spectrum. Norman (1996)) detected 1.7 absorption at an impact parameter of 26 kpe from a starburst galaxy. but it is not known whether the system has the type of kinematic structure we are observing at high redshift.," In a low–resolution spectrum, Norman \nocite{Norman96}) ) detected $W_r=1.7$ absorption at an impact parameter of $26$ kpc from a starburst galaxy, but it is not known whether the system has the type of kinematic structure we are observing at high redshift."
 Also. emission has been seen out to an impact parameter of 11 kpe in Ms2 (Devine&Bally 1999)). indicating the presence of cold material out to that radius.," Also, emission has been seen out to an impact parameter of $11$ kpc in $82$ \cite{Devine99}) ), indicating the presence of cold material out to that radius."
" Radi of 10 kpe or greater will produce the observed .N(:) for moderate L,,;,, and C; factors of a few.", Radii of $10$ kpc or greater will produce the observed $N(z)$ for moderate $L_{min}$ and $C_t$ factors of a few.
 We expect 1x;C;<5 based on the speed and duration of the superwind., We expect $1 \la C_t \la 5$ based on the speed and duration of the superwind.
" Although we can't place a useful constraint on fyi, from physical considerations. we argue 0<3«0.2 by considering the pressure mechanisms acting on the expanding superbubble."," Although we can't place a useful constraint on $L_{min}$ from physical considerations, we argue $0 \la \beta < 0.2$ by considering the pressure mechanisms acting on the expanding superbubble."
 Observations of local starburst galaxies tell us that 5zd<2h.," Observations of local starburst galaxies tell us that $5
\la R^* \la 25$."
 Using these physical arguments. we can furtherconstrain parameterspace by examining Figure 2..," Using these physical arguments, we can furtherconstrain parameterspace by examining Figure \ref{fig:dndz}. ."
" In orderto obtain AN(:)=0.15 forreasonable values of Cy. we expect that IU~10 kpe and logL,,;,x; 2.5."," In orderto obtain $N(z)=0.15$ forreasonable values of $C_t$ , we expect that $R^* \sim
10$ kpc and $\log L_{min} \la -2.5$ ."
 The calculation is not particularlysensitive to? within the chosen range. so we can'tplace any further constraint on it from Figure 2..," The calculation is not particularlysensitive to $\beta$ within the chosen range, so we can'tplace any further constraint on it from Figure \ref{fig:dndz}. ."
 The timescale factor (619) cannot be constrained from Figure 2. either., The timescale factor $C_t$ ) cannot be constrained from Figure \ref{fig:dndz} either.
 It should be recognized that the calculations presented here are very rough., It should be recognized that the calculations presented here are very rough.
 We can only determinethat the parameters needed to produce the observed N(:) of 1.>15 absorption systems are consistent with the expected propertiesof superwinds at + 1.3., We can only determinethat the parameters needed to produce the observed $N(z)$ of $W_r>1.8$ absorption systems are consistent with the expected propertiesof superwinds at $z \sim 1.3$ .
 Primordial Nucleosynthesis in Light ofWA/AP H. Cyburt!. Brian D. Fields? andKeith A. Olive? Richard ! Deparliment ofPhysics. Univers,"18pt The primordial light element abundances are predicted accurately and robustly by the theory of Big Bang Nucleosynthesis (BBN) \cite{bbn,sarkar}, describing the first 3 minutes of the hot early universe."
ily of Illinois. Urbana. IL61801 ?Cenler for Theoretical Deparliment ofAstronomy. Astr," This hot big bang model also predicts a relic photon background, produced when nuclei recombined to form neutral atoms some 400,000 years later."
ophysics. University ofHlinois. Urbana. IL 61801 William £Fine Theorelical Physics Inslilule. University," The Cosmic Microwave Background (CMB), and its anisotropies carry key information about the content of the universe and early structure growth."
 of Minnesota. MN 55453. USA Minneapolis. Abstract nucleosvuthesis long providedthe primary determination of thecosmic barvon Digbang has density Qph?. or equivalently the barvon-to-photon ratio.7.," In particular, both BBN and the CMB are sensitive to the baryon content in the universe and because they are governed by different physics, BBN and the CMB can be used as independent measures of the cosmic baryon density, $\rho_{\rm B}\propto
\omb h^2$, or equivalently the baryon-to-photon ratio, $\eta$."
 Recently. data onCMDaniso- have become increasinglysensitiveto 7.The of these (woindependen," The comparison of the baryon density predictions from BBN and the CMB is a fundamental test of big bang cosmology \cite{st}, and its underlying assumptions, which include: a nearly homogeneous, isotropic universe, with gravity described by General Relativity and microphysics described by the Standard Model of particle In the standard model, we fix the number of neutrino flavors to three, and we allow this number to vary in order to test models beyond the standard model."
t tropies comparison measures," Furthermore, standard BBN relies on a network of nuclear reactions which are taken from low energy cross section measurements."
 providesa kevtes, Any deviation from concordance points to either unknown systematics or the need for new physics.
t lorbig bang cosmology. The firstrelease," Up till now, there has been tentative agreement between the baryon density predictions from BBN and the CMB, barring the internal tension between BBN derived limits from deuterium and 7 observations."
 ofresults [rom the Wilkinson. Microwave Anisolropy Probe(WAIAP) marksa milestone in (histest. With," With the first data release from the Wilkinson Microwave Anisotropy Probe (WMAP), the anisotropies in the CMB have been measured to unprecedented accuracy \cite{wmap}."
 the precisionof WAITAP.the CAIBnow offersa significantly stronger constraint on iy., This new precision allows for a CMB-based determination of the baryon density which is significantly tighter than current BBN analysis yields.
Wedis- cussthecurrent, One no longer needs to use BBN as a probe of the baryon density.
 state ofBBN and element observations (Gncluding theirpossible theory light," Instead, the CMB baryon density can be used as an input for BBN, and the light element abundance observations can be used to test particle physics and nuclear astrophysics \cite{cfo2,kssg}."
 lingering svstematicerrors)., This paper is organized as follows.
 The resulting BBN barvon density predictionis in overall," In section \ref{sect:bbn}, we discuss the state of affairs of primordial nucleosynthesis before WMAP."
 agree- thesewith observations one canobtainnew ins," We then explain how the post-WMAP CMB compares with BBN in section \ref{sect:cmb}, , and go on to constrain astrophysics (section \ref{sect:bbn+cmba}) ) and particle physics (section \ref{sect:bbn+cmbp}) )."
ight intopost-DDN nucleosynthesis, We conclude with a discussion of our results and aspirations for the future.
 processes associated testthe nonstandard pl," The baryon density (or the baryon-to-photon ratio, $\eta \equiv \eta_{10}/10^{10}$ ) is the sole parameter in the standard model of BBN."
yvsics and astvoplivsies. Finally.one can possibilityof αἱ ihe time ofBBN.now with alllight elements available asprobes.," Prior to the recent measurements of the microwave background power spectrum, the best available method for determining the baryon density of Universe was the concordance of the BBN predictions and the observations of the light element abundances of D, 3, 4, and 7."
 Indeed. withthe WAIAP precision deuterium beginningtorivalος sensitivity nonstandard physics. 7. is already to and additional D/II measurements can," A high-confidence upper limit to the baryon density has long been available \cite{rafs} from observations of local D/H abundance determinations (giving roughly $\eta_{10} < 9.0$ ), but a reliable lower bound to $\eta$, much less a precise value, has been more elusive to obtain."
 improve (his further, Lower bounds to $\eta$ have been derived (1) onthe basis of D + 3
 improve (his further., Lower bounds to $\eta$ have been derived (1) onthe basis of D + 3
«©. Where Dy is. the luuinosity. distance. at redshift 2 aud voy. is the observed frequency (?)..,", where $D_\mathrm{L}$ is the luminosity distance at redshift $z$ and $\nu_\mathrm{obs}$ is the observed frequency \citep{Solomon1997}."
 A comparison of the CO LO maps with optical aud the radio positions (Fie. 1)), A comparison of the CO $1-0$ maps with optical and the radio positions (Fig. \ref{fig:contours}) )
 shows a suiall offset of ~0.3” from the CO peak position in the case of BzIs-li71., shows a small offset of $\sim0.3\arcsec$ from the CO peak position in the case of BzK-4171.
 This is well within the range expected given the low sienificance of the detection., This is well within the range expected given the low significance of the detection.
" For the other sources. the CO emission is cousistent ( 0.2"") with the position of the radio aud optical source."," For the other sources, the CO emission is consistent $<0.2\arcsec$ ) with the position of the radio and optical source."
 Our observations of the CO Ll0 line emission cau he used to directly measure the amount of molecular gas and star formation efficiency in the Dzk ealaxics., Our observations of the CO $1-0$ line emission can be used to directly measure the amount of molecular gas and star formation efficiency in the BzK galaxies.
 The estimation of the molecular gas masses is typically done by using a CO luminosity to eas mass conversion factor. aco.," The estimation of the molecular gas masses is typically done by using a CO luminosity to gas mass conversion factor, $\alpha_\mathrm{CO}$."
 Comparing observations with simulations of star-formine disk galaxies that reproduced the observed CO 2.1 line shapes aud UV. morphologies of three BzIx ealaxies (two of which are iu our sample}. 7.estimated aeo=362308AL. US kins t pe?) |. close to the Galactic disk o.," Comparing observations with simulations of star-forming disk galaxies that reproduced the observed CO $2-1$ line shapes and UV morphologies of three BzK galaxies (two of which are in our sample), \citet{Daddi2009} estimated $\alpha_\mathrm{CO}=3.6\pm0.8\ M_\sun$ (K km $^{-1}$ $^{2}$ $^{-1}$, close to the Galactic disk $\alpha$."
 Asstuning this value of aco. we compute he Ty masses eiven in Table 2..," Assuming this value of $\alpha_\mathrm{CO}$, we compute the $_2$ masses given in Table \ref{table:properties}."
 The star formation cfiicicncey of galaxies is defined as he ratio between the IR luuinosity aud the CO 1.0 uninosty. SFE=Lin/Log.," The star formation efficiency of galaxies is defined as the ratio between the IR luminosity and the CO $1-0$ luminosity, $=L_\mathrm{IR}/L_\mathrm{CO}'$."
" Using the values for the IR unuimositv from ?.. we find SFE=13.112 and LLL. (Is aus pet) | for DZK-H171. DzS-21000 aud BzIs-16000, respectively,"," Using the values for the IR luminosity from \citet{Daddi2009}, we find $=43,\ 142$ and 44 $L_\sun$ (K km $^{-1}$ $^2$ $^{-1}$ for BzK-4171, BzK-21000 and BzK-16000, respectively."
" We can also compute the time in which he eas would be coustuned if the current SFR remains constant. r4,= A(ILJ/SER."," We can also compute the time in which the gas would be consumed if the current SFR remains constant, $\tau_\mathrm{gas}=M(\mathrm{H}_2)/$ SFR."
 Using the SFRs found o 72 we find eas consmuption lifetimes of ~0.20.8 Gar (see Table 2)).," Using the SFRs found by \citet{Daddi2009}, we find gas consumption lifetimes of $\sim0.2-0.8$ Gyr (see Table \ref{table:properties}) )."
 These values are comparable to those ound by? and aresimilar those found for comparable ealaxies at redshifts ~ ο]., These values are comparable to those found by \citet{Daddi2009} and aresimilar those found for comparable galaxies at redshifts $\sim1-3$ \citep{Tacconi2010}.
 Iu this section we study the properties of the molecular eas in our Dzk galaxies., In this section we study the properties of the molecular gas in our BzK galaxies.
 All of our sources have xeviouslv been detected in the CO 2.1 cinission line., All of our sources have previously been detected in the CO $2-1$ emission line.
 However. oulv. BzIs-21000 has been detected in the CO 352 line (?)..," However, only BzK-21000 has been detected in the CO $3-2$ line \citep{Dannerbauer2009}."
 Figure 5 shows the velocity iuteerated CO line fluxes of BzIk-21000 as a function of rotational quantum uuuboer. J.," Figure \ref{fig:lvg} shows the velocity integrated CO line fluxes of BzK-21000 as a function of rotational quantum number, $J$ ."
 Also shown are the CO 1.0 2d CO 5E integrated ine fluxes of Dzls-I1171 and BzIk-16000. normalized to he CO 2.Liuteusitv of DzK-21000 for comparison. aud he normalized CO intensities for the iuuer disk of the Alilkv Way (72).. the Antenna overlap region (7). and the spiral galaxy NCGC69L6 (7?)..," Also shown are the CO $1-0$ and CO $2-1$ integrated line fluxes of BzK-4171 and BzK-16000, normalized to the CO $2-1$ intensity of BzK-21000 for comparison, and the normalized CO intensities for the inner disk of the Milky Way \citep{Fixsen1999}, , the Antenna overlap region \citep{Zhu2003} and the spiral galaxy NGC6946 \citep{Bayet2006}. ."
" From the velocity integrated Lue fluxes. we compute he brightucss temperature line ratios as roy=To4/TiyGMBg)«Gyνο). where To, and Tyy are the xiehtuess temperatures. fo, aud Jyy are the inteerated fluxes. ancl voy and 49 are the observed frequencies of the CO2 Llandl 0 emission lines. respectively."," From the velocity integrated line fluxes, we compute the brightness temperature line ratios as $r_{21}=T_{21}/T_{10}=(I_{21})/I_{10})\times(\nu_{10}/\nu_{21})^2$ , where $T_{21}$ and $T_{10}$ are the brightness temperatures, $I_{21}$ and $I_{10}$ are the integrated fluxes, and $\nu_{21}$ and $\nu_{10}$ are the observed frequencies of the CO $2-1$ and $1-0$ emission lines, respectively."
 For LTE. we expect this ratio to be ray=1.," For LTE, we expect this ratio to be $r_{21}=1$ ."
 In our sources. we ucasure brightuess temperature line ratios of 080035. 1.22/095 and Ο.Ε35 for DzK-I171. BzK-21000. aud DzIx-16000. respectively.," In our sources, we measure brightness temperature line ratios of $0.80_{-0.22}^{+0.35}$ , $1.22_{-0.36}^{+0.61}$ and $0.41_{-0.13}^{+0.23}$ for BzK-4171, BzK-21000 and BzK-16000, respectively."
 At the significanceof ourdetections. it is not possible o conclude whether the emissiou in the individual DzI ealaxies is thermalized ornot up to J=2. ?..," At the significanceof ourdetections, it is not possible to conclude whether the emission in the individual BzK galaxies is thermalized ornot up to $J=2$ \citet{Dannerbauer2009}."
" ? (ee.273... 2.. 5.. ὃν, ?.."," \citet{Flower2001} \citep[e.g.,][]{Weiss2005b, Weiss2007}. \citet{Dannerbauer2009}, \ref{fig:lvg}. \citet{Dannerbauer2009}, \citet{Dannerbauer2009}."
pixel on the direct CCD.,pixel on the direct CCD.
 Thus. we consider (he scale at the slit to be determined to better than1954.," Thus, we consider the scale at the slit to be determined to better than."
".. We directly measured the scale at the detector using UCAC?2 stars in M67 and obtained a scale of 0.765""+0.003"" per pixel based upon repeated measurements.", We directly measured the scale at the detector using UCAC2 stars in M67 and obtained a scale of $0.765\arcsec \pm 0.003\arcsec$ per pixel based upon repeated measurements.
 So. this value is also known to much better than14.," So, this value is also known to much better than."
.. The data were reduced in à manner similar to that of Massey Foltz (2000)., The data were reduced in a manner similar to that of Massey Foltz (2000).
 They were first corrected for the bias level bv removing the average value in the overscan strip on a row-by-row basis., They were first corrected for the bias level by removing the average value in the overscan strip on a row-by-row basis.
 This removed some otherwise troublesome banding present in the data., This removed some otherwise troublesome banding present in the data.
 We examined an average bias [rame and found no residual counts or structure greater than 1 electron., We examined an average bias frame and found no residual counts or structure greater than 1 electron.
 The data were trimmed to 2531 pixels in the wavelength direction., The data were trimmed to 2531 pixels in the wavelength direction.
 Data outside of this region had poor focus or too few counts per exposure in the UV., Data outside of this region had poor focus or too few counts per exposure in the UV.
 We trimmed the data to either 45 or το binned pixels in the spatial direction depending on which decker was used., We trimmed the data to either 45 or 70 binned pixels in the spatial direction depending on which decker was used.
 A bad pixel mask was constructed from the division of long and short exposures of an internal quartz lamp. and was used to remove the few bad columns aud occasional bad pixel by linear interpolation.," A bad pixel mask was constructed from the division of long and short exposures of an internal quartz lamp, and was used to remove the few bad columns and occasional bad pixel by linear interpolation."
 Dome flats were used to correct lor pixel to pixel sensitivity variations. (he response of the grating in (he wavelength direction. and first-order vieneing in (he spatial direction.," Dome flats were used to correct for pixel to pixel sensitivity variations, the response of the grating in the wavelength direction, and first-order vignetting in the spatial direction."
 We then fit a fanction to the twilight flats to further correct for the «lit illumination function which. on average. represented around a change.," We then fit a function to the twilight flats to further correct for the slit illumination function which, on average, represented around a change."
 Additionally. we created a “master” skv image bv combining the blank skv images for each night.," Additionally, we created a “master"" sky image by combining the blank sky images for each night."
 A low order function was then fit to the spatial variance of this image and all of the images were then divided by this fit as a further spatial correction. twpically <1%.," A low order function was then fit to the spatial variance of this image and all of the images were then divided by this fit as a further spatial correction, typically $<$."
. Finally. HeNeÀr lamp exposures were used (o provide wavelength calibrations.," Finally, HeNeAr lamp exposures were used to provide wavelength calibrations."
 since it was vital that our “blank skv images be completely devoid of stars. we strove to position our slit as Far away [rom surrounding stars as possible.," Since it was vital that our “blank sky"" images be completely devoid of stars, we strove to position our slit as far away from surrounding stars as possible."
 Llowever. very cim stars did occasionally make their way into one of our frames.," However, very dim stars did occasionally make their way into one of our frames."
" Thus. we combined our three consecutive images using a discrepant pixel rejection algorithm (avsigclip"") using ""imcombine"" routine."," Thus, we combined our three consecutive images using a discrepant pixel rejection algorithm (“avsigclip"") using “imcombine"" routine."
 This removed cosmic rays and the spectra of any. Taint. resolved star.," This removed cosmic rays and the spectra of any faint, resolved star."
 The standard. star observations were extracted using a moderately. wide extraction aperture. and we tracecl the spectrum along the detector.," The standard star observations were extracted using a moderately wide extraction aperture, and we traced the spectrum along the detector."
 The same trace was used for the comparison exposure in order to provide a wavelength scale., The same trace was used for the comparison exposure in order to provide a wavelength scale.
 The standards were taken from Massey. οἱ ((1988). ancl we constructed a wavelength-dependent sensitivity curve using these data.," The standards were taken from Massey et (1988), and we constructed a wavelength-dependent sensitivity curve using these data."
 The scatter of our (tvpicallv 10) standards: was ~0.03 magnitudes., The scatter of our (typically 10) standards was $\sim$ 0.03 magnitudes.
 If the observations from two consecutive nights were involved. we combined the data using a," If the observations from two consecutive nights were involved, we combined the data using a"
is enhanced in the presence of shocks due to its injection in the gas phase from the erain mantles (Zinchenkoetal.2000).,is enhanced in the presence of shocks due to its injection in the gas phase from the grain mantles \citep{Zinchen00}.
. This paper presents a follow up study of the CS/IINCO ralio towards a sample of prototvpe galaxies with different nuclear activitv., This paper presents a follow up study of the CS/HNCO ratio towards a sample of prototype galaxies with different nuclear activity.
 Although. CS has been extensively observed in external galaxies (Baanetal.2008).. INCO had only been detected in four galaxies prior to (this work (Nguven-Q-Hieuetal.1991:Wane2004).," Although CS has been extensively observed in external galaxies \citep{Baan08}, HNCO had only been detected in four galaxies prior to this work \citep{Nguyen91,Wang04}."
. Observations were carried out. with the IRLAM 30mm telescope on Pico Veleta. Spain. during three observing periods [rom summer 2005 through summer 2007.," Observations were carried out with the IRAM m telescope on Pico Veleta, Spain, during three observing periods from summer 2005 through summer 2007."
 Table 1 shows the sample of ealaxies wilh their coordinates and (he rest Irequencies of the observed molecular transilions., Table \ref{tab:sourceandlines} shows the sample of galaxies with their coordinates and the rest frequencies of the observed molecular transitions.
 Observations were perlormed in svmmnetrical wobbler switched mode with a frequeney of Wiz and a beam throw of 4 in azimuth., Observations were performed in symmetrical wobbler switched mode with a frequency of Hz and a beam throw of $4'$ in azimuth.
 As spectrometers we used the MMIIz filter banks for the 31min transitions aud the 256x4 MMIIZ filler banks for those ab 2 and 1.3mumam., As spectrometers we used the $512\times1$ MHz filter banks for the mm transitions and the $256\times4$ MHz filter banks for those at 2 and mm.
" Pointing accuracy was estimated to be of ~3"" from frequent continuum Cross scans on nearby pointing sources.", Pointing accuracy was estimated to be of $\sim3''$ from frequent continuum cross scans on nearby pointing sources.
 Data were calibrated using the standard dual load svsleni and main beam temperatures were obtained as Typ(ζωDap)Ty. where Boy is tabulated in Table 1. and Foy are 0.95. 0.93. and 0.91 for 3. 2. and 1.2nmuin. respectively.," Data were calibrated using the standard dual load system and main beam temperatures were obtained as $T_{\rm MB}=(F_{\rm eff}/B_{\rm eff})T^*_{\rm A}$, where $B_{\rm eff}$ is tabulated in Table \ref{tab:sourceandlines} and $F_{\rm eff}$ are 0.95, 0.93, and 0.91 for 3, 2, and mm, respectively."
" Calibration uncertainties are estimaled to be < 15%,", Calibration uncertainties are estimated to be $<15\%$ .
 The observed spectra for each source are shown in Fig. 1.., The observed spectra for each source are shown in Fig. \ref{fig.spectra}.
 The IINCO 5—4 and 10—9 lines were observed simultaneously with the ΟΡΟ 1—0 and 2—I lines. respectively.," The HNCO $5-4$ and $10-9$ lines were observed simultaneously with the $^{18}$ O $1-0$ and $2-1$ lines, respectively."
 This allows a reliable determination of the IINCO relative abundance. as no uncertainties due to pointing drifts and/or calibration are involved.," This allows a reliable determination of the HNCO relative abundance, as no uncertainties due to pointing drifts and/or calibration are involved."
 For some of the sources with the larger observed linewidths. the LINCO and CO lines appear moderately blended.," For some of the sources with the larger observed linewidths, the HNCO and $^{18}$ O lines appear moderately blended."
 Such is the case ol T7469. 11068. and 2220.," Such is the case of 7469, 1068, and 220."
 Gaussian shapes have been fitted to the observed profiles., Gaussian shapes have been fitted to the observed profiles.
 Table 2. compiles the derived fitted parameters., Table \ref{tab.gaussfit} compiles the derived fitted parameters.
 For the non-detectecl transitions. upper limits are tabulated where it was considered a 3o level and an approximate linewidth similar to those of the detected CS and IINCO transitions. or that of CO in the case of 55194.," For the non-detected transitions, upper limits are tabulated where it was considered a $3\sigma$ level and an approximate linewidth similar to those of the detected CS and HNCO transitions, or that of $^{18}$ O in the case of 5194."
 Rotational temperatures and molecular column densities have been derived. assuming local thermodvnamic equilibrium (LTE) and optically thin emission., Rotational temperatures and molecular column densities have been derived assuming local thermodynamic equilibrium (LTE) and optically thin emission.
 As derived for CS 3—2in NGC2253 (Martinetal.2005) we only might expect the emission of CS /—5—4 to be significantly optically thick., As derived for CS $J=3-2$ in 253 \citep{Martin05} we only might expect the emission of CS $J=5-4$ to be significantly optically thick.
 However. our observation of C345 will be less affected bv the opacity effects.," However, our observation of C34S will be less affected by the opacity effects."
" We have accounted for the dilution of the source in the telescope beam bv assuming an averaged emissionextent of 10"" [or all sources.", We have accounted for the dilution of the source in the telescope beam by assuming an averaged emissionextent of $10''$ for all sources.
 This simplification might affect the determination of the column densities for sources much smaller than 10 , This simplification might affect the determination of the column densities for sources much smaller than $10''$ 
@ between reverse shock and radial direction.,$\phi$ between reverse shock and radial direction.
" For spherical explosions this angle is always 7/2, since the reverse shock can only be perpendicular to the radius vector."," For spherical explosions this angle is always $\pi/2$, since the reverse shock can only be perpendicular to the radius vector."
" In an oblique shock the velocity can be decomposed into two components: tangential (uj) and perpendicular (u,) to the shock.", In an oblique shock the velocity can be decomposed into two components: tangential $u_{\parallel}$ ) and perpendicular $u_{\perp}$ ) to the shock.
" The tangential component of the velocity is continuous through an oblique shock (Landau&Lifshitz,1959).", The tangential component of the velocity is continuous through an oblique shock \cite[]{Landau}.
". Following the notation introduced in Fig. 3,,"," Following the notation introduced in Fig. \ref{fig:analytic2d},"
" this implies that: with being the radial and lateral components of the velocity of the shocked matter (u;,), respectively."," this implies that: with being the radial and lateral components of the velocity of the shocked matter $u_{\mathrm{rs}}$ ), respectively."
" The perpendicular component of the velocity, u,, is changed according to the Rankine-Hugoniot conditions."," The perpendicular component of the velocity, $u_{\perp}$, is changed according to the Rankine-Hugoniot conditions."
" The mass conservation condition, including the angle dependence, is: The momentum continuity condition for an oblique shock is: where only the perpendicular components of the velocities enter."," The mass conservation condition, including the angle dependence, is: The momentum continuity condition for an oblique shock is: where only the perpendicular components of the velocities enter."
" We can thus write a relation between the pressure and the angle ¢: where AP=P,—Py is the pressure jump at the reverse shock (note that usually Py« Pi) uy is the radial wind"," We can thus write a relation between the pressure and the angle $\phi$: where $\Delta P=P_{\mathrm{rs}}-P_{\mathrm{w}}$ is the pressure jump at the reverse shock (note that usually $P_{\mathrm{w}} \ll
P_{\mathrm{rs}}$ ), $u_{\mathrm{w}}$ is the radial wind"
In Sect.,In Sect.
 ?? we describe the implementations of radiation (Sect. ??)), \ref{Sect:implementations} we describe the implementations of radiation (Sect. \ref{Sect:radtrans}) )
 and cosmic chemistry evolution (Sect. ?2?7))., and cosmic chemistry evolution (Sect. \ref{Sect:chemistry}) ).
 In Sect. 22...," In Sect. \ref{Sect:simulations},"
 we test our implementation by performing analyses of the Strómamgren. sphere. problem. (Sect. ??)), we test our implementation by performing analyses of the Strömmgren sphere problem (Sect. \ref{Sect:ss}) )
 in a static (Sect. ?22)), in a static (Sect. \ref{sec:static}) )
 and dynamic (Sect. 2?)), and dynamic (Sect. \ref{sec:dyn}) )
 density field. and chemical abundance evolution (Sect. ??)).," density field, and chemical abundance evolution (Sect. \ref{Sect:abundances}) )."
 We then apply our method. to. cosmological structure formation simulations (Sect. ??))., We then apply our method to cosmological structure formation simulations (Sect. \ref{Sect:cosmo}) ).
 We summarize. discuss and conclude in Sect. ??..," We summarize, discuss and conclude in Sect. \ref{Sect:discussion}."
 We use the parallel tree ΧρονΟΙ (smoothed particle hvdrodsnamics) code GADGETS. an. extenced version of the publicly available code (?).. and moclify it in order to couple chemistry evolution and RL.," We use the parallel tree N-body/SPH (smoothed particle hydrodynamics) code , an extended version of the publicly available code \cite[][]{Springel2005}, and modify it in order to couple chemistry evolution and RT."
 In the following paragraphs. we give the details about the implementations of the RL (Sect. 22))," In the following paragraphs, we give the details about the implementations of the RT (Sect. \ref{Sect:radtrans}) )"
 and chemistry (Sect. ?27)), and chemistry (Sect. \ref{Sect:chemistry}) )
 parts. and. in the next section. we will show results from our test runs.," parts, and, in the next section, we will show results from our test runs."
 To follow the propagation of radiation we use the implementation of ICE in (7). and expand it to a multi-[requeney. scheme., To follow the propagation of radiation we use the implementation of RT in \cite[][]{Petkova2009} and expand it to a multi-frequency scheme.
 The original implementation is based on a moment method. where the closure relation is the optically thin variable IExdldington tensor. suggested. by 7..," The original implementation is based on a moment method, where the closure relation is the optically thin variable Eddington tensor, suggested by \cite{GA2001}."
 Jo follow the transport of radiation. we solve the equation of anisotropic οβίο for the photon number density per frequency (7): tity [it ΕΕ dd pid where fois time. ay and ory are the coordinate components. e is the speed of light. si) is the absorption coellicient.  are the components of the Eddington tensor. s-(v) is the source function. and the Einstein summation convention is adopted for all exponents ὁ and |j.," To follow the transport of radiation, we solve the equation of anisotropic diffusion for the photon number density per frequency $n_\gamma(\nu)$: = c ( ) - ) + ), where $t$ is time, $x_i$ and $x_j$ are the coordinate components, $c$ is the speed of light, $\kappa(\nu)$ is the absorption coefficient, $h^{ij}$ are the components of the Eddington tensor, $s_\gamma(\nu)$ is the source function, and the Einstein summation convention is adopted for all exponents $i$ and $j$."
 The Eddington tensor is obtained by summing up the contributions from the sources of ionizing photons and. its components are given by = where [ae xl is the radiation. pressure tensor and. ps is the stellar clensity., The Eddington tensor is obtained by summing up the contributions from the sources of ionizing photons and its components are given by = where ) = ^3 x' ') is the radiation pressure tensor and $\rho_{\ast}$ is the stellar density.
 “Phe tensor is computed. via a tree ancl effectively removes the dependenee of the scheme on the number of ionizing sources an advantage in cosmological ancl galaxy formation simulations., The tensor is computed via a tree and effectively removes the dependence of the scheme on the number of ionizing sources – an advantage in cosmological and galaxy formation simulations.
 The source term is treated in a [ashion. where photons are [first “injected” into. the. medium surrounding the sources. and are then cdilfused via equation (1).," The source term is treated in a fashion, where photons are first “injected” into the medium surrounding the sources, and are then “diffused” via equation \ref{eqn:rt}) )."
 Solving the equation for all particles in the simulation reduces to a linear svstem ofequations. which we solve implicitly by using a Conjugate-Ciradient scheme. that ensures robustness and stability even for large timesteps.," Solving the equation for all particles in the simulation reduces to a linear system of equations, which we solve implicitly by using a Conjugate-Gradient scheme, that ensures robustness and stability even for large timesteps."
 Por our multi-frequeney extension we need to transform. the photon number density to ionizing intensity ancl vice versa., For our multi-frequency extension we need to transform the photon number density to ionizing intensity and vice versa.
 Since the photoheating and. photoionization rates in equations (7)) (discussed. more in detail in Sect. ??)), Since the photoheating and photoionization rates in equations \ref{rad_rates}) ) (discussed more in detail in Sect. \ref{Sect:chemistry}) )
 are obtained by integrating the intensity over frequency. we use a single photon number density in cach frequency. bin.," are obtained by integrating the intensity over frequency, we use a single photon number density in each frequency bin."
" The photon number density. per frequency. is. derived from the ionizing intensity. £(7). as ( d"" where 4x isthe= solid angle dinancl P, is the Planck constant."," The photon number density per frequency is derived from the ionizing intensity, $I(\nu)$, as ) =, where $4\pi$ isthe full solid angle and $h_p$ is the Planck constant."
 For any particle and at any timestep. the ICE equation (1)) is then solved for each frequency. bin.," For any particle and at any timestep, the RT equation \ref{eqn:rt}) ) is then solved for each frequency bin."
 The intensity of the radiative source. £(7). depends on the particular problems treated.," The intensity of the radiative source, $I(\nu)$, depends on the particular problems treated."
 Por. stellar sources. a common. simple ancl suitable approximation (which we will also adopt in the following) is a black-bods speetrum (sce Fig. 1)).," For stellar sources, a common, simple and suitable approximation (which we will also adopt in the following) is a black-body spectrum (see Fig. \ref{fig:BB}) ),"
 with ellective temperature dependent on the assumed stellar population., with effective temperature dependent on the assumed stellar population.
 Phis treatment allows us to take into account contributions from a wide frequency range. even xow the L-ionization energv of 13.6 eV. Indeed. as evident rom the plot in Fie.," This treatment allows us to take into account contributions from a wide frequency range, even below the H-ionization energy of 13.6 eV. Indeed, as evident from the plot in Fig."
 1. the low-energy tail of the black-hocky spectrum contributes to the Lyman-Werner band and that will cefinitely. allect the molecular evolution of the gas (see ihrer), \ref{fig:BB} the low-energy tail of the black-body spectrum contributes to the Lyman-Werner band and that will definitely affect the molecular evolution of the gas (see later).
 We note that dealing with radiation below ~ 13.6 eV is avery debated. and complicated: problem (c.g. TITUCPTTTPTTTTT). because of the many lines involved. (76) in the LAW band.," We note that dealing with radiation below $\sim$ 13.6 eV is a very debated and complicated problem \cite[e.g.][]{ThoulWeinberg1996,Haiman1997,Haiman1997_Erratum,OmukaiNishi1999,Machacek2001,Kitayama2001,Ricotti2002a,Ricotti2002b,Mackey2003,Shapiro2004,Dijkstra2004,SusaUmemura2004,Stacy2011arXiv}, because of the many lines involved (76) in the LW band."
 Pull. detailed modeling of RP in such regimes is bevond the aims of this work. and. at some levels. it might be superfluous (c.g.2).. since the ionizing lux at high redshift (2) is domunatec by radiation [roni neighboring haloes (e.g. 2).. rather than from the soft-UV. background in the E. band.," Full, detailed modeling of RT in such regimes is beyond the aims of this work, and, at some levels, it might be superfluous \cite[e.g.][]{Ricotti2001}, since the ionizing flux at high redshift $z$ ) is dominated by radiation from neighboring haloes \cite[e.g.][]{Ciardi2000b}, , rather than from the soft-UV background in the LW band."
 Thus. Le photoclissociation is simply accounted for by using (e.g.?) the radiativerate obtained from integration of the source intensity over," Thus, $_2$ photodissociation is simply accounted for by using \cite[e.g.][]{Abel_et_al1997,Ricotti2001,Yoshida2003,Ahn2007,Maio2007,WhalenNorman2008} the radiativerate obtained from integration of the source intensity over"
0.75. and <20% complete at 0.5...,$0.75 M_{\odot}$ and $< 20$ complete at $0.5 M_{\odot}$.
 Considered separately the two fields show similar ALFs down a similar completeness limit. despite an exposure difference of a [actor of two.," Considered separately the two fields show similar XLFs down a similar completeness limit, despite an exposure difference of a factor of two."
 This is a product ofthe Ly mass relation which is level between 1. 10 M. and then drops rapidly at lower masses will a high dispersion (?).., This is a product of the $L_X$ – mass relation which is level between 1 – 10 $_{\odot}$ and then drops rapidly at lower masses with a high dispersion \citep{prei05a}.
 Devond the completeness limit. the NLF falls off quicker in the north-western field (han it does in the central field due to (he different in X-ray exposure and the lack οἱ The compilation of a large sample of cluster members wilh near-IR. photometry aud litted. pre-MIS isochrones allows stellar masses to be estimated [or a large ancl relatively complete sample.," Beyond the completeness limit, the XLF falls off quicker in the north-western field than it does in the central field due to the different in X-ray exposure and the lack of The compilation of a large sample of cluster members with near-IR photometry and fitted pre-MS isochrones allows stellar masses to be estimated for a large and relatively complete sample."
 This then allows the mass function of sources in Cvg OD? to be determined., This then allows the mass function of sources in Cyg OB2 to be determined.
 Individual stellar masses were caleulatecd based on the positions of the sources in the (4. J— H) CMD by tracing an extineGon vector back to the theoretical MS or pre-MS isochrones described in Section 3.1..," Individual stellar masses were calculated based on the positions of the sources in the $J$, $J-H$ ) CMD by tracing an extinction vector back to the theoretical MS or pre-MS isochrones described in Section \ref{s-cmd}."
 For this purpose we assume a distance to (νο OB? of 1.45 kpe ?.., For this purpose we assume a distance to Cyg OB2 of 1.45 kpc \cite{hans03}.
 We will initially assume Chat all stars in each field were born coevallv. ignoring any possible age spread. therefore allowing a direct relationship between the position of the source in the CMD and its mass and extinction.," We will initially assume that all stars in each field were born coevally, ignoring any possible age spread, therefore allowing a direct relationship between the position of the source in the CMD and its mass and extinction."
 For this we will use the best-fitting ages determined in section 3.1. for DM = 10.3., For this we will use the best-fitting ages determined in Section \ref{s-cmd} for DM = 10.8.
 Because of the form of the pre-MS isochrone in the near-IB CMD a mumber of sources have degenerate solutions lor their masses., Because of the form of the pre-MS isochrone in the near-IR CMD a number of sources have degenerate solutions for their masses.
" This degeneracy was removed. by dereddening these sources using (their X-ray spectral-fitted. hydrogen: column densities and the relationVy=2.2x10?A, ? (e.g.??) and then finding the closest solution on their redclening locus."," This degeneracy was removed by dereddening these sources using their X-ray spectral-fitted hydrogen column densities and the relation$N_H = 2.2 \times 10^{21} A_V$ $^{-2}$ \citep[e.g.][]{gore75,ryte96} and then finding the closest solution on their reddening locus."
 Table 1. lists the masses and extinctions lor all sources in νο OB? with near-IR. photometry determined using (his method., Table \ref{t-masses} lists the masses and extinctions for all sources in Cyg OB2 with near-IR photometry determined using this method.
 Masses derived using (his method will be dependent on a number of factors., Masses derived using this method will be dependent on a number of factors.
 The J- magnitude errors. as shown in Figure 2.. are small. ancl will therefore produce only a small error in the derived mass (at J~I7. where A/=0.65AZ.. (the typical J-band error of 0.024 mages corresponds to an error of only 0.02 M. ).," The $J$ -band magnitude errors, as shown in Figure \ref{nearir_cmd}, are small, and will therefore produce only a small error in the derived mass (at $J \sim 17$, where $M = 0.65 M_{\odot}$, the typical $J$ -band error of 0.024 mags corresponds to an error of only 0.02 $_{\odot}$ )."
 Other photometric discrepancies. such as treating a binary star as à single star or not considering the effects of variability will affect the derived stellar mass slightly more.," Other photometric “discrepancies”, such as treating a binary star as a single star or not considering the effects of variability will affect the derived stellar mass slightly more."
" The influence of circiumstellar material on the stellar masses is reduced by our use of the J—I color as opposed to the HJ—I, color in deriving masses [rom near-IR. colors.", The influence of circumstellar material on the stellar masses is reduced by our use of the $J-H$ color as opposed to the $H-K_s$ color in deriving masses from near-IR colors.
 The age of the region. estimated in Section 3.1.. will also allect the derived masses. ancl (his is discussed later.," The age of the region, estimated in Section \ref{s-cmd}, will also affect the derived masses, and this is discussed later."
 Finally. (he choice of pre-M$ isochrones could potentially have a signilicant effect.," Finally, the choice of pre-MS isochrones could potentially have a significant effect."
 SCudies show (hat using different isochrones can produce mass differences of up to a [actor two (?).. though this elfect is strongest at. low lüasses.," Studies show that using different isochrones can produce mass differences of up to a factor two \citep{hill04}, , though this effect is strongest at low masses."
determined from the kinetic temperature are σα. relative to the nouthermal line widths Αοντ (1.77 aud kaus}). obtained by subtracting in quadrature the thermal line width from the intrinsic line width averaged over the core.,"determined from the kinetic temperature are small relative to the nonthermal line widths $\Delta$$v_{\rm NT}$ (1.77 and ), obtained by subtracting in quadrature the thermal line width from the intrinsic line width averaged over the core."
 Further supported by substantial core masses. the two ccores are reminiscent of the ‘turbulent. massive dese cores foriung clusters or groups of stars in the Jijina et al," Further supported by substantial core masses, the two cores are reminiscent of the `turbulent, massive dense cores' forming clusters or groups of stars in the Jijina et al."
 samples. although none of the two cores secnis to have more than 30 enibedaec stars associated.," samples, although none of the two cores seems to have more than 30 embedded stars associated."
 This is supported by the distribution of he YSO caucicdates shown in rof20231| 3110-bolo.. in which a least six (IRSI. 2 to 6) appear to be associatec with the northern core aud another two with the southern oue (11 aud 12).," This is supported by the distribution of the YSO candidates shown in \\ref{20231+3440-bolo}, in which at least six (IRS1, 2 to 6) appear to be associated with the northern core and another two with the southern one (11 and 12)."
 Towards the northern Core. there seclus to be a temperature eradicut frou the core center to the outermost laver.," Towards the northern core, there seems to be a temperature gradient from the core center to the outermost layer."
 The detection of the (L1) line of vvields a kinetie temperature of ~30 IIs at the position of 1220231.," The detection of the (4,4) line of yields a kinetic temperature of $\sim$ K at the position of 20231."
 This value is an average over the beam size of 407 (—0.2ppc) and is likely a lower luuit for the reeion οςΠαο] surrounding 1220231. since the 1.1) ine was only detected towards the IRAS )osition aud nay not have been spatially resolved.," This value is an average over the beam size of $''$ $\sim$ pc) and is likely a lower limit for the region immediately surrounding 20231, since the (4,4) line was only detected towards the IRAS position and may not have been spatially resolved."
 The average kinetic eniperature over the rest of the core is ~ Kk. For regions where iis detectable. the density is ou the order of 10!vorce..," The average kinetic temperature over the rest of the core is $\sim$ K. For regions where is detectable, the density is on the order of $10^{\rm 4}$."
 At lower deusities (107.? )orec)). an excitation temmpcrature of ~ ISIN is traced wCHO.. decreasing further to ~ KK. towards the outermost laver of the clouds (see rofunbieut)).," At lower densities $10^{\rm 2-3}$ ), an excitation temperature of $\sim$ K is traced by, decreasing further to $\sim$ K towards the outermost layer of the clouds (see \\ref{ambient}) )."
 The far-infrared Iuniuositv of the IRAS source. calculated from the IRAS fux. is Lpyp=l96 L. (at a clistance of lkkpe)h," The far-infrared luminosity of the IRAS source, calculated from the IRAS flux, is $L_{\rm FIR}$ =196 $\solum$ (at a distance of kpc)."
 This luminosity is higher than the mimi value set bv the mechanical luninosity requirement., This luminosity is higher than the minimum value set by the mechanical luminosity requirement.
 By adopting the ATLay relationship of Shepherd CChurchwell (1996)). the huuimositv of the outflow source i I220231 is predicted to be. greater than LLL.," By adopting the $\dot{M}-L_{\rm bol}$ relationship of Shepherd Churchwell \cite{Shepherd96}) ), the luminosity of the outflow source in 20231 is predicted to be greater than $\solum$."
 WW ithiotheerrorrange. itsuggeststhatthein chfiopedky /olvatid REOR awRTact Vesteian ," Within the error range, it suggests that the infrared source in question can provide sufficient mechanical power to drive the CO outflow."
Source IRSI. located at (3%. 0%). coincides well with the IRAS source [1220231 with A.=9.76 uunae and LFἐν=1. unnae.," Source IRS1, located at $''$ , $''$ ), coincides well with the IRAS source 20231 with $K_{\rm s}$ mag and $H-K_{\rm s}$ mag."
" luuuediatelv next to IRSL. a fainter εν το nag) companion source 2 was found at 1"", 11""). appearing much redder with fFAY =2.21 mae."," Immediately next to IRS1, a fainter $K_{\rm s}$ =13.33 mag) companion source 2 was found at $''$, $''$ ), appearing much redder with $H-K_{\rm s}$ =2.21 mag."
 Ave they physically related?, Are they physically related?
 Aud which one is responsible for the outflow?, And which one is responsible for the outflow?
 Considering the chuupiuess iu outflow structure. are perhaps both stars driving the outflow?," Considering the clumpiness in outflow structure, are perhaps both stars driving the outflow?"
" It is worth noting that the position difference between source 2 aud ΜΙΑ ΕΕ 5"", which is mareinally within the pointing uncertainty of the 870422 observations."," It is worth noting that the position difference between source 2 and SMM1 is $''$, which is marginally within the pointing uncertainty of the $\mu$ m observations."
 The question theu arises on how IRSI. source 2 aud SMMA are plivsically related.," The question then arises on how IRS1, source 2 and SMM1 are physically related."
" Cousidering the relatively large beam (22"") of the 870722 observations. higher resolution dust coutiuuua and molecular line observatious as well as some deeper NIR tages are needed to auswer these questions."," Considering the relatively large beam $''$ ) of the $\mu$ m observations, higher resolution dust continuum and molecular line observations as well as some deeper NIR images are needed to answer these questions."
 Tu the southern core. we did not find such YSO candidates close Τε» SMIAI2.," In the southern core, we did not find such YSO candidates close to SMM2."
" Although there is a much weaker nunae) A, source located at M. 180), its nature is unknow siice it was not detected in J aud II aud we cannot place it ¢mu the color-color diagram."," Although there is a much weaker mag) $K_{\rm s}$ source located at $''$ $''$ ), its nature is unknow since it was not detected in $J$ and $H$ and we cannot place it on the color-color diagram."
 Most likely the driving source of the southern outflow is still deeply embedded in the coud., Most likely the driving source of the southern outflow is still deeply embedded in the cloud.
 It is also less hpnuuimous thia its counterpart(s) of the northern outflow., It is also less luminous than its counterpart(s) of the northern outflow.
 Protostars evolve roni Class00 to Class L. IT. IIT.," Protostars evolve from 0 to Class I, II, III."
" Class00 sources, the voungest protostars are characterized bv MioLuaz 01M.""ILL GOLas is the euvelope mass). no detectable emission at waveleugths shorter than  san. and the presence of outflow (André et al. 1993.. 200033."," 0 sources, the youngest protostars, are characterized by $M_{\rm env}/L_{\rm bol} > 
0.1$ $\solmass/\solum$ $M_{\rm env}$ is the envelope mass), no detectable emission at wavelengths shorter than $\sim$ $\mu$ m, and the presence of outflow (André et al. \cite{Andre93}, \cite{Andre00}) )."
 At esent. 12 00 sources have been ideutified (Audiré et al. 20003).," At present, 42 0 sources have been identified (André et al. \cite{Andre00}) )."
" A reasonably good estimate of Mj cau be provided w the streusth of the optically thin jan continu, cluission iu the 22"" beam (~00.lLppe. the typical size of xotostellar euvelopes in the Taurus cloud)."," A reasonably good estimate of $M_{\rm env}$ can be provided by the strength of the optically thin $\mu$ m continuum emission in the $''$ beam $\sim$ pc, the typical size of protostellar envelopes in the Taurus cloud)."
 Following the nethod used in rofdust.. we can estimate A444 for SNIATL and SAINI? to © about 9 audsolhuass.. with their peak flux densities of 1.67 alc Ll. respectively.," Following the method used in \\ref{dust}, we can estimate $M_{\rm env}$ for SMM1 and SMM2 to be about 9 and, with their peak flux densities of 1.67 and $^{-1}$, respectively."
 It is. however. worth noting that p= 15 AERE come 1 correspoudinely). a value lower than the one used for mass caleulatious iu rofdust.. is found to be more suitable to estimate the masses traced by the dust around protostars (e.g. Visser et al. 1998.. 2001)).," It is, however, worth noting that $\beta$ = 1.5 $\kappa_{\rm 870\mu m}$ = $^{\rm 2}$ $^{\rm -1}$ correspondingly), a value lower than the one used for mass calculations in \\ref{dust}, is found to be more suitable to estimate the masses traced by the dust around protostars (e.g. Visser et al. \cite{Visser98}, \cite{Visser01}) )."
" Moreover. the averaged dust temperature within a 22"" beam could be higher than tle Ones used in rofdust.."," Moreover, the averaged dust temperature within a $''$ beam could be higher than the ones used in \\ref{dust}."
 Both effects lead to lower masses., Both effects lead to lower masses.
Considerimg frarcedsoug icalpacntéodricctheC we can safelv conclude that AZμις0.01 for SMALL. typical of a Il source.,"Considering additionally that 20231 may not be at the core center, we can safely conclude that $M_{\rm env}/L_{\rm bol}<0.04$ for SMM1, typical of a I source."
 The detection of 1220231 at pau and gan and the moderate strength of its CO outflow also sugeest SMMEI to be a ~ II YSO., The detection of 20231 at $\mu$ m and$\mu$ m and the moderate strength of its CO outflow also suggest SMM1 to be a $\sim$ I YSO.
 To better constrain the properties of SMM2. we first estimate the lower limit to Moy. sry = (ολους + is most likely an upper limit if we take the assuuption from. Ilildebrand (1983)). bie. ry=0.1(250Αμ) ," To better constrain the properties of SMM2, we first estimate the lower limit to $M_{\rm env}$ $\kappa_{\rm 870\mu m}$ = $^{2}$ $^{-1}$ is most likely an upper limit if we take the assumption from Hildebrand \cite{Hildebrand83}) ), i.e. $\kappa_{\rm \lambda} = 0.1(250/ \lambda (\mu m))^{\rm \beta}$ "
morphology of the Galactic bar.,morphology of the Galactic bar.
" The technique, based on using RC giants as accurate distance indicators across different lines of sight, was first applied by ? and adopted later by several authors to trace the bar morphology at different Galactic latitudes (e.g.?22).."," The technique, based on using RC giants as accurate distance indicators across different lines of sight, was first applied by \citet[][]{stanek97} and adopted later by several authors to trace the bar morphology at different Galactic latitudes \citep[e.g.][]{babusiaux05, rattenbury07, cabrera07}."
 ? applied this technique to the VVV survey data to detect the edge of the Galactic stellar disk., \citet{minniti11} applied this technique to the VVV survey data to detect the edge of the Galactic stellar disk.
" Here, we use it to test whether the change in the slope in the orientation of the Galactic bar observed by N05 at b=+1° is also evident in our data at b= +1°, as well as at b=—1°."," Here, we use it to test whether the change in the slope in the orientation of the Galactic bar observed by N05 at $b=+1^\circ$ is also evident in our data at $b=+1^\circ$ , as well as at $b=-1^\circ$."
" We corroborate the measurements of N05, which suggests that there is a distinct structure in the inner regions of the Galactic bar that appears to be symmetric with respect to the Galactic plane."," We corroborate the measurements of N05, which suggests that there is a distinct structure in the inner regions of the Galactic bar that appears to be symmetric with respect to the Galactic plane."
" For this study, we use the near-IR JK photometry from the VVV publicsurvey!."," For this study, we use the near-IR JK photometry from the VVV public."
. A detailed description of the survey and the data can be found in ?.., A detailed description of the survey and the data can be found in \citet[][]{vvv10}.
" In particular, the photometric calibration and dereddened magnitudes were calculated as described in ?,, hence are only briefly described here."," In particular, the photometric calibration and dereddened magnitudes were calculated as described in \citet[][]{gonzalez11b}, hence are only briefly described here."
 Multi-band catalogs were produced by a cross-match of sources between single-band catalogs produced at the Cambridge Astronomical Survey Unit (CASU) using the STILTS code (?).., Multi-band catalogs were produced by a cross-match of sources between single-band catalogs produced at the Cambridge Astronomical Survey Unit (CASU) using the STILTS code \citep[][]{taylor06}.
" For this work, we analyzed a total of 28 tiles, containing about 30 million measured sources, which cover the survey region between —1.4?«b<—0.4? and +0.7°«b«1.7? at longitudes across the range —10?«/10? (Fig.1))."," For this work, we analyzed a total of 28 tiles, containing about 30 million measured sources, which cover the survey region between $-1.4^\circ<b<-0.4^\circ$ and $+0.7^\circ<b<+1.7^\circ$ at longitudes across the range $-10^\circ<l<10^\circ$ \ref{red}) )."
 The photometric calibration was obtained by sources of VVV with thoseof 2MASS flagged with high quality photometry., The photometric calibration was obtained by cross-matching sources of VVV with thoseof 2MASS flagged with high quality photometry.
" This produced the final VVV J, H, and K, photometric catalogs fully consistent with the 2MASS photometric system."," This produced the final VVV J, H, and $K_s$ photometric catalogs fully consistent with the 2MASS photometric system."
 The calibrated VVV tile catalogues were then dereddened and used to build the luminosity functions for each of the tiles., The calibrated VVV tile catalogues were then dereddened and used to build the luminosity functions for each of the tiles.
 The extinction correction was done following the prescriptions described in ?.., The extinction correction was done following the prescriptions described in \citet[][]{gonzalez11b}.
" However, for the present analysis, we adopted the ? extinction law, where A,=0.528-E(J—Ks) instead of the standardvalues of ?,, as the latter does not seem to be consistent with observations in the"," However, for the present analysis, we adopted the \citet[][]{nishiyama09} extinction law, where $A_k=0.528\cdot E(J-K_s)$ instead of the standardvalues of \citet[][]{cardelli89}, , as the latter does not seem to be consistent with observations in the"
r=2 (,r = 2 ( t) =. (
GRB central engine starts operating at /=0).,GRB central engine starts operating at $t=0$ ).
 Thus. if there is a delay of the switching ou of the GBR engine bytime .N. the resulting GRB shock slows down for a time A’. aud ouly later starts to accelerate.," Thus, if there is a delay of the switching on of the GBR engine bytime $\Delta t$, the resulting GRB shock slows down for a time $\Delta t$, and only later starts to accelerate."
" The GRB shock reaches the edge of the expaucing core at time aud radius στο Re = (va vo)? AP}pen where The time /, (or /g) aud the radius Z2. give the typical scales of the problem.", The GRB shock reaches the edge of the expanding core at time and radius = ( + )^2 - t. R_c = _c ( ( + )^2 - ) v_0 where t_0=_c The time $t_c$ (or$t_0$ ) and the radius $R_c$ give the typical scales of the problem.
 Iu case of time delay between the SN explosion aud the activation of the GARB engine. the time it takes for the GRB shock to reach the edge of the expanding core (this time is the main coustraint ou the moclel) is thegeometrical mean of the dyuauical time (3.2)) and thedelay tine M.," In case of time delay between the SN explosion and the activation of the GRB engine, the time it takes for the GRB shock to reach the edge of the expanding core (this time is the main constraint on the model) is thegeometrical mean of the dynamical time \ref{t0}) ) and thedelay time $\Delta t$."
" The intrinsic dynamical time {ρ and distance at which the GRB shock reaches the surface of the core (Lor zero delay. A?— 0) is fy"" = lOsec ! 3) | τ) | τ) |"," The intrinsic dynamical time $t_0$ and distance at which the GRB shock reaches the surface of the core (for zero delay, $\Delta t=0$ ) is t_0 = 40 ) ) ) )"
the Orion region. to analyze the ages and masses of the stars.,"the Orion region, to analyze the ages and masses of the stars."
 The advantage of using these stars is that unlike lower mass stars. they move significantly in the log7.—L diagram on a timescale of Myrs.," The advantage of using these stars is that unlike lower mass stars, they move significantly in the $\log T_{\mathrm{eff}}-\log L$ diagram on a timescale of Myrs."
 Given a set of evolutionary models. one can therefore derive a relatively precise evolutionary age even if the observational errors are large.," Given a set of evolutionary models, one can therefore derive a relatively precise evolutionary age even if the observational errors are large."
 On the other hand. the theoretical evolution of these massive stars ts still poorly understood. and assumptions to derive log7.[ui and logL from observations introduce relatively large errors.," On the other hand, the theoretical evolution of these massive stars is still poorly understood, and assumptions to derive $\log T_{\mathrm{eff}}$ and $\log L$ from observations introduce relatively large errors."
 For the Orion OB] associations. we include the stars listed in Brownetal. (1994). whereas Dolan&Mathieu(2001) was used fort Ort.," For the Orion OB1 associations, we include the stars listed in \citet{Brown1994}, , whereas \citet{Dolan2001} was used for $\lambda$ Ori."
 Orion hosts ο stars altogether., Orion hosts 7 O stars altogether.
 Their properties were analyzed in previous studies. using photometric data interpreted using local thermodynamic equilibrium (LTE) models (Kuruez1992) that were not corrected for line-blanketing.," Their properties were analyzed in previous studies, using photometric data interpreted using local thermodynamic equilibrium (LTE) models \citep{Kurucz1992}
 that were not corrected for line-blanketing."
 The results provided by such analysis are. however. very unreliable for massive stars.," The results provided by such analysis are, however, very unreliable for massive stars."
 We therefore derive new properties based on spectroscopy rather than photometry. and using line-blanketed non-LTE models rather than LTE: We use the recent catalogue of Mafz-Apellánizetal.(2004) to identify the spectral types of the O stars.," We therefore derive new properties based on spectroscopy rather than photometry, and using line-blanketed non-LTE models rather than LTE: We use the recent catalogue of \citet{Maiz2004} to identify the spectral types of the O stars."
 We then use the line-blanketed models of Martinsetal.(2005). to estimate their effective temperatures (using the observational scale). luminosities and surface gravities.," We then use the line-blanketed models of \citet{Martins2005} to estimate their effective temperatures (using the observational scale), luminosities and surface gravities."
 We increased the sample by adding the two very bright B stars Ce Ori A and « Ort) from Searleetal.(2008)., We increased the sample by adding the two very bright B stars $\epsilon$ Ori A and $\kappa$ Ori) from \citet{Searle2008}.
 For the Orion Nebula Cluster a more detailed study of the five most massive Trapezium stars was performed by Simón-Díazetal. (2006).. and we use their results for these five stars.," For the Orion Nebula Cluster a more detailed study of the five most massive Trapezium stars was performed by \citet{Simon-diaz2006}, and we use their results for these five stars."
 In figure ] the stars are shown in an logTay-L plot. where they are compared to four different sets of stellar evolutionary. tracks and isochrones. with (upper panels and lower left panel) and without (lower right panel) including the effects of rotation.," In figure \ref{fig:ostars} the stars are shown in an $\log T_{\mathrm{eff}}-\log L$ plot, where they are compared to four different sets of stellar evolutionary tracks and isochrones, with (upper panels and lower left panel) and without (lower right panel) including the effects of rotation."
 Stellar models including rotation. are taken from Meynet&Maeder(2005) and the models without inclusion of rotation from Meynetetal.(1997);Schalleral.(1992);Limongi&Chieti (2006).," Stellar models including rotation are taken from \citet{Meynet2005} and the models without inclusion of rotation from \citet{Meynet1997,Schaller1992,Limongi2006}."
. From this plot the masses and ages of the individual stars can be derived., From this plot the masses and ages of the individual stars can be derived.
 The masses implied for the stars do not vary significantly between the models. but à systematic. shift in ages between the non-rotating and the rotating models is apparent.," The masses implied for the stars do not vary significantly between the models, but a systematic shift in ages between the non-rotating and the rotating models is apparent."
 For the stars in groups OBIb.e and 2t Ort. the average stellar age is 0.8 Myr higher for models including rotation than for the ones without. whereas the five stars in group OBId are on average ~0.7 Myr younger for the models with rotation.," For the stars in groups OB1b,c and $\lambda$ Ori, the average stellar age is 0.8 Myr higher for models including rotation than for the ones without, whereas the five stars in group OB1d are on average $\sim0.7$ Myr younger for the models with rotation."
 There are no significant differences between the results obtained from the three different non-rotating models., There are no significant differences between the results obtained from the three different non-rotating models.
 The results for the models including rotation are given in table 2.., The results for the models including rotation are given in table \ref{tab:ostars}.
 For many decades O-star research has been subject to a severe mass discrepancy (e.g.Herreroetal.1992)... where spectroscopic masses (derived from log g) and evolutionary masses (derived from the luminosity. and the mass-Iuminosity relation) were highly discrepant. in some cases by more than506t.," For many decades O-star research has been subject to a severe mass discrepancy \citep[e.g.][]{Herrero1992}, where spectroscopic masses (derived from log g) and evolutionary masses (derived from the luminosity, and the mass-luminosity relation) were highly discrepant, in some cases by more than."
. Here we re-investigate this issue for Orion’s massive star population (see figure 2))., Here we re-investigate this issue for Orion's massive star population (see figure \ref{fig:masses}) ).
 It is comforting to notice that there no longer appears to be any significant mass-discrepancy., It is comforting to notice that there no longer appears to be any significant mass-discrepancy.
" It is clear that properties of the massive stars in the groups OBIb-d and ,| Ori are consistent with ages of a few Myr. whereas there are no very massive stars in OBla. in agreement with a higher age of - 10 Myr."," It is clear that properties of the massive stars in the groups OB1b-d and $\lambda$ Ori are consistent with ages of a few Myr, whereas there are no very massive stars in OB1a, in agreement with a higher age of $\sim$ 10 Myr."
 The 4-5 Myr ages of the stars in OBIbe and 2 Ori fall approximately in the middle of the age estimates derived from the less massive stars. with no evidence for the much lower age of 1.7 Myr for OBIb found by Brown (1994).," The 4-5 Myr ages of the stars in OB1bc and $\lambda$ Ori fall approximately in the middle of the age estimates derived from the less massive stars, with no evidence for the much lower age of 1.7 Myr for OB1b found by \citet{Brown1994}."
. The most massive star in OBId is found to be the youngest., The most massive star in OB1d is found to be the youngest.
 The stars in OBId are all consistent with an age below 2 Myr., The stars in OB1d are all consistent with an age below 2 Myr.
 In table | we summarize the assumptions on the different stellar groups as we use them in the following., In table \ref{tab:regs} we summarize the assumptions on the different stellar groups as we use them in the following.
 We emphasize that there are considerable uncertainties on the umbers given in table 1.. which should be evident from the discussion above and from figure 1..," We emphasize that there are considerable uncertainties on the numbers given in table \ref{tab:regs}, which should be evident from the discussion above and from figure \ref{fig:ostars}."
 As the numbers are gathered from a large number of sources with varying assumptions and methodology. and many of these lack reliable estimates of the uncertainties. we have not included error estimates in the table.," As the numbers are gathered from a large number of sources with varying assumptions and methodology, and many of these lack reliable estimates of the uncertainties, we have not included error estimates in the table."
 However. in the following analysis. we do estimate the sensitivity of our results to our assumptions.," However, in the following analysis, we do estimate the sensitivity of our results to our assumptions."
 We also compile a list of stars with masses between 8 and 20 M... for each of the 5 subgroups (fromBrownetal.1994;Dolan&Mathieu2001:Hernándezetal. 2005).. and assign the assumed average age per group.," We also compile a list of stars with masses between 8 and 20 $M_{\odot}$ for each of the 5 subgroups \citep[from][]{Brown1994,Dolan2001,Hernandez2005}, and assign the assumed average age per group."
 We note that the use of Kuruez(1992) atmosphere models in these earlier studies is not quite appropriate for these relatively massive stars. so that the uncertaintyon these estimates increases significantly.," We note that the use of \citet{Kurucz1992} atmosphere models in these earlier studies is not quite appropriate for these relatively massive stars, so that the uncertaintyon these estimates increases significantly."
 However. as the output of kinetic energy. matter. and UV radiation from these B stars is relatively small. compared to the more massive O-type stars. this is not important for our study.," However, as the output of kinetic energy, matter, and UV radiation from these B stars is relatively small, compared to the more massive O-type stars, this is not important for our study."
on erain surfaces. though we do argue its presence will uot siguificautly alter our fincdines.,"on grain surfaces, though we do argue its presence will not significantly alter our findings."
 The presence of dust aud its effect on cooling las been discussed as a possible catalyst for the star formation iode trausition., The presence of dust and its effect on cooling has been discussed as a possible catalyst for the star formation mode transition.
 Schneideretal.(2006) and Schneider&ΕΕ(2009) found that dust induced fragmentation can decrease the Pop II fragmentation mass scale by about four orders of magnitude over that accessible with inetal fue structure lines oulv., \citet{SCH06} and \citet{SO09} found that dust induced fragmentation can decrease the Pop II fragmentation mass scale by about four orders of magnitude over that accessible with metal fine structure lines only.
 Jappsenoetal.(20095) suggested that ictallicity docs not affect the fraeimeutation of eas with hot initial conditions. similar to the envirowmment probed iu this study;," \citet{JAP09} suggested that metallicity does not affect the fragmentation of gas with hot initial conditions, similar to the environment probed in this study."
 We attribute the differeuce iu our couclusious to our examination of a slightly different pliysical regie aud to our inclusion of a soft UV. backeround that stifles IT) cooling (assup-ported.e.g.byShaneetal. 2009j.," We attribute the difference in our conclusions to our examination of a slightly different physical regime and to our inclusion of a soft UV background that stifles $\textrm{H}_2$ cooling \citep[as supported, e.g., by][]{SHA09}."
. Takiusg euidauce from galaxy formation simulations. we follow isobarically evolving gas in au expanding shocked slab to study its thermal evolution aud fragmentation.," Taking guidance from galaxy formation simulations, we follow isobarically evolving gas in an expanding shocked slab to study its thermal evolution and fragmentation."
 Our model is designed to reflect the flkument-dominated inflow topology of cold accretion flows. whereas Jappsenctal.(20095) examine the collapse iuto a spherically- centrally concentrated halo poteutial.," Our model is designed to reflect the filament-dominated inflow topology of cold accretion flows, whereas \citet{JAP09} examine the collapse into a spherically-symmetric, centrally concentrated halo potential."
 In our isoharically evolving case. the fieht coupling between density aud temperature will increase the importance of the role of the cooling rate iu determining the fal outcome of fragnientatiou.," In our isobarically evolving case, the tight coupling between density and temperature will increase the importance of the role of the cooling rate in determining the final outcome of fragmentation."
" This aside. if we include molecule formation aud molecular cooling (I. aud ΠΟ) by setting Jo,=10. our results aeree with Jappsenctal.(20094). in that metal line cooling docs not affect the fragmentation propertics of the evolving eas."," This aside, if we include molecule formation and molecular cooling $\textrm{H}_2$ and HD) by setting $J_{21} = 10$, our results agree with \citet{Jappsen:09a} in that metal line cooling does not affect the fragmentation properties of the evolving gas."
 This emphasizes the importance of a LAW soft UV. backerouud in modeling the formation of Pop II stars in the first ealaxies., This emphasizes the importance of a LW soft UV background in modeling the formation of Pop II stars in the first galaxies.
 The first galaxies are suspected to be the first structures where turbulence begins to play a inajor role. dviven by high Mach-unuber cold streams penctrating o the protogalactic core (Crceifetal.2008:Wise&Abel 2007).," The first galaxies are suspected to be the first structures where turbulence begins to play a major role, driven by high Mach-number cold streams penetrating to the protogalactic core \citep{GB08, WA07}."
. It is the iuterplav of turbulence aud self eravity which is suspected to be responsible for the shape of 1e present-day IME. especially the lieh mass power law xtension (Padoan Nordluud 2002: Mac Low lessen 2001: Melee Ostriker 2007).," It is the interplay of turbulence and self gravity which is suspected to be responsible for the shape of the present-day IMF, especially the high mass power law extension (Padoan Nordlund 2002; Mac Low Klessen 2004; McKee Ostriker 2007)."
 Thus. it is likelvthat stax ornmation inside the first galaxies will be characterized oa stellar mass distribution that for the first time in the history of the universe resembles alreacy the present-day IME.," Thus, it is likely that star formation inside the first galaxies will be characterized by a stellar mass distribution that for the first time in the history of the universe resembles already the present-day IMF."
 Specifically. we can expect turbulence to introduce density perturbations ou the order of M. sugecsting within our above model that fragments as low asc 0.3AL. uuelt form.," Specifically, we can expect turbulence to introduce density perturbations on the order of ${\cal M}^{2}$, suggesting within our above model that fragments as low as $\sim0.3 \,M_\odot$ might form."
" Such stars. below the mass ΓΗ, of 0.8AL. required to survive for the age of the universe. would still exist today. aud could be probed by Stellar Archaeology (Freheletal.2009.andrefercucestherein)."," Such stars, below the mass limit of $0.8
\,M_\odot$ required to survive for the age of the universe, would still exist today, and could be probed by Stellar Archaeology \citep[][and references therein]{FRE09}."
 To predict the detailed shape of the Pop., To predict the detailed shape of the Pop.
 TD IME insice he first galaxies. the source and impact of the turbulence reeds to be studied with realistic umunuerical simulations.," II IMF inside the first galaxies, the source and impact of the turbulence needs to be studied with realistic numerical simulations."
 Tere. we have coustrained some of the key physical xocesses that govern star formation iu high-redshitt xotosalaxies within an idealized analytical framework hat allowed us to explore the relevaut parameter space.," Here, we have constrained some of the key physical processes that govern star formation in high-redshift protogalaxies within an idealized analytical framework that allowed us to explore the relevant parameter space."
" This work needs to be followed wp bv detailed sinulations. iucludiusg a απο of iugredieuts ignored rere, such as high optical depth effects. IT and Te ionizing radiation (Ricottietal.2002).. turbulence. feedback. effects (ACN. stellar outflows. ote)."," This work needs to be followed up by detailed simulations, including a number of ingredients ignored here, such as high optical depth effects, H and He ionizing radiation \citep{RIC02}, turbulence, feedback effects (AGN, stellar outflows, etc.),"
 and yossibly cosmic rays from the first SNe (Jascheetal.2007:Stacy&Bronuun 2007).," and possibly cosmic rays from the first SNe \citep{JCE07, SB07}."
. It needs to be emphasized that the estimates preseuted in this paper are derived with the Bounor-Ehert mass aud a simplified treatinent of the post-shock dvuamics., It needs to be emphasized that the estimates presented in this paper are derived with the Bonnor-Ebert mass and a simplified treatment of the post-shock dynamics.
 To truly probe the fragmentation mass scale in the first ealaxics one must use multidimensional numerical simulations., To truly probe the fragmentation mass scale in the first galaxies one must use multidimensional numerical simulations.
" The goal of understanding the couples first stages of ealaxv formation secius now within reach. using state-ofthe-art three dimensional racliation-lycdrodvuamical «λαΊος, together with realistic cosmological initial conditions."," The goal of understanding the complex first stages of galaxy formation seems now within reach, using state-of-the-art three dimensional radiation-hydrodynamical simulations, together with realistic cosmological initial conditions."
 Such calculations are crucial to make useful predictions for the(., Such calculations are crucial to make useful predictions for the.
"JWST). This work was supported in part by NSF eraut. AST-ηςτοῦ, aud bv NASA ΑΤΕΡ erant NNXOSAL106. (for V.BB.)."," This work was supported in part by NSF grant AST-0708795, and by NASA ATFP grant NNX08AL43G (for B.)."
 The authors thaws Farah Prasla aud Chliistopher Lindner for useful conversations and echnical help., The authors thank Farah Prasla and Christopher Lindner for useful conversations and technical help.
 We thank Sean Couch for adding deutermi chemistry., We thank Sean Couch for adding deuterium chemistry.
 We also thauk Nazi Οι aud Uniberto Maio for valuable comments., We also thank Kazu Omukai and Umberto Maio for valuable comments.
 SS. thanks L.PP.DD for her never-eudiug patience., S. thanks D for her never-ending patience.
 This research js nade use of NASA's Astroplivsies Data Syste., This research has made use of NASA's Astrophysics Data System.
"Jets are ""pipelines"" through which energy aud matter originating from the central region of ACNsS can flow out from the galaxy and. as in FRIT radio ealaxies. reach the radio-lobes (οιο, Beegclman. Blandford Rees 1981).","Jets are “pipelines” through which energy and matter originating from the central region of AGNs can flow out from the galaxy and, as in FRII radio galaxies, reach the radio-lobes (e.g. Begelman, Blandford Rees 1984)."
 The comprelieusion of such structures represcuts a ereat challenge for Astrophysics: he ultimate goals include the unuderstaudius of the plivsical processes able to xoduce such enerectics and collimated outlows aud the complex dynamics of he jet and its interaction with the cuvironment., The comprehension of such structures represents a great challenge for Astrophysics: the ultimate goals include the understanding of the physical processes able to produce such energetics and collimated outlows and the complex dynamics of the jet and its interaction with the environment.
 Iu the last decade. thanks to new instruments (ii particular the οταν clescope EGRET. the TeV Cherenkov telescopes aud Chandra). this field las received a ereat inpulse.," In the last decade, thanks to new instruments (in particular the $\gamma
$ -ray telescope EGRET, the TeV Cherenkov telescopes and ), this field has received a great impulse."
" In the following I briefly present our current view of he principal plivsical processes acting in jets. from the iunerinost portion of he jet close to the central ""engine"" to the external regions."," In the following I briefly present our current view of the principal physical processes acting in jets, from the innermost portion of the jet close to the central “engine” to the external regions."
 Finally I discuss sole works m progress regarding the counection between the inner portion of he jet and the outer regions., Finally I discuss some works in progress regarding the connection between the inner portion of the jet and the outer regions.
 It is now venerally accepted that the blazar “phenomenon (highly polarised and rapidly variable radio/optical continu) is due to a relativisticjet pointing close to the line of sight (e.g. Urrv Padovani 1995).," It is now generally accepted that the blazar ""phenomenon"" (highly polarised and rapidly variable radio/optical continuum) is due to a relativistic jet pointing close to the line of sight (e.g. Urry Padovani 1995)."
 Relativistic effects strongly amplity the enutted non-thenual continuum produced close to the central DII (at 4<0.1 pe. Fig.l) that can dominate over the thermal coutribution from the disk or the Broad. Line," Relativistic effects strongly amplify the emitted non-thermal continuum produced close to the central BH (at $d<0.1$ pc, Fig.1) that can dominate over the thermal contribution from the disk or the Broad Line"
olfset from the one-to-one line by ~0.5 dex. are within the scatter of the full sample.,"offset from the one-to-one line by $\sim$ 0.5 dex, are within the scatter of the full sample."
 A clear trend of decreasing. E/Fe] with increasing οΗ] is scen in Fig. 3.., A clear trend of decreasing [E/Fe] with increasing [Fe/H] is seen in Fig. \ref{fealpha}.
 Por GC's associated with NGC 3379. Pierce (2005h) used the index-index plots to confirm the suggestion of a trend in the 47. fit a-clement abunelances.," For GCs associated with NGC 3379, Pierce (2005b) used the index-index plots to confirm the suggestion of a trend in the $\chi^2$ fit $\alpha$ -element abundances."
 Similar index-index. plots lor NGC 4649 GCs do not show the trend. that is seen in the fitted: parameters., Similar index-index plots for NGC 4649 GCs do not show the trend that is seen in the fitted parameters.
 In. the case presented. here there is the added complication of age differences between GCs. whereas the NGC 3379 GCs of Pierce ((2005b) were found. to be universally old.," In the case presented here there is the added complication of age differences between GCs, whereas the NGC 3379 GCs of Pierce (2005b) were found to be universally old."
 lt should be noted that we find no trend of a-clement abundance ratios with age., It should be noted that we find no trend of $\alpha$ -element abundance ratios with age.
 One of the more important factors for the \ fitting analysis used in this work is the determination of errors., One of the more important factors for the $\chi$ fitting analysis used in this work is the determination of errors.
 Uncertainties in the background: subtraction of sky and ealaxy light introduces Lick index errors in acelition to the easily. quantifiable Poisson noise., Uncertainties in the background subtraction of sky and galaxy light introduces Lick index errors in addition to the easily quantifiable Poisson noise.
 The relative effect of these errors increases for [ainter GC's. so in reality not only do fainter GC's have larger index errors. but also those errors are increasingly. uncerestimated.," The relative effect of these errors increases for fainter GCs, so in reality not only do fainter GCs have larger index errors, but also those errors are increasingly underestimated."
 Assuming Gaussian. errors due to photon noise. of measurements should. be within 2e.," Assuming Gaussian errors due to photon noise, of measurements should be within $\sigma$."
 For most objects we measure 16 indices. which means that when we apply a 2c clip. only 1 index measurement should. be exeluded on average per object.," For most objects we measure $\sim$ 16 indices, which means that when we apply a $\sigma$ clip, only 1 index measurement should be excluded on average per object."
 For the application of «7. fitting to extragalactic (ος this is clearly. not the case as we are often forced. to exclude 3-7 indices at greater than 30 before a stable result is obtained., For the application of $\chi^2$ fitting to extragalactic GCs this is clearly not the case as we are often forced to exclude 3-7 indices at greater than $\sigma$ before a stable result is obtained.
 Here we are also assuming that the SSP models are perfect., Here we are also assuming that the SSP models are perfect.
 Both flux calibration and calibration to the Lick svstem introduce further errors and uncertainties., Both flux calibration and calibration to the Lick system introduce further errors and uncertainties.
 The main manifestation of these unaccounted for errors is the increased dilliculty in constraining ages and a-clement abundance ratios for fainter GCs., The main manifestation of these unaccounted for errors is the increased difficulty in constraining ages and $\alpha$ -element abundance ratios for fainter GCs.
 In general. metallicitics are less susceptible to these ellects because of the large number (210) of preclominantly metallicity sensitive indices available.," In general, metallicities are less susceptible to these effects because of the large number $>$ 10) of predominantly metallicity sensitive indices available."
 By contrast. there are only 3. primarily age indicators (Lo. the 112. H5. ane 115 lines) ancl only a few strongly sensitive a-clement indices.," By contrast, there are only 3 primarily age indicators (i.e. the $\beta$, $\gamma$ and $\delta$ lines) and only a few strongly sensitive $\alpha$ -element indices."
 This underestimation of errors probably occurs in all extra-galactic GC samples., This underestimation of errors probably occurs in all extra-galactic GC samples.
 For example. the large and homogeneous sample of Puzia (2004) has index errors," For example, the large and homogeneous sample of Puzia (2004) has index errors"
per single CPU.,per single CPU.
 This means that the granularity (ratio of computation to communication) of the parallel problem drops strongly with an increasing number of processors., This means that the granularity (ratio of computation to communication) of the parallel problem drops strongly with an increasing number of processors.
 The resulting speedup factors and efficiencies of this test are shown in Fig. 9.., The resulting speedup factors and efficiencies of this test are shown in Fig. \ref{Performance}.
" The runs during this test are performed on a grid consisting of 32,768+n grid cells (e.g. a 64x8n grid), where n is again the number of processors used."," The runs during this test are performed on a grid consisting of $*n$ grid cells (e.g. a $64 \mbox{ x } 64 \mbox{ x } 8n$ grid), where $n$ is again the number of processors used."
" Each processor covers therefore a subdomain containing 32,768 grid cells respectively during all runs, independent of the number of processors used."," Each processor covers therefore a subdomain containing 32,768 grid cells respectively during all runs, independent of the number of processors used."
 This test shows the efficiency achievable when using more processors to run a bigger problem., This test shows the efficiency achievable when using more processors to run a bigger problem.
" This is a realistic setup for our three-dimensional radiative hydrodynamics studies of collapsing massive pre-stellar cores, which are at the current limit of our clusters."," This is a realistic setup for our three-dimensional radiative hydrodynamics studies of collapsing massive pre-stellar cores, which are at the current limit of our clusters."
 The resulting speedup factors and efficiencies are shown in Fig. 9.., The resulting speedup factors and efficiencies are shown in Fig. \ref{Performance}.
" The constant grid test shows a clear speedup for the fixed problem, so it is simply possible to compute a fixed problem faster by using more processors."," The constant grid test shows a clear speedup for the fixed problem, so it is simply possible to compute a fixed problem faster by using more processors."
 The growing grid case shows a high efficiency of more than during all runs., The growing grid case shows a high efficiency of more than during all runs.
" This speedup seems to be higher than the speedup of any actual freely available three-dimensional hydrodynamics code for spherical grids (well known in the astrophysical community, e.g. Pluto2, Flash2.5, and Zeus-MP1.5), which we tested during the summer 2007 in an accretion disk setup in hydrostatic equilibrium."," This speedup seems to be higher than the speedup of any actual freely available three-dimensional hydrodynamics code for spherical grids (well known in the astrophysical community, e.g. Pluto2, Flash2.5, and Zeus-MP1.5), which we tested during the summer 2007 in an accretion disk setup in hydrostatic equilibrium."
" In this sense, the resulting parallel speedup is high enough for the planned integration of this radiation transfer module into a (magneto-) hydrodynamics framework."," In this sense, the resulting parallel speedup is high enough for the planned integration of this radiation transfer module into a (magneto-) hydrodynamics framework."
" Finally, we can recommend the usage of such an implicit modern KSP solver method leading to fast convergence of the radiative diffusion problem (at least for the setup discussed) while simultaneously offering high parallel efficiency."," Finally, we can recommend the usage of such an implicit modern KSP solver method leading to fast convergence of the radiative diffusion problem (at least for the setup discussed) while simultaneously offering high parallel efficiency."
" Admittedly, attention should be paid to the general fact that such an approximate solver method strongly depends on the physical problem at hand as well as on the specified accuracy or abort criterion."," Admittedly, attention should be paid to the general fact that such an approximate solver method strongly depends on the physical problem at hand as well as on the specified accuracy or abort criterion."
" To test the approximate radiation transport scheme also in dynamical interaction with a streaming fluid, we perform two standard radiative shock tests."," To test the approximate radiation transport scheme also in dynamical interaction with a streaming fluid, we perform two standard radiative shock tests."
 We adopt the setup of the supercritical and subcritical radiative shock tests for the VISPHOT code in ?.., We adopt the setup of the supercritical and subcritical radiative shock tests for the VISPHOT code in \citet{Ensman:1994p10128}.
" These radiative shock tests were already repeated in tests of the TITAN code (??),, ZEUS-2D (?),, as well as ZEUS-MP (?).."," These radiative shock tests were already repeated in tests of the TITAN code \citep{Sincell:1999p10169, Sincell:1999p10170}, , ZEUS-2D \citep{Turner:2001p1152}, as well as ZEUS-MP \citep{Hayes:2006p1133}."
 Analytic approximations for this kind of problem are given by ?.., Analytic approximations for this kind of problem are given by \citet{ZelDovich:1967p10174}.
" To follow the motion of the gas, we solve (additionally to the radiation transport equations of Sect. 2))"," To follow the motion of the gas, we solve (additionally to the radiation transport equations of Sect. \ref{sect:theory}) )"
 the equations of compressible hydrodynamics in conservative form with the acceleration source term from the radiation transport derived in Sect. 3.3.4.., the equations of compressible hydrodynamics in conservative form with the acceleration source term from the radiation transport derived in Sect. \ref{sect:radiativeforce}.
" The evolution of the gas density p, the gas velocity i, the thermal pressure P, and the total energy E is computed using the open source magneto-hydrodynamics code Pluto3 (?).."," The evolution of the gas density $\rho$ , the gas velocity $\vec{u}$, the thermal pressure $P$, and the total energy $E$ is computed using the open source magneto-hydrodynamics code Pluto3 \citep{Mignone:2007p3421}."
" Pluto is a high-order Godunov solver code, i.e. it uses a shock capturing Riemann solver within a conservative finite volume scheme."," Pluto is a high-order Godunov solver code, i.e. it uses a shock capturing Riemann solver within a conservative finite volume scheme."
 Our default configuration consists further of a Harten-Lax-VanLeer (hll) Riemann solver and a so-called “minmod” flux limiterusing piecewise linear interpolation (plm) and a Runge-Kutta2 (RK2) time integration, Our default configuration consists further of a Harten-Lax-VanLeer (hll) Riemann solver and a so-called “minmod” flux limiterusing piecewise linear interpolation (plm) and a Runge-Kutta2 (RK2) time integration
Revniviseyοἱal.(2004) detected a significant X-ray variability with time scales as short as 100 s with RATE in 2004.,\citet{revnivtsev04} detected a significant X-ray variability with time scales as short as 100 s with RXTE in 2004.
 The absence or weakness of a rapid X-ray. variability had been explained in terms of the X-rav-emitting jet as long as or longer than 101 em., The absence or weakness of a rapid X-ray variability had been explained in terms of the X-ray-emitting jet as long as or longer than $10^{12}$ cm.
 Together with the QPO-like feature in the power density spectrum. (his shot-like variability implies the presence of X-ray sources smaller than LOY? em in the system.," Together with the QPO-like feature in the power density spectrum, this shot-like variability implies the presence of X-ray sources smaller than $10^{12}$ cm in the system."
 Considering that these shots coincide a massive jet ejeclion event. we further assume that they are related to the ejection in the following discussion.," Considering that these shots coincide a massive jet ejection event, we further assume that they are related to the ejection in the following discussion."
 since the spectral fit is consistent wilh a decrease of the absorption hydrogen column density during the evolution of the shots. we attribute the rise of the shots to the decrease of attenuating matter. or in other words. the emergence of an. N-rav-enmitting small plasma bullet from behind attenuating matter.," Since the spectral fit is consistent with a decrease of the absorption hydrogen column density during the evolution of the shots, we attribute the rise of the shots to the decrease of attenuating matter, or in other words, the emergence of an X-ray-emitting small plasma bullet from behind attenuating matter."
 Each shot literally corresponds to a shot of a small plasma bullet rom the nozzle., Each shot literally corresponds to a shot of a small plasma bullet from the nozzle.
 This interpretation is different from that of the X-ray variability seen in GRS 19154-105. which is explained in terms of (he rapid removal ancl replenishment of malter forming (the inner part of an accretion disk (Bellonietal.1997)..," This interpretation is different from that of the X-ray variability seen in GRS 1915+105, which is explained in terms of the rapid removal and replenishment of matter forming the inner part of an accretion disk \citep{belloni97}."
 Since both thermal and non-thermal spectral models are consistent with the observed spectrum. it is difficult to determine the emission mechanism.," Since both thermal and non-thermal spectral models are consistent with the observed spectrum, it is difficult to determine the emission mechanism."
 Bul in either case. physical «quantities of the emitting bullets would be derived as follows.," But in either case, physical quantities of the emitting bullets would be derived as follows."
 Given a spherical. (hin-thermal. freely expanding plasma bullet with a temperature T(/). a radius RU)=exp. an expanding velocity (44= const..," Given a spherical, thin-thermal, freely expanding plasma bullet with a temperature $T(t)$, a radius $R(t) = v_{\rm exp}t$, an expanding velocity $v_{\rm exp} =$ const.,"
 and a total number of electrons NV.= const..," and a total number of electrons $N_{\rm
e} =$ const.,"
 the cooling would be governed with the equation where X=N;/.N. is (he ratio of the total number of ions to that of electrons assumed {ο be 0.93117. Ay is the Doltzmann constant. aud > is (he adiabatic index. assumed to be 5/3.," the cooling would be governed with the equation where $X = N_{\rm i}/N_{\rm e}$ is the ratio of the total number of ions to that of electrons assumed to be 0.93117, $k_{\rm B}$ is the Boltzmann constant, and $\gamma$ is the adiabatic index, assumed to be 5/3."
 The first terii on the right-hand side corresponds (to radiative cooling. and the coellicient A(T) is defined so that ACP)Nαπ/3)N;/(47/3) equals to the emitted power per unit volume.," The first term on the right-hand side corresponds to radiative cooling, and the coefficient $\Lambda(T)$ is defined so that $\Lambda(T) N_{\rm e}/(4
\pi R^3/3) N_{\rm i}/(4 \pi R^3/3)$ equals to the emitted power per unit volume."
 The last term corresponds to expansion: For expanding plasma will a volume V(/). ↕⊳∖⇁≺⇂≼↲↕⋅↕∖↽≼↲≼⊔⋟↕⋅∪∐↓⊔∐↲↕⋅≼↲↥≀↧↴∐∪∐↕↴↜↴|— constant.," The last term corresponds to expansion: For expanding plasma with a volume $V(t)$, is derived from the relation $TV^{\gamma-1} =$ constant."
 Substituting V.—4x17/3 to Eq. (4)). ⊔∐↲≺∢∪∪∐∐≸≟↕⋅≀↧↴," Substituting $V
= 4 \pi R^3/3$ to Eq. \ref{eq:adiabatic}) ),"
∩↲∣↽≻∡∖↽≼↲⇀↸↕↽≻≀↧↴∐⊳∖⊽↕∪∐⋅↙∣↕⇁∕∕∣↙∣∕∶−⊑↽⊰≼⋝↶⇌↴−⊥⇄⋝⊺∣⋎≺⋅⇀∖↓⋝∕∕∣∫↘⋝↥⊳∖⊽∪∣↽≻↥≀↧↴↥∐≼↲≼⇂⋅∖∖↽∐↕≺∢∐↕⊳∖⇁≼↲≺⇂∏↕∖↽≀↧↴↥≼↲∐↥↥∪ ⊔∐↲↥≀↧⊔∖⇁↥↥≼↲↕⋅∐↓∪↓≯⊏≺⇂⋅⋜⋝⊑↽⊰⇄⋝⇄⋝⋅↴," the cooling rate by expansion, $ dT/dt = -3 (\gamma-1) T v_{\rm exp}/R$ is obtained, which is equivalent to the last term of Eq. \ref{eq:cooling}) )."
∏∐↲∐∐∐↲↕↽≻≀↧↴↕⋅≀↧↴∐∐↲∩↲↕⋅∕↥⊳∖⊽≼⇂≼↲↓∎↓∐≼↲≼⇂⋝∖⊽∪⊔⋯↥∣∶∩≀↧↴↥∫↘⋝∶∪⋅≀↧↴∐∐∪∏≸≟∐," The time parameter $t$ is defined so that $t = 0$ at $R =
0$ , although"
priors for this spectroscopy-free cosnology test were constructed. under the assunptiou of a “worst-case scenario. with no host eaaxy photo-z estimates at all.,"priors for this spectroscopy-free cosmology test were constructed under the assumption of a “worst-case scenario,” with no host galaxy photo-z estimates at all."
 In reality. many SNe from future wide-field) surveys wil have good photoimoetric redsufts from their host galaxies. which call significantly improve the SOFT parameter cstimeat¢*.," In reality, many SNe from future wide-field surveys will have good photometric redshifts from their host galaxies, which can significantly improve the SOFT parameter estimates."
 Those uture wide-fied survevs will also have nuci larger data san]es. helpiug to reduce the uieer estimate uncertainties tha arise fron 111100111 effects," Those future wide-field surveys will also have much larger data samples, helping to reduce the parameter estimate uncertainties that arise from random effects."
 As t1C siuuple SIZO dncreases. LOWCVCL. systematic uncertainties will »'ei to dominate.," As the sample size increases, however, systematic uncertainties will begin to dominate."
 In Section 5 we will cousider »otential LOications of the SOFT inethod that uav help Oo nuninize svstclatic errors., In Section \ref{sec:BiasCorrections} we will consider potential modifications of the SOFT method that may help to minimize systematic errors.
" One of the primary reasous for developing a tool such as SOFT is to deal with the extremely large SN data sets frou a new generation of synoptic surveys,", One of the primary reasons for developing a tool such as SOFT is to deal with the extremely large SN data sets from a new generation of synoptic surveys.
 A principal scicuce goal for these next eeueration surveys is fo Improve constraiuts on a time-variable dark euerev (DE) «quation of state., A principal science goal for these next generation surveys is to improve constraints on a time-variable dark energy (DE) equation of state.
 Iu this section we ask: Tow uuch of an improvement can be made with the precision provided by SOFT?, In this section we ask: How much of an improvement can be made with the precision provided by SOFT?
 As a foundation for our simulations we ust first adopt a DE model in which the equation of state parameter. ais a fiction of the scale factor a. and therefore varies over cosmic time.," As a foundation for our simulations we must first adopt a DE model in which the equation of state parameter, $w$, is a function of the scale factor $a$, and therefore varies over cosmic time."
" A simple and conmuouly used parameterization for wa) is to assume a linear form (7?ju For our simulations we add the additional restriction ofa flat universe (Q),.=00)."," A simple and commonly used parameterization for $w(a)$ is to assume a linear form \citep{Chevallier:2001,Linder:2003}: For our simulations we add the additional restriction of a flat universe 0)."
 The Fricciuann equation in this case is: To investigate the informative power of future SN data sets. wo use a series of Monte Carlo siaulations iu which the real SOFT results from our validation tests servo as seed points for creating larecr sinulated data sets;," The Friedmann equation in this case is: To investigate the informative power of future SN data sets, we use a series of Monte Carlo simulations in which the real SOFT results from our validation tests serve as seed points for creating larger simulated data sets."
 Our goal is to iiic the observational data set that might be produced by PSI. DES. LSST. or another large and deep SN survey.," Our goal is to mimic the observational data set that might be produced by PS1, DES, LSST, or another large and deep SN survey."
 The SDSS and SNLS data provide a good baseline for simulating those future survevs because they have simular light curve sapling aud cover a simular redshift rauee., The SDSS and SNLS data provide a good baseline for simulating those future surveys because they have similar light curve sampling and cover a similar redshift range.
 We create nine Monte Carlo data sets. labeled A through L using the time-varving DE model with," We create nine Monte Carlo data sets, labeled A through I, using the time-varying DE model with"
"(2011), but is at odds with several earlier studies in the literature (Somerville2002;Kravtsovetal.",", but is at odds with several earlier studies in the literature \citep{Somerville2002, Kravtsov2004b}."
 The difference is largely due to two factors., The difference is largely due to two factors.
" First, the 2004)..previous work that focused on the range of the classical dwarf galaxies of the Milky Way found little reionization dependence; our results agree to the extent that the bright end of our luminosity function (classical dSph regime with 10°<L«105 L5) does not change either with large scale (different reionization model) or small scale versus instantaneous) changes in reionization."," First, the previous work that focused on the range of the classical dwarf galaxies of the Milky Way found little reionization dependence; our results agree to the extent that the bright end of our luminosity function (classical dSph regime with $10^{5}<L<10^{8}\,L_{\odot}$ ) does not change either with large scale (different reionization model) or small scale (patchy versus instantaneous) changes in reionization."
" The (patchydifference at the faint end is explained by the various assumptions about how reionization influences the available supply of cold gas in small halos — our model assumes an abrupt end to star formation in halos smaller than a cutoff Όμιας, whereas the filtering mass formalism will lead to a gradual suppression in star formation, and a much weaker reionization dependence."," The difference at the faint end is explained by the various assumptions about how reionization influences the available supply of cold gas in small halos – our model assumes an abrupt end to star formation in halos smaller than a cutoff $v_{max}$, whereas the filtering mass formalism will lead to a gradual suppression in star formation, and a much weaker reionization dependence."
" In that sense, we have chosen a maximum effect, and the results of our study can be viewed as an upper limit to the impact of patchiness of reionization."," In that sense, we have chosen a maximum effect, and the results of our study can be viewed as an upper limit to the impact of patchiness of reionization."
" We also note that since all but the largest subhalos in our simulation finish their star formation around reionization, our results are consistent with some ultra-faint dwarf galaxies having formed around the epoch of"," We also note that since all but the largest subhalos in our simulation finish their star formation around reionization, our results are consistent with some ultra-faint dwarf galaxies having formed around the epoch of"
our measurements on both the cluster sample and the random control sample.,our measurements on both the cluster sample and the random control sample.
 The results are shown in Figure 10 and Figure 11 The results from the random control sample show that y is consistently zero.," The results are shown in Figure \ref{fig:gammaz} and Figure \ref{fig:gammaz_random}
 The results from the random control sample show that $\gamma$ is consistently zero."
" From the cluster sample, we detect a clear BCG alignment and its strength decreases as redshift increases."," From the cluster sample, we detect a clear BCG alignment and its strength decreases as redshift increases."
" From the figures, we can also see that is almost the same no matter how the PAs of BCGs yare measured."," From the figures, we can also see that $\gamma$ is almost the same no matter how the PAs of BCGs are measured."
 This has two important implications: 1., This has two important implications: 1.
 the PAs of BCGs are well measured by both isophotal fit and model fit; 2., the PAs of BCGs are well measured by both isophotal fit and model fit; 2.
 the diffuse light of satellite galaxies does not affect the PA measurement of the BCG., the diffuse light of satellite galaxies does not affect the PA measurement of the BCG.
" Before we can conclude the redshift dependence of y, we still need to do one more test."," Before we can conclude the redshift dependence of $\gamma$, we still need to do one more test."
" That is, if the axis ratio (b/a) of the BCG and cluster become systematically smaller due to the decreased at higher redshift, the measured strength of ""y will S/Ndecrease too."," That is, if the axis ratio $b/a$ ) of the BCG and cluster become systematically smaller due to the decreased S/N at higher redshift, the measured strength of $\gamma$ will decrease too."
" To calculate the cluster b/a, we use the method as described in ??.."," To calculate the cluster $b/a$ , we use the method as described in \citet{kim02,ostholt10}. ."
" For clusters, the axis ratio is defined as b/a=(1—/Q?+U?)/(1+/Q?U?), with the stokes parameters Q=Mz,—My, and U= 2M;,."," For clusters, the axis ratio is defined as $b/a = (1-\sqrt{Q^2+U^2})/(1+\sqrt{Q^2+U^2})$, with the stokes parameters $Q=M_{xx}-M_{yy}$ and $U=2 M_{xy}$ ."
" The radius-weighted second moments are given by Mz,=(x?/r?), My,= and M,= with r?=2?4y?."," The radius-weighted second moments are given by $M_{xx}=\left<x^2/r^2\right>$, $M_{yy}=\left<y^2/r^2\right>$ and $M_{xy}=\left<xy/r^2\right>$ with $r^2=x^2+y^2$."
 x and y are (y?/r?)the distances between (xy/r?)the satellite galaxies and BCG in the tangent plane., $x$ and $y$ are the distances between the satellite galaxies and BCG in the tangent plane.
" For BCGs, we use the measured b/a in SDSS pipeline based on isophotal fit, exponential fit and DeVoucular fit."," For BCGs, we use the measured $b/a$ in SDSS pipeline based on isophotal fit, exponential fit and DeVoucular fit."
" In Figure 12,, we plot the b/a in each redshift bin of size 0.05."," In Figure \ref{fig:ba}, we plot the $b/a$ in each redshift bin of size 0.05."
" From the results, the axis ratio does not depend on redshift in a statistically significant way."," From the results, the axis ratio does not depend on redshift in a statistically significant way."
" Furthermore, we also checked that both the BCGs' PAs and cluster PAs are distributed randomly, as show in the right panel of Figure 13.."," Furthermore, we also checked that both the BCGs' PAs and cluster PAs are distributed randomly, as show in the right panel of Figure \ref{fig:pa}."
" Therefore, the evolution of y in Figure 10 should not result from the S/N variation of the PA measurements."," Therefore, the evolution of $\gamma$ in Figure \ref{fig:gammaz} should not result from the S/N variation of the PA measurements."
 We measure the BCG alignment vs the r band absolute magnitudes of the BCG., We measure the BCG alignment vs the $r$ band absolute magnitudes of the BCG.
" The results are presented in Figure 14 From the plot, we see that 7 strongly depends on the BCGs absolute magnitude."," The results are presented in Figure \ref{fig:gamma_ramag}
 From the plot, we see that $\gamma$ strongly depends on the BCGs absolute magnitude."
" To further show that this is not due to S/N of the measurement of BCGs shape, we plot the axis ratio b/a of BCGs and clusters as a function of the BCGs r band absolute magnitude in Figure 15.."," To further show that this is not due to S/N of the measurement of BCGs shape, we plot the axis ratio $b/a$ of BCGs and clusters as a function of the BCGs $r$ band absolute magnitude in Figure \ref{fig:ba_absmag}."
 There is no dependence of b/a on the BCGs absolute magnitude., There is no dependence of $b/a$ on the BCGs absolute magnitude.
" From the above results, we see that the depends on both redshiftand the BCG absolute magnitude."," From the above results, we see that the $\gamma$ depends on both redshiftand the BCG absolute magnitude."
"y To show thismore clearly, we bin the cluster samples into photoz bins of size 0.05 and absolute magnitudebins of size 0.5."," To show thismore clearly, we bin the cluster samples into photoz bins of size 0.05 and absolute magnitudebins of size 0.5."
We believe that the probable explanation for the phenomenon shown in Figures5. and 5.1 is In the presence of an extra-tidal stellar halo or tidal tail.,We believe that the probable explanation for the phenomenon shown in Figures\ref{profconf} and \ref{extrat} is in the presence of an extra-tidal stellar halo or tidal tail.
 Doubt resides in the unknown gradient of the background field stars., Doubt resides in the unknown gradient of the background field stars.
 To resolve this we need to map the whole cluster and a large area surrounding the cluster., To resolve this we need to map the whole cluster and a large area surrounding the cluster.
 This would also allow us to find the exact level of field stars., This would also allow us to find the exact level of field stars.
 Our star counts stop at 33/(2« r4). from the center of M55 while the tidal tails of Grillmairetal.(1995). stop at ~2.5:[ry.," Our star counts stop at $\simeq2\times r_t$ ), from the center of M55 while the tidal tails of \cite{Grillmair95}
 stop at $\simeq 2.5 \div 4\, r_t$."
 Consequently. we cannot correctly subtract the contribution of the field stars from our star counts.," Consequently, we cannot correctly subtract the contribution of the field stars from our star counts."
 We can give only an estimate of the exponent of the power law. fxra fitting the profiles at r=1.27;.," We can give only an estimate of the exponent of the power law, $f\propto r^{-\alpha}$, fitting the profiles at $ r > 1.2\,r_t$."
 Without subtracting any background counts o.~0.7ck0.3. while subtracting different levels of background stars the slope varies in the interval 0.7<a<1.7: the highest value comes out after subtracting the outermost value of the density profiles.," Without subtracting any background counts $\alpha\sim0.7\pm0.3$, while subtracting different levels of background stars the slope varies in the interval $0.7<\alpha<1.7$: the highest value comes out after subtracting the outermost value of the density profiles."
 When it will be available a better estimate of the background/foreground level of the sky it will be possible to assign a value to the slope of the gradient of stars: actually our range. à.=0.7: 1.7. is in," When it will be available a better estimate of the background/foreground level of the sky it will be possible to assign a value to the slope of the gradient of stars: actually our range, $\alpha=0.7 \div 1.7$ , is in"
stars with high values of the covering factor display a larger amount of blue-shift in the X-ray line profiles.,stars with high values of the covering factor display a larger amount of blue-shift in the X-ray line profiles.
 Note that for many objects the derived from. the fit errors can be appreciable., Note that for many objects the derived from the fit errors can be appreciable.
 Unfortunately. the complexity of the model fits and the non-uniform quality of the data limit the accuracy on the derivation of the plotted. qauntities.," Unfortunately, the complexity of the model fits and the non-uniform quality of the data limit the accuracy on the derivation of the plotted qauntities."
 An additional source of uncertainty comes from the ‘cloudiness’ parameter that. depends on the accuracy of the cooling curve (see eq. 5))., An additional source of uncertainty comes from the `cloudiness' parameter that depends on the accuracy of the cooling curve (see eq. \ref{eq:spec}) ).
 However. the key. point is that all the objects were analvzed in a uniform wav.," However, the key point is that all the objects were analyzed in a uniform way."
 Thus. future improvements in the atomic data (ic. cooling curve) might only shift the scale. but they will not allect the observed trend that we believe is rather robust.," Thus, future improvements in the atomic data (i.e. cooling curve) might only shift the scale, but they will not affect the observed trend that we believe is rather robust."
 More importantly. as can be seen in Fig.," More importantly, as can be seen in Fig."
 4 appreciable red shifts of the spectral lines are not observed., \ref{fig:cloudy} appreciable red shifts of the spectral lines are not observed.
 The observed. correlation between the total stellar ‘cloudiness’ and the spectral line shifts. reveals additional details about the X-ray emitting zone in hot massive stars., The observed correlation between the total stellar `cloudiness' and the spectral line shifts reveals additional details about the X-ray emitting zone in hot massive stars.
 For example. from Fig.," For example, from Fig."
" 4. and for typical mass-loss rates (Al,=0.1 1) and wind velocities (eyo71.5— 2.5). in most cases the ""eloudiness parameter is small (9: 1)."," \ref{fig:cloudy} and for typical mass-loss rates $\dot{M}_6 \approx 0.1 - 1$ ) and wind velocities $v_{1000}
\approx 1.5 - 2.5$ ), in most cases the `cloudiness' parameter is small $\delta \leq 1$ )."
 In other words. dense clumps/clouds do not completely. cover he N-ray skv of massive stars.," In other words, dense clumps/clouds do not completely cover the X-ray `sky' of massive stars."
 This also means that. the RDI instabilities (and the ALCWS as well) do not allect a rig part of their stellar winds., This also means that the RDI instabilities (and the MCWS as well) do not affect a big part of their stellar winds.
" Comparing the results for single and multiple svstems. we note that the latter show higher values of the ""cloudiness? xwameter: this could. result. [rom additional sources of Χ-rav emission. such as colliding wind shocks in binary stars (Luo.AleCray&MacLow.1990: Stevens.Blondin&Pol-lock 1992: Myasnikov&Zhekov 1993))."," Comparing the results for single and multiple systems, we note that the latter show higher values of the `cloudiness' parameter: this could result from additional sources of X-ray emission, such as colliding wind shocks in binary stars \citealt{luo_90}; \citealt{st_92}; \citealt{myas_93}) )."
 We have to keep in mind that the ‘cloudiness’ parameter is also à measure of the ellicieney of the X-ray production., We have to keep in mind that the `cloudiness' parameter is also a measure of the efficiency of the X-ray production.
 Pherefore. if an extra source of X-ravs exists in some object. then it will result in an ellectively larger number of shocks representing the additional emission.," Therefore, if an extra source of X-rays exists in some object, then it will result in an effectively larger number of shocks representing the additional emission."
 “Vhis is the case for a binary svstem. where a higher value of that parameter is expected. in comparison to a single star with the same spectral line shift.," This is the case for a binary system, where a higher value of that parameter is expected in comparison to a single star with the same spectral line shift."
 Finally. the fact that no appreciable redshift of the X- line profiles is observed. in any object. indicates that the cistribution of the absorbers in OB stars likely has a spherical (or axial) symmetry.," Finally, the fact that no appreciable redshift of the X-ray line profiles is observed in any object indicates that the distribution of the absorbers in OB stars likely has a spherical (or axial) symmetry."
 Future observations with a high spectral resolution and a good photon statistics will give us an opportunity to further test. these conclusions and to study the X-ray gas. kinematics in greater cletail., Future observations with a high spectral resolution and a good photon statistics will give us an opportunity to further test these conclusions and to study the X-ray gas kinematics in greater detail.
 They will also show whether the ‘cloucliness’ parameter for a given object. changes with time which might be an important characteristic of the mechanism that drives the wind instabilities responsible for the A-ray emission. from. niisslve stars., They will also show whether the `cloudiness' parameter for a given object changes with time which might be an important characteristic of the mechanism that drives the wind instabilities responsible for the X-ray emission from massive stars.
 Using the public archive. we have analvzed the rav spectra of a sample of 15 massive OB stars.," Using the public archive, we have analyzed the X-ray spectra of a sample of 15 massive OB stars."
 Phe basic assumption in this study is that the N-ray. emission. [rom, The basic assumption in this study is that the X-ray emission from
 ⊤∣↴⊖∁∪⋯∣⊃⋯⋪⋯⋯⋋↾⋂⋔⊖∥⋯⇈⋋∣≻∕⊥⋅≏↧⋯↿∣≻∕⇉↳∐⋋∁⋅≏⋯↿∐∏∣⊃∣↴⋝⇁⋋≣∁∐∣∖⇁∐∣∐⊜⋋⋯⊟↳∣∐⋅≏↧⊓⋂∏⋋⋀∣∍−−⋀∣−↓∖∖⇁∣↴⊜∣⋪⊜⋔⊖⊓∏∐∣∥⋯≣↾⋋∪↑↴⋯↾⊖∶↔⊺∣⋪∐⊓∪∏ are found.,The comparisons to the limits $\rho_{l1}$ and $\rho_{l2}$ discard unphysical values in Equations \ref{eq_lastlim1}- \ref{eq_lastlim2} where the final limits of integration are found.
 With the integration boundaries now well defined. (1.D2) can easily be obtained through numerical integration.," With the integration boundaries now well defined, $\mu(b_1,b_2)$ can easily be obtained through numerical integration."
with which different maegnuetars could be detected. aud thereby to answer the question. If there are may more magnetars m the Galaxy. what must they look like?,"with which different magnetars could be detected, and thereby to answer the question, If there are many more magnetars in the Galaxy, what must they look like?"
 Iu the subsections below. we use the results of surveys most sensitive to each class of object.," In the subsections below, we use the results of surveys most sensitive to each class of object."
 For standard ANPs. we use our own survey of aand ddata.," For standard AXPs, we use our own survey of and data."
 For SGRs. the best coustraiuts are provided by allsky eanunarav burst monitors.," For SGRs, the best constraints are provided by all-sky gamma-ray burst monitors."
 For transient ANPs. simular results are found using our own archival survey. and past surveys with aandASCA.," For transient AXPs, similar results are found using our own archival survey, and past surveys with and."
. The standard ANPs are the easiest population to constrain. because they are casily-detectable throughout he Galaxy.," The standard AXPs are the easiest population to constrain, because they are easily-detectable throughout the Galaxy."
 Our survey of archival aand oobservations is complete for finding staudard ANPs or SHY of the vouns stellar population iu the Galaxy., Our survey of archival and observations is complete for finding standard AXPs for $\approx$ of the young stellar population in the Galaxy.
 Before estimating a total nuuber of standard ANPs. rowever. we need to establish how many known examples ie within our random survey of the Galaxy.," Before estimating a total number of standard AXPs, however, we need to establish how many known examples lie within our random survey of the Galaxy."
 Ouly one source Was ideutified in au observation im which it was rot the tareet: CNOU J161710.2.155216 in Westerluud Lt (Munoetal.2006)., Only one source was identified in an observation in which it was not the target: CXOU J164710.2–455216 in Westerlund 1 \citep{mun06}.
. The other sources detected i our survey were observed as the targets of aand oobservatious because they were previously kuowu. and some thought must be taken before they cau be considered as part of a raudonm sample.," The other sources detected in our survey were observed as the targets of and observations because they were previously known, and some thought must be taken before they can be considered as part of a random sample."
 Three of the standard AXPS originally were identified sereudipitousl diving observations of other sources: LE 1018.15937 diving observations of the Carina uchula (Seward.Charles.o&Simale1986).. LE 2259|586 chairing obscrvatious of a supernova roiinaut. Cregorv I981).. aud LE 1811015 during oobservations of a supernova remnant (Vashisht&Got-thelf 1997).," Three of the standard AXPS originally were identified serendipitously during observations of other sources: 1E 1048.1–5937 during observations of the Carina nebula \citep{scs86}, 1E 2259+586 during observations of a supernova remnant \citep{fg81}, and 1E 1841–045 during observations of a supernova remnant \citep{vg97}."
. In the first case. the separation on the sky between the magnetar aud the central position. of the original target were 20.5°.. which makes it unlikely that the magnetar would have serendipitously fallen in the field of view of a oor oobservation.," In the first case, the separation on the sky between the magnetar and the central position of the original target were $\ga$, which makes it unlikely that the magnetar would have serendipitously fallen in the field of view of a or observation."
 Iu the latter two cases. the magnetars are close euough to the supernova ποιαές that one could have discovered them with oor oobservations. if oue makes the reasonable assuuption that the supernova remnant would be a suffücieutlv colmpclling target to have been observed.," In the latter two cases, the magnetars are close enough to the supernova remnants that one could have discovered them with or observations, if one makes the reasonable assumption that the supernova remnant would be a sufficiently compelling target to have been observed."
 Therefore. we claim that 3 known magnuetars lie i the random sample of the Galaxy that we surveved.," Therefore, we claim that 3 known magnetars lie in the random sample of the Galaxy that we surveyed."
 snowing that there are 3 easily-detectable maguetars that can be fouud in our search of of the voune stars in the Ctalaxw. we can determine the most likely total munber of such objects in the Galaxy using the binomial istribution.," Knowing that there are 3 easily-detectable magnetars that can be found in our search of of the young stars in the Galaxy, we can determine the most likely total number of such objects in the Galaxy using the binomial distribution."
 The probability that » pulsars out of a total population N would lic iu a fraction f£ of the Calaxy is: This can be inverted using Ώανος theorem to eive the total uuniber of maeuetars NV. eiven that 7=3 maguetars ave found with the fraction £50.05 of the Calaxy: The most likely value and coufideuce iuterval for the total umber of ensilv-detectable magnetars is 59172," The probability that $n$ pulsars out of a total population $N$ would lie in a fraction $f$ of the Galaxy is: This can be inverted using Bayes' theorem to give the total number of magnetars $N$, given that $n$ =3 magnetars are found with the fraction $f$ =0.05 of the Galaxy: The most likely value and confidence interval for the total number of easily-detectable magnetars is $59^{+92}_{-32}$."
 Given that the number of known Galactic niaguetars is 12. there could be 17!- waiting to be discovered.," Given that the number of known Galactic magnetars is 12, there could be $47^{+92}_{-32}$ waiting to be discovered."
 The Galactic rate of core-collapse supernovae 1s ~0.010.01 | (Cappallareetal.1993:vandenBorel&McChive199 1).. aud the radio pulsar birth rate has been recently estimated to be between z0.011 yr| etal.2006) and ©0.03 ve| (Faucher-Cignére&Kaspi 2006).," The Galactic rate of core-collapse supernovae is $\sim$ 0.01--0.04 $^{-1}$ \citep{cap93,vdbm94}, and the radio pulsar birth rate has been recently estimated to be between $\approx$ 0.014 $^{-1}$ \citep{lor06} and $\approx$ 0.03 $^{-1}$ \citep{fgk06}."
 If magnetars have typical lifetimes of —105 yr (Isouveliotouetal.1999:Cacuslerot1999)... then with somewhere between 27 aud 160 in the Calaxy. the magnetar birth rate would be betweeu 0.003 and 0.016 +.," If magnetars have typical lifetimes of $\sim$$10^{4}$ yr \citep{kou99,ggv99}, then with somewhere between 27 and 160 in the Galaxy, the magnetar birth rate would be between 0.003 and 0.016 $^{-1}$."
" The lower bouud is cousiderably sualler tha the pulsar birth rate. as would be expected if maguctars desceud from 30M, sstars (co...Gaensleretal.2005)."," The lower bound is considerably smaller than the pulsar birth rate, as would be expected if magnetars descend from $>$ stars \citep[e.g.,][]{gae05}."
. However. at the upper range. niagnoetars that resemble the standard ANPs could have a birth rate nearly equal to that of radio pulsars.," However, at the upper range, magnetars that resemble the standard AXPs could have a birth rate nearly equal to that of radio pulsars."
 An SCR can be identified if it produces inultiple bright soft gamma-ray bursts L.2001).," An SGR can be identified if it produces multiple bright soft gamma-ray bursts \citep[$\ga$$10^{40}$,."
 Over the course of 2:25 (210Mergsvears of monitoring. 3 Galactic SCRs have been confinnied (audoneintheLAICWoods&Thoupson200601.," Over the course of $\approx$ 25 years of monitoring, 3 Galactic SGRs have been confirmed \citep[and one in the LMC][]{wt06}."
 Their bursts typically last “(hds (Ctógüsetal.2001).. so they are bright cuough to be detected from auvwhere in the Calaxy.," Their bursts typically last $\sim$ 0.1s \citep{gog01}, so they are bright enough to be detected from anywhere in the Galaxy."
 Therefore. to estimate their total uuuber. we ouly need to determine the rate at which SGRs produce detectable bursts.," Therefore, to estimate their total number, we only need to determine the rate at which SGRs produce detectable bursts."
" For anv monitoring period of leneth 7. if we cefine an ""outburst as containing multipleindividual soft eaunia- bursts. an SCR will be identified if it produces one"," For any monitoring period of length $T$ , if we define an “outburst” as containing multiple individual soft gamma-ray bursts, an SGR will be identified if it produces one"
The right panel of Figure 3 plots (ue) (calculated from He and np using equation (9) in Graham&Driver (2005))) against γε for all bulges in our sample.,The right panel of Figure 3 plots $\left\langle \mu_{\rm e} \right\rangle$ (calculated from $\mu_{\rm e}$ and $n_{\rm b}$ using equation (9) in \cite{gra05}) ) against $r_{\rm e}$ for all bulges in our sample.
 Bulges with Séssic index above and below 2 are given by solid and open symbols respectively., Bulges with Séssic index above and below 2 are given by solid and open symbols respectively.
" According to method MOI, there are 14 classical bulges (ny> 2) and 61 pseudo-bulges (n,« 2) in our sample."," According to method M01, there are 14 classical bulges $n_{\rm b}>2$ ) and 61 pseudo-bulges $n_{\rm b}<2$ ) in our sample."
 The solid line in Fig., The solid line in Fig.
" 3 gives the dividing line between pseudo-bulges and classical bulges based on method M02, which results in 23 classical bulges and 52 pseudo-bulges."," 3 gives the dividing line between pseudo-bulges and classical bulges based on method M02, which results in 23 classical bulges and 52 pseudo-bulges."
" We can find that most M02-based pseudo-bulges are consistent with MO1-based results, while M02-based classical bulge sample is about 1.6 times large than MOI-based one."," We can find that most M02-based pseudo-bulges are consistent with M01-based results, while M02-based classical bulge sample is about 1.6 times large than M01-based one."
" This difference will affect our results to some extent, and we'll discuss it later."," This difference will affect our results to some extent, and we'll discuss it later."
" Based on the fitting results of STARLIGHT, we can obtain/derivel the following parameters for the bulges in our sample: mean stellar age, mean stellar metallicity, the contribution of flux and mass from different SSPs, and stellar velocity dispersion."," Based on the fitting results of STARLIGHT, we can obtain/derive the following parameters for the bulges in our sample: mean stellar age, mean stellar metallicity, the contribution of flux and mass from different SSPs, and stellar velocity dispersion."
 Both mass- and light-weighted mean stellar ages and metallicities are estimated., Both mass- and light-weighted mean stellar ages and metallicities are estimated.
 These properties can provide us very useful probes for the SFH studies., These properties can provide us very useful probes for the SFH studies.
" In the left panels of Figure 4, we plot the distributions of two mean stellar ages (mass- and light-weighted mean ages; Cid05) estimated for all of the bulges in our sample, as the dashed and solid histograms show the results for pseudo-bulges and classical bulges, respectively."," In the left panels of Figure 4, we plot the distributions of two mean stellar ages (mass- and light-weighted mean ages; Cid05) estimated for all of the bulges in our sample, as the dashed and solid histograms show the results for pseudo-bulges and classical bulges, respectively."
" The weighted mean stellar age is defined as, and the light-weighted mean stellar age is, where 4; and x; represent the fractional contributions to the stellar mass and luminosity of the SSP with age f; respectively."," The mass-weighted mean stellar age is defined as, and the light-weighted mean stellar age is, where $\mu_j$ and $x_j$ represent the fractional contributions to the stellar mass and luminosity of the SSP with age $t_j$ respectively."
" N, is the number of SSPs.", $N_\star$ is the number of SSPs.
" It is easy to understand that (t,)y is associated with the mass assembly history of galaxies, whereas (f,); is strongly affected by the recent SFH of a given galaxy."," It is easy to understand that $\left< t_\star \right>_M$ is associated with the mass assembly history of galaxies, whereas $\left<t_\star \right>_L$ is strongly affected by the recent SFH of a given galaxy."
 The fitting results of these two kinds of ages for our bulges are summarized in, The fitting results of these two kinds of ages for our bulges are summarized in
one switches to JWST/MIRI observations at >5.5 uum and continue to deteriorate almost monotonically all the way up to the 25 jum limit of MIRI.,one switches to JWST/MIRI observations at $\geq 5.5\ \mu$ m and continue to deteriorate almost monotonically all the way up to the 25 $\mu$ m limit of MIRI.
" Hence, detections of high-redshift galaxies in the MIRI filters will be very expensive in terms of observing time, compared to those in NIRCam filters."," Hence, detections of high-redshift galaxies in the MIRI filters will be very expensive in terms of observing time, compared to those in NIRCam filters."
" On average, the relative contribution from nebular continuum grows with increasing rest-frame wavelength, and this compensates for some of the sensitivity loss in the MIRI bands."," On average, the relative contribution from nebular continuum grows with increasing rest-frame wavelength, and this compensates for some of the sensitivity loss in the MIRI bands."
" For galaxies without nebular emission (type C), the decline in mass sensitivity"," For galaxies without nebular emission (type C), the decline in mass sensitivity"
it uses the following cuapirically derived formula to correct for the slight. skewness in the pixel distribution (ic. an excess of brighter pixels) that is conuuonlv seen due to contamination bv other objects in the image.,"it uses the following empirically derived formula to correct for the slight skewness in the pixel distribution (i.e., an excess of brighter pixels) that is commonly seen due to contamination by other objects in the image."
 This formula generally works well if the pixel values have a continuous distribution. as demonstrated iu our tests on the dithered star damages. however. it behaves poorly if the pixels are quantized because then the median value is also quantized.," This formula generally works well if the pixel values have a continuous distribution, as demonstrated in our tests on the dithered star images, however, it behaves poorly if the pixels are quantized because then the median value is also quantized."
 The amplitude of the error in the background estimate depends on how closely oue of the quantized levels happens to match the true background level., The amplitude of the error in the background estimate depends on how closely one of the quantized levels happens to match the true background level.
 Iu the worst case. where the true value les half way between 2 of the quautized levels (and assuuime that the mean value lies very close to the true background level. which is usually the case in our inages). then the error is equal to 1.25 times the iutensitv spacing between adjacent quantized levels.," In the worst case, where the true value lies half way between 2 of the quantized levels (and assuming that the mean value lies very close to the true background level, which is usually the case in our images), then the error is equal to 1.25 times the intensity spacing between adjacent quantized levels."
 Ou average. tle RAIS error in the background estimate introduced by this effect will be (2«1.25)/12=0.72 times the quantized spacing.," On average, the RMS error in the background estimate introduced by this effect will be $ (2 \times 1.25) / \sqrt{12} = 0.72 $ times the quantized spacing."
 It is ionic that equation 13 is intended to provide amore accurate backeround estimate. than simply using the imecian valuc alone. but it actually mereases the errors by a factor of 2.5 i£ the image is significantly quanutized.," It is ironic that equation \ref{eq:mode} is intended to provide a more accurate background estimate than simply using the median value alone, but it actually increases the errors by a factor of 2.5 if the image is significantly quantized."
 It should be emphasized that while this particular problem applies specifically to the way SExtractor estimates the background intensity. it is likely that sa.uilar problems would arise with other astrononucal data analvsis packages unless thev are specifically designed to deal with quantized data.," It should be emphasized that while this particular problem applies specifically to the way SExtractor estimates the background intensity, it is likely that similar problems would arise with other astronomical data analysis packages unless they are specifically designed to deal with quantized data."
 Another way to view this problem is that many aleoritlius are not well behaved ifthe noise is unuder-suupled., Another way to view this problem is that many algorithms are not well behaved if the noise is under-sampled.
 Ditheriug helps to eliminate this problemi because it preserves the natural distribution of the pixel values. as shown in Figure 2," Dithering helps to eliminate this problem because it preserves the natural distribution of the pixel values, as shown in Figure 2."
 As a final test. it is important to establish that there are no subtle svstematic zero-poit biases in the measured iagnuitudoes in the quautized images.," As a final test, it is important to establish that there are no subtle systematic zero-point biases in the measured magnitudes in the quantized images."
 This is demoustrated in Figure 8. which plots the can mnaenitude residual (true magnitude müuus nieasured magnitude) for the 6250 simulated star Huages within each 0.5 magnitude bin after quantizing the nuages with a range of different q values.," This is demonstrated in Figure 8, which plots the mean magnitude residual (true magnitude minus measured magnitude) for the 6250 simulated star images within each 0.5 magnitude bin after quantizing the images with a range of different q values."
 The upper panel shows the mean residuals in the subtractively dithered images. and the lower paucl shows the residuals iu the nou-cdithered quantized iaages.," The upper panel shows the mean residuals in the subtractively dithered images, and the lower panel shows the residuals in the non-dithered quantized images."
 The thicker line in both panels was derived frou the original nuquantized dmaees and shows that there is a sanall iutrisic negativo bias (-0.02 mae) iu the SExtractor magnitudes of the faintest stars., The thicker line in both panels was derived from the original unquantized images and shows that there is a small intrisic negative bias (-0.02 mag) in the SExtractor magnitudes of the faintest stars.
 The cause of this small measurement bias. which is less than 1/10th the statistical error on a single magnitude measurement. is unkuown. but it uuelt be due to the algorithms that SExtractor uses to measure the fainter stars. or perhaps due to the particular set of SExtractor configuration paraueters that we used in these tests.," The cause of this small measurement bias, which is less than 1/10th the statistical error on a single magnitude measurement, is unknown, but it might be due to the algorithms that SExtractor uses to measure the fainter stars, or perhaps due to the particular set of SExtractor configuration parameters that we used in these tests."
 The Huportant point here is that a very simular pattern of residuals is ποσα (nu the upper panel) in the coarsely quantized and dithered images. which shows that there are no significant additional magnitude biases in these quantized images.," The important point here is that a very similar pattern of residuals is seen (in the upper panel) in the coarsely quantized and dithered images, which shows that there are no significant additional magnitude biases in these quantized images."
 For q=2. the mean residuals match those iu the nuquantized images so closely that the points lic within the thickness of the line in the figure.," For $q \ge 2$, the mean residuals match those in the unquantized images so closely that the points lie within the thickness of the line in the figure."
 If dithering is not applied. however. then siguificaut biases iu the magnitude residuals may be present in the quantized damages. as shown iu the lower panel of Figure 8.," If dithering is not applied, however, then significant biases in the magnitude residuals may be present in the quantized images, as shown in the lower panel of Figure 8."
 This effect is entirely due to the systematic errors caused by the use of the median function in estimating the backerouncl iuteusitv level. as previously discussed.," This effect is entirely due to the systematic errors caused by the use of the median function in estimating the background intensity level, as previously discussed."
 The second experiuenut investigates how well faint simulated Caussian stars (as described iu 8.1)) that ave below the detection threshold of a single image can be measured after co-adding 250 simular niages together., The second experiment investigates how well faint simulated Gaussian stars (as described in \ref{s:setup}) ) that are below the detection threshold of a single image can be measured after co-adding 250 similar images together.
 To first order. one would expect that this experiment should detect stars that are about 2.5logY250=3.0 magnitudes fainter than in the single images.," To first order, one would expect that this experiment should detect stars that are about $2.5 \log{\sqrt{250}} = 3.0$ magnitudes fainter than in the single images."
 For comparison. we also generated quantized co-added images by quantizing cach of the 250 individual images (using a range of q values. with aud without subtractive ditherie)o before co-adding thei.," For comparison, we also generated quantized co-added images by quantizing each of the 250 individual images (using a range of q values, with and without subtractive dithering) before co-adding them."
 The iiaguitude aud position of the stars in cach of these co-added tages were then measured with the SExtractor program. just as in the first experiment.," The magnitude and position of the stars in each of these co-added images were then measured with the SExtractor program, just as in the first experiment."
 Figure 9 shows the results of the photometric meastvements in the co-added images., Figure 9 shows the results of the photometric measurements in the co-added images.
 Other than the fact that the lines in the plots exhibit more statistical scatter. since they were derived," Other than the fact that the lines in the plots exhibit more statistical scatter, since they were derived"
typical uuniber of a particles closest neighbors.,typical number of a particle's closest neighbors.
 This choice of AZ(.j.k) cusures that we always take into account a sufficient nuniber of particles for making the adaptively-sinoothed field ou the exid.," This choice of $M(i,j,k)$ ensures that we always take into account a sufficient number of particles for making the adaptively-smoothed field on the grid."
" The siioothedauterpolated value AC.jh) at the exid site (.4.Kk). which corresponds to a sioothl-averaegimeg of the quautities ον carried out by individual particles p. is defined as: where W,, ave additional weights to be determined for each particle and S is the smoothing kernel function."," The smoothed-interpolated value $\tilde{A}(i,j,k)$ at the grid site $(i,j,k)$, which corresponds to a smooth-averaging of the quantities $A_p$ carried out by individual particles $p$ , is defined as: where $W_p$ are additional weights to be determined for each particle and $\mathcal{S}$ is the smoothing kernel function."
" We determine the weights by euforciug that the suu of “lyj over all grid sites iust be the same as tlie sui of 4, over all particles."," We determine the weights by enforcing that the sum of $\tilde{A}_{i,j,k}$ over all grid sites must be the same as the sum of $A_p$ over all particles."
" This vields. for [IN particles. The last equality is true if Finally, we define the smoothing kerucl to be the typical SPII compact-support spline (Alonaghan1992).. We now compute both the mass density fluctuation field €.jk) and the displacement field Wi.j.&) in Enderian coordinates."," This yields, for $N$ particles, The last equality is true if Finally, we define the smoothing kernel to be the typical SPH compact-support spline \citep{mon92}, We now compute both the mass density fluctuation field $\delta(i,j,k)$ and the displacement field $\mathbf{\Psi}(i,j,k)$ in Eulerian coordinates."
" In the case of /-body simulations. the mass density fluctuation field is obtained by putting a nass gn,= Lou cach particle p. thus where we the conservation of the quantity Mun=MmU.medk). aud defined NV, the uuuber of grid sites."," In the case of $N$ -body simulations, the mass density fluctuation field is obtained by putting a mass $m_p=1$ on each particle $p$, thus where we used the conservation of the quantity $\sum m_p=\sum \tilde{m}(i,j,k)$, and defined $N_\text{g}$ the number of grid sites."
 In the case of observations. one could in principle use any tracer of the mass that is available. such as the huninosity or the number of galaxies.," In the case of observations, one could in principle use any tracer of the mass that is available, such as the luminosity or the number of galaxies."
 The displacementfield is obtained by averaging the displaceiieut carried by cach of the tracer particles., The displacementfield is obtained by averaging the displacement carried by each of the tracer particles.
 We thus obtain where l ds the result of applying the adaptive filter to compute the nmuuber of tracers on the erid site (ipby.," We thus obtain where $\tilde{1}$ is the result of applying the adaptive filter to compute the number of tracers on the grid site $(i,j,k)$."
 We that even though in N-body simulations (pb)—mt.notejk). this is not the case for observations.," We note that even though in $N$ -body simulations $\tilde{1}(i,j,k)=\tilde{m}(i,j,k)$, this is not the case for observations."
 We obtain the divergence of the displacement fold iu Fourier space. as with the previous CIC method.," We obtain the divergence of the displacement field in Fourier space, as with the previous CIC method."
 Figure shows V αν a function of ó and lu(l|à) using the adaptive SPII smoothing method with a cell size of L6h I\Ipe (lower uniddle plot)., Figure shows $\grad\cdot\bPsi$ as a function of $\delta$ and $\ln(1+\delta)$ using the adaptive SPH smoothing method with a cell size of 1.6 $^{-1}$ Mpc (lower middle plot).
 We note that both the CIC and SPIT methods produce very similar results., We note that both the CIC and SPH methods produce very similar results.
 The additional advantage of the SPITinethod is that exid cells with zero particles are not an issuc. as they are for CIC. since AM= particles are always included in the binning.," The additional advantage of the SPH method is that grid cells with zero particles are not an issue, as they are for CIC, since $M_\text{min}=32$ particles are always included in the binning."
" The vertical artifact near lu(116).du(l|6);=2 marks the transition where Mj, becomes important. above which the adaptive method behaves effectively the sune as the CIC inethod."," The vertical artifact near $\ln(1+\delta)-\langle\ln(1+\delta)\rangle=2$ marks the transition where $M_\text{min}$ becomes important, above which the adaptive method behaves effectively the same as the CIC method."
 Note however that this is a very siuall feature that is exaggerated by the logarithiuic color scaling ou the plot., Note however that this is a very small feature that is exaggerated by the logarithmic color scaling on the plot.
 The Voronoi tessellation aud its dual. the Delaunay tessellation. divide au N-climensional space iuto a fully volume-coverius set of cells based on the underlying particle distribution (see e.g. vandeWeveacrt(1991))).," The Voronoi tessellation and its dual, the Delaunay tessellation, divide an $N$ -dimensional space into a fully volume-covering set of cells based on the underlying particle distribution (see e.g. \citet{van94}) )."
 The resulting distribution of cells is such that the volume of the cells is inversely proportional to the density of the particle Seld at the location of cach sampled particle. leading to a natural and adaptive density estimator (theWeveaert&Schaap 2009).," The resulting distribution of cells is such that the volume of the cells is inversely proportional to the density of the particle field at the location of each sampled particle, leading to a natural and adaptive density estimator \citep[the Delaunay Tessellation Field Estimator, DTFE;][]{sch00,pel03,van09}."
. In the case of the Delaunay tessellation. cach particle is surrounded by a set of tetrahedra of which it makes up one of the vertices.," In the case of the Delaunay tessellation, each particle is surrounded by a set of tetrahedra of which it makes up one of the vertices."
 The voluue of oue tetrahedron. T. is a function of the positions of the three other vertices for a particle at the orien: The density is then eiveu by the inverse of the volume of the set of tetrahedra surrounding cach particle. V=SO; lr.," The volume of one tetrahedron, $T$, is a function of the positions of the three other vertices for a particle at the origin: The density is then given by the inverse of the volume of the set of tetrahedra surrounding each particle, $V = \sum_T V_T$ ."
" We choose to normalize the inverse volumes by 1/013 instead of (/V5 Gvhich gives a meau-zero density field) jecause the DTFE density distribution has a prominent ail at hieh densities,", We choose to normalize the inverse volumes by $1/\langle V \rangle$ instead of $\langle 1/V \rangle$ (which gives a mean-zero density field) because the DTFE density distribution has a prominent tail at high densities.
 This cau be seen in Figure 3.. in which we plot the distribution functions of the CIC u(l|8)ἐπ|]38) aud the DTFE hnu((V5/V)= u(l16).," This can be seen in Figure \ref{fig:pdf}, in which we plot the distribution functions of the CIC $\ln(1+\delta)-\langle\ln(1+\delta)\rangle$ and the DTFE $\ln(\langle V \rangle / V) = \ln(1+\delta)$ ."
 TheCIC distribution is uch more svuuuetrical hau the D'TFE. which has a shoulder at high densities.," The CIC distribution is much more symmetrical than the DTFE, which has a shoulder at high densities."
 Note that the mean of the DIFE distribution has not con subtracted so that its peak is niuch closer to zero., Note that the mean of the DTFE distribution has not been subtracted so that its peak is much closer to zero.
 We also plot a traustormed DTFE distribution function in which we weight the original distribution function * the vohuue: Por)=(WPA)αιΕν this cHectively transforius the (nassweighted) Lagraugiui DTFE distribution iuto a (volume-weielted) Eulerian distribution that closely resembles the CIC distribution., We also plot a transformed DTFE distribution function in which we weight the original distribution function by the volume: $P(x) = (V/\langle V \rangle)P(\ln(\langle V \rangle / V))$; this effectively transforms the (mass-weighted) Lagrangian DTFE distribution into a (volume-weighted) Eulerian distribution that closely resembles the CIC distribution.
 The Delaunay tessellation also allows a calculation of the divergence of Wat the location of every particle by using Ganss’s theorem. [Vedi=fo nds.," The Delaunay tessellation also allows a calculation of the divergence of $\bPsi$at the location of every particle by using Gauss's theorem, $\int_V\grad\cdot\,\bPsi\,dV = \int_S\bPsi\cdot\,{\bf n}\,dS$ ."
 Replacing the integrals with discrete suns. we have where we take Wr to be the average of the W values of the three particles making the outside face of the," Replacing the integrals with discrete sums, we have where we take $\bPsi_T$ to be the average of the $\bPsi$ values of the three particles making the outside face of the"
At micelle age the mass of white cwarfs that remain in the cluster may exceed a third. of the total mass of the cluster: consequently. if white cwarls receive a kick comparable to the velocity dispersion of the cluster (???).. the total kinetic energy of the kicks may approach of the binding energy of the cluster as shown in Fig. 1..,"At middle age the mass of white dwarfs that remain in the cluster may exceed a third of the total mass of the cluster; consequently, if white dwarfs receive a kick comparable to the velocity dispersion of the cluster \citep{2008MNRAS.383L..20D,Heyl07kickgc,Heyl07kickobs}, the total kinetic energy of the kicks may approach of the binding energy of the cluster as shown in Fig. \ref{fig:binding}. ."
" Specifically. ? found that an initial distribution of white-dwarf progenitors with ara=0.50 and a typical kick velocity of a,=Lddope could explain the observations (?).."," Specifically, \citet{Heyl07kickobs} found that an initial distribution of white-dwarf progenitors with $\sigma_\rmscr{TO}=0.5\sigma$ and a typical kick velocity of $\sigma_k=1.84\sigma_\rmscr{TO}$ could explain the observations \citep{2008MNRAS.383L..20D}."
 Essentially. voung white chwarls receive a kick of the same order as the velocity cüspersion of the cluster.," Essentially, young white dwarfs receive a kick of the same order as the velocity dispersion of the cluster."
" Furthermore. unlike neutron stars whose kicks nearly abwavs cause them to leave the cluster, most of the voung white dwarfs remain in the cluster to heat it up (only about two percent escape within a Crossing time)."," Furthermore, unlike neutron stars whose kicks nearly always cause them to leave the cluster, most of the young white dwarfs remain in the cluster to heat it up (only about two percent escape within a crossing time)."
 These results provide an estimate of the total power in white-dwarl kicks. where dNfdi is the number of stars per unit mass in the cluster (the mass function). M is the total mass of stars in the cluster. m is the mean mass of stars in the cluster. z(m) is the duration of the main sequence for a star in the cluster. (he age of the cluster). and €=(ao)zz(0.85.," These results provide an estimate of the total power in white-dwarf kicks, where $dN/dm$ is the number of stars per unit mass in the cluster (the mass function), $M$ is the total mass of stars in the cluster, $\bar
m$ is the mean mass of stars in the cluster, $\tau(m)$ is the duration of the main sequence for a star in the cluster, (the age of the cluster), and $\zeta=\left(v_\rmscr{kick}/\sigma\right)^2\approx 0.85$ ."
 7 give the initial-[inal mass relation in the numerator of the rightmost expression., \citet{1983ARA&A..21..271I} give the initial-final mass relation in the numerator of the rightmost expression.
 7T estimate the current mass function for a region near the half-light radius of NGC 6397 to be where the slope of the mass function today is given by a—0.13 and τοzOSAL. (70z12 Gye is the current age of the cluster) and dInz/dinms3.75 (?) for a cluster of the age ancl metallicity of NGC 6397., \citet{2007arXiv0708.4030R} estimate the current mass function for a region near the half-light radius of NGC 6397 to be where the slope of the mass function today is given by $\alpha=0.13$ and $m_\rmscr{TO}\approx 0.8\msun$ $\tau_0\approx 12$ Gyr is the current age of the cluster) and $d\ln \tau/d\ln m\approx -3.75$ \citep{1991ApJS...76..525S} for a cluster of the age and metallicity of NGC 6397.
 Integrating Eq. (3)), Integrating Eq. \ref{eq:massfunction}) )
 over the masses of the stars in the cluster gives the mean mass of a star in the cluster (assuming a«xland neroΠΕ tho minimum mass of a star). SO for the current observations of NGC 6397.," over the masses of the stars in the cluster gives the mean mass of a star in the cluster (assuming $\alpha<1$ and $m_\rmscr{TO} \gg m_\rmscr{min}$, the minimum mass of a star), so for the current observations of NGC 6397."
 1n a binary a fraction of the energy of the kick is used to change the orbital parameters €2).., In a binary a fraction of the energy of the kick is used to change the orbital parameters \citep{Heyl07kickbin}.
 H£ the masses of the primary anc secondary are similar due to dynamical biasing (e.g.2).. the total kick to the binary is about of the kick impartec to a single star. so given that the fraction of binaries is smal in the cluster as a whole and the correction to the kick [or binaries is also small. the energeties of changing the orbits of binaries will be ignored.," If the masses of the primary and secondary are similar due to dynamical biasing \citep[e.g.][]{1993MNRAS.262..800M}, the total kick to the binary is about of the kick imparted to a single star, so given that the fraction of binaries is small in the cluster as a whole and the correction to the kick for binaries is also small, the energetics of changing the orbits of binaries will be ignored."
 On the other hand. the binaries provide an importan energy source for the cluster (in fact the only energy. source if one excludes the kicks).," On the other hand, the binaries provide an important energy source for the cluster (in fact the only energy source if one excludes the kicks)."
 The interaction of a binary with a single star can result in an exchange or the dissolution of the binary. but generally it results in an increase in the kinetic energv of final single star (like a kick) at the expense of the increased bincing energy of the binary.," The interaction of a binary with a single star can result in an exchange or the dissolution of the binary, but generally it results in an increase in the kinetic energy of final single star (like a kick) at the expense of the increased binding energy of the binary."
 The velocity increment of the singleton is generally random (also like a kick). so these (wo energy sources are similar ancl possibly comparably important to the evolution of the cluster.," The velocity increment of the singleton is generally random (also like a kick), so these two energy sources are similar and possibly comparably important to the evolution of the cluster."
" ? gives an estimate for the power from binaries of per relaxation time. where Ny,is the numberof binaries."," \citet{Spit87} gives an estimate for the power from binaries of per relaxation time, where $N_b$is the numberof binaries."
 Combining these results vields, Combining these results yields
TllowhichwasusedinthePaperlanalysis. andiwoC SOs: J11002-6210«0n4./19 L145LI,"which was used in the Paper I analysis, and two CSOs: J1400+6210 and J1944+5448."
ST heinlegraliontimesontlie andapprorimalelyfiveminidesonthelenssysten," The integration times on the various sources were typically one minute on the phase calibrator and the CSOs, two minutes on 1633+741, and approximately five minutes on the lens system."
tN either CSOwasobsercved forthe ει Πο fseason2: lSwasobsercved from 998 February ol908.JuneOlehileJ1100--6210wasobserved from ΟΟΣΑ 21ο., Neither CSO was observed for the full length of season 2; J1944+5448 was observed from 1998 February 13 to 1998 June 01 while J1400+6210 was observed from 1998 May 12 to 1998 October 19.
 005 ῶσΙol Aand," The observations for season 3 were similar to those of season 2, but with a different set of secondary flux calibrators."
191-2 EESandaddedsiicC SOslollielwousediullieseason20bservalions, We dropped 1633+741 and J1944+5448 and added six CSOs to the two used in the season 2 observations.
 DE heincreaseiuthemuiunberof goods , The increase in the number of good secondary flux calibrators provided a better estimate of the errors in the absolute flux density calibration.
J10354-5628. 11182-2592L. 71211440Ls. 7151541051. 71823471938. and J19415-1022.," The additional CSOs used were: J1035+5628, J1148+5924, J1244+4048, J1545+4751, J1823+7938, and J1945+7055."
 Beceuselliereweremoresour: secand," Because there were more sources observed per epoch than in the first two seasons, the average integration time per source dropped slightly."
B1608+ 606wasobserved fora fewinimes., The phase calibrator and CSOs typically were observed for 45-60 sec and B1608+656 was observed for a few minutes.
 The data were calibrated using eustomized procedures that acted as an interface to tasks in the NRAO data reduction package. AIPS.," The data were calibrated using customized procedures that acted as an interface to tasks in the NRAO data reduction package, AIPS."
 For cousistency. the data from all three observing seasons were calibrated in the same way.," For consistency, the data from all three observing seasons were calibrated in the same way."
 Therefore. the seasou IL data were recalibrated.," Therefore, the season 1 data were recalibrated."
 The overall flux deusity calibration was tied to 3313., The overall flux density calibration was tied to 343.
 As discussed in FOL. 33123 is not au ideal calibrator due to some low surlace-brightuess emission surrouudiug the central component.," As discussed in FT01, 343 is not an ideal calibrator due to some low surface-brightness emission surrounding the central component."
 However. it was ;»ossible to correct for the changes in the total measured flux density of 30-3313 as the VLA configuration changecl (see 'elsec prralourves)).," However, it was possible to correct for the changes in the total measured flux density of 343 as the VLA configuration changed (see \\ref{sec_finalcurves}) )."
 The calibration procedure for each epoch of observation began with careful data editing., The calibration procedure for each epoch of observation began with careful data editing.
 Bad inteerations on the calibrators. indicated by cliscrepant amplitudes or phases. were deleted.," Bad integrations on the calibrators, indicated by discrepant amplitudes or phases, were deleted."
 Any autenua which exhibited a large uumber of bad integratious during an epoch was [flagged Lor he entire epoch., Any antenna which exhibited a large number of bad integrations during an epoch was flagged for the entire epoch.
 The autenua system temperatures were also used as a diagnostic to discover owl integrations. which were then flagged.," The antenna system temperatures were also used as a diagnostic to discover bad integrations, which were then flagged."
 Oue anteunua iu particular (anteuua 3) had system eniperatures that were. on average. a [actor of three higher than those of the other auteunas.," One antenna in particular (antenna 3) had system temperatures that were, on average, a factor of three higher than those of the other antennas."
 Because this behavior was seen during all three seasons of observations. we flagged. auteuua 3 jefore doiug any calibration.," Because this behavior was seen during all three seasons of observations, we flagged antenna 3 before doing any calibration."
 Alter the bad data had. been flagged. the antenna gain phases aud amplitudes were determined through self-calibration on the bright. compact calibrator sources.," After the bad data had been flagged, the antenna gain phases and amplitudes were determined through self-calibration on the bright, compact calibrator sources."
 For all of the CSOs and the pliase calibrator. we used a poiut source model to do the self calibration.," For all of the CSOs and the phase calibrator, we used a point source model to do the self calibration."
makes the orbital angular velocity at the mass-shedding limit increase for binary systems with massive neutron stars.,makes the orbital angular velocity at the mass-shedding limit increase for binary systems with massive neutron stars.
" Because of this effect, the orbital angular velocity at the closest separation is about 0.038 for Mo=2.4Mo whereas it is about 0.054 for Mo=3.0Mo."," Because of this effect, the orbital angular velocity at the closest separation is about 0.038 for $M_0=2.4 M_{\odot}$ whereas it is about 0.054 for $M_0=3.0 M_{\odot}$."
 We can understand this behavior by using Equation (61))., We can understand this behavior by using Equation \ref{eq:omega_tid}) ).
" By substituting each total mass and circumferential radius, we obtain the ratio of the orbital angular velocity as The actual ratio of the orbital angular velocity at the closest separation we obtained is This value agrees again with the estimated ratio given in Equation (64))."," By substituting each total mass and circumferential radius, we obtain the ratio of the orbital angular velocity as The actual ratio of the orbital angular velocity at the closest separation we obtained is This value agrees again with the estimated ratio given in Equation \ref{eq:omega_ratio}) )."
" We construct quasi-equilibrium sequences for three cases of total mass, three mass ratios for each total mass, and 18 EOSs."," We construct quasi-equilibrium sequences for three cases of total mass, three mass ratios for each total mass, and 18 EOSs."
" For all the sequences, we do not find the turning point of the binding energy and total angular momentum, which represents the innermost stable circular orbit of the binary system."," For all the sequences, we do not find the turning point of the binding energy and total angular momentum, which represents the innermost stable circular orbit of the binary system."
" Instead, the sequences terminate at the mass-shedding limit of a less massive star. ("," Instead, the sequences terminate at the mass-shedding limit of a less massive star. ("
"For equal-mass binaries, two neutron stars reach the mass-shedding limit at the same time.)","For equal-mass binaries, two neutron stars reach the mass-shedding limit at the same time.)"
" As explained before, we stop constructing the sequences at x~0.6 because our spectral method code cannot handle a cusp-like figure which appears at the mass-shedding limit."," As explained before, we stop constructing the sequences at $\chi \sim 0.6$ because our spectral method code cannot handle a cusp-like figure which appears at the mass-shedding limit."
 This implies that the closest separation with the largest value of MoQ we can calculate is not the actual endpoint of the sequence., This implies that the closest separation with the largest value of $M_0 \Omega$ we can calculate is not the actual endpoint of the sequence.
" 'To determine the orbital angular velocity at the mass-shedding limit, we extrapolate a curve of the mass-shedding indicator x as a function of MoQ."," To determine the orbital angular velocity at the mass-shedding limit, we extrapolate a curve of the mass-shedding indicator $\chi$ as a function of $M_0 \Omega$."
 'The procedure isas follows: we first make a fitting polynomial equation of x as a functionof ΜοΏ for sequences., The procedure isas follows: we first make a fitting polynomial equation of $\chi$ as a functionof $M_0 \Omega$ for sequences.
" Then, we extrapolate the fitting polynomial equationto x=O and determine the value of Mo) at x=0."," Then, we extrapolate the fitting polynomial equationto $\chi=0$ and determine the value of $M_0 \Omega$ at $\chi=0$."
 The extrapolated value of Mo) at x=0 is defined as MoQus.," The extrapolated value of $M_0 \Omega$ at $\chi=0$ is defined as $M_0
\Omega_{\rm ms}$."
 Figure 19 shows such extrapolated curves for the piecewise polytropic EOS with Γι=3.0 and logyP1=13.45 (PwPoly30-1345).," Figure \ref{fig19} shows such extrapolated curves for the piecewise polytropic EOS with $\Gamma_1=3.0$ and $\log_{10}
P_1=13.45$ (PwPoly30-1345)."
" The thick (black) solid, thick (red) dashed, and thick (blue) dot-dashed curves denote the computed sequences for equal-mass binary neutron stars with masses of ΜΑΡΑ=MNR, 1.20Mo, 1.35Mo, and 1.50Mo, respectively."," The thick (black) solid, thick (red) dashed, and thick (blue) dot-dashed curves denote the computed sequences for equal-mass binary neutron stars with masses of $M_{\rm
ADM}^{\rm NS1}=M_{\rm ADM}^{\rm NS2}=1.20 M_{\odot}$ , $1.35
M_{\odot}$ , and $1.50 M_{\odot}$ , respectively."
" The thin (black) dotted, thin (red) dashed, and thin (blue) dot-dashed"," The thin (black) dotted, thin (red) dashed, and thin (blue) dot-dashed"
surface density distribution has a central maxima.,surface density distribution has a central maximum.
 The nolecular gas disk is more extended to the northeast thaw o the southwest., The molecular gas disk is more extended to the northeast than to the southwest.
 This morphology is in close agreement with our observations., This morphology is in close agreement with our observations.
 However. both sides of the extended nodel molecular eas disk ave slightly beut to the south. a vchavior which is not clearly observed.," However, both sides of the extended model molecular gas disk are slightly bent to the south, a behavior which is not clearly observed."
 In agreement with observations. no molecular gas is found in the extraplanuar soutliwestern eas tail.," In agreement with observations, no molecular gas is found in the extraplanar southwestern gas tail."
 NGC L330 was observed at [85 GIIz during 6 bh £0 iin ou December d aud 3. 2009 with the Verv Large Array (VLA) of the National Badio. Astrouauw Observatory in the D array configuration.," NGC 4330 was observed at 4.85 GHz during 6 h 40 min on December 1 and 3, 2009 with the Very Large Array (VLA) of the National Radio Astronomy Observatory in the D array configuration."
 The baud passes were 2«450 MIIz., The band passes were $2\times 50$ MHz.
 We used 3€286 as the fix calibrator and ISL)116 as the phase calibrator. the latter of which was observed every 10 nin.," We used 3C286 as the flux calibrator and 1254+116 as the phase calibrator, the latter of which was observed every 40 min."
 Maps were made for both wavelengths using the AIPS task IMAGR with ROBUST=3., Maps were made for both wavelengths using the AIPS task IMAGR with ROBUST=3.
" The final cleaned maps were convolved to a lea size of 15”«I8"".", The final cleaned maps were convolved to a beam size of $18'' \times 18''$.
 The rus levels of the polarized enüssiou is 13 pdx., The rms levels of the polarized emission is 13 $\mu$ Jy.
 We obtain apparent D vectors bv rotating the observed E vector by 907. uncorrected for Faraday rotation.," We obtain apparent B vectors by rotating the observed E vector by $90^{\circ}$, uncorrected for Faraday rotation."
 The observed radio contimmiun emission ou the cobuuu density distribution is shown in Fig. 7.., The observed radio continuum emission on the column density distribution is shown in Fig. \ref{fig:n4330_cont_hi}. .
 The upturn observed in Ha /UV (Fie., The upturn observed in $\alpha$ /UV (Fig.
 11of Abramson et al., 14 of Abramson et al.
 2011) and CO is clearly visible iu the total power eniissiou., 2011) and CO is clearly visible in the total power emission.
 Moreover. the total power emission shows an asvinetry with respec to the major axis.," Moreover, the total power emission shows an asymmetry with respect to the major axis."
 The enüssiou is more extended on the southeastern dowuwind side than ou the northwestern windward side., The emission is more extended on the southeastern downwind side than on the northwestern windward side.
 The extraplanar tail is not detected a 6 ci., The extraplanar tail is not detected at 6 cm.
 However. the total cunission bends strougly to the south at the western border of the galactic eas disk.," However, the total emission bends strongly to the south at the western border of the galactic gas disk."
 This behavior is not visible at auv other wavelength except a 20 cm (Fig., This behavior is not visible at any other wavelength except at $20$ cm (Fig.
 20 of Abramson et al., 20 of Abramson et al.
 2011)., 2011).
 We can ouly speculate that the cosmic rav gas. having a low column density. is stripped more effideutlv than the neutral gas.," We can only speculate that the cosmic ray gas, having a low column density, is stripped more efficiently than the neutral gas."
o This effect has already been suggested by Vollmer et al. (, This effect has already been suggested by Vollmer et al. (
2009) for NGC L138 and Crowl et al. (,2009) for NGC 4438 and Crowl et al. (
2005) in NGC £102.,2005) in NGC 4402.
 ILowewver. oue would expect a compression of the comic rav gas. Which is in contradiction with the abseuce of polarization in this region.," However, one would expect a compression of the comic ray gas, which is in contradiction with the absence of polarization in this region."
 Alternatively. there might be chhanced diffusion of comic rav clectrous into the tail reeion due to. e.g.àY an outflow.," Alternatively, there might be enhanced diffusion of comic ray electrons into the tail region due to, e.g., an outflow."
 The observed polarized radio contiuunni enission together with the magnetic field vectors ou the column density distribution are shown in the upper panel of Fig. 5.., The observed polarized radio continuum emission together with the magnetic field vectors on the column density distribution are shown in the upper panel of Fig. \ref{fig:n4330_hi_pi}.
 The poluized radio continu Cluission is mainly found iu the immer part of the gas disk., The polarized radio continuum emission is mainly found in the inner part of the gas disk.
 Its total extent alous the galaxy major axis is ~1'., Its total extent along the galaxy's major axis is $\sim 1'$.
 The emission is alinost sviuuetric with respect to the major and minor axis., The emission is almost symmetric with respect to the major and minor axis.
 Two maxima are observed which follow the spiral inus detected in CO (Fig. 6))., Two maxima are observed which follow the spiral arms detected in CO (Fig. \ref{fig:n4330_hi_co}) ).
 We do not observe an asvuuuetric ridge of polarized radio contiuuuni enission as we did iu all other rain pressure affected Vireo spiral ealaxies (Vollmer et al., We do not observe an asymmetric ridge of polarized radio continuum emission as we did in all other ram pressure affected Virgo spiral galaxies (Vollmer et al.
 2007)., 2007).
 Ou the leading side of the interaction we observe a faint upturn of the polarized radio continuum enission (12 23 20 |11 22 20) which is inside the Πα /total power radio continui upturn., On the leading side of the interaction we observe a faint upturn of the polarized radio continuum emission (12 23 20 +11 22 20) which is inside the $\alpha$ /total power radio continuum upturn.
" The maeuetic field vectors are not xwallel to the ealactic disk as one nieht expect it for an edee-on galaxy (see. ο,ὃς,o Iaause 2009)."," The magnetic field vectors are not parallel to the galactic disk as one might expect it for an edge-on galaxy (see, e.g., Krause 2009)."
 The iiagnoetic field of the ealaxvs western side has a characteristic N-structure. which is observed in edge-on spiral ealaxics with a high star formation activity (oe. NGC 253. Ieesen et al.," The magnetic field of the galaxy's western side has a characteristic X-structure, which is observed in edge-on spiral galaxies with a high star formation activity (e.g., NGC 253, Heesen et al."
 2009)., 2009).
 The fold iu the rorthern aud castern part of the X is compressed by ram xessure., The field in the northern and eastern part of the X is compressed by ram pressure.
 Ou the other haud. the maeuetic field in the cast of the ealaxy center is tilted clockwise by 30° with respect to the disk plane.," On the other hand, the magnetic field in the east of the galaxy center is tilted clockwise by $\sim 30^{\circ}$ with respect to the disk plane."
 There can be two reasous for lis tilt: (3) bending of the ealactic regular maguetic field or (u) enhanced Faraday rotation ou the eastern side of he galactic disk., There can be two reasons for this tilt: (i) bending of the galactic regular magnetic field or (ii) enhanced Faraday rotation on the eastern side of the galactic disk.
 A rotation neasure of. 4.190 2 is required. to rotate the E vectors by 30° which seeuis yossible (see below)., A rotation measure of $-130$ $^{-2}$ is required to rotate the E vectors by $30^{\circ}$ which seems possible (see below).
 Otnuanowska-Alazur Vollmer (2003) studiedthe evolution of the large-scale maguetic ficld during a rai, Otmianowska-Mazur Vollmer (2003) studiedthe evolution of the large-scale magnetic field during a ram
 Otnuanowska-Alazur Vollmer (2003) studiedthe evolution of the large-scale maguetic ficld during a rai., Otmianowska-Mazur Vollmer (2003) studiedthe evolution of the large-scale magnetic field during a ram
There has been significant recent interest in the interaction οποσα radio sources and clusters.,There has been significant recent interest in the interaction between radio sources and clusters.
 This has been driven o» observations with both the and satellites which have demonstrated clearly that the presence of a powerful FR-LE radio source very. significantly: allects he ICM/IGM in the vicinity of the source., This has been driven by observations with both the and satellites which have demonstrated clearly that the presence of a powerful FR-II radio source very significantly affects the ICM/IGM in the vicinity of the source.
 For example. or the best. studied: cases of €vgnus A (Corilli.Perley&IHLuris1994:Smithetal.2002). and 3€842 inPerseus (Fabianetal.2000:: Fabianetal. 2002)). cavities in the X-ray emitting gas coincident with the radio cocoon are clearly observed. and for Cvegnus A the elfects of a strong row shock can be clearly seen.," For example, for the best studied cases of Cygnus A \citep*{Carilli et al,Smith et al} and 3C84 inPerseus \citealt{Fabian et al2000}; \citealt{Fabian et al2002}) ), cavities in the X-ray emitting gas coincident with the radio cocoon are clearly observed and for Cygnus A the effects of a strong bow shock can be clearly seen."
 Recent reviews of the N-ray observational data on racdio-source/cluster interactions are eiven in AleNamara(2002) ancl MeNamaractal.(2000).," Recent reviews of the X-ray observational data on radio-source/cluster interactions are given in \citet{McNamara2002}
 and \citet{McNamara et al2000}."
. This interaction between the radio source and the ICM has lech a number of authors to consider whether radio sources could solve the so-called 7cooling-IHow problem” (e.g. Binney&DBegelman 2002.. hereafter RIB). in which the cool eas expected to accumulate at the cluster centre as a result of cooling is not detected.," This interaction between the radio source and the ICM has led a number of authors to consider whether radio sources could solve the so-called “cooling-flow problem” (e.g. \citealt*{BinneyTabor, McNamara et al2000, Reynolds et al,
Churazov et al, Quilis et al, Bohringer et al, RuszkowskiBegelman,
BrighentiMathews, RHB}, hereafter RHB), in which the cool gas expected to accumulate at the cluster centre as a result of cooling is not detected."
 A number of authors have discussed. the heating of the LOCAL by radio sources in the context. of the overall energy budget for the cluster (e.g. Binney&Tabor1995:Iwaiser&Alexancler 1999: RIB: Alexander2002 and references. therein).," A number of authors have discussed the heating of the ICM by radio sources in the context of the overall energy budget for the cluster (e.g. \citealt{BinneyTabor, KaiserAlexander1999}; RHB; \citealt{Alexander} and references therein)."
 Churazovetal.(2002) discuss/— the energv balance between the cooling How and the AGN on the basis that there is some feedback between the cooling How (which results in matter accreting onto à supermassive black hole) and the resulting mechanical power of the ACN.," \citet{Churazov et
al2002} discuss the energy balance between the cooling flow and the AGN on the basis that there is some feedback between the cooling flow (which results in matter accreting onto a supermassive black hole) and the resulting mechanical power of the AGN."
 This could. also be responsible for the intermitteney. of the radio source as inferred in some observations (MeNamaraetal.2000:FabianOwen&Eilek 1995).," This could also be responsible for the intermittency of the radio source as inferred in some observations \citep{McNamara et al2000_1, Fabian et al2000,
OwenEilek}."
 The energy input from powerful FR-LE radio sources is certainly sullicient to have a significant elfect on the cluster. however the lifetimes of FR-LL radio sources are of. order 100 Myr (e.g. Alexander&Leahy 1987)). they are therefore transient events in the lifetime of a cooling Low (Fabian 1904).," The energy input from powerful FR-II radio sources is certainly sufficient to have a significant effect on the cluster, however the lifetimes of FR-II radio sources are of order 100 Myr (e.g. \citealt{AlexanderLeahy}) ), they are therefore transient events in the lifetime of a cooling flow \citep{Fabian}."
. Xn important question is therefore whether a radio source can have a long-term ellect on the cluster: for this reason it is necessary to consider the evolution of the remnants of dead: radio sources (ie. after the jets cease energy injection into the lobes)., An important question is therefore whether a radio source can have a long-term effect on the cluster; for this reason it is necessary to consider the evolution of the remnants of dead radio sources (i.e. after the jets cease energy injection into the lobes).
 During these latter stages of evolution the dvnamies of the remnants of the radio source will be dominated: by buovaney forces (Cull&Northover 1973)., During these latter stages of evolution the dynamics of the remnants of the radio source will be dominated by buoyancy forces \citep{GullNorthover}. .
. A number of studies have considered. the evolution of buovant plasma bubbles within a cluster., A number of studies have considered the evolution of buoyant plasma bubbles within a cluster.
 For example, For example
the region between 0.065≤z«Q0. 200g140€«i210° and —3°<66? SF(Dengetal]uf. hich is a small fraction of the ootprint.,"the region between $0.065 \leq z \leq 0.09$ , $140^\circ \leq \alpha \leq 210^\circ$ and $-3^\circ \leq \delta \leq 6^\circ$ \citep{2006ChJAA...6...35D} which is a small fraction of the SDSS footprint."
" The observed quadrant to quadrant variations of do not seem to depart much from the GQED, so the fypresence(N) of a large supercluster probably does not affect the observed form of {ν(Ν)."," The observed quadrant to quadrant variations of $f_V(N)$ do not seem to depart much from the GQED, so the presence of a large supercluster probably does not affect the observed form of $f_V(N)$."
 This result is in agreement with an earlier analysis of the 2MASS catalog by (2005) where it was found that the inclusion of the Shapley supercluster did not make a large difference on the agreement with the GQED., This result is in agreement with an earlier analysis of the 2MASS catalog by \cite{2005ApJ...626..795S} where it was found that the inclusion of the Shapley supercluster did not make a large difference on the agreement with the GQED.
 Therefore these large superclusters may be natural consequences of gravitational interactions among galaxies., Therefore these large superclusters may be natural consequences of gravitational interactions among galaxies.
" Since the “great wall” probably does not make a large contribution to the counts-in-cells statistics, the difference in N and b between the high and low redshift ranges could be due to evolution or selection."," Since the “great wall” probably does not make a large contribution to the counts-in-cells statistics, the difference in $\overline{N}$ and $b$ between the high and low redshift ranges could be due to evolution or selection."
 Further pursuit of these possibilities requires more detailed models., Further pursuit of these possibilities requires more detailed models.
 Here we note that the difference is consistent across quadrants which rules out cosmic variance as a dominant cause., Here we note that the difference is consistent across quadrants which rules out cosmic variance as a dominant cause.
" We also note that the difference in lookback time between the middle of the low and high redshift ranges is about 0.7 Gyr, which is close to the amount of time a merging pair ofgalaxies takes to"," We also note that the difference in lookback time between the middle of the low and high redshift ranges is about 0.7 Gyr, which is close to the amount of time a merging pair ofgalaxies takes to"
There has been renewed interest in //QSOs since the detection of parsec-scale X-ray jets aud variable 5-ray. emission (?)..,There has been renewed interest in $\mu$ QSOs since the detection of parsec-scale X-ray jets \citep{2007RMxAC..27..122C} and variable $\gamma$ -ray emission \citep{2009Sci...326.1512F}.
 The nature of the hieh-enerey emission for two ruicro-cquasars. aand1+61303.. has been much debated. e.g. the emission could truly be generated in a pQSO jet (?).. or possibly it could be generated by the interaction of a young pulsar wind with the wind of the coripanion (???).. w," The nature of the high-energy emission for two micro-quasars, and, has been much debated, e.g., the emission could truly be generated in a $\mu$ QSO jet \citep{2008MNRAS.383..467K}, or possibly it could be generated by the interaction of a young pulsar wind with the wind of the companion \citep{2004A&A...413.1019L,2006smqw.confE..52D,2006A&A...456..801D}. ."
iwas is entified as an HMXB by ? based on the positional coincidence of an X-ray. source with an O7V star (V— 11.5). projected near the Calactic bulge (/21628816. 6=--2502).," was first identified as an HMXB by \citet{1997A&A...323..853M} based on the positional coincidence of an X-ray source with an O7V star $V=11.5$ ), projected near the Galactic bulge $l=16\fdg8816$, $b=-1\fdg2892$ )."
 Using optica auc diinfra-red spectroscopy. ? found the comparion star to be type O6.52V(L). variable in the IR but uot in the optical.," Using optical and infra-red spectroscopy, \citet{2001A&A...376..476C} found the companion star to be type O6.5V(f), variable in the IR but not in the optical."
" ? ineasured line radial velociies and fouud binary period 2,4,=Lidd ancl stbstautial eccentricity € 0.[.", \cite{2001ApJ...558L..43M} measured line radial velocities and found binary period $P_{\rm orb}=4.1$ d and substantial eccentricity $e=0.4$ .
" UsireOm detailed. time-resolved. spectroscopy. aud atiospleric mocleling of the companion. ? refined the binary parameer (Py,=3.906 d.e =t)0) aud concluded that the system must harbor a high-mass compact object. probably a BH. for aiiufe red distauce of 2.5x0.1 kkpe."," Using detailed time-resolved spectroscopy and atmospheric modeling of the companion, \citet{2005MNRAS.364..899C} refined the binary parameters $P_{\rm orb}=3.906$ d, $e=0.35$ ) and concluded that the system must harbor a high-mass compact object, probably a BH, for an inferred distance of $2.5\pm 0.1$ kpc."
 The couclusion was. however. late| disputed by 2?) who argue that tlie NS option still canuot be dinissed.," The conclusion was, however, later disputed by \citet{2006A&A...456..801D} who argued that the NS option still cannot be dismissed."
 Usiug high-precision. long time base-line photometry from theMOST satelite and e&eround-based spectroscopy. ? further refined the orbital characteristics. preferring a sliguly lower eccentricity e0.2[0.05 ard component masses 268. (or the O-star and 1.744. for he compact object.," Using high-precision, long time base-line photometry from the satellite and ground-based spectroscopy, \citet{2011MNRAS.411.1293S} further refined the orbital characteristics, preferring a slightly lower eccentricity $e=0.24\pm0.08$ and component masses $M_\odot$ for the O-star and $M_\odot$ for the compact object."
 Thus. the iattwe of the compact object in LS 5039 remains unknown.," Thus, the nature of the compact object in LS 5039 remains unknown."
 Au unresolved. non-thermal variable radio source was [ist detected by 2..," An unresolved, non-thermal, variable radio source was fist detected by \citet{1998A&A...338L..71M}."
 Using the high angular resolution of VLBA. the source was resolved. and ‘jets’ observed by ?:: the souCO Was herelore classified as a ΟΡΟ.," Using the high angular resolution of VLBA, the source was resolved, and `jets' observed by \citet{2000Sci...288.2340P}; the source was therefore classified as a $\mu$ QSO."
" ?./— measured the system. proper motion. (12 using adio aud optical astrometry) aud. based ou is 1ο tangential velocity. called the system rulaw""uv. Le. with enough velocity to leave the Galactic disk."," \citet{2002A&A...384..954R} measured the system proper motion $\approx$ $^{-1}$, using radio and optical astrometry) and, based on its high tangential velocity, called the system `runaway', i.e., with enough velocity to leave the Galactic disk."
 The proper motion vector can be traced back o the supernova remnant. (SNR) CU6.5—1.1., The proper motion vector can be traced back to the supernova remnant (SNR) $-$ 1.1.
 Subsequent radio observations by ο showed that he resolved emission of LS 5039 varies in intensity. aud that the position augle of the elongated eatures chiauges.," Subsequent radio observations by \citet{2008A&A...481...17R} showed that the resolved emission of LS 5039 varies in intensity, and that the position angle of the elongated features changes."
 LS 5039 has been extensively observed in N-rays. mainly to study its variability aud spectrum.," LS 5039 has been extensively observed in X-rays, mainly to study its variability and spectrum."
 The X-ray. emission is modulated at the orbital period., The X-ray emission is modulated at the orbital period.
 The light-curve produced [rom X-ray data taken iu 1999-2007 was [οι to be remarkably stable (?).. although some aperiodic variability has been reported earlier with (??)..," The light-curve produced from X-ray data taken in 1999-2007 was found to be remarkably stable \citep{2009ApJ...697L...1K}, although some aperiodic variability has been reported earlier with \citep{2003A&A...405..285R,1999A&A...347..518R}."
 Both aand hhave been detected at higher euergies., Both and have been detected at higher energies.
 LS 5039 has been detected with HESS (7?).. (?) audFeri (?).. with a spectrum similar to 7?-ray. pulsars.," LS 5039 has been detected with HESS \citep{2006A&A...460..743A}, \citep{2009A&A...494L..37H} and \citep{2009ApJ...706L..56A}, with a spectrum similar to $\gamma$ -ray pulsars."
 The higli-energylight curves show moclulatious at the orbital period. peaking at superior coujuuction (see? for a review).," The high-energylight curves show modulations at the orbital period, peaking at superior conjunction (see\citealt{2009IJMPD..18..347B} for a review)."
 In this paper we report the results of a kks imagine observation of, In this paper we report the results of a ks imaging observation of
We find that many bulge dominated progenitors experienced minor mergers in between (wo major merger events.,We find that many bulge dominated progenitors experienced minor mergers in between two major merger events.
 The morphology of these objects is somewhat ambieuous and may depend on several parameters like (he impact parameter of the infalling satellites., The morphology of these objects is somewhat ambiguous and may depend on several parameters like the impact parameter of the infalling satellites.
 ILowever. 1 15 clear that. these galaxies will rather look like lenticular galaxies (han classical spirals.," However, it is clear that these galaxies will rather look like lenticular galaxies than classical spirals."
 If lenticulars make up a large fraction of progenitors of present day ellipticals with —2]. numerical simulations of the formation of giant elliptical galaxies should start. with progenitors which were disturbed by minor mergers and should not use relaxed spiral galaxies (e.g.Burkert&Naab2003).," If lenticulars make up a large fraction of progenitors of present day ellipticals with $M_B \lesssim
-21 $ , numerical simulations of the formation of giant elliptical galaxies should start with progenitors which were disturbed by minor mergers and should not use relaxed spiral galaxies \citep[e.g.][]{bn03}."
. Independent of the fate of satellite stars in minor mergers. more than 50% of present day ellipticals brighter than Mg~—158 in clusters μας a last major merger which was nol a merger between (wo classical spiral galaxies.," Independent of the fate of satellite stars in minor mergers, more than $50 \%$ of present day ellipticals brighter than $ M_B \sim -18$ in clusters had a last major merger which was not a merger between two classical spiral galaxies."
 Despite all the successes of simulations of merging spirals in explaining elliptical galaxies our results indicate (hat only low mass elliplicals are represented by such simulations., Despite all the successes of simulations of merging spirals in explaining elliptical galaxies our results indicate that only low mass ellipticals are represented by such simulations.
 More simulations of sp-e 2000) ancl e-e mergers are required to address the question of the formation of ellipticals via merging adequately., More simulations of sp-e \citep[e.g.][]{nb00} and e-e mergers are required to address the question of the formation of ellipticals via merging adequately.
of accreted matter depending on IGM parameters for a Milky-Way-like galaxy is calculated semianalytically.,of accreted matter depending on IGM parameters for a Milky-Way-like galaxy is calculated semianalytically.
 In $3... it is explained that other factors of the non-conservative potential. for example approaches to individual stars. produce a much lower effect that is totally negligible.," In \ref{.other}, it is explained that other factors of the non-conservative potential, for example approaches to individual stars, produce a much lower effect that is totally negligible."
 In. $4.. statisties with observational data are performed in order to see whether barred galaxies have larger masses.," In \ref{.observations}, statistics with observational data are performed in order to see whether barred galaxies have larger masses."
 We analyse the variations of the energy in particles that follow orbits in certain kinds of non-conservative potentials: those in which the gravitational force varies with time., We analyse the variations of the energy in particles that follow orbits in certain kinds of non-conservative potentials: those in which the gravitational force varies with time.
 This happens. for instance. in a barred galaxy. because the rotation of a non-axisymmetric structure produces variations in the potential due to the bar with respect to an inertial frame.," This happens, for instance, in a barred galaxy, because the rotation of a non-axisymmetric structure produces variations in the potential due to the bar with respect to an inertial frame."
 However. the rotating dise has a stationary potential since the axial distribution of mass does not change.," However, the rotating disc has a stationary potential since the axial distribution of mass does not change."
 If the bar rotates with angular velocity ω. the variation in the energy of a particle along its path (orbit) ts: in orbitcylindrical coordinates. where F is the gravitational force produced by the bar.," If the bar rotates with angular velocity $\omega$, the variation in the energy of a particle along its path (orbit) is: in cylindrical coordinates, where $\vec{F}$ is the gravitational force produced by the bar."
 If we change to the variable wt (that is. we adopt the frame that is moving with the bar): If the orbits of particles begin at infinite distance and finish at infinite distance: The Jacobi integral Is conserved.," If we change to the variable $\phi '=\phi -\omega t$ (that is, we adopt the frame that is moving with the bar): If the orbits of particles begin at infinite distance and finish at infinite distance: The Jacobi integral is conserved."
 Let us consider a monodimensional bar., Let us consider a monodimensional bar.
" This is an approximate deseription. of real 3D-bars because the major axis Is considerably larger than the other axis—otherwise. they would not be bars—as can be observed. for instance. in the galaxies NGC 1300. NGC 7479. NGC 4123. NGC 1433. NGC 4999, ete. ("," This is an approximate description of real 3D-bars because the major axis is considerably larger than the other axis—otherwise, they would not be bars—as can be observed, for instance, in the galaxies NGC 1300, NGC 7479, NGC 4123, NGC 1433, NGC 4999, etc. ("
Sandage Bedke 1994) or in our own Galaxy (L6ppez-Corredoira et al.,Sandage Bedke 1994) or in our own Galaxy (Lóppez-Corredoira et al.
 2001. 2007).," 2001, 2007)."
 The mass density distribution will be 4(/) as a function of the distance / to its centre., The mass density distribution will be $\lambda (l)$ as a function of the distance $l$ to its centre.
 The azimuthal component of the gravitational force produced by this bar of radius Ro on a particle of mass 7i will be: If we assume ο)=constantοἱ. the integral can be solved: Therefore. if we want to calculate the gain/loss of energy of the particle. we must just know its orbit (1) and use expressions (4)) and (6)) to calculate AE.," The azimuthal component of the gravitational force produced by this bar of radius $R_0$ on a particle of mass $m$ will be: If we assume $\lambda (l)={\rm constant}=\lambda $, the integral can be solved: Therefore, if we want to calculate the gain/loss of energy of the particle, we must just know its orbit $\vec{r}(t)$ and use expressions \ref{deltaE}) ) and \ref{Fphi}) ) to calculate $\Delta E$."
 For our problem. we use semianalytical calculations.," For our problem, we use semianalytical calculations."
 The solution ofeqs. (4)). (6))," The solution of eqs. \ref{deltaE}) ), \ref{Fphi}) )"
 is calculated numerically. and the orbit of each particle itself ts 1ot solved numerically as an outcome of a numerical simulation in which all particles interact with each other but as the umerical integration of its motion equation.," is calculated numerically, and the orbit of each particle itself is not solved numerically as an outcome of a numerical simulation in which all particles interact with each other but as the numerical integration of its motion equation."
 Indeed. we cai consider the gravitational potential of the infalling particles as due only to the components of the galaxies and neglect the 1teraction due to other IGM particles.," Indeed, we can consider the gravitational potential of the infalling particles as due only to the components of the galaxies and neglect the interaction due to other IGM particles."
 Analytically. we cannot caleulate the orbit of a particle in a galactic potential: the integrals are too complex to find the solution.," Analytically, we cannot calculate the orbit of a particle in a galactic potential; the integrals are too complex to find the solution."
" But we can calculate r(f) simply by numerical calculation of the differential equation F=4,4. the total acceleration produced by the total potential of the galaxy."," But we can calculate $\vec{r}(t)$ simply by numerical calculation of the differential equation $\ddot{\vec{r}}=\vec{a}_{galaxy}$, the total acceleration produced by the total potential of the galaxy."
 It is then straightforward to obtain r'(7) (the position in the frame that is moving with the bar) from r(r) by using &=—ct., It is then straightforward to obtain $\vec{r}'(t)$ (the position in the frame that is moving with the bar) from $\vec{r}(t)$ by using $\phi '=\phi-\omega t$.
 In this case. of course. for the calculation of the orbit. all the potentials are to be taken into account not only the potential of the bar.," In this case, of course, for the calculation of the orbit, all the potentials are to be taken into account not only the potential of the bar."
 We can approximate this potential as the sum of several components: We give analytical expressions for these acceleration terms as integrals., We can approximate this potential as the sum of several components: We give analytical expressions for these acceleration terms as integrals.
 All these integrals will be performed numerically with the Simpson algorithm. and the solution to the differential equation F=αμ Will be carried out with a variable step depending on the acceleration: The Jacobi integral H ts conserved for each orbit within variations of ~0.1%.," All these integrals will be performed numerically with the Simpson algorithm, and the solution to the differential equation $\ddot{\vec{r}}=\vec{a}_{galaxy}$ will be carried out with a variable step depending on the acceleration: The Jacobi integral $H$ is conserved for each orbit within variations of $\sim 0.1$."
 The accuracy in the orbit calculation was also checked by testing that the orbit is approximately the same when decreasing this step Ar by a factor of 50 (Ar= ): the difference in the position of both calculations —after a travelled path of more than 1000 kpe (once the particle fell from a distance +o towards the centre and. after that. it crosses the shell at r=ro: with ro=400—500 kpe) is ~0.4 kpe on average.," The accuracy in the orbit calculation was also checked by testing that the orbit is approximately the same when decreasing this step $\Delta t$ by a factor of 50 $\Delta t=\frac{1 s}{a({\rm m/s^2})+10^{-12}}$ ): the difference in the position of both calculations after a travelled path of more than 1000 kpc (once the particle fell from a distance $r_0$ towards the centre and, after that, it crosses the shell at $r=r_0$; with $r_0=400-500$ kpc) is $\sim 0.4$ kpc on average."
 These errors are hot important for the present calculations because we do not require too much accuracy in the orbit: it is only used for the path integral of eq. (4))., These errors are not important for the present calculations because we do not require too much accuracy in the orbit; it is only used for the path integral of eq. \ref{deltaE}) ).
 Moreover. à small random error added to the orbit ts equivalent to a small random variation of the initial conditions. which in comparison with the range of impact parameters (0-200 kpc) is negligible.," Moreover, a small random error added to the orbit is equivalent to a small random variation of the initial conditions, which in comparison with the range of impact parameters (0-200 kpc) is negligible."
 We approximate the halo as spherical. ie. we neglect the ellipticity: We then use a truncated flat model by Battaglia et al. (," We approximate the halo as spherical, i.e. we neglect the ellipticity: We then use a truncated flat model by Battaglia et al. ("
2005):,2005):
Castro-Tirado et ((1992) reported the discovery of the hard-N-rayv. transient source 11915|105. using the WATCL instrument on theGRANAY satellite.,"Castro-Tirado et (1992) reported the discovery of the hard-X-ray transient source 1915+105, using the WATCH instrument on the satellite."
 Its. X-ray emission at both high and low energies has proved to have a rich structure — sec. e.g. Paciesas et ((1996) and Greiner et ((1996).," Its X-ray emission at both high and low energies has proved to have a rich structure – see, e.g., Paciesas et (1996) and Greiner et (1996)."
 In the radio regime. the source is no less remarkable: Mirabel guez (1994) discovered a double-sided relativistic ejection of racdio-emitting material.," In the radio regime, the source is no less remarkable; Mirabel guez (1994) discovered a double-sided relativistic ejection of radio-emitting material."
 Acopting a model based on svmametrical ejection. they derive an angle to the line of sight of TO degrees and a velocity of ejection of 0.92e.," Adopting a model based on symmetrical ejection, they derive an angle to the line of sight of 70 degrees and a velocity of ejection of $c$."
 The distance. from 21-em absorption. is estimated to be 12.5 kpe. consistent with the relativistic-expansion moclel.," The distance, from 21-cm absorption, is estimated to be 12.5 kpc, consistent with the relativistic-expansion model."
 iguez et ((1995) and Foster et ((1996) have presented Ilux-density monitoring data at a range of frequencies., guez et (1995) and Foster et (1996) have presented flux-density monitoring data at a range of frequencies.
 From this monitoring. it was apparent that the [lux density in the radio regime varies on many. time-scales. and we started a systematic monitoring program at 15 Cillz with the νο Telescope in 1995 August.," From this monitoring, it was apparent that the flux density in the radio regime varies on many time-scales, and we started a systematic monitoring program at 15 GHz with the Ryle Telescope in 1995 August."
 One surprising feature. apparently periodic oscillations with periods in the range 2040 min. has been reported in two LAU Circulars (Pooley 19905. 1996).," One surprising feature, apparently periodic oscillations with periods in the range 20–40 min, has been reported in two IAU Circulars (Pooley 1995, 1996)."
 This phenomenon. and other patterns of variation including the relationship to theTE monitoring data. are considered in more detail in this paper.," This phenomenon, and other patterns of variation including the relationship to the monitoring data, are considered in more detail in this paper."
 The Ryle Telescope (RL: Jones 1991). the upgraded Cambridge 5-kim ‘Telescope. is usecl primarily for observations related to microwave-backerouncd studies.," The Ryle Telescope (RT: Jones 1991), the upgraded Cambridge 5-km Telescope, is used primarily for observations related to microwave-background studies."
 ]t is an EW synthesis telescope for which the majority of observations have durations of 12 h. In the inevitable gaps in that program. projects such as monitoring of variable sources are often carried out.," It is an E–W synthesis telescope for which the majority of observations have durations of 12 h. In the inevitable gaps in that program, projects such as monitoring of variable sources are often carried out."
 AIL observations reported here are centred. on. 15.2 Gllz with a bandwidth of 350. MlIZ., All observations reported here are centred on 15.2 GHz with a bandwidth of 350 MHz.
 The linearlv-polarized feeds are sensitive to Stokes L1O: no allempt was mace to measure polarization properties., The linearly-polarized feeds are sensitive to Stokes I+Q; no attempt was made to measure polarization properties.
 Since much of the work of the telscope is at. modes resolutions. the four mobile aerials are usually set in a compact arrav configuration within 100 m of the neares ixed aerial: the resulting LO baselines give a resolution of some 30 arcsec at 15 CGllz when mapping.," Since much of the work of the telscope is at modest resolutions, the four mobile aerials are usually set in a compact array configuration within 100 m of the nearest fixed aerial; the resulting 10 baselines give a resolution of some 30 arcsec at 15 GHz when mapping."
 Atmospheric ohase fluctuations are not a serious. problem on. these vasclines., Atmospheric phase fluctuations are not a serious problem on these baselines.
 Most of the data reported in this paper are derive rom the compact array and not the longer baselines which were also available., Most of the data reported in this paper are derived from the compact array and not the longer baselines which were also available.
 One cilliculty arises in the compact array rom the declination of this particular source. in that some antennas become severely shadowed at extreme hour angles.," One difficulty arises in the compact array from the declination of this particular source, in that some antennas become severely shadowed at extreme hour angles."
 In practice only hour angles within 3h ofthe meridian were normally used. to avoid. shadowing., In practice only hour angles within 3h of the meridian were normally used to avoid shadowing.
 Phe observations were interleaved with those ofa calibrator. D1920|154. using a 15 | 2.5 minute evele. so that the instrumental phase variations can be determined and removed.," The observations were interleaved with those of a calibrator, B1920+154, using a 15 + 2.5 minute cycle, so that the instrumental phase variations can be determined and removed."
 The Dux-density scale is set » nearby observations of 3€48 or 3€286. and is believed to conform to the scale of Baars et (01977).," The flux-density scale is set by nearby observations of 3C48 or 3C286, and is believed to conform to the scale of Baars et (1977)."
 The measured lux densitv of DI9201|154 was used as a check that the system was working well: they show that the day-to-day calibration of the παν density scale is consistent within 32 »eent rms., The measured flux density of B1920+154 was used as a check that the system was working well; they show that the day-to-day calibration of the flux density scale is consistent within 3 percent rms.
 Data are normally integrated. over 32-second (sidereal) intervals. although several observations were mace," Data are normally integrated over 32-second (sidereal) intervals, although several observations were made"
Therefore. we donet expect CNO-processiug to have a laree impact ouAT.. but it nmüsht have impact ou the terminal velocities.,"Therefore, we do expect CNO-processing to have a large impact on, but it might have impact on the terminal velocities."
 Finally. we would like to add that our caleulatious for around Tig=25000IK have only been performed forone value of M. LE. and T/Te abuudauce.," Finally, we would like to add that our calculations for around $\teff = 25~000~\rm K$ have only been performed for value of $M_*$, $L_*$ and H/He abundance."
 lis expected to depeud on these stellar parameters. so calculating niass-loss rates for a wider rauge of stellar paralcters will provide valuable information on the size of the bistabilityjΠΠ) Ine aand ad will allow us to constrain its amplitude aud location in the IRD.," is expected to depend on these stellar parameters, so calculating mass-loss rates for a wider range of stellar parameters will provide valuable information on the size of the bi-stability jump in and and will allow us to constrain its amplitude and location in the HRD."
where the subscripts s. e. p and / label quantities for entropy. vorlicily. pressure waves and third mode.,"where the subscripts $s$ , $v$ , $p$ and $t$ label quantities for entropy, vorticity, pressure waves and third mode."
 Upstream (here are neither entropy nor vorlicily perturbations: We must use (hese expressions in the perturbed RankineIIugoniot., Upstream there are neither entropy nor vorticity perturbations: We must use these expressions in the perturbed Rankine–Hugoniot.
" Furthermore. we can write one ofthe two components of df, in terms of the other one. throughhoyQU,0. where hou=hy and hy,=w/t (see eqs. 13))."," Furthermore, we can write one ofthe two components of $\delta\!\vec{v}_{2v}$ in terms of the other one, through$\vec{k}_{2v}\cdot\delta\!\vec{v}_{2v}=0$, where $k_{2vy}\equiv k_y$ and $k_{2vx}=\omega/v_2$ (see eqs. \ref{vorticitysolution}) )."
 Then we can simplify our svstem by eliminating the shock displacement ¢. (he remaining component of (he velocity perturbation due to vorlicily. and oli..," Then we can simplify our system by eliminating the shock displacement $\zeta$, the remaining component of the velocity perturbation due to vorticity, and $\delta\!V_{1s}$."
 One equation remains. linking only pressure waves and (hire modes’ perturbations: Now. eqs.," One equation remains, linking only pressure waves and third modes' perturbations: Now, eqs."
 34 hold both for pressure waves and third modes., \ref{homogeneoussolution} hold both for pressure waves and third modes.
 We can use them to write the above equation in terms of volume perturbations., We can use them to write the above equation in terms of volume perturbations.
" We remark Chat each mode has its own 2 and its own , but. for given δὴand w. they are fixed by the dispersion relation. eq. 24.."," We remark that each mode has its own $\vec{z}$ and its own $k_x$ but, for given $k_y$and $\omega$, they are fixed by the dispersion relation, eq. \ref{reldisp}. ."
 We obtain:, We obtain:
accretion histories from the Millennium and Millenium-IL simulations. combined with two additional. smaller. cosmological simulations.,"accretion histories from the Millennium and Millenium-II simulations, combined with two additional, smaller, cosmological simulations."
" We use the ""splitting"" merger tree construction algorithm deseribed in refs:merger, reessethodandinGO09. andverif vitsreliabilitybyreprodIMGdepliotelveltibef expeated tef . independe."," We use the ""splitting"" merger tree construction algorithm described in \\ref{s:merger_trees_method} and in G09, and verify its reliability by reproducing our results by following individual particle histories alone, independent of merger tree construction algorithms."
 We find that the contributions of all resolved mergers (up to mass ratios z: 10°) to the total growth rate of halos do not exceed 60%. regardless of halo mass and redshift.," We find that the contributions of all resolved mergers (up to mass ratios $\approx10^{5}$ ) to the total growth rate of halos do not exceed $60\%$, regardless of halo mass and redshift."
" Most of themerger contribution comes from small mass ratio (""major"") mergers (e.g. ]«x10 contribute z30% of the total growth). while ""very minor"" mergers add very little mass (e.g. 10°cx« contribute just a few percent to the total halo growth)."," Most of the contribution comes from small mass ratio (""major"") mergers (e.g. $1<x<10$ contribute $\approx30\%$ of the total growth), while ""very minor"" mergers add very little mass (e.g. $10^{3}<x<10^{5}$ contribute just a few percent to the total halo growth)."
 We find that the power-law index of the merger rate is such that if the merger rate is extrapolated beyond the maximum resolved mass ratio z10°. the total contribution ofall mergers saturates at ~60%.," We find that the power-law index of the merger rate is such that if the merger rate is extrapolated beyond the maximum resolved mass ratio $\approx10^{5}$, the total contribution of mergers saturates at $\approx60\%$."
 This suggests that a significant mass fraction of halos may be accreted in a genuinely smooth way., This suggests that a significant mass fraction of halos may be accreted in a genuinely smooth way.
 Our results have important implications for galaxy formation models and the modes of baryonic accretion., Our results have important implications for galaxy formation models and the modes of baryonic accretion.
 If z:40% of the dark matter that 1s accreted onto a halo was never previously bound in any merging smaller halos. then at least z40% of the baryons must also be accreted smoothly - as gas that was never previously heated by feedback processes or converted to stars.," If $\approx40\%$ of the dark matter that is accreted onto a halo was never previously bound in any merging smaller halos, then at least $\approx40\%$ of the baryons must also be accreted smoothly - as gas that was never previously heated by feedback processes or converted to stars."
" For the baryons. this z40% is a strong lower limit since halos with 7,;.«IO0K likely cannot retain their gas."," For the baryons, this $\approx40\%$ is a strong lower limit since halos with $T_{vir}<10^4K$ likely cannot retain their gas."
" The common assumption that halos with 7,<10 cannot retain their gas also makes our results insensitive toK the limited resolution of the simulations we use. because we resolve all halos above this limit (at z=3)."," The common assumption that halos with $T_{vir}<10^4K$ cannot retain their gas also makes our results insensitive to the limited resolution of the simulations we use, because we resolve all halos above this limit (at $z\lesssim3$ )."
" The implication is that a very large fraction of the baryonic matter falling into a halo must be pristine ""cold"" IGM gas. with T>107K set by do"," The implication is that a very large fraction of the baryonic matter falling into a halo must be pristine ""cold"" IGM gas, with $T\gtrsim10^4K$ set by IGM photoheating."
s fas iis] otl lhreafovrlvene stars or to have become significantly enriched with metals. no matter what the star-formation efficiency. and history of the baryons in any of the merging halos.," This gas is not expected to have formed stars or to have become significantly enriched with metals, no matter what the star-formation efficiency and history of the baryons in any of the merging halos."
 We thank Raul Angulo. Mike Boylan-Kolchin. Jerry Ostriker. Jie Wang and Simon White for advice and comments on the manuscript.," We thank Raul Angulo, Mike Boylan-Kolchin, Jerry Ostriker, Jie Wang and Simon White for advice and comments on the manuscript."
 We are grateful to Eyal Neistein. for enlightening discussions and for kindly providing his code for computing EPS merger rates., We are grateful to Eyal Neistein for enlightening discussions and for kindly providing his code for computing EPS merger rates.
 We acknowledge the anonymous referee for a report that guided us towards significant improvement of the paper., We acknowledge the anonymous referee for a report that guided us towards significant improvement of the paper.
 The Millennium and Millennium-Il Simulations databases and the web application providing online access to them were constructed as part of the activities of the German Astrophysical Virtual Observatory., The Millennium and Millennium-II Simulations databases and the web application providing online access to them were constructed as part of the activities of the German Astrophysical Virtual Observatory.
 We thank Gerard Lemson for helping us taking the most advantage of those databases. and Michaela Hirschmann for invaluable assistance with the USM simulation.," We thank Gerard Lemson for helping us taking the most advantage of those databases, and Michaela Hirschmann for invaluable assistance with the USM simulation."
 We thank the DFG for support via German- Project Cooperation grant STE]869/1-1.GE625/15-1., We thank the DFG for support via German-Israeli Project Cooperation grant STE1869/1-1.GE625/15-1.
 SG acknowledges the PhD fellowship of the International Max Planck Research School in Astrophysies., SG acknowledges the PhD fellowship of the International Max Planck Research School in Astrophysics.
properly taken into account.,properly taken into account.
 We have determined the expression of the Lagrangian density in the variational framework developed by Brandon Carter ancl co-workers., We have determined the expression of the Lagrangian density in the variational framework developed by Brandon Carter and co-workers.
 We have also shown how to make the correspondence with non-relativistic mocels by applving the 4D covariant formulation of Newtonian hyelrocnamics of ?.., We have also shown how to make the correspondence with non-relativistic models by applying the 4D covariant formulation of Newtonian hydrodynamics of \cite{CCI-04}.
 We have determined all the coellicients of these models consistently with the microscopic approach., We have determined all the coefficients of these models consistently with the microscopic approach.
 In the perspective of describing not only the liquid. core of neutron stars but also the crust lavers. we have emploved the nuclear energy. density functional theory which has been already successfully applied to study both isolated nuclei and infinite nuclear matter.," In the perspective of describing not only the liquid core of neutron stars but also the crust layers, we have employed the nuclear energy density functional theory which has been already successfully applied to study both isolated nuclei and infinite nuclear matter."
 As an example. we have calculated the composition. the equation of state and the entrainment matrix of neutron star core for three dillerent nuclear models: the popular SLy4 model for which the equation of state of both the crust and the liquid core has been already tabulated (2). ane the more recent LNS and NRAPR. models which have been entirely constructed from recent realistic many body calculations.," As an example, we have calculated the composition, the equation of state and the entrainment matrix of neutron star core for three different nuclear models: the popular SLy4 model for which the equation of state of both the crust and the liquid core has been already tabulated \citep{haensel-04} and the more recent LNS and NRAPR models which have been entirely constructed from recent realistic many body calculations."
 For comparison. we have also considered. relativistic (w mean field models that have been first applied. by 2...," For comparison, we have also considered relativistic $\sigma-\omega$ mean field models that have been first applied by \citet{comer-03}."
 We have improved their models by refitting the parameters in order to obtain a better agreement with nuclear data. but still we coulc not reach the same level of accuracy as the non-relativistic models mentioned. above.," We have improved their models by refitting the parameters in order to obtain a better agreement with nuclear data, but still we could not reach the same level of accuracy as the non-relativistic models mentioned above."
 This would require the introduction of additional meson fields. especially the rho meson.," This would require the introduction of additional meson fields, especially the rho meson."
 Josices self-meson couplings should be taken into account., Besides self-meson couplings should be taken into account.
 Numorica calculations with both elfective energy density functionals and relativistic mean field mocdels have shown that the dvnamica elfective nucleon masses arising from entrainment effects are smaller than the ordinary mass in the Newtonian case., Numerical calculations with both effective energy density functionals and relativistic mean field models have shown that the dynamical effective nucleon masses arising from entrainment effects are smaller than the ordinary mass in the Newtonian case.
 Relativistic ellects increase effective masses. since all forms of internal energy. contribute to the mass.," Relativistic effects increase effective masses, since all forms of internal energy contribute to the mass."
 A rather unexpected. consequence which has not been usually discussed in the literature. is that relativistic effective masses can be even larger than the bare mass in the liquid core of neutron stars.," A rather unexpected consequence which has not been usually discussed in the literature, is that relativistic effective masses can be even larger than the bare mass in the liquid core of neutron stars."
 This work was financially supported by ENRS (Belgium)., This work was financially supported by FNRS (Belgium).
 The author is grateful to Brandon Carter for valuable comments during the completion of this work., The author is grateful to Brandon Carter for valuable comments during the completion of this work.
taking some of the data on V10S2 Ser.,taking some of the data on V1082 Sgr.
 Johu Southworth provided a timely aud. helpful referee report., John Southworth provided a timely and helpful referee report.
 As always. we thank the Tohono O'odliun Nation for letting us use their mountain for a while.," As always, we thank the Tohono O'odham Nation for letting us use their mountain for a while."
2= 0.6) in MCO9 (catalog B).,$z= 0.46$ ) in MC09 (catalog B).
 Therefore. the MCO9 catalog D. provides a representative sample of candidates aud allows for the [ist time the exploration of the physical conditions in CGs through the past ~5 Gyr.," Therefore, the MC09 catalog B provides a representative sample of candidates and allows for the first time the exploration of the physical conditions in CGs through the past $\sim 5$ Gyr."
 For the great majority of the CG candidates. the spectra of just one galaxy. was obtained by SDSS.," For the great majority of the CG candidates, the spectra of just one galaxy was obtained by SDSS."
 To reduce (he degree of random projected associalions. we restricted our study to the 23 svstems with at least two members with concordant determination of spectroscopic redshifts at 2>0.3.," To reduce the degree of random projected associations, we restricted our study to the 23 systems with at least two members with concordant determination of spectroscopic redshifts at $z>0.3$."
" Here. we present (he results [or three such at redshifts 0.31 (NIC4629). 0.38 (MC'T697). and 0.36 (AIC13069),"," Here, we present the results for three such at redshifts 0.31 (MC4629), 0.38 (MC7697), and 0.36 (MC13069)."
 This paper is organized as follows: after this introduction. Section 2 presents the basic issues of the observations aud data processing. while the redshift estimations and the main observational properties are considered in Section 3.," This paper is organized as follows: after this introduction, Section 2 presents the basic issues of the observations and data processing, while the redshift estimations and the main observational properties are considered in Section 3."
 Section. + presents the main kinematic and dynamical properGes., Section 4 presents the main kinematic and dynamical properties.
 The main conclusions are presented in Section 4., The main conclusions are presented in Section 4.
 Table 1 presents a summary of the photometric and spectroscopic observations presented in (his paper., Table 1 presents a summary of the photometric and spectroscopic observations presented in this paper.
 Using the 2.5 m INT (ORAL La Palma. Spain). images of a field centred in each of the three CG candidates were obtained.," Using the 2.5 m INT (ORM, La Palma, Spain), images of a field centred in each of the three CG candidates were obtained."
 The images were bias subtracted. flat field corrected and combined usingIRAF?.," The images were bias subtracted, flat field corrected and combined using."
. The images for the CG candidate \IC4629 were (taken in photometric conditions. whilst during the observations of MCT697. and AIC13069 there were evidence for the presence of some high clouds.," The images for the CG candidate MC4629 were taken in photometric conditions, whilst during the observations of MC7697 and MC13069 there were evidence for the presence of some high clouds."
 An approximate, An approximate
Our wicle-ficlel L4-Gllz image also shows a relatively faint extended radio source which we have called0.,Our wide-field 1.4-GHz image also shows a relatively faint extended radio source which we have called.
59.. Unlike0.84... it. does not have a clear shell-LHike morphology.," Unlike, it does not have a clear shell-like morphology."
 Although the current data cdo not. reliably determine its radio spectral index. a relatively Dat spectrum. with o in the range of 0.3 to O is suggested refsgvobs)).," Although the current data do not reliably determine its radio spectral index, a relatively flat spectrum, with $\alpha$ in the range of $-0.3$ to 0 is suggested \\ref{sgyobs}) )."
" The source is present on the Climpse Sum infrared images. and listec as 00.5894 in the GLIMPSEL sourcelist""."," The source is present on the Glimpse $8 \, \mu$ m infrared images, and listed as $-$ 00.5894 in the GLIMPSEII source."
.. We therefore tentatively identify aas an rregion., We therefore tentatively identify as an region.
 Al EF. Bietenholz. Hl. €. Matheson. $8. Sali-Llarb and N. Bartel acknowledge support. by. the Natural Sciences and Enginecring Research Council (NSERC).," M. F. Bietenholz, H. C. Matheson, S. Safi-Harb and N. Bartel acknowledge support by the Natural Sciences and Engineering Research Council (NSERC)."
 S. Sali-Hlarb acknowledge support by the Canada Research Chairs program., S. Safi-Harb acknowledge support by the Canada Research Chairs program.
 This research. mace use of NASA's Astrophysics Data System., This research made use of NASA's Astrophysics Data System.
is present at a level of ~10—20% for the smallest systems.,is present at a level of $\sim 10 - 20\%$ for the smallest systems.
" However, when we restrict ourselves to galaxies at the center of FOF groups (~75—85% of galaxies at z=2 and ~95—98% at z—5, depending on stellar mass), the excess bias approaches that obtained fordark matter haloes alone (section 3.2))."," However, when we restrict ourselves to galaxies at the center of FOF groups $\sim 75-85
\%$ of galaxies at $z=2$ and $\sim 95-98 \%$ at $z=5$, depending on stellar mass), the excess bias approaches that obtained fordark matter haloes alone (section \ref{sub:haloes}) )."
" The differing results obtained for haloes and the galaxy population must therefore be due to the physics of the merger of galaxies, which goes beyond that of halo merging."," The differing results obtained for haloes and the galaxy population must therefore be due to the physics of the merger of galaxies, which goes beyond that of halo merging."
 This is still a topic of active research in galaxy formation modelling., This is still a topic of active research in galaxy formation modelling.
 The large clustering amplitude of quasars observed by ? at high redshift appears to suggest that these objects live in very massive haloes.," The large clustering amplitude of quasars observed by \citet{shen07}
 at high redshift appears to suggest that these objects live in very massive haloes."
" In Figure 7,, the bias associated with FOF halo merger events for different mass ranges and at different redshifts, is compared to the observed quasarbias!,, as calculated by ?.."," In Figure \ref{fig:bias_haloes_QSO}, the bias associated with FOF halo merger events for different mass ranges and at different redshifts, is compared to the observed quasar, as calculated by \citet{shen09}."
" The high observed clustering is compatible with the clustering associated with the most massive DM haloes, which, at least up to z»4, we find to be in better agreement with the analytical predictions of ?,, rather than those of ?,, though still somewhat higher at the highest redshifts."," The high observed clustering is compatible with the clustering associated with the most massive DM haloes, which, at least up to $z\sim4$, we find to be in better agreement with the analytical predictions of \citet{jing98}, rather than those of \citet{sheth01}, though still somewhat higher at the highest redshifts."
" As discussed in Section ??,, the high observed clustering signal forces quasar models to adopt extreme values for some of the relevant parameters, such as assuming very low scatter in the L-Mualo rrelation, high duty cycles, and high radiative efficiencies (??).."," As discussed in Section \ref{sec:intro}, the high observed clustering signal forces quasar models to adopt extreme values for some of the relevant parameters, such as assuming very low scatter in the $L$ relation, high duty cycles, and high radiative efficiencies \citep{White08,ShankarCrocce}."
" However, an excess bias applying specifically to quasar hosts compared with random haloes of the same mass might reduce the need for such strong assumptions (?).."," However, an excess bias applying specifically to quasar hosts compared with random haloes of the same mass might reduce the need for such strong assumptions \citep{wyithe09}."
" The results of the previous sections for massive haloes and galaxies represent a challenge to this attractive explanation, at least if the excess bias is to be of merger origin."," The results of the previous sections for massive haloes and galaxies represent a challenge to this attractive explanation, at least if the excess bias is to be of merger origin."
" Figure 7 suggests that quasars at z>2 live in haloes ~10?57! which is broadly consistent with the average host halo mass estimatedMc, for lower redshift quasars (e.g.,?).."," Figure \ref{fig:bias_haloes_QSO} suggests that quasars at $z>2$ live in haloes $\sim 10^{13} ~h^{-1}
\rm{M}_{\odot}$ which is broadly consistent with the average host halo mass estimated for lower redshift quasars \citep[e.g.,][]{croom05}."
" If bright quasars have no significant excess bias due to their merger-driven nature, as our results suggest, then either there is another unknown source of excess bias, or, more simply, their clustering must trace the clustering of their host DM haloes and the discrepancy mentioned above must be explained in some other way."," If bright quasars have no significant excess bias due to their merger-driven nature, as our results suggest, then either there is another unknown source of excess bias, or, more simply, their clustering must trace the clustering of their host DM haloes and the discrepancy mentioned above must be explained in some other way."
 At this point it is therefore important to carry out a simple consistency check tosee if there are enough massive haloes to host the luminous quasars actually observed in SDSS at z= 3., At this point it is therefore important to carry out a simple consistency check tosee if there are enough massive haloes to host the luminous quasars actually observed in SDSS at $z\gtrsim 3$ .
" In Figure 8,, we compare the number density of observed"," In Figure \ref{fig:number_densities}, , we compare the number density of observed"
exists a lower-triangular L such that LL”=B.,exists a lower-triangular $\coh{L}{}$ such that $\coh{L}{}\coh{L}{}^H=\coh{B}{}$.
 For any unitary U. we then have: Therefore. given a single polarized calibrator. we still have an ambiguity factor of LUL7'!," For any unitary $\jones{U}{}$, we then have: Therefore, given a single polarized calibrator, we still have an ambiguity factor of $\coh{L}{} \jones{U}{} \coh{L}{}^{-1}$!"
 Physical examples of this are somewhat more elaborate. but perhaps the simplest one is that à source with Q polarization only is insensitive to a certain combination of dipole rotation and gain adjustment.," Physical examples of this are somewhat more elaborate, but perhaps the simplest one is that a source with $Q$ polarization only is insensitive to a certain combination of dipole rotation and gain adjustment."
 Indeed. for pg.[(/*9=01-09. We ehuero[have =VO0τη2. and.and given a rotational U. the resulting ambiguity factor ts The upshot of this 1s that unambiguous calibration of the polarization response of an interferometer requires. polarized calibrator sources. and/or additional assumptions about the sky (e.g. V=0. which was à common assumption in the pre-RIME era).," Indeed, for $\coh{B}{}=\matrixtt{I+Q}{0}{0}{I-Q},$ we have $L=\matrixtt{\sqrt{I+Q}}{0}{0}{\sqrt{I-Q}},$ and, given a rotational $\jones{U}{}$, the resulting ambiguity factor is The upshot of this is that unambiguous calibration of the polarization response of an interferometer requires polarized calibrator sources, and/or additional assumptions about the sky (e.g. $V=0$, which was a common assumption in the pre-RIME era)."
 ? explores these issues in more detail., \citet{ME5} explores these issues in more detail.
 We should note that though the matrix equations above may seem somewhat complicated. they are far more succinct and complete than any sealar equations that have been used to deseribe polarization calibration prior to the RIME.," We should note that though the matrix equations above may seem somewhat complicated, they are far more succinct and complete than any scalar equations that have been used to describe polarization calibration prior to the RIME."
 Once again. the RIME provides a rigorous mathematical language to describe what is otherwise an extremely tricky problem.," Once again, the RIME provides a rigorous mathematical language to describe what is otherwise an extremely tricky problem."
 Most of the problems associated with DDEs are already pointed to by Eq. (1)., Most of the problems associated with DDEs are already pointed to by Eq. \ref{eq:me-allsky}) ).
 The fundamental assumption of traditional selfeal is that DDEs are trivial. meaning that: DDEs are a multiplication in. the /m plane. which corresponds to a convolution in its Fourier counterpart. the ay plane.," The fundamental assumption of traditional selfcal is that DDEs are trivial, meaning that: DDEs are a multiplication in the $lm$ plane, which corresponds to a convolution in its Fourier counterpart, the $uv$ plane."
" That is. in the presence of non-trivial DDEs E, (including a non-trivial W,, term). the observed visibility is actually a of the sky coherency."," That is, in the presence of non-trivial DDEs $\jones{E}{p}(\vec l)$ (including a non-trivial $W_p$ term), the observed visibility is actually a of the sky coherency."
" Assuming G,=| for the moment. Eq. (1))"," Assuming $\jones{G}{p}\equiv1$ for the moment, Eq. \ref{eq:me-allsky}) )"
" then gives us: where ""o"" is a matrix convolution (te. following the same rules as matrix multiplication. with each elementary multiplication replaced by a convolution). and the convolution kernels U,, are Fourier transforms of the sky-Jones terms £,."," then gives us: where $\circ$ ” is a matrix convolution (i.e. following the same rules as matrix multiplication, with each elementary multiplication replaced by a convolution), and the convolution kernels $\jones{U}{p}$ are Fourier transforms of the sky-Jones terms $\jones{E}{p}$."
" We can rewrite this equation to emphasize the time variability. and the fact that any given interferometer pq only samples one point w,, of the «v plane at a time: This equation captures the heart of the DDE problem: DDEs convolve the ""ideal"" visibilities. with (in the general case) a different kernel per every antenna and time sample."," We can rewrite this equation to emphasize the time variability, and the fact that any given interferometer $pq$ only samples one point $\vec u_{pq}$ of the $uv$ plane at a time: This equation captures the heart of the DDE problem: DDEs convolve the “ideal” visibilities, with (in the general case) a different kernel per every antenna and time sample."
 Instead of sampling one wv plane (X). we have a separate iv plane per each pg and time interval (Χρ). and we're sampling each such plane at only one (or at most a handful) of points.," Instead of sampling one $uv$ plane $\coh{X}{}$ ), we have a separate $uv$ plane per each $pq$ and time interval $\coh{X}{pq}[t]$ ), and we're sampling each such plane at only one (or at most a handful) of points."
 Convolution is not uniquely reversible at the best of times: with such limited sampling it is even less tractable., Convolution is not uniquely reversible at the best of times; with such limited sampling it is even less tractable.
 This is the reason why (in the sense of Sect. 1.1)), This is the reason why (in the sense of Sect. \ref{sec:implicit-me-newstar}) )
 To be more precise. they may exist in the mathematical sense. but recovering them is an inverse (and ill-posed) problem.," To be more precise, they may exist in the mathematical sense, but recovering them is an inverse (and ill-posed) problem."
 In this section. I will first consider the two common sources of DDEs: the ionosphere and the primary beam. and then discuss some proposed methods of dealing with them.," In this section, I will first consider the two common sources of DDEs: the ionosphere and the primary beam, and then discuss some proposed methods of dealing with them."
" The primary beam gain. commonly designated as the E-Jones. is the single most ubiquitous DDE (since every telescope. after all. has à beamshape of some kind). and probably the most The implicit simplifying assumption of 2GC packages ts that the interferometer observes an ""apparent sky”: that is. some true sky B(/.ii). attenuated by a LEG.nl."," The primary beam gain, commonly designated as the $E$ -Jones, is the single most ubiquitous DDE (since every telescope, after all, has a beamshape of some kind), and probably the most The implicit simplifying assumption of 2GC packages is that the interferometer observes an “apparent sky”: that is, some true sky $\coh{B}{}(l,m)$, attenuated by a $|E(l,m)|^2$."
 Given a reasonably accurate model for the beam. the final images can be multiplied by [E(/.in| to correct the flux scale (at the cost of Increasing the Image noise away from centre).," Given a reasonably accurate model for the beam, the final images can be multiplied by $|E(l,m)|^{-2}$ to correct the flux scale (at the cost of increasing the image noise away from centre)."
 In RIME terms. this classical assumption corresponds to an E-Jones that is a trivial DDE (1.e. constant in time. and same across all stations). but also the same for both receivers and thus scalar: EG./.m)=ΕΙm).," In RIME terms, this classical assumption corresponds to an $E$ -Jones that is a trivial DDE (i.e. constant in time, and same across all stations), but also the same for both receivers and thus scalar: $\jones{E}{p}(t,l,m) \equiv E(l,m)$."
" We can then commute the E term in the apparent sky equation (1)). which becomes a simple multiplication of the true sky B by EE""=ΕΙ. (Incidentally. this also shows why classical selfeal does not concern itself with the complex phase of the primary beam.)"," We can then commute the $E$ term in the apparent sky equation \ref{eq:me-allsky}) ), which becomes a simple multiplication of the true sky $\coh{B}{}$ by $EE^\herm=|E|^2.$ (Incidentally, this also shows why classical selfcal does not concern itself with the complex phase of the primary beam.)"
 Real-life beams deviate from these assumptions in a number of ways. some of them less well understood than others.," Real-life beams deviate from these assumptions in a number of ways, some of them less well understood than others."
 The WSRT primary beam is commonly approximated as: where C has a very mild dependence on v (1.e. is effectively constant for a given band)., The WSRT primary beam is commonly approximated as: where $C$ has a very mild dependence on $\nu$ (i.e. is effectively constant for a given band).
 This model is only valid for the main, This model is only valid for the main
The discovery of a massive quasar at a redshift of =7.085 bv Mortlock et al. (,The discovery of a massive quasar at a redshift of $z=7.085$ by Mortlock et al. (
20115) has a nunuber of inaportant duplications to both this paper. and to existing comological models.,"2011b) has a number of important implications to both this paper, and to existing comological models."
" First. as stated by the authors, it establishes tha there is an appreciable un-ionized fraction at this redshift. in contrast with the WALAP result. (IXo1natsu et al."," First, as stated by the authors, it establishes that there is an appreciable un-ionized fraction at this redshift, in contrast with the WMAP result (Komatsu et al."
 2011)., 2011).
" Second. its spectruni establishes that the broad line region has chemical abundances similar to solar. even though the universe is only 0.77 Cr old at this epoch, implying a large conversion of barvons into heavy elements in its vicinity."," Second, its spectrum establishes that the broad line region has chemical abundances similar to solar, even though the universe is only 0.77 Gyr old at this epoch, implying a large conversion of baryons into heavy elements in its vicinity."
" Third. the estimated black hole mass. 2\ LOPAL, inplies very prompt collapse."," Third, the estimated black hole mass, $2 \times 10^9$ $_{\odot}$ implies very prompt collapse."
 If built up at the Eddington rate from an initial mass of order LOOAL. πο wold uced about 3\10? vr to do this!," If built up at the Eddington rate from an initial mass of order $100$ $_{\odot}$, we would need about $3 \times 10^8$ yr to do this!"
" This inyplics that the host halo. Af~ LottAL, was not only collapsed but had. formed a super-dense core by DoLO. supporting +1¢ possibility of monolithic collapse of massive halos iu the early universe."," This implies that the host halo, $M \sim 10^{11}$ $_{\odot}$ was not only collapsed but had formed a super-dense core by $z \sim 10$, supporting the possibility of monolithic collapse of massive halos in the early universe."
" Monolithic collapse. the production of niassive black holes; as well as possibly concentrated regions of star formation suggestsOO that all three sources of UV photons may be important for re-ionization, and that the current paradigui of massive halo formation is likely incomplete"," Monolithic collapse, the production of massive black holes, as well as possibly concentrated regions of star formation suggests that all three sources of UV photons may be important for re-ionization, and that the current paradigm of massive halo formation is likely incomplete"
Iu teris of above notations. the action of the QFT-110del in curved space with is as follows: where A is determined by the infinite red-shiftiug condition we have discussed in above. ie. by following equatiou where gay is the effective metric describing the effects of noncommutative equation of notion ó7|o|=0 in the range of fryAxrixrg|A}.,"In terms of above notations, the action of the QFT-model in curved space with is as follows: where $\Delta$ is determined by the infinite red-shifting condition we have discussed in above, i.e., by following equation where $\widetilde{g}_{\mu\nu}$ is the effective metric describing the effects of noncommutative equation of motion $\delta
I[\phi]=0$ in the range of $\{r_H-\Delta<r<r_H+\Delta \}$."
 We address the QET-aaodel with the quautwm horizon (C18)). (50)) is quite differeut from the QFT-imodel with classical vorizon ( for iustance. the brick wall 1iodel|5])).," We address the QFT-model with the quantum horizon \ref{Nac}) \ref{Delta}) ) is quite different from the QFT-model with classical horizon ( for instance, the brick wall )."
 The fields in the action (618)) are , The fields in the action \ref{Nac}) ) are non-commutative.
And this properties are naturally charactered by the Plauck leneth. ic... p.," And this properties are naturally charactered by the Planck length, i.e., $\Theta\equiv l_p^2$ ."
 Distiuguisliug from other brick wall-tvpe iiodes. there is uo any free parameter im the heory defined. by 18))-(50)).," Distinguishing from other brick wall-type modes, there is no any free parameter in the theory defined by \ref{Nac}) \ref{Delta}) )."
 We evaluate the start product in the action of (18)) uxing eq.(17)) aud cast the action in he ordinary product., We evaluate the start product in the action of \ref{Nac}) ) using \ref{sp1}) ) and cast the action in the ordinary product.
 Dy this. the noncommutative effect can be absorbed iuto an equivaleut vackeround metric.," By this, the noncommutative effect can be absorbed into an equivalent background metric."
 In other words. we first take the semi-classical quantum effect into consideration.," In other words, we first take the semi-classical quantum effect into consideration."
 This effect is then realized through the non-comuutative eeomietry., This effect is then realized through the non-commutative geometry.
 Finally. lis effect is further through an effective background but in an ordinary geometry.," Finally, this effect is further through an effective background but in an ordinary geometry."
" For a eiven energv mode. ie.. assuming the WISB approximation wave function κοο”...""Yinoe). the effective metric⋅∙ can∙ be either read∙ from the∙ action (actually sinpler) or from the following equation of motion for the scalar field) once the star product is evaluated: where (SZ.gg!)ae’pss stands for 0.O0.gg). ote."," For a given energy mode, i.e., assuming the WKB approximation wave function $\phi(t,r,\theta,\varphi)=e^{-it\omega
-i\int k(r) dr}Y_{lm}(\theta,\varphi)$ , the effective metric can be either read from the action (actually simpler) or from the following equation of motion for the scalar field once the star product is evaluated: where $(\sqrt{ -g}g^{tt}),_{\underbrace{r\cdots r}\limits_{n}}$ stands for $\underbrace{{\pa_r\cdots \pa_r}}\limits_{n}(\sqrt{
-g}g^{tt})$, etc."
 For the scalar field with given energv o. the above equation becomes The noucouuautative field action is nonlocal. which is iuclude with infinity orders of the differential operate.," For the scalar field with given energy $\omega$, the above equation becomes The noncommutative field action is nonlocal, which is include with infinity orders of the differential operate."
 Under WIXB approximation. the OQ expiusiou terms in the equation," Under WKB approximation, the $\Theta-$ expansion terms in the equation"
due to the deviation from the exact edgeon siehtliue of Ai~17.,due to the deviation from the exact edge–on sightline of $\Delta i \sim 7^\circ$.
 LLLO2 is a member of the Virgo. cluster (cf., 4402 is a member of the Virgo cluster (cf.
 Diugeeli et al. 1985))., Binggeli et al. \cite{BiSa}) ).
 Dozeus of relatively bright reeions are embedded iu DIC., Dozens of relatively bright regions are embedded in DIG.
 This DIG is supposed. to originate from cluission that is leaking through the reeions heated bv hot ο and D stars., This DIG is supposed to originate from emission that is leaking through the regions heated by hot O and B stars.
 The Πα image is shown in Fig. 6.., The $\alpha$ image is shown in Fig. \ref{F6}.
 The visual appearance of LL102 is sinuilar to the recently stucied Vireo cluster member ealaxv 11522 (IXeunev Koopiiaun 1999)).," The visual appearance of 4402 is similar to the recently studied Virgo cluster member galaxy 4522 (Kenney Koopmann \cite{
KeKo}) )."
 They clan that they have detected eDIG up to 3kkpc above the ooOalactic plane., They claim that they have detected eDIG up to kpc above the galactic plane.
 However. the inclination of that galaxy is fay away frou beius edgeon. so the observed enmiüssiou iight be emission from the disk.," However, the inclination of that galaxy is far away from being edge–on, so the observed emission might be emission from the disk."
 The Πα flux of L11402 has been estimated aud has a value of ⋟↽↼↽1.17.«10Peresàtem»7 aud frou. the derived. Te huumositv the star formation rate (SFR) has heen determined which is SER=(0.07MM.vrt.," The $\alpha$ flux of 4402 has been estimated and has a value of $\rm{1.47 \times 10^{-13}\,erg\,s^{-1}\,cm^{-2}}$ and from the derived $\alpha$ luminosity the star formation rate $SFR$ ) has been determined which is $SFR = \rm{0.07\,M_{\sun}\,yr^{-1}}$."
 This edgeon galaxy is also a member of the Vireo cluster DDingeeli et al. 1985::, This edge–on galaxy is also a member of the Virgo cluster Binggeli et al. \cite{BiSa};
 Welou et al. 198 D) , Helou et al. \cite{HeHo}) )
and Teerikorpi et al. (1992)), and Teerikorpi et al. \cite{TeBo}) )
 give a distance of MMpc to this galaxy., give a distance of Mpc to this galaxy.
 Recently new BR.baud photometry became available for this ealaxy and other members of the Vireo Cluster (Schroeder Visvanathan 1996))., Recently new R–band photometry became available for this galaxy and other members of the Virgo Cluster (Schroeder Visvanathan \cite{ScVi}) ).
 Oosterloo Shostak (1993)) list it as a binary pair with in their study., Oosterloo Shostak \cite{OoSh}) ) list it as a binary pair with in their study.
 L1631 shows an interesting DIC morphology., 4634 shows an interesting DIG morphology.
 A bright eDIC laver is detected. which reaches distances of —1.lkkpe above the ealactic plane.," A bright eDIG layer is detected, which reaches distances of $\sim$ kpc above the galactic plane."
 We show our Ho [Nu image in Fig. 7.., We show our $\alpha$ ] image in Fig. \ref{F7}.
 In addition to the eDIG laver. several filaments reach iuto the halo. simular to the ones discovered in the edgeou spiral (Dettinar 1993)).," In addition to the eDIG layer, several filaments reach into the halo, similar to the ones discovered in the edge–on spiral (Dettmar \cite{De93}) )."
" These pluies are more frequent than iu 55775, although fainter iu iutensity on average."," These plumes are more frequent than in 5775, although fainter in intensity on average."
 Furthermore several regious iu the disk can be identified. aud iu the southeasterü part a possible dust region absorbs parts of the oenüsson frou the disk.," Furthermore several regions in the disk can be identified, and in the south–eastern part a possible dust region absorbs parts of the emission from the disk."
 Tuterestinely the visible regious in the disk sce not aligned in a plauc., Interestingly the visible regions in the disk seem not aligned in a plane.
 This wieght be an orientation effect duc o the galaxy inclination of 83°., This might be an orientation effect due to the galaxy inclination of $83\degr$.
 ITowever. the position of 1e regions along the plane scatter randomly. which wieht indicate that the disk is disturbed.," However, the position of the regions along the plane scatter randomly, which might indicate that the disk is disturbed."
 Therefore au oeiteraction of 1631 with ucighhbouring galaxies in je Virgo cluster secs likely., Therefore an interaction of 4634 with neighbouring galaxies in the Virgo cluster seems likely.
 Tn the vicinity of 11631 another Virgo spiral is ocated. namely £1633.," In the vicinity of 4634 another Virgo spiral is located, namely 4633."
" Both galaxies have simular radial velocities. (Avz112]ans 1). therefore a direct interaction seenis verv likely,"," Both galaxies have similar radial velocities $\rm{\Delta v 
\approx 112\,km\,s^{-1}}$ ), therefore a direct interaction seems very likely."
 The preseuce of a bar is reported in the literature. which could also be a source of disturbance.," The presence of a bar is reported in the literature, which could also be a source of disturbance."
 About 10 bright regious can be identifier in the disk which are eiibedded in DIG., About 10 bright regions can be identified in the disk which are embedded in DIG.
 Some of the filaments reaching iuto the halo. which are seen in our Ho image. cau be traced back to the disk.," Some of the filaments reaching into the halo, which are seen in our $\alpha$ image, can be traced back to the disk."
 This would be cousisteut with theoretical models (Cehiuuevs with the chimmevs as the interface between disk aud halo.," This would be consistent with theoretical models ('chimneys'), with the chimneys as the interface between disk and halo."
 At least one region protudes from the disk., At least one region protudes from the disk.
 This is the secoucd bright enission reegioninthe very northeru part of the disk. which is slightly offset from the disk.," This is the second bright emission region in the very northern part of the disk, which is slightly offset from the disk."
lack of detectable x-ray emission bv. Musielak. Porter and Davis (1995) renders the accretion scenario unsatisfactorvy al present.,"lack of detectable x-ray emission by Musielak, Porter and Davis (1995) renders the accretion scenario unsatisfactory at present."
 We note. though. that new. more sensitive x-ray observations of 3356 have recently been scheduled with the observatory.," We note, though, that new, more sensitive x-ray observations of 356 have recently been scheduled with the observatory."
 “Phe detection. of hard. x-rav emission. and possibly x-ray variability. on the same timescale as the optical oscillations reported here would give credibility to the chromospheric activity. and/or accretion models.," The detection of hard x-ray emission, and possibly x-ray variability on the same timescale as the optical oscillations reported here would give credibility to the chromospheric activity and/or accretion models."
 CSB acknowledges the support of a PPARC studentship., CSB acknowledges the support of a PPARC studentship.
 MRB. CLAN. and PRAL also acknowledge the support of PPARC.," MRB, GAW and TRM also acknowledge the support of PPARC."
 We thank the anonymous referee. for. helpful comments., We thank the anonymous referee for helpful comments.
 The Jacobus Ixaptevn Telescope is operated. on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Itoque de los Muchachos of the Instituto ce Astrolisica de Canarias., The Jacobus Kapteyn Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.
 Vhis research has mace use of the SLIAIBAD database. operated at CDS. Strasbourg. France.," This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France."
from the attenuation estimate.,from the attenuation estimate.
 Table 4 summarizes those parameters., Table \ref{tab:pahvsZ} summarizes those parameters.
 We also note that there is an anticorrelation between M(PAH)/M(dust) and Av., We also note that there is an anticorrelation between M(PAH)/M(dust) and Av.
 A possibility would be that it is due to the color of the ISRE., A possibility would be that it is due to the color of the ISRF.
" However, it is lower than the variations we are probing."," However, it is lower than the variations we are probing."
" For example, Fig."," For example, Fig."
" 3 of demonstrates the effect of the color of the ISRF on the PAH spectrum, for two extreme cases."," 3 of demonstrates the effect of the color of the ISRF on the PAH spectrum, for two extreme cases."
" The variation is at most a factor of 3, and it is certainly lower in this sample: we are probing variations of 2 order of magnitude in M(PAH)/M(dust)."," The variation is at most a factor of 3, and it is certainly lower in this sample: we are probing variations of 2 order of magnitude in M(PAH)/M(dust)."
 The reason of this anticorrelation most likely reflects the systematic effect of the determination of Av., The reason of this anticorrelation most likely reflects the systematic effect of the determination of Av.
" If we consider the V band flux over 8 um in our sample, it does not vary drastically: F,(V)/F,(8)«0.1, 505 being lower (0.02) and NGC 245 (0.25)."," If we consider the V band flux over 8 $\mu$ m in our sample, it does not vary drastically: $F_\nu(V)/F_\nu(8)\simeq0.1$, SQ5 being lower (0.02) and NGC 245 higher (0.25)."
" At first order, the value of Av will determine the higherfraction of absorbed luminosity in the UV-visible, relative to the V band."," At first order, the value of Av will determine the fraction of absorbed luminosity in the UV-visible, relative to the V band."
" Since, the V band to 8 um flux does not vary a lot, Av will determine the absorbed luminosity relative to the 8 um band."," Since, the V band to 8 $\mu$ m flux does not vary a lot, Av will determine the absorbed luminosity relative to the 8 $\mu$ m band."
" Finally, the value of M(PAH)/M(dust) will depend directly on the 8 um to absorbed luminosity ratio."," Finally, the value of M(PAH)/M(dust) will depend directly on the 8 $\mu$ m to absorbed luminosity ratio."
" Therefore, when Av is low, 8 um/absorbed luminosity is going to be high, and therefore, M(PAH)/M(dust) is going to be high."," Therefore, when Av is low, 8 $\mu$ m/absorbed luminosity is going to be high, and therefore, M(PAH)/M(dust) is going to be high."
 Fig., Fig.
 23 is a way to help discriminate the values of Av which are clearly too low compared to the known 8 um emission., \ref{fig:pahvsZ} is a way to help discriminate the values of Av which are clearly too low compared to the known 8 $\mu$ m emission.
 A very low value of Av NGC 5291 Av=0.2) would all the observed luminosity(e.g. to be put in the PAHs., A very low value of Av (e.g. NGC 5291 Av=0.2) would require all the observed luminosity to be put in the PAHs.
" There requirewould be no room for far-IR dust emission (Fig. 14)),"," There would be no room for far-IR dust emission (Fig. \ref{fig:fit-NGC5291N-mass}) ),"
" which is difficult to understand theoretically, and has never been observed at the scale of a galaxy."," which is difficult to understand theoretically, and has never been observed at the scale of a galaxy."
" The modeling of the fluxes at 3.6 wm and 4.5 um by the photospheric and nebular models is not always very satisfying, in particular for the regions for which the luminosity is dominated by the population formed in the collision debris."," The modeling of the fluxes at 3.6 $\mu$ m and 4.5 $\mu$ m by the photospheric and nebular models is not always very satisfying, in particular for the regions for which the luminosity is dominated by the population formed in the collision debris."
" To exhibit the physical cause, we have plotted the ratio of the modeled to the observed bands versus the observed 8 jum band emission (which traces star formation) normalized to the emission of the model at 3.6 um, which can be seen as a specific star formation rate."," To exhibit the physical cause, we have plotted the ratio of the modeled to the observed bands versus the observed 8 $\mu$ m band emission (which traces star formation) normalized to the emission of the model at 3.6 $\mu$ m, which can be seen as a specific star formation rate."
" In Figure 24 we see that as the specific star formation rate increases, the fit of the 3.6 um and 4.5 um bands degrades progressively."," In Figure \ref{fig:fit-quality} we see that as the specific star formation rate increases, the fit of the 3.6 $\mu$ m and 4.5 $\mu$ m bands degrades progressively."
 The Pearson correlation coefficient is r=—0.71 (resp., The Pearson correlation coefficient is $r=-0.71$ (resp.
 r=—0.72) for the 3.6 jum (resp., $r=-0.72$ ) for the 3.6 $\mu$ m (resp.
 4.5 um) band., 4.5 $\mu$ m) band.
 have made an extensive study on the origin of the non-stellar 4.5 um excess in dwarf galaxies investigating several possibilities., have made an extensive study on the origin of the non-stellar 4.5 $\mu$ m excess in dwarf galaxies investigating several possibilities.
" They have shown this excess is likely a combination of nebular emission (Βτ-α line and continuum) and high optical depth — which would redden the 3.6 um to 4.5 um color -, making the presence of dust emission unnecessary."," They have shown this excess is likely a combination of nebular emission $\alpha$ line and continuum) and high optical depth – which would redden the 3.6 $\mu$ m to 4.5 $\mu$ m color –, making the presence of dust emission unnecessary."
 However we cannot rule out that the contamination of the 3.6 um and 4.5 um bands by dust emission is a possibility in star forming regions in collision debris., However we cannot rule out that the contamination of the 3.6 $\mu$ m and 4.5 $\mu$ m bands by dust emission is a possibility in star forming regions in collision debris.
 A high optical depth may be a factor in NGC 5291N and NGC 7252NW as we have shown that there are hints of embedded star forming regions., A high optical depth may be a factor in NGC 5291N and NGC 7252NW as we have shown that there are hints of embedded star forming regions.
" Our UV to near-infrared model already takes into account the nebular emission, both the Br-a line and the continuum, so the detected excess is unlikely to be of nebular origin in its entirety."," Our UV to near-infrared model already takes into account the nebular emission, both the $\alpha$ line and the continuum, so the detected excess is unlikely to be of nebular origin in its entirety."
 This leads us to interpret this excess as the effect of the emission of the dust (the continuum as well as the emission lines) excited and heated by massive stars., This leads us to interpret this excess as the effect of the emission of the dust (the continuum as well as the emission lines) excited and heated by massive stars.
" This emission is probably coming from very small grains fluctuating in temperature, rather than hot because the equilibrium temperature of the latter (27700K) grains,would correspond to grains too close to stellar sources (51 a.u."," This emission is probably coming from very small grains fluctuating in temperature, rather than hot grains, because the equilibrium temperature of the latter $\simeq$ 700K) would correspond to grains too close to stellar sources $\simeq$ 1 a.u."
 of an O4 star)., of an O4 star).
" When the specific star formation rate is high, there are proportionally many more young stars that are able to make the small grains fluctuate to higher temperatures than the rest of the stellar population."," When the specific star formation rate is high, there are proportionally many more young stars that are able to make the small grains fluctuate to higher temperatures than the rest of the stellar population."
" As a consequence, the dust emission at short wavelength becomes non-negligible compared to the stellar emission."," As a consequence, the dust emission at short wavelength becomes non-negligible compared to the stellar emission."
" As a consequence, the 3.6 um and 4.5 um bands cannot be good tracers of the mass of the evolved stellar population, especially in regions that have a high specific star formation rate."," As a consequence, the 3.6 $\mu$ m and 4.5 $\mu$ m bands cannot be good tracers of the mass of the evolved stellar population, especially in regions that have a high specific star formation rate."
" In addition, the objects that have the highest excess at 3.6 um and 4.5 um are also those with a negligible evolved stellar population that can contribute to those bands, making it easier for the dust to dominate."," In addition, the objects that have the highest excess at 3.6 $\mu$ m and 4.5 $\mu$ m are also those with a negligible evolved stellar population that can contribute to those bands, making it easier for the dust to dominate."
 An uncertainty may be, An uncertainty may be
using a version of GRAFIC (?) modified to accept power spectra generated by CMBFAST (?)..,using a version of GRAFIC \citep{Bertschinger2001} modified to accept power spectra generated by CMBFAST \citep{Seljak1996}.
 We normalized the power spectrum using og=0.74.," We normalized the power spectrum using $\sigma_8 =
0.74$."
 We included adiabatic gas dynamics for the baryons using a perfect-gas equation of state with adiabatic index y=5/3 and mean particle mass determined using interpolation from collisional ionization equilibrium tables for primordial gas from ?.., We included adiabatic gas dynamics for the baryons using a perfect-gas equation of state with adiabatic index $\gamma = 5/3$ and mean particle mass determined using interpolation from collisional ionization equilibrium tables for primordial gas from \citet{Sutherland1993}.
" Although no additional physics is included in this first calculation, we initialized the gas temperature at z; to a constant value of 9100 K, corresponding to a preheating entropy of 250 keV cm? at a redshift of 3."," Although no additional physics is included in this first calculation, we initialized the gas temperature at $z_i$ to a constant value of 9100 K, corresponding to a preheating entropy of 250 keV $^2$ at a redshift of 3."
" This level of preheating is adequate to reproduce the observed X-ray luminosity-temperature relation (?) for clusters of galaxies, although details of the scatter in this relation and its correlation with other cluster properties such as the presence of cold cores are not constrained to match observations."," This level of preheating is adequate to reproduce the observed X-ray luminosity-temperature relation \citep{Bialek2001}
 for clusters of galaxies, although details of the scatter in this relation and its correlation with other cluster properties such as the presence of cold cores are not constrained to match observations."
 We ran our simulation using the FLASH code version 3.3 (??) using a new direct multigrid Poisson solver (?) with 1024? dark matter particles and a uniform base mesh.," We ran our simulation using the FLASH code version 3.3 \citep{Fryxell2000b,Dubey2008} using a new direct multigrid Poisson solver \citep{Ricker2008a} with $^3$ dark matter particles and a uniform $^3$ base mesh."
 The piecewise-parabolic method (?) was used to solve the Euler equations of gas dynamics., The piecewise-parabolic method \citep{COLELLA1984} was used to solve the Euler equations of gas dynamics.
" To achieve the resolution necessary to estimate the level of turbulence within clusters, we used adaptive mesh refinement within 100 preselected regions."," To achieve the resolution necessary to estimate the level of turbulence within clusters, we used adaptive mesh refinement within $100$ preselected regions."
 Each region was 50h-!Mpc on side centered on a halo identified using a lower-resolutiona precursor run., Each region was $50 \hmpc$ on a side centered on a halo identified using a lower-resolution precursor run.
 The halos were selected to uniformly sample the range of resolvable halos using mass function weighting to ensure a representative sample in the full simulation., The halos were selected to uniformly sample the range of resolvable halos using mass function weighting to ensure a representative sample in the full simulation.
" Within the preselected regions we used a dark matter particle refinement criterion, allowing no more than 100 dark matter particles within a zone."," Within the preselected regions we used a dark matter particle refinement criterion, allowing no more than $100$ dark matter particles within a zone."
 We refined to a maximum resolution of 32h! kpc., We refined to a maximum resolution of $32 \hkpc$ .
" Estimates of the integral scale of turbulence in clusters suggests a power law spectrum from spatial scales of 0.8 to 8 kpc, with no visible turnover suggesting that the integral scale is larger than 8 kpc (?),,and that our resolution should allow us to determine the level of turbulent dissipation."," Estimates of the integral scale of turbulence in clusters suggests a power law spectrum from spatial scales of $0.8$ to $8$ kpc, with no visible turnover \citep{Kuchar2011}, suggesting that the integral scale is larger than 8 kpc and that our resolution should allow us to determine the level of turbulent dissipation."
" Since the refined regions were larger than the halos on which they were centered, we captured a total of 131 high-resolution clusters."," Since the refined regions were larger than the halos on which they were centered, we captured a total of $131$ high-resolution clusters."
" We ran the code on the Cray XT5 machine at Oak Ridge National Laboratory, where the simulation required approximately 450,000 CPU-hours on 16,000 processors."," We ran the code on the Cray XT5 machine at Oak Ridge National Laboratory, where the simulation required approximately 450,000 CPU-hours on 16,000 processors."
 Output files containing both particle and gas information were written beginning at z=2.0 at every Az=0.25 for the purposes of mock skygeneration.," Output files containing both particle and gas information were written beginning at $z=2.0$ at every $\Delta z =
0.25$ for the purposes of mock skygeneration."
 We created halo catalogs from the simulation outputs using the friends-of-friends technique with a linking length parameter b=0.2 (FOF)and considered only halos with at least 3000 particles (ie. an FOF dark matter mass of 2x10145-! Mo)., We created halo catalogs from the simulation outputs using the friends-of-friends (FOF) technique with a linking length parameter $b = 0.2$ and considered only halos with at least $3000$ particles (i.e. an FOF dark matter mass of $2 \times 10^{14} \hmsol$ ).
 Our base-grid spatial resolution is sufficient to ensure accurate counts of halos with this many particles throughout the range of redshifts we consider here (??)..," Our base-grid spatial resolution is sufficient to ensure accurate counts of halos with this many particles throughout the range of redshifts we consider here \citep{Heitmann2005,Lukic2007}."
 shows our mass function for all halos in the simulation volume compared against the best fit of ?.., shows our mass function for all halos in the simulation volume compared against the best fit of \citet{Warren2006}.
" We find fewer high-mass objects relative to the Warren fit, but this is not unexpected (see,forexample,"," We find fewer high-mass objects relative to the Warren fit, but this is not unexpected \citep[see, for example,][]{Knebe2011}."
" Also, we tend to over-produce low mass objects, even ?)..below our resolvability limit."," Also, we tend to over-produce low mass objects, even below our resolvability limit."
" However, note that even though we produce too many low-mass objects relative to the Warren fit below our resolution limit, our mass function still turns away from the expected slope, and thus we cannot fully trust the number counts below this threshold."," However, note that even though we produce too many low-mass objects relative to the Warren fit below our resolution limit, our mass function still turns away from the expected slope, and thus we cannot fully trust the number counts below this threshold."
 There were ~4000 resolvable objects at z—0.0., There were $\sim 4000$ resolvable objects at $z=0.0$.
" To make comparisons with the observational analysis of ?;hereafterCBS06, we compute a spherical overdensity radius R, for each of our halos."," To make comparisons with the observational analysis of \citet[][hereafter CBS06]{Cassano2006}, we compute a spherical overdensity radius $R_v$ for each of our halos."
" For the high-resolution sample (i.e., the adaptively-refined halos within the 100 predefined regions), we compute overdensities including both just dark matter and with dark matter plus gas."," For the high-resolution sample (i.e., the adaptively-refined halos within the $100$ predefined regions), we compute overdensities including both just dark matter and with dark matter plus gas."
" For the remaining fixed-resolution halos outside the predefined regions, we only include dark matter in the overdensity calculation since the gas data in these halos were poorly resolved."," For the remaining fixed-resolution halos outside the predefined regions, we only include dark matter in the overdensity calculation since the gas data in these halos were poorly resolved."
 In Section 6 we discuss our procedure for assigning radio power to these lower-resolution halos., In Section \ref{sec:rh_counts} we discuss our procedure for assigning radio power to these lower-resolution halos.
" We use the same definition of overdensity as in CBS06, namely ?:: where w(z)=Ω/(Σ)1—1."," We use the same definition of overdensity as in CBS06, namely \citet{Kitayama1996}: where $\omega(z) \equiv \Omega_f(z)^{-1} -1$."
" Here, The virial mass, M,, follows as M,=(4/3)tAcpm(z)R3, where P~m(z) is the mean mass density: The most massive cluster in our simulation has a mass M,—1.2x10%57!Mo."," Here, The virial mass, $M_v$, follows as $M_v = (4/3) \pi \Delta_c
\rho_m(z) R_v^3$, where $\rho_m(z)$ is the mean mass density: The most massive cluster in our simulation has a mass $M_v = 1.2 \times 10^{15}
\hmsol$."
" We identify gas zones within R, for each halo and associate them with the halo in which they are found.", We identify gas zones within $R_v$ for each halo and associate them with the halo in which they are found.
" We create two-dimensional maps of projected density and projected turbulent pressure, m;v2, where m; is the mass in the cell i and the average velocity is defined as the difference between the measured velocity in the cell and the bulk velocity averaged over300 kpc regions, Vi=—Vaoo "," We create two-dimensional maps of projected density and projected turbulent pressure, $m_i v_i^2$, where $m_i$ is the mass in the cell $i$ and the average velocity is defined as the difference between the measured velocity in the cell and the bulk velocity averaged over300 kpc regions, ${\bf v}_i \equiv {\bf v}_i - {\bf \bar{v}}_{\rm 300~kpc}$ ."
This is a strategy for removing bulk motions similar to kpc.? (an alternative approach to remove bulk velocities from this calculation is discussed in ?))., This is a strategy for removing bulk motions similar to \citet{Vazza2010a} (an alternative approach to remove bulk velocities from this calculation is discussed in \citealt{Paul2011}) ).
 We use these projections in two ways: to create simulated, We use these projections in two ways: to create simulated
spectra are shown for each transition. the lits are good through most of the mapped regions.,"spectra are shown for each transition, the fits are good through most of the mapped regions."
 The TSC model is a parameterized model. and hence the search space to obtain the best fit model is quite large.," The TSC model is a parameterized model, and hence the search space to obtain the best fit model is quite large."
 For this reason. observational constraints when available. were used to set the initial value of (he infall parameters in (he fitting process.," For this reason, observational constraints when available, were used to set the initial value of the infall parameters in the fitting process."
" The initial value of the infall radius r;,; was constrained using the ratio of main beam temperatures towards (he central source obtained from JCAIT and WIT.", The initial value of the infall radius $_{inf}$ was constrained using the ratio of main beam temperatures towards the central source obtained from JCMT and HHT.
 As shown in (1993).. it is possible to constrain the emitting source size from the ratio of the main beam temperatures of (he same (transition obtained al (wo different telescopes with different beam sizes.," As shown in \citet{nwb98}, it is possible to constrain the emitting source size from the ratio of the main beam temperatures of the same transition obtained at two different telescopes with different beam sizes."
 Al 267 GlIz. the main beam efficiencies are 0.6 and 0.71. and beam sizes are and respectively for JCNIT and HIT. which can be used to obtain the emitting source size of SMAI4 to be10.," At 267 GHz, the main beam efficiencies are 0.6 and 0.71, and beam sizes are and respectively for JCMT and HHT, which can be used to obtain the emitting source size of SMM4 to be."
"5"".. This size is in verv g00d agreement with the core size derived from nolecular emission observed with high angular resolution aperture svuthesis observations dllogerheijdeetal1999).", This size is in very good agreement with the core size derived from molecular emission observed with high angular resolution aperture synthesis observations \citep{hog99}.
". Now that rj, is constrained. if the time since onset of collapse t; is known. (he initial value of (he effective sound speed e can be determined."," Now that $_{inf}$ is constrained, if the time since onset of collapse $_{inf}$ is known, the initial value of the effective sound speed $a$ can be determined."
 I is now believed that the pure infall phase belore the onset of molecular outflows is extremely short-lived or ion-existent (Andreetal1993:Saracenoοἱal..1996).," It is now believed that the pure infall phase before the onset of molecular outflows is extremely short-lived or non-existent \citep{and93,sar96}."
. Hence the dynamical time-scale of the observed outflows can be used as a good indicator of νε, Hence the dynamical time-scale of the observed outflows can be used as a good indicator of $_{inf}$.
 From the projected ELLY obes in the JCNIT CO data shown in Figure 3. and the maximum flow. velocity. we derive an outflow dynamical timescale of ~10! vears. which was used as the initial value of t;y in the model fits.," From the projected EHV lobes in the JCMT CO data shown in Figure \ref{intco} and the maximum flow velocity, we derive an outflow dynamical timescale of $\sim 10^4$ years, which was used as the initial value of $_{inf}$ in the model fits."
 The angles subtended by the rotational axis in and out of the plane of the skv are also input. parameters (to the models., The angles subtended by the rotational axis in and out of the plane of the sky are also input parameters to the models.
 The angle in the plane of the skv is taken (o be 45° (east of north) from the appearance of the outflow lobes in Figure 3.., The angle in the plane of the sky is taken to be $45\arcdeg$ (east of north) from the appearance of the outflow lobes in Figure \ref{intco}.
 We initially assumed (that the outflow was in the plane of the sky. and (he best-fit models are consistent with this interpretation.," We initially assumed that the outflow was in the plane of the sky, and the best-fit models are consistent with this interpretation."
" The best value of v;,,5 was chosen from the linewidth of our LM observations.", The best value of $_{turb}$ was chosen from the linewidth of our $^{13}$ $^+$ observations.
 For our model fits we used a temperature distribution profile of, For our model fits we used a temperature distribution profile of
The most generic case to consider is isotropic turbulence without a large-scale homogeneous maegnetic-iekl component.,The most generic case to consider is isotropic turbulence without a large-scale homogeneous magnetic-field component.
 The calculations should broadly describe situations in which 0DXBy. as is often invoked [or voung SNRs.," The calculations should broadly describe situations in which $\delta B \gg B_0$, as is often invoked for young SNRs."
 Figure 2 shows the degree of polarization as a function of frequency lor a selection of maegnetic-field models with Kolmogorov and fat turbulence spectra., Figure \ref{f2} shows the degree of polarization as a function of frequency for a selection of magnetic-field models with Kolmogorov and flat turbulence spectra.
" Ir all cases the polarized intensiv was beam-integrated"" over an area of 20 by 20 cells."," In all cases the polarized intensity was ""beam-integrated"" over an area of 20 by 20 cells."
 We find the behavior of polarized raclio-svuchrotron emission well characterized by the following statements:, We find the behavior of polarized radio-synchrotron emission well characterized by the following statements:
moments of population. beginning from a master-equation standpoint.,"moments of population, beginning from a master-equation standpoint."
 This allows the calculation of accurate production rates., This allows the calculation of accurate production rates.
 However. in the deterministic regime. the method gives accurate production rates. but can produce inaccurate populations (Barzel Biham. 2007b: B. Barzel. private comm.).," However, in the deterministic regime, the method gives accurate production rates, but can produce inaccurate populations (Barzel Biham, 2007b; B. Barzel, private comm.)."
 It is currently unclear how this would affect the behaviour of large chemical networks., It is currently unclear how this would affect the behaviour of large chemical networks.
 Also. the scheme is untested against networks that include activation energies. such as are necessary in the methanol-producing system.," Also, the scheme is untested against networks that include activation energies, such as are necessary in the methanol-producing system."
 Attempts have been made previously (Caselli et al., Attempts have been made previously (Caselli et al.
 1998: Shalabiea et al., 1998; Shalabiea et al.
 1998; Stantcheva et al., 1998; Stantcheva et al.
 2001) to rectify the inaccuracies of the rate-equation method by modifying the rate coefficients of gram-surface production rates according to a set of simple rules: Casellietal.(2002) also devised a more complex modification scheme for reactions involving activation energy barriers., 2001) to rectify the inaccuracies of the rate-equation method by modifying the rate coefficients of grain-surface production rates according to a set of simple rules; \cite{caselli02} also devised a more complex modification scheme for reactions involving activation energy barriers.
 These modifications were largely empirical. and were not universally successful: convergence with exact techniques was achieved only for low temperatures. where atomic hydrogen is the only mobile reactant.," These modifications were largely empirical, and were not universally successful; convergence with exact techniques was achieved only for low temperatures, where atomic hydrogen is the only mobile reactant."
 The comparison of techniques conducted by Rae et al. (, The comparison of techniques conducted by Rae et al. (
2003). using a standardised two-reactant system. found that the method was in general no more accurate than the standard rate-equation approach.,"2003), using a standardised two-reactant system, found that the method was in general no more accurate than the standard rate-equation approach."
 Here is presented a new method of modification of the production rates. different from previous techniques.," Here is presented a new method of modification of the production rates, different from previous techniques."
" This method modifies not the ratecoefficient. but the functional form of the production rate itself. adopting production rates derived for the extreme ""small-grain"" regime."," This method modifies not the rate, but the functional form of the production rate itself, adopting production rates derived for the extreme “small-grain” regime."
 The method switches smoothly to a rate-equation treatment where appropriate., The method switches smoothly to a rate-equation treatment where appropriate.
 The scheme retains its functional dependence on averaged population values. (V). rather than analysing individual states. N. allowing it to be easily implemented in standard gas-grain codes.," The scheme retains its functional dependence on averaged population values, $\langle N \rangle$, rather than analysing individual states, $N$, allowing it to be easily implemented in standard gas-grain codes."
 The purpose of the new method is not primarily to produce a match to the results of exact methods. but to improve accuracy in large chemical networks that cannot be modelled with exact techniques.," The purpose of the new method is not primarily to produce a match to the results of exact methods, but to improve accuracy in large chemical networks that cannot be modelled with exact techniques."
 Section 2 outlines the rates for surface processes., Section 2 outlines the rates for surface processes.
 Basic modified rates are formulated in Section 3., Basic modified rates are formulated in Section 3.
 Sections 4 and 5 detail further modifications to the basic rates., Sections 4 and 5 detail further modifications to the basic rates.
 Section 6 applies the method to reaction systems with activation energies., Section 6 applies the method to reaction systems with activation energies.
 A discussion follows in Section 7. and conclusions in Section 8.," A discussion follows in Section 7, and conclusions in Section 8."
" In the systems to be analysed in this paper. three basic grain-surface processes are considered: accretion of gas-phase atoms onto the grains: evaporation of grain-surface species into the gas phase: and reaction between species on the grain surfaces,"," In the systems to be analysed in this paper, three basic grain-surface processes are considered: accretion of gas-phase atoms onto the grains; evaporation of grain-surface species into the gas phase; and reaction between species on the grain surfaces."
 Here. the aceretion rate is defined simply as an average flux of atoms/molecules per second.," Here, the accretion rate is defined simply as an average flux of atoms/molecules per second."
 This obviates the need to trace any kind of gas-phase chemistry in the following tests., This obviates the need to trace any kind of gas-phase chemistry in the following tests.
" The evaporation rate of species A is governed by the lifetime against evaporation of one particle. 74,4)."," The evaporation rate of species $A$ is governed by the lifetime against evaporation of one particle, $t_{evap}(A)$."
 Assuming a binding energy EpCA) (in Kelvin). and a grain temperature T4. the rate coefficient for evaporation 1s: where vis the vibrational frequency of the atom/molecule in its binding site. typically of the order of 10! s! (eg. Hasegawa et al.," Assuming a binding energy $E_{D}(A)$ (in Kelvin), and a grain temperature $T_d$, the rate coefficient for evaporation is: where $\nu$ is the vibrational frequency of the atom/molecule in its binding site, typically of the order of $10^{12}$ $^{-1}$ (e.g., Hasegawa et al."
 1992)., 1992).
 Hence the total evaporation rate (in s!) Is: where (N(A)) 1s the average surface population of species A., Hence the total evaporation rate (in $^{-1}$ ) is: where $\langle N(A) \rangle$ is the average surface population of species $A$.
 It is assumed that surface reactions take place via the Langmuir-Hinshelwood mechanism: reaction occurs when two reactants diffusing over the grain surface meet in the same binding site., It is assumed that surface reactions take place via the Langmuir-Hinshelwood mechanism: reaction occurs when two reactants diffusing over the grain surface meet in the same binding site.
" The rate at which reaction occurs Is: where ορ) and Rj,,(8) are the average rates of thermal hopping between binding sites for each reactant. S is the number of binding sites on the grain. and ay, is an efficiency factor that accounts for any activation energy required to react."," The rate at which reaction occurs is: where $R_{hop}(A)$ and $R_{hop}(B)$ are the average rates of thermal hopping between binding sites for each reactant, $S$ is the number of binding sites on the grain, and $\kappa _{AB}$ is an efficiency factor that accounts for any activation energy required to react."
" If diffusion is assumed to occur via thermal hopping. the rate is simply where E, is the strength of the barrier (in Kelvin) between binding sites."," If diffusion is assumed to occur via thermal hopping, the rate is simply where $E_{b}$ is the strength of the barrier (in Kelvin) between binding sites."
 If. in the case of atomic hydrogen. movement between sites is assumed to occur through quantum tunnelling. different expressions pertain: see Hasegawaetal.(1992).," If, in the case of atomic hydrogen, movement between sites is assumed to occur through quantum tunnelling, different expressions pertain; see \cite{hasegawa}."
. Where an activation energy is required for reaction to occur. the efficiency. Κιμ. Is typically described by a Boltzmann factor. or an expression for quantum-tunnelling efficiency. whichever is the more efficient.," Where an activation energy is required for reaction to occur, the efficiency, $\kappa _{AB}$, is typically described by a Boltzmann factor, or an expression for quantum-tunnelling efficiency, whichever is the more efficient."
 Alternatives to these simple expressions have been put forward that take account of competition between reaction and diffusion out of the binding site (Awad et al., Alternatives to these simple expressions have been put forward that take account of competition between reaction and diffusion out of the binding site (Awad et al.
 2005. Chang et al.," 2005, Chang et al."
 2007); however. for the purposes of comparison to older results. these more recent developments are ignored.," 2007); however, for the purposes of comparison to older results, these more recent developments are ignored."
 Using rate equations to solve a grain-surface chemical network. the production rate (in s!) of the products of the reaction between species A and B is defined as: or. in the case of homogeneous reactants. As stated above. the accuracy of this definition breaks down when stochastic effects become important.," Using rate equations to solve a grain-surface chemical network, the production rate (in $^{-1}$ ) of the products of the reaction between species $A$ and $B$ is defined as: or, in the case of homogeneous reactants, As stated above, the accuracy of this definition breaks down when stochastic effects become important."
" The difference between the production rate. R,,,,LAB). and the reaction rate. Kap. should be noted."," The difference between the production rate, $R_{prod}(AB)$, and the reaction rate, $k_{AB}$, should be noted."
 The former is the subject of the modifications proposed in this paper: the latter 1s strictly defined above in equation (3). and is not adjusted in any way.," The former is the subject of the modifications proposed in this paper; the latter is strictly defined above in equation (3), and is not adjusted in any way."
 The expectation value. (NC). of the grain-surface population of species / may be defined simply as: where Pa(/) is the probability of finding N atoms/molecules of species / on the gram. at any arbitrary moment.," The expectation value, $\langle N(i) \rangle$, of the grain-surface population of species $i$ may be defined simply as: where $P_{N}(i)$ is the probability of finding $N$ atoms/molecules of species $i$ on the grain, at any arbitrary moment."
 The quantity «ΝΟ may be considered to be the average population of, The quantity $\langle N(i) \rangle$ may be considered to be the average population of
the O depletion amounts to a factor of ~2 or more.,the O depletion amounts to a factor of $\sim 2$ or more.
 Why should BP Tau and TW Iva exhibit distinctly dilferent O depletion in (heir accreting plasma?, Why should BP Tau and TW Hya exhibit distinctly different O depletion in their accreting plasma?
 We propose Chat this reflects the different ages and evolutionary states of these stars., We propose that this reflects the different ages and evolutionary states of these stars.
 There is some controversy concerning the age of BP Tan. though this is entirely the result of its uncertain Lipparcos parallax.," There is some controversy concerning the age of BP Tau, though this is entirely the result of its uncertain Hipparcos parallax."
 The Hipparcos data inclicate a distance of only 42-70 pe (flo range)well in front of the Taurus cloud at 140 pe in which it is generally thought to reside (Wichmannοἱal.1998:FavataDertout1999).," The Hipparcos data indicate a distance of only 42-70 pc $\pm
1\sigma$ range)—well in front of the Taurus cloud at 140 pc in which it is generally thought to reside \citep{Wichmann.etal:98,Favata.etal:98,Bertout.etal:99}."
.. Dased on this distance. Favataetal.(1993). estimated BP Tatu to be as old as 35 Myr through comparison with evolutionary (racks.," Based on this distance, \citet{Favata.etal:98} estimated BP Tau to be as old as 35 Myr through comparison with evolutionary tracks."
 However. both Wichmannetal.(1993). and. etal.(1999). refute the Lipparcos distance based on its low statistical significance.," However, both \citet{Wichmann.etal:98} and \citet{Bertout.etal:99} refute the Hipparcos distance based on its low statistical significance."
 find that the astrometric [it to the Iipparcos data for the distance of the Taurus cloud of 140 pc. instead of 42-70 pc. represents only a 26 deviation. and point oul that BP Tau is rather faint for the nominal distance to be reliable.," \citet{Bertout.etal:99} find that the astrometric fit to the Hipparcos data for the distance of the Taurus cloud of 140 pc, instead of 42-70 pc, represents only a $2\sigma$ deviation, and point out that BP Tau is rather faint for the nominal distance to be reliable."
 Thev also show the llipparcos distance of 32-52 pe for for DF Tau.the other Taurus star found by to be of anomalous proximityto be highly uncertain owing to binarity and photometric variability., They also show the Hipparcos distance of 32-52 pc for for DF Tau—the other Taurus star found by \citet{Favata.etal:98} to be of anomalous proximity—to be highly uncertain owing to binarity and photometric variability.
 Allowing for a somewhat smaller distance than 140 pe. but not as extreme as (he Lipparcos value. Simonetal.(2000) estimate a range of 2-10 Myr.," Allowing for a somewhat smaller distance than 140 pc, but not as extreme as the Hipparcos value, \citet{Simon.etal:00} estimate a range of 2-10 Myr."
 However. all other observational evidence points to BP Tau lving in the Taurus cloud. including radial velocity. and proper motion (ILartznann&Stauffer1989:Bertoutοἱal.1999).. extinction of Ay~0.5 (eg.Gullbringetal.19962:Muzerolle2003.andreferencestherein) and strong interstellar Na I absorption (Gullbringetal.," However, all other observational evidence points to BP Tau lying in the Taurus cloud, including radial velocity and proper motion \citep{Hartmann.Stauffer:89,Bertout.etal:99}, extinction of $A_V \sim 0.5$ \citep[e.g.\ ][and references
therein]{Gullbring.etal:96b,Muzerolle.etal:03} and strong interstellar Na I absorption \citep{Gullbring.etal:96}."
1996b).. Gullbringetal.(1993). estimate the age to be 0.6 Myr.," \citet{Gullbring.etal:98}
 estimate the age to be 0.6 Myr."
 In contrast. (he distance and age of TW Iva are much more secure: with an age of e»10 Myr (e.g.Zuckerman&Song2004).. TW Iva appears significantly older (han BP Tau.," In contrast, the distance and age of TW Hya are much more secure: with an age of $\sim 10$ Myr \citep[e.g.\ ][]{Zuckerman.Song:04}, TW Hya appears significantly older than BP Tau."
 TW Ilva is in fact one of the oldest CTS known to be still accreting., TW Hya is in fact one of the oldest CTTS known to be still accreting.
 More importantly. near infra-red measurements also show the inner disks of (he (wo stars to be quite different.," More importantly, near infra-red measurements also show the inner disks of the two stars to be quite different."
" Veiling measurements for BP Tau show a very large excess of0.6 at 2.2; (Muzerolleetal. 2003).. and A—L=0.5740.23 (Ixenvon&Hartmann1995)- (vpical of the accreting stars in Γωναις, oof which have A—L colours in the range 0.35-1.2 (Aleverοἱal."," Veiling measurements for BP Tau show a very large excess of0.6 at $2.2\mu$ m \citep{Muzerolle.etal:03}, and $K-L=0.57\pm 0.23$ \citep{Kenyon.Hartmann:95}- —typical of the accreting stars in Taurus, of which have $K-L$ colours in the range 0.35-1.2 \citep{Meyer.etal:97}."
1997).. lind (hat BP Tau has an optically thick disk whose dust truncation radius is essentially at the corotation radius [rom which magnetospheric accretion is thought to take placematerial from both gas and dust will therefore accrete aud (his material will not be depleted., \citet{Muzerolle.etal:03} find that BP Tau has an optically thick disk whose dust truncation radius is essentially at the corotation radius from which magnetospheric accretion is thought to take place—material from both gas and dust will therefore accrete and this material will not be depleted.
 Instead. TW Iva has very little near-infrared excess shortsvard of 10jan. with A—L= (Silkoetal.2000:Calvet2002:Uchida 2004)..," Instead, TW Hya has very little near-infrared excess shortward of $\mu$ m, with $K-L=0.25$ \citep{Sitko.etal:00,Calvet.etal:02,Uchida.etal:04}. ."
 This is more tvpical of ἐν—L for the stars in Taurus that are in the range —0.05-0.25 for similar spectral, This is more typical of $K-L$ for the stars in Taurus that are in the range $-0.05$ -0.25 for similar spectral
em™.,$^{-3}$.
 Using a quiescent plasma electron number density (the region outside the loop) of |+0.5x10° em? in line with previous estimates (see. e.g. Fludra et al.," Using a quiescent plasma electron number density (the region outside the loop) of $1\pm 0.5
\times 10^8$ $^{-3}$ in line with previous estimates (see, e.g. Fludra et al."
" 1999, Ugarte-Urra et al."," 1999, Ugarte-Urra et al."
 2002). we can determine the loop filling factor to be 3.70.4.," 2002), we can determine the loop filling factor to be $3.7{\pm}0.4$."
 For brightly emitting coronal loops. it can be assumed that all of the emission measure comes directly from the loop itself.," For brightly emitting coronal loops, it can be assumed that all of the emission measure comes directly from the loop itself."
 However. for relatively dim loops. similar to the one under investigation here. a significant portion of the emission will come from plasma in the immediate vicinity of the loop.," However, for relatively dim loops, similar to the one under investigation here, a significant portion of the emission will come from plasma in the immediate vicinity of the loop."
 As a result. the derived electron number densities will represent the upper boundaries of actual values.," As a result, the derived electron number densities will represent the upper boundaries of actual values."
 Coronal seismology. initiated αεί high-resolution observations of waves and oscillations in coronal structures became available. can provide relatively accurate estimates of quantities that cannot be measured directly or are below the instrument’s resolution limit.," Coronal seismology, initiated after high-resolution observations of waves and oscillations in coronal structures became available, can provide relatively accurate estimates of quantities that cannot be measured directly or are below the instrument's resolution limit."
 Using a combination of observations and theoretical models. answers to the problems of the magnitudes and structuring of coronal magnetic fields. density scale-heights. ete..," Using a combination of observations and theoretical models, answers to the problems of the magnitudes and structuring of coronal magnetic fields, density scale-heights, etc.,"
 have since been recovered (Nakariakovetal.1999;Andries2005.2009;Verth2008:Ruderman&Erdéllyi 2009).," have since been recovered \citep{nakariakov1999,andries2005,andries2009,VerthErdelyiJess2008,
RudermanErdelyi2009}."
". In this context. one of the most promising methods for investigating the internal structure of coronal loops 1s based on the P,/P» ratio of the fundamental (Pj) to first harmonic (P3) modes of an oscillation."," In this context, one of the most promising methods for investigating the internal structure of coronal loops is based on the $P_1/P_2$ ratio of the fundamental $P_1$ ) to first harmonic $P_2$ ) modes of an oscillation."
 In à homogeneous. non-stratified atmosphere the period ratio is. 2.," In a homogeneous, non-stratified atmosphere the period ratio is 2."
 However. longitudinal variations in the properties of the plasma (1.e. variations along the loop) can make this ratio to deviate either below or above 2.," However, longitudinal variations in the properties of the plasma (i.e. variations along the loop) can make this ratio to deviate either below or above 2."
 It is believed that magnetic effects produce a ratio that 1s greater than 2 because of the magnetic divergence caused by changes in the cross-sectional area of the loop (DeMoortel&Brady2007:O'Sheaetal. 2007).," It is believed that magnetic effects produce a ratio that is greater than 2 because of the magnetic divergence caused by changes in the cross-sectional area of the loop \citep{DeMoortelBrady2007,oshea2007}."
. In this case. the magnetic effect on the period of oscillation dominates any other effects. such as density stratification.," In this case, the magnetic effect on the period of oscillation dominates any other effects, such as density stratification."
 In contrast. if the ratio of the two periods is less than 2. then the change is attributed. to density stratification effects along the coronal loop.," In contrast, if the ratio of the two periods is less than 2, then the change is attributed to density stratification effects along the coronal loop."
" Several examples have been published where the P,/P* ratio 1s within the interval 1.5—1.9 (McEwanetal.2006:VanDoorsselaereetal. 2008).. Andries"," Several examples have been published where the $P_1/P_2$ ratio is within the interval $1.5-1.9$ \citep{mcewan2006,vandoorsselaere2007,ruderman2008,VerthErdelyi2008,VerthErdelyiJess2008}."
"etal.(2005) show how a one-to-one relationship exists between the P,/P»s ratio and the density scale-height.", \cite{andries2005} show how a one-to-one relationship exists between the $P_1/P_2$ ratio and the density scale-height.
 The dependence of the period ratio on L/xH. where H is the density scale-height. is shown in4.," The dependence of the period ratio on $L/{\pi}H$, where $H$ is the density scale-height, is shown in."
. According to Andriesetal.(2005).. the dependence of the period ratio on the density stratification does not depend on other loop parameters or the magnetic field strength.," According to \cite{andries2005}, the dependence of the period ratio on the density stratification does not depend on other loop parameters or the magnetic field strength."
 As a result. the same dependence can be demonstrated for a variety of density profiles generated inside the same coronal loop.," As a result, the same dependence can be demonstrated for a variety of density profiles generated inside the same coronal loop."
 For the coronal loop under current investigation. we find that ΡΙ/5.=1.8220.02. corresponding to a density scale height H=7343 Mm.," For the coronal loop under current investigation, we find that $P_1/P_2 = 1.82{\pm}0.02$, corresponding to a density scale height $H = 73{\pm}3$ Mm."
 This value ts consistentwith those found by VanDoorsselaereetal.(2007)., This value is consistentwith those found by \citet{vandoorsselaere2007}.
. Assuming that the loop is in hydrostatic equilibrium. the density scale height i5 directly proportional to the temperature. T. according to the equation H=47(—_)Thus. for our present analysis we obtain a loop temperature of T=1.5z0.6 MK. which is within TRACE's temperature response for the 171 channel. and towards the central portion of the 195 channel's temperature response curve (Aschwanden2004;Phillipsetal.," Assuming that the loop is in hydrostatic equilibrium, the density scale height is directly proportional to the temperature, $T$, according to the equation Thus, for our present analysis we obtain a loop temperature of $T =
1.5{\pm}0.6$ MK, which is within TRACE's temperature response for the 171 channel, and towards the central portion of the 195 channel's temperature response curve \citep{aschwanden,phillips}."
2005).. Nevertheless. the visibility of the coronal loop 1 both the 171 and 195 bandpasses. in addition to a derived loop temperature within the TRACE instrument’s temperature response function. suggests that the loop under investigatio is in hydrostatic equilibrium (Andriesetal.2005).," Nevertheless, the visibility of the coronal loop in both the 171 and 195 bandpasses, in addition to a derived loop temperature within the TRACE instrument's temperature response function, suggests that the loop under investigation is in hydrostatic equilibrium \citep{andries2005}."
 On the basis of the period of the fundamental mode (501 s). following the methods of Verwichteetal.(2004).. it i$ possible to calculate the kink speed. ος. of the wave to be ey.=2L/Piundanenal=29148.2 kms7!.," On the basis of the period of the fundamental mode (501 s), following the methods of \citet{verwichte2004}, it is possible to calculate the kink speed, $c_K$, of the wave to be $c_K =
2L/P_{\mathrm{fundamental}} = 291{\pm}8.2$ $^{-1}$."
" The kink speed can then be related to the magnetic field strength. B. by the equation wherep; andp, are the internal and external loop densities. respectively. 4 is the permeability of free space. and the magnetic field strength inside and outside the loop is assumed to be identical."," The kink speed can then be related to the magnetic field strength, $B$, by the equation where $\rho_i$ and $\rho_e$ are the internal and external loop densities, respectively, $\mu$ is the permeability of free space, and the magnetic field strength inside and outside the loop is assumed to be identical."
 Thus. we estimate the magnetic field strength the coronal loop to be 2.0x0.7 G. which is towards the lower-end of statistical studies compiled by Nakartakov and Aschwandenetal. (2002)..," Thus, we estimate the magnetic field strength the coronal loop to be $2.0{\pm}0.7$ G, which is towards the lower-end of statistical studies compiled by \citet{Nak01} and \citet{asch02}. ."
 The existence of two distinet periods in. the. loop. under investigation has been explained and investigated assuming that the two periods belong to the fundamental and first, The existence of two distinct periods in the loop under investigation has been explained and investigated assuming that the two periods belong to the fundamental and first
9 We perform X minimization fits using the UV spectrum and the photometrie data of 553W091. and the results are following.," 	We perform $\chi^{2}$ minimization fits using the UV spectrum and the photometric data of 53W091, and the results are following."
 We have carried out a weighted 47 test to the UV spectrum of 553W091. using the following definition. where N and c4 are the number of spectral bins and the observational errors. respectively.," 	We have carried out a weighted $\chi^{2}$ test to the UV spectrum of 53W091, using the following definition, where $N$ and $\sigma_{\lambda}$ are the number of spectral bins and the observational errors, respectively."
 Figure 10 shows the measured values of reduced 4 of various models., 	Figure 10 shows the measured values of reduced $\chi^{2}$ of various models.
 A smaller value \7 indicates a better , 	A smaller value of $\chi^{2}$ indicates a better fit.
The spectra are normalized at 3150 A(theof average flux in the fit.range of 3000 — 3300 A)). but the test was quite insensitive to the choice of the normalization point. as long as the normalization flux is the mean flux in a reasonably wide (AA>50 A)) range.," 	The spectra are normalized at 3150 (the average flux in the range of 3000 – 3300 ), but the test was quite insensitive to the choice of the normalization point, as long as the normalization flux is the mean flux in a reasonably wide $\Delta\lambda \gtrsim 50$ ) range."
 We modified the error value at 4973.47 (1948.85 in the rest-frame) with an approval from the observers., 	We modified the error value at 4973.47 (1948.85 in the rest-frame) with an approval from the observers.
 It was 2 orders of magnitude smaller than other values. thus 47 tests were heavily dominated by the single point. producing unreasonable results.," 	It was 2 orders of magnitude smaller than other values, thus $\chi^{2}$ tests were heavily dominated by the single point, producing unreasonable results."
 We assume that it was an artifact., 	We assume that it was an artifact.
 We replaced it with an interpolated value from the adjacent bins., 	We replaced it with an interpolated value from the adjacent bins.
10 Figure 10 shows that OS has very little effect on the age estimates based on the UV spectrum. as illustrated earlier in Figure 7.," 	Figure 10 shows that OS has very little effect on the age estimates based on the UV spectrum, as illustrated earlier in Figure 7."
 The discussion of the effects of metallicity mixtures requires a bit of clarification first., 	The discussion of the effects of metallicity mixtures requires a bit of clarification first.
 The mean metallicity of the majority of stars in giant elliptical galaxies is often believed to be approximately twice solar., 	The mean metallicity of the majority of stars in giant elliptical galaxies is often believed to be approximately twice solar.
 If we use such a large metallicity for the single abundance population synthesis. then we would tend to underestimate the UV flux of this galaxy significantly and thus the age (<1.0 Gyr).," 	If we use such a large metallicity for the single abundance population synthesis, then we would tend to underestimate the UV flux of this galaxy significantly and thus the age $< 1.0$ Gyr)."
 This is because even in such metal-rich (<Z»z 2 Z..)) galaxies the main UV sources are probably metal-poor (see Figure 9)., 	This is because even in such metal-rich $<\!\!Z\!\!>\approx$ 2 ) galaxies the main UV sources are probably metal-poor (see Figure 9).
 In this sense. the effect of the use of metallicity mixtures is very large.," 	In this sense, the effect of the use of metallicity mixtures is very large."
 As one can see in Figure 10. solar abundance models mimic metal-rich (2 Z..) composite models reasonably.," 	As one can see in Figure 10, solar abundance models mimic metal-rich (2 $Z_{\odot}$ ) composite models reasonably."
 Composite models indicate larger ages (1.9 — 2.1 Gyr) than solar abundance models (1.8 Gyr) by approximately10%., 	Composite models indicate larger ages (1.9 – 2.1 Gyr) than solar abundance models (1.8 Gyr) by approximately.
.. This suggests that the solar abundance. used by various groups including Spinrad et al. (," 	This suggests that the solar abundance, used by various groups including Spinrad et al. ("
1997). might be a reasonable approximation in the UV population synthesis ofvoung giant elliptical galaxies. even though it is still a factor of two smaller than the likely mean metallicity of stars in giant elliptical galaxies (c.£..,"1997), might be a reasonable approximation in the UV population synthesis of giant elliptical galaxies, even though it is still a factor of two smaller than the likely mean metallicity of stars in giant elliptical galaxies (c.f.,"
 Angeletti Gianonne 1999)., Angeletti Gianonne 1999).
 When the three c confidence ranges are included. our age estimates based on the 4 test using the UV spectrum alone are approximately L8 Gyr (solar abundance model with OS) through 1.9*5* Gyr (infall model with OS). where the errors are internal only and do not include observational errors.," 	When the three $\sigma$ confidence ranges are included, our age estimates based on the $\chi^{2}$ test using the UV spectrum alone are approximately $1.8^{+0.2}_{-0.1}$ Gyr (solar abundance model with OS) through $1.9^{+0.6}_{-0.1}$ Gyr (infall model with OS), where the errors are internal only and do not include observational errors."
 Thus. they are inconsistent with that of Spinrad et al. (," 	Thus, they are inconsistent with that of Spinrad et al. ("
1997) with more than a three 7 confidence (99.7%)).,1997) with more than a three $\sigma$ confidence ).
stars (88.6 %)) (see Tables 1 through 3).,stars (88.6 ) (see Tables 1 through 3).
" We have cross- the AKARI BSC counterparts for 1548 O-rich stars (51.5 %)), 675 C-rich stars (57.8 %)), 86 S stars (23.8 %)) and 18 silicate carbon stars (51.4 %))."," We have cross-identified the $AKARI$ BSC counterparts for 1548 O-rich stars (51.5 ), 675 C-rich stars (57.8 ), 86 S stars (23.8 ) and 18 silicate carbon stars (51.4 )."
" We use AKARI PSC data at twobands (9 and 18 uim) and BSC data at four bands (65, 90, 140 and 160 jim)."," We use $AKARI$ PSC data at twobands (9 and 18 $\mu$ m) and BSC data at four bands (65, 90, 140 and 160 $\mu$ m)."
 In Fig., In Fig.
" 1, AKARI and IRAS PSC fluxes are compared for the cross-identified objects."," 1, $AKARI$ and $IRAS$ PSC fluxes are compared for the cross-identified objects."
 We plot only the objects with good quality (q—3) data at any wavelengths., We plot only the objects with good quality (q=3) data at any wavelengths.
 It is evident that there is a close correlation between two sets of data., It is evident that there is a close correlation between two sets of data.
 Some objects on the left panel of Fig., Some objects on the left panel of Fig.
 1 are too far off from the general trend., 1 are too far off from the general trend.
 This may be because they are large amplitude pulsators or because they are not AGB stars (possibly post-AGB stars)., This may be because they are large amplitude pulsators or because they are not AGB stars (possibly post-AGB stars).
 We mark the candidates for AGB stars (see Section 4.2) on both panels of Fig., We mark the candidates for post-AGB stars (see Section 4.2) on both panels of Fig.
 1., 1.
 We find that the large scatters happen only on the left panel for the candidate stars probably because the shapes of their SEDs are somewhat different from those for typical AGB stars., We find that the large scatters happen only on the left panel for the candidate stars probably because the shapes of their SEDs are somewhat different from those for typical AGB stars.
 IRAS LRS (A = 8—22 yum) data can be used for comparison with AKARI fluxes at 9 and 18 ym. We use interpolated values of the spectral fluxes at 9 and 18 um using a cubic spline method., $IRAS$ LRS $\lambda$ = $-$ 22 $\mu$ m) data can be used for comparison with $AKARI$ fluxes at 9 and 18 $\mu$ m. We use interpolated values of the spectral fluxes at 9 and 18 $\mu$ m using a cubic spline method.
 In Fig., In Fig.
" 2, we compare the fluxes at 9 and 18 um obtained from 1RAS LRS data with those from AKARI data for 922 O-rich stars and 703 C-rich stars in the sample."," 2, we compare the fluxes at 9 and 18 $\mu$ m obtained from $IRAS$ LRS data with those from $AKARI$ data for 922 O-rich stars and 703 C-rich stars in the sample."
 Dim sources are brighter in /RAS LRS than in AKARI PSC., Dim sources are brighter in $IRAS$ LRS than in $AKARI$ PSC.
 The difference could be attributed to the difference in the spatial resolution as Ishihara et al. (, The difference could be attributed to the difference in the spatial resolution as Ishihara et al. (
2010) pointed out to explain a similar phenomenon.,2010) pointed out to explain a similar phenomenon.
" [RAS LRS measures the total flux of the dim emission because of the larger aperture size (15’ x6’), whereas AKARI measures the flux of the peak emission with a smaller aperture (i9"" beam size)."," $IRAS$ LRS measures the total flux of the dim emission because of the larger aperture size $\arcmin$$\times$ $\arcmin$ ), whereas $AKARI$ measures the flux of the peak emission with a smaller aperture $\arcsec$ beam size)."
 We find that the effect of dim sources brighter with IRAS LRS data is more enhanced at 18 wm if compared with the effect at 9 ym. This could be due to the fact that the detectable image size at 18 jum is much larger than the one at 9 jum for dusty AGB stars., We find that the effect of dim sources brighter with $IRAS$ LRS data is more enhanced at 18 $\mu$ m if compared with the effect at 9 $\mu$ m. This could be due to the fact that the detectable image size at 18 $\mu$ m is much larger than the one at 9 $\mu$ m for dusty AGB stars.
 We may also use SO Short Wavelength Spectrometer (SWS; A = 2.4—45.4 um) data for comparison with AKARI fluxes at 9 and 18 jum. Sloan et al. (, We may also use $ISO$ Short Wavelength Spectrometer (SWS; $\lambda$ = $-$ 45.4 $\mu$ m) data for comparison with $AKARI$ fluxes at 9 and 18 $\mu$ m. Sloan et al. (
2003) presented the ISO SWS catalog which contains the high resolution spectral data for 1271 observations.,2003) presented the $ISO$ SWS catalog which contains the high resolution spectral data for 1271 observations.
 We have cross-identified 121 O-rich stars (185 observations) and 68 C-rich stars (105 observations) from the ISO SWS catalog by finding the closest counterpart in the position within 30”., We have cross-identified 121 O-rich stars (185 observations) and 68 C-rich stars (105 observations) from the $ISO$ SWS catalog by finding the closest counterpart in the position within $\arcsec$ .
" Unlike IRAS LRS data, most ISO SWS spectral data show severe scatters and/or noises."," Unlike $IRAS$ LRS data, most $ISO$ SWS spectral data show severe scatters and/or noises."
" Therefore, we obtain the [SO SWS fluxes at 9 and 18 jm using linear least squares regression in the wavelength range of 0.1 jum from the central"," Therefore, we obtain the $ISO$ SWS fluxes at 9 and 18 $\mu$ m using linear least squares regression in the wavelength range of 0.1 $\mu$ m from the central"
resulting spectral classification is provided with an uncertainty of no more than one luminosity subclass.,resulting spectral classification is provided with an uncertainty of no more than one luminosity subclass.
 The spectral type is precise up to one subtype., The spectral type is precise up to one subtype.
" Some of the identified features exhibit a 10-20 ddisplacement with respect to the nominal values, consistent with the instrumental resolution."," Some of the identified features exhibit a 10-20 displacement with respect to the nominal values, consistent with the instrumental resolution."
" Greater displacements, up to a maximum of 29A,, are found corresponding to lines characterized by a complex profile, such as Bry, or placed in a region of strong telluric absorption, such as bothH1 205581 aand Bry."," Greater displacements, up to a maximum of 29, are found corresponding to lines characterized by a complex profile, such as $\gamma$, or placed in a region of strong telluric absorption, such as both 581 and $\gamma$."
" In the next section we will classify the spectra, showing the features we were able to identify, with the corresponding equivalent width."," In the next section we will classify the spectra, showing the features we were able to identify, with the corresponding equivalent width."
" Although it was pointed out (?) that equivalent widths may show variations between stars, we report them for completeness."," Although it was pointed out \citep{hanson96} that equivalent widths may show variations between stars, we report them for completeness."
 The values we calculated are affected by an average 15% error., The values we calculated are affected by an average $\%$ error.
" For each object, a figure displays the spectrum we obtained, together with some comparative spectra from the atlas of ? in a separate box."," For each object, a figure displays the spectrum we obtained, together with some comparative spectra from the atlas of \citet{hanson96} in a separate box."
 Table 2 summarizes the line identifications for all the observed targets., Table \ref{lines} summarizes the line identifications for all the observed targets.
" The source was discovered by IBIS/ISGRI in the first Galactic Plane Survey performed by INTEGRAL (?),, which measured a flux of 3.8 + 0.3 mCrab in the 20-40 keV range."," The source was discovered by IBIS/ISGRI in the first Galactic Plane Survey performed by INTEGRAL \citep{bird04}, , which measured a flux of 3.8 $\pm$ 0.3 mCrab in the 20–40 keV range."
" Instead, only the upper limit of <4 mCrab was obtained in the 40-100 keV band."," Instead, only the upper limit of $<4$ mCrab was obtained in the 40–100 keV band."
 Subsequent Chandra observations allowed the identification of the optical/infrared counterpart., Subsequent Chandra observations allowed the identification of the optical/infrared counterpart.
 This was associated with USNO-B1.0 0384-0560857 = 2MASS J16204627-5130060 by ?.., This was associated with USNO-B1.0 0384-0560857 = 2MASS J16204627-5130060 by \citet{tom06}.
" The power-law spectral fit provided Ng=3.7*15x10” cm? and photon index equal to 0.5705, indicating an intrinsically hard source."," The power-law spectral fit provided $N_{H} = 3.7^{+1.4}_{-1.2} \times 10^{22}$ $^{-2}$ and photon index equal to $0.5^{+0.6}_{-0.5}$, indicating an intrinsically hard source."
" The lower limit to the stellar temperature was estimated toK,, revealing the presence of a very hot, massive star."," The lower limit to the stellar temperature was estimated to, revealing the presence of a very hot, massive star."
" From the fit of optical/IR spectral energy distributions, the distance was estimated to be between 3-10 kpc (3-9 kpc in the case of a supergiant classification)."," From the fit of optical/IR spectral energy distributions, the distance was estimated to be between 3-10 kpc (3-9 kpc in the case of a supergiant classification)."
" Subsequent optical spectroscopy from ? refined the distance estimate to 4.6 kpc. ?,,"," Subsequent optical spectroscopy from \citet{mas06} refined the distance estimate to 4.6 kpc. \citet{negue07},"
" from optical observations, constrained the spectral type to earlier than Figure {| shows the Ks, spectrum we obtained, with identified spectral features marked."," from optical observations, constrained the spectral type to earlier than Figure \ref{fig:IGRJ16207} shows the $K_{s}$ spectrum we obtained, with identified spectral features marked."
" The spectrum shows no metal lines (no or iv), strong He1205581 eemission, absorption at 1126 aand moderately strong Bry absorption."," The spectrum shows no metal lines (no or ), strong 581 emission, absorption at 126 and moderately strong $\gamma$ absorption."
 The atomic transitions observed are the typical of OB star spectra., The atomic transitions observed are the typical of OB star spectra.
" The 205581 lline is a prominent feature in supergiant stars, so that it is considered an important tracer of stars with extended atmospheres."," The 581 line is a prominent feature in supergiant stars, so that it is considered an important tracer of stars with extended atmospheres."
" It becomes weak or even disappears in main sequence stars and it is observed in emission in B type supergiants, whereas it is in absorption in O type supergiants (?).. TheH"," It becomes weak or even disappears in main sequence stars and it is observed in emission in B type supergiants, whereas it is in absorption in O type supergiants \citep{hanson96}."
"e1211126 lline is present in late O — early B For what was outlined above, and by comparing the relative strengths of the identified lines with those of ??,, we estimate the spectral type of the IGR J16207—5129 counterpart to be B1 Ia. This allows us to classify the system as a SGXRB, as also inferred by ?.."," The 126 line is present in late O – early B For what was outlined above, and by comparing the relative strengths of the identified lines with those of \citet{hanson96,hanson05}, we estimate the spectral type of the IGR J16207–5129 counterpart to be B1 Ia. This allows us to classify the system as a SGXRB, as also inferred by \citet{negue07}."
 The source was discoveredby INTEGRAL during its only observed X-ray flare on 2004 September 6th-7th (?).., The source was discoveredby INTEGRAL during its only observed X-ray flare on 2004 September 6th-7th \citep{lut04}.
" Using data of XMM/Newton, ? found pulsations with period P, = 228 s in the X-ray flux and high photoabsorption, with Ny~7x10? cm""."," Using data of XMM/Newton, \citet{lut05} found pulsations with period $P_{s}$ = 228 s in the X-ray flux and high photoabsorption, with $N_{H} \sim 7 \times 10^{23}$ $^{-2}$."
" The single star falling in the XMM/Newton error circle was identified by ? as the counterpart to the X-ray source, and associated with 2MASS J16463526-4507045."," The single star falling in the XMM/Newton error circle was identified by \citet{zur04} as the counterpart to the X-ray source, and associated with 2MASS J16463526-4507045."
" From an optical spectrum, ? classified the source as a Bl Ib supergiant, subsequently refining their classification to Β0.5 Ib (?).."," From an optical spectrum, \citet{negue06} classified the source as a B1 Ib supergiant, subsequently refining their classification to B0.5 Ib \citep{negue07-a}."
 They also estimated the distance of the source to 8 kpc., They also estimated the distance of the source to 8 kpc.
" Our IR data suggest a different spectral Figure 2 shows the Ks, spectrum we obtained, with identified spectral features marked."," Our IR data suggest a different spectral Figure \ref{fig:IGRJ16465} shows the $K_{s}$ spectrum we obtained, with identified spectral features marked."
" The spectrum shows 205581 iin quite strong absorption; a feature at 207730 iis possibly identifiable with a faint blend of the transitions at 6690, 7780 and 8830À,, which appear in the atlas from ? only in the very high S/N spectra."," The spectrum shows 581 in quite strong absorption; a feature at 730 is possibly identifiable with a faint blend of the transitions at 690, 780 and 830, which appear in the atlas from \citet{hanson96} only in the very high S/N spectra."
"We observeHer 1126 and Bry, both in strong absorption.","We observe 126 and $\gamma$ , both in strong absorption."
 We agree with ? in the classification of the counterpart as an early supergiant., We agree with \citet{negue07-a} in the classification of the counterpart as an early supergiant.
" However, we suggest that the observed"," However, we suggest that the observed"
 refsec:discussion.., \\ref{sec:discussion}.
" +=0.3014 2=0.3145. ez.=4000 +. refsec:discussion.. 1420.6. Dec.=30724007. 0.80000+0.00033 RA.ο Dec.=30724207. 2=0.31870+0.00033 1121L9  68225 Ll, S.0.75 3.0.072 ~20 5. 2=0.31 +«0.31 0.31 5.. z-90% 2.«0.31. "," $z = 0.3014$ $z = 0.3148$ $\Delta cz = 4000$ $^{-1}$ \\ref{sec:discussion}, ${\rm R.A.} =
00\hd14\md20.6\sd$ ${\rm Dec.} = -30^\circ24\md00\sd$ $z=0.30000\pm0.00033$ ${\rm R.A.}=00\hd14\md22.0\sd$ ${\rm Dec.} =
-30^\circ24\md20\sd$ $z=0.31870\pm0.00033$ $1121^{+176}_{-88}$ $^{-1}$ $682^{+97}_{-75}$ $^{-1}$ $8.0^{+2.7}_{-1.2}$ $3.0^{+0.9}_{-0.7}$ $\sim$ \ref{fig:zhist_img} $z=0.31$ $z<0.31$ $z>0.31$ \ref{fig:zhist_img}, $>90$ $z < 0.31$ "
by means of a linear relation.,by means of a linear relation.
 Once attained (he deepest optical depth point 7; al the end of (he forward-elimination. we can impose the bottom boundary condition (eq. [," Once attained the deepest optical depth point $\tau_{NL}$ at the end of the forward-elimination, we can impose the bottom boundary condition (eq. ["
"5] later on) to both the RT process and the cubic spline chain: in other words we can close the linear relation between οτν4) and 5,(7N1) on the one hand. between Si(ty,1) and οτν) on the other.","5] later on) to both the RT process and the cubic spline chain; in other words we can close the linear relation between $S_{\nu}(\tau_{NL-1})$ and $S_{\nu}(\tau_{NL})$ on the one hand, between $S^{\prime\prime}_{\nu}(\tau_{NL-1})$ and $S^{\prime\prime}_{\nu}(\tau_{NL})$ on the other."
 This allows us to recover (he munerical values of the source functions and their second. derivatives at the bottom. as well as those of the set ofthe incident upgoing specilic intensities LAND}.," This allows us to recover the numerical values of the source functions and their second derivatives at the bottom, as well as those of the set ofthe incident upgoing specific intensities $\lbrace I^{+}(\tau_{NL},\mu_{J}), J = 1,ND\rbrace$ ."
 Then. in a succesive back-substitution scheme. we are in a position to compute at each depth point the numerical values of the source functions and their second derivatives by using the above linear relations. whose coefficients have been stored during the previous forward-elimination.," Then, in a succesive back-substitution scheme, we are in a position to compute at each depth point the numerical values of the source functions and their second derivatives by using the above linear relations, whose coefficients have been stored during the previous forward-elimination."
 Thanks to that we have at hand a unique algorithm to solve each specilic RT problem under the imposed constraint that the specilic source functions as well as their fist and second derivatives be continuous at all the points of the grid chosen lor the geometrical representation of the stellar atmosphere., Thanks to that we have at hand a unique algorithm to solve each specific RT problem under the imposed constraint that the specific source functions as well as their first and second derivatives be continuous at all the points of the grid chosen for the geometrical representation of the stellar atmosphere.
 In such a way we can get rid of the instabilities (hat may arise in the case of extreme variations of (he source functions without paving anv extra computational cost., In such a way we can get rid of the instabilities that may arise in the case of extreme variations of the source functions without paying any extra computational cost.
 For the sake of an easier presentation of the new more precise version of the IAI announced in Section 1. we will consider (he simplest instance (hat vel contains all the difficulties intrinsic to. RT astroplivsical problems. namely (he transport of monochromatic radiation through a plane-parallel medium in which matter particles can scatter. absorb and emit photons.," For the sake of an easier presentation of the new more precise version of the IIM announced in Section 1, we will consider the simplest instance that yet contains all the difficulties intrinsic to RT astrophysical problems, namely the transport of monochromatic radiation through a plane-parallel medium in which matter particles can scatter, absorb and emit photons."
 In the previous works above quoted the original formulation was applied to much more general instances., In the previous works above quoted the original formulation was applied to much more general instances.
 The version presented here can be easily applied to such cases., The version presented here can be easily applied to such cases.
 Following the customary notation. the RT equations that describe the evolution of the upgoing intensities /.(7.j() and the cowngoing intensities /.(7.j() are Üem where 7 denotes the optical depth and ris the cosine of the angle formed by the direction of propagation with the perpendicular to the plane-parallel lavers (jj=cos@.0<yrx1) 3em The source finetion is a weighted mean between the thermal source 2(7) and the mean intensiv J(7). namely," Following the customary notation, the RT equations that describe the evolution of the upgoing intensities $I^{+}(\tau,\mu)$ and the downgoing intensities $I^{-}(\tau,\mu)$ are 0em where $\tau$ denotes the optical depth and $\mu$ is the cosine of the angle formed by the direction of propagation with the perpendicular to the plane-parallel layers $\mu \equiv \cos \theta, 0 \leq \mu \leq 1)$ 3em The source function is a weighted mean between the thermal source $B({\tau})$ and the mean intensity $J(\tau)$ , namely"
SAAO telescope by end of January 2004 on ten sources confirm their extragalactic nature (Leipski et al.,SAAO telescope by end of January 2004 on ten sources confirm their extragalactic nature (Leipski et al.
 2004 in prep.)., 2004 in prep.).
 The observations reveal two type-1 AGN and two type-2 AGN. one of which (ISOCPO08080. refspectra)) has a high [OIIIJAS007 luminosity above 10 L. and can be classified as QSO-2.," The observations reveal two type-1 AGN and two type-2 AGN, one of which (ISOCP08080, \\ref{spectra}) ) has a high $\lambda$ 5007 luminosity above $^{\rm 8}$ $_{\odot}$ and can be classified as QSO-2."
 Furthermore. we find two reddened LINER and four extremely reddened emission-line galaxies.," Furthermore, we find two reddened LINER and four extremely reddened emission-line galaxies."
 Example spectra are given in Fig. 2.., Example spectra are given in Fig. \ref{spectra}.
" The visual extinction of the emission-line galaxies as inferred from the ratio H,,/H.;10 is A= 3mag: actually ely is expected to be much stronger when derived from data at longer wavelengths. as found m many dust-enshrouded IR. sources (e.g. Haas et al."," The visual extinction of the emission-line galaxies as inferred from the ratio $_\alpha$ $_\beta > 10$ is $A_V \ge 3\,$ mag; actually $A_V$ is expected to be much stronger when derived from data at longer wavelengths, as found in many dust-enshrouded IR sources (e.g. Haas et al."
 2001)., 2001).
 The redshift range is 0.1<:x0.5., The redshift range is $ 0.1 \le z \le 0.5$.
 Evidence is growing that LINER galaxies contain an AGN (e.g. Satyapal et al., Evidence is growing that LINER galaxies contain an AGN (e.g. Satyapal et al.
 2004)., 2004).
 Also the four emission-line galaxies may contain an AGN. since their flux ratio Fyy/Fri. - 100 1s below that found for known pure starburst IR galaxies.," Also the four emission-line galaxies may contain an AGN, since their flux ratio $F_{60}/F_{LW2}$ $<$ 100 is below that found for known pure starburst IR galaxies."
 Therefore. the ongoing results with a fraction of (4/10) optically identifyable classical AGN are consistent with our prediction that most of the ISOCP excess sources are AGN.," Therefore, the ongoing results with a fraction of (4/10) optically identifyable classical AGN are consistent with our prediction that most of the ISOCP excess sources are AGN."
 Alternatively. we would have to postulate a new population of dust-enshrouded unusually cool. star-forming galaxies.," Alternatively, we would have to postulate a new population of dust-enshrouded unusually cool star-forming galaxies."
 We have discovered a sample of unique MIR excess sources., We have discovered a sample of unique MIR excess sources.
 Various arguments suggest that they likely contain an AGN., Various arguments suggest that they likely contain an AGN.
 The ongoing optical spectroscopy indicates of the sample to be classical AGN and the remaining part to be dust-enshrouded sources., The ongoing optical spectroscopy indicates of the sample to be classical AGN and the remaining part to be dust-enshrouded sources.
 They appear enigmatic in terms of having a high MIR/NIR flux ratio. but relatively low FIR upper limits.," They appear enigmatic in terms of having a high MIR/NIR flux ratio, but relatively low FIR upper limits."
 Since a moderate FIR/MIR flux ratio is more typical for AGN. it argues against pure starbursts.," Since a moderate FIR/MIR flux ratio is more typical for AGN, it argues against pure starbursts."
 This conjecture has to be confirmed., This conjecture has to be confirmed.
 Because of the high extinction. optical observations might not be able to see the true AGN or starburst or composite nature of those sources.," Because of the high extinction, optical observations might not be able to see the true AGN or starburst or composite nature of those sources."
 Therefore. future observations with XMM-Newton. the VLA and IR spectroscopy with the Spitzer Space Telescope are planned.," Therefore, future observations with XMM-Newton, the VLA and IR spectroscopy with the Spitzer Space Telescope are planned."
 If all 80 ISOCP MIR excess sources turn out to be AGN and if 32 of them (= 40%%)) are classical AGN which could have been identified also in optical surveys. then the number counts of AGN may increase by a factor of up to 80/32 = 2.5 due to the inclusion of dusty AGN.," If all 80 ISOCP MIR excess sources turn out to be AGN and if 32 of them (= ) are classical AGN which could have been identified also in optical surveys, then the number counts of AGN may increase by a factor of up to 80/32 = 2.5 due to the inclusion of dusty AGN."
 Clearly. a reliable comparison will have to wait until spectra of more ISOCP sources are obtained.," Clearly, a reliable comparison will have to wait until spectra of more ISOCP sources are obtained."
 The emphasis of this letter is on presenting a promising strategy how to find the presumed missing AGN., The emphasis of this letter is on presenting a promising strategy how to find the presumed missing AGN.
" The selection of MIR excess sources via the 77.A, and AEAT2 colour-colour diagrams in combination with the low 60j/m upper flux limits turns out to be efficient in. separating starbursts from AGN.", The selection of MIR excess sources via the $H-K_{\rm s}$ and $K_{\rm s}-LW2$ colour-colour diagrams in combination with the low $\mu$ m upper flux limits turns out to be efficient in separating starbursts from AGN.
" It will establish a long sought-after technique for selecting the full population of AGN largely free of extinction,", It will establish a long sought-after technique for selecting the full population of AGN largely free of extinction.
 We thank Michael Strauss and Nadia Zakamska for their constructive and detailed referee report., We thank Michael Strauss and Nadia Zakamska for their constructive and detailed referee report.
 This research is based on the Data Archives of ISO. 2MASS. USNO-B. UCAC. IRAS. NVSS and FIRST.," This research is based on the Data Archives of ISO, 2MASS, USNO-B, UCAC, IRAS, NVSS and FIRST."
 The NED. SIMBAD and the VisieR Service were used.," The NED, SIMBAD and the VisieR Service were used."
 This work is supported by the Nordrhein-Westfllisehe Akademie der Wissenschaften. funded by the Federal State and the Federal Republic of Germany.," This work is supported by the Nordrhein-Westfällische Akademie der Wissenschaften, funded by the Federal State and the Federal Republic of Germany."
 BC thanks the South African National Research Foundation NRF for tinancial support., BC thanks the South African National Research Foundation NRF for financial support.
AA)) at time-resolutions down to 3 minutes.,) at time-resolutions down to 3 minutes.
 They derived a long period (10499) from radial velocity variations in the optical emission lines., They derived a long period 9) from radial velocity variations in the optical emission lines.
 They also mace note of the relative weakness of the Balmer line emission. which they deemed due to a high temperature ancl high mass accretion rate in the disc and suggested: a classification of old. nova or nova-like variable — a view in keeping with Schild's (1969) comment that the object displaved: some characteristics indicative of an old nova.," They also made note of the relative weakness of the Balmer line emission, which they deemed due to a high temperature and high mass accretion rate in the disc and suggested a classification of old nova or nova-like variable – a view in keeping with Schild's (1969) comment that the object displayed some characteristics indicative of an old nova."
 Since this time. QU Car has been classified in catalogues (Ritter Ixolb 1998. Downes et al.," Since this time, QU Car has been classified in catalogues (Ritter Kolb 1998, Downes et al."
 2001) as a nova-like variable.Evplover ), 2001) as a nova-like variable. )
 low-dispersion spectra reveal broad blueshifted UV absorption lines in aandCIV. with an emission component in aand (Ixnigge. Woods Drew 1994). indicative of an optically thick disc accompanied by mass outflow.," low-dispersion spectra reveal broad blueshifted UV absorption lines in and, with an emission component in and (Knigge, Woods Drew 1994), indicative of an optically thick disc accompanied by mass outflow."
 Ixnigee et al. (, Knigge et al. (
1994). noted variation in the Iline caused. by a periodic increase in the strength. of the emission. component. but were unable to decide whether this variablity. was linked το the orbital phase.,"1994) noted variation in the line caused by a periodic increase in the strength of the emission component, but were unable to decide whether this variablity was linked to the orbital phase."
 They. also commented on the strength of the T1371 absorption line and the 11640 emission both unusually strong for high-state non-magnetic CV (LInMCV)., They also commented on the strength of the 1371 absorption line and the 1640 emission – both unusually strong for high-state non-magnetic CV (HnMCV).
 The data that are analysed in this paper were obtained as part of an observing campaign to detect. spectral signatures of cdisc-wind variability. of short timescales., The data that are analysed in this paper were obtained as part of an observing campaign to detect spectral signatures of disc-wind variability of short timescales.
 These signatures are predicted to show up as highly time-variable fine structure components in wind-formed UV lines (Proga. Stone Drew 1998).," These signatures are predicted to show up as highly time-variable fine structure components in wind-formed UV lines (Proga, Stone Drew 1998)."
 To achieve the necessary time and waveleneght resolution. the Space Telescope. Imaging Spectrograph (STIS) on the )) was emploved with an echelle grating in photon-counting (ΤΙΝΗΣΟΤΕΛ) mode.," To achieve the necessary time and wavelenght resolution, the Space Telescope Imaging Spectrograph (STIS) on the ) was employed with an echelle grating in photon-counting (TIME-TAG) mode."
 This allows a time-resolution of down to ~ 10s and velocity resolution of down to IO0kms with the tracde-oll that higher time-resolution will result in a reduced uscable spectral resolution ancl vice-versa.," This allows a time-resolution of down to $\sim10\,$ s and velocity resolution of down to $\sim10$, with the trade-off that higher time-resolution will result in a reduced useable spectral resolution and vice-versa."
 On examining the results of the observations we were struck by the wavs in which QU Car distinguished itself from the other targets in the programme (the nova-like variables EX. Vel ancl V3885 Ser. presented in Hartley ct al.," On examining the results of the observations we were struck by the ways in which QU Car distinguished itself from the other targets in the programme (the nova-like variables IX Vel and V3885 Sgr, presented in Hartley et al."
 2002)., 2002).
 In this paper we seek to present the current. observations and then re-examine archive data. with a view to establishing a physical origin for the unusual features noted.," In this paper we seek to present the current observations and then re-examine archive data, with a view to establishing a physical origin for the unusual features noted."
 In section 2. we describe the observations and cata extraction processes., In section \ref{s:obs} we describe the observations and data extraction processes.
 The results are then presented in two wavs: in section 3 we describe the time-averaged spectrum obtained at each epoch of observation. then in section d. we re-present the data as spectral time-series at 30-sec. time- and as continuum light curves.," The results are then presented in two ways: in section \ref{s:mean} we describe the time-averaged spectrum obtained at each epoch of observation, then in section \ref{s:timevar} we re-present the data as spectral time-series at 30-sec time-resolution and as continuum light curves."
 Finally. in section 6 we complare QU Car with other non-magnetic HnMCV and. consider the origin of QU Car's UV line spectrum.," Finally, in section \ref{s:discuss} we complare QU Car with other non-magnetic HnMCV and consider the origin of QU Car's UV line spectrum."
 Observations were performed by the STIS instrument on the with the far ultraviolet. (LUV). NLANEA. detector AA))., Observations were performed by the STIS instrument on the with the far ultraviolet (FUV) MAMA detector ).
 Phe E140M echelle erating with a central wavelength of wwas used., The E140M echelle grating with a central wavelength of was used.
 This configuration provides a resolution of ~kms (1t ~ 23000)., This configuration provides a resolution of $\sim13\kms$ (R $\sim$ 23000).
" Each observation was performed in a single telescope orbit for the maximum available time. with the detector set to time-tag mode and using the arcsec.0.2"" aaperture."," Each observation was performed in a single telescope orbit for the maximum available time, with the detector set to time-tag mode and using the $\times0.2\,$ aperture."
 “Phe cates and exposure lengths of our observations are given in table 2.., The dates and exposure lengths of our observations are given in table \ref{tab:obs_dates}.
 All data calibration was performed with software. using the package produced by the Space Telescope Science. Institute (SPSel).," All data calibration was performed with software, using the package produced by the Space Telescope Science Institute (STScI)."
 Time-tag is à photon counting mode. which provides an events stream with 125-55 time-resolution.," Time-tag is a photon counting mode, which provides an events stream with $\mu$ s time-resolution."
 This can be integrated. over any selected. time resolution (time bin) to produce a set of raw images of the echelle output. from which a 1-D spectrum is extracted and calibrated.," This can be integrated over any selected time resolution (time bin) to produce a set of raw images of the echelle output, from which a 1-D spectrum is extracted and calibrated."
 The calibration. including doppler correction for the telescope's motion. was performed with S'TScls package. using the suggested best reference files.," The calibration, including doppler correction for the telescope's motion, was performed with STScI's package, using the suggested best reference files."
 igure 1 shows the summed spectrum for cach observation (hereafter. called datasets. Ql. Q2. and. Q3).," figure \ref{fig:qucar} shows the summed spectrum for each observation (hereafter called datasets Q1, Q2 and Q3)."
 QU Car's UV lines appear to be characterised. by strong absorption eatures in T1240. and T1371. less. prominent T1398 absorption. and emission in. 11176. 11549 and 11640.," QU Car's UV lines appear to be characterised by strong absorption features in 1240 and 1371, less prominent 1398 absorption, and emission in 1176, 1549 and 1640."
 Phe narrowness of QU Car's ine features ds striking., The narrowness of QU Car's line features is striking.
 “Pypical terminal velocities of outllows in high-state CV that commonly determine UV ine widths can be up toFi., Typical terminal velocities of outflows in high-state CV that commonly determine UV line widths can be up to.
 Indeed it is usual to ind broad blueshifted absorption in the stronger resonance ine profiles in non-eclipsing svstems., Indeed it is usual to find broad blueshifted absorption in the stronger resonance line profiles in non-eclipsing systems.
 Here. however. the line oofiles rarely extend to more than ~+1000kms+. and show rather little P Cvgni behaviour.," Here, however, the line profiles rarely extend to more than $\sim\pm1000$, and show rather little P Cygni behaviour."
 The STIS datasets. oller. an insight into the finer structure of lines that have previously only been identifiable in low-resolution data., The STIS datasets offer an insight into the finer structure of lines that have previously only been identifiable in low-resolution data.
 Llowever. before describing the character of the observed. profiles. we first consider whether it is possible to correct the spectra for line of sight (LOS)," However, before describing the character of the observed profiles, we first consider whether it is possible to correct the spectra for line of sight (LOS)"
racius. high internal entropy. ancl large effective temperature.,"radius, high internal entropy, and large effective temperature."
 Such an object is not necessarily one that would be the result of any particular planet Formation moclel., Such an object is not necessarily one that would be the result of any particular planet formation model.
 This model planet is allowed to radiate and Cool over time., This model planet is allowed to radiate and cool over time.
 Since there have been no detections vet of voung planets with measured masses. (he applicability. of (his initial condition is untested. although there are data from more massive objects.," Since there have been no detections yet of young planets with measured masses, the applicability of this initial condition is untested, although there are data from more massive objects."
 A pair of eclipsing. voung (I1Myr) brown clwarls with known dynamical masses (57 and 36 Jupiter masses (Mj)) indeed have radii exceeding five limes that of Jupiter (Stassunοἱal.2006).. confirming (hat voung massive brown clwarls. at least. are in fact large and hot.," A pair of eclipsing, young $\sim 1\,\rm Myr$ ) brown dwarfs with known dynamical masses (57 and 36 Jupiter masses $\rm M_J$ )) indeed have radii exceeding five times that of Jupiter \citep{Stassun06}, confirming that young massive brown dwarfs, at least, are in fact large and hot."
 But giant planets that formed in a disk around a primary star. or even isolated planet-mass objects. mav have experienced very different initial conditions.," But giant planets that formed in a disk around a primary star, or even isolated planet-mass objects, may have experienced very different initial conditions."
 Evolution (racks computed in the usual wav.even (hough thev do not necessarily rellect anv particular planet formation theorvhave been used to evaluate detection strategies for irue giant planets orbiting solar (vpe stars (e.g..Burrows2005).. and (hev have been used to characterize isolated. verv low mass brown dwarls. Chauvinetal.(2004).," Evolution tracks computed in the usual way–even though they do not necessarily reflect any particular planet formation theory–have been used to evaluate detection strategies for true giant planets orbiting solar type stars \citep[e.g.,][]{Burrows05}, and they have been used to characterize isolated, very low mass brown dwarfs. \citet{Chauvin04},"
. lor example. reported on the detection of a faint companion to the M8 brown dwarf (hereafter 241A881207) in TW IIvdrae with an estimated age of 8 Myr.," for example, reported on the detection of a faint companion to the M8 brown dwarf (hereafter 2MASS1207) in TW Hydrae with an estimated age of 8 Myr."
" Using its observed luminosity and applying published evolution tracks. thev estimated a mass of just 5M, for the mass of the companion."," Using its observed luminosity and applying published evolution tracks, they estimated a mass of just $5\,\rm M_J$ for the mass of the companion."
 The early modelers certainlv did not foresee that direct. detectiouns of putative voung planets would be compared against the models at exceptionally voung ages. at Limes when the model planet may not vet have forgotten its hot start.," The early modelers certainly did not foresee that direct detections of putative young planets would be compared against the models at exceptionally young ages, at times when the model planet may not yet have forgotten its hot start."
 Stevenson(1982) wrote (hat evolution calculations 7...cannot be expected to provide accurate information on the first LO? 105 vears of evolution because of the artificiality of an initially adiabatic. homologously stale.”," \citet{stevenson82} wrote that evolution calculations “...cannot be expected to provide accurate information on the first $10^5$ $10^8$ years of evolution because of the artificiality of an initially adiabatic, homologously state.”"
 More recently. Daraffeetal.(2002) examinecl (he uncertainties in evolution tracks of brown dwarls al voung ages and cautioned about the applicability of evolution models al ages less than a few million vears. on the lower end of Stevenson's uncertainty range.," More recently, \citet{Baraffe02} examined the uncertainties in evolution tracks of brown dwarfs at young ages and cautioned about the applicability of evolution models at ages less than a few million years, on the lower end of Stevenson's uncertainty range."
 Wuchterl(2005). has also expressed concern (hat standard evolution models do not capture the early evolution correctly., \citet{Wuchterl05} has also expressed concern that standard evolution models do not capture the early evolution correctly.
 Given (he clear imperatives to interpret observations of voung. low mass objects and {ο plan for future direct detections of giant. planets formed in orbit about solar (wpe stars. (here is a need to connect models of eiant planet formation to gian planet evolution.," Given the clear imperatives to interpret observations of young, low mass objects and to plan for future direct detections of giant planets formed in orbit about solar type stars, there is a need to connect models of giant planet formation to giant planet evolution."
 Our goals here are both to help fill the void in physically. plausible models of extrasolar ejant planets (EGPs) at voung ages and to better quantily the age bevond which the evolution models are robust and applicable., Our goals here are both to help fill the void in physically plausible models of extrasolar giant planets (EGPs) at young ages and to better quantify the age beyond which the evolution models are robust and applicable.
 We aim to understand whether or not (he current eeneration of evolution models can reliably predict the luminosity of giant. planets al voung, We aim to understand whether or not the current generation of evolution models can reliably predict the luminosity of giant planets at young
After phase aud amplitude calibration. we combined the data with «different central frequencies into an expanded data-set of 271 spectral chamucls of 2.5 MIIz each. calculating the proper statistical weight of each channel individually.,"After phase and amplitude calibration, we combined the data with different central frequencies into an expanded data-set of 271 spectral channels of 2.5 MHz each, calculating the proper statistical weight of each channel individually."
 The outer channels of the spectral cube therefore have larger uncertaiuties (sce Fig. 8))., The outer channels of the spectral cube therefore have larger uncertainties (see Fig. \ref{B3COposa}) ).
" To determine: the total -1.3 um fins density,: D3 J2330|23927 was observed iu service mode with he I17-chauucl Max Planck Bolometer array at the IRAM 3018. telescope on Pico: Veleta. Spain."," To determine the total 1.3 mm flux density, B3 J2330+3927 was observed in service mode with the 117-channel Max Planck Bolometer array at the IRAM 30m telescope on Pico Veleta, Spain."
 The effective bandwidth centre for steep ↕∐∖↥⋅↕⊔⋜↧↕↴∖↴↻↸∖↸⊳⊓⋅⋜↧↕↴∖↴∿⊇⋅↱⊐∩≼∶, The effective bandwidth centre for steep thermal spectra is $\sim$ 250 GHz.
∐∑∙↖↖⊽↸∖∪↴⋝↴∖↴↸∖↥⋅↖⇁↸∖≼↧↑↕∐∖↴∖↴≺∏∐⋅↸⊳↸∖ with the arrav’s central channel. using the standard .ON-OFF? chopsobservingi sequence. in: which: the secondary uivrOr in azimuth by aat a rate of 2 Uz.," We observed the source with the array's central channel, using the standard 'ON-OFF' observing sequence, in which the secondary mirror chops in azimuth by at a rate of 2 Hz."
 We adopted a calibration factor of» .35000 counts per Jausky. which we estimate is accurate o within20%.," We adopted a calibration factor of 35000 counts per Jansky, which we estimate is accurate to within."
.. The observations were split in 2 sessions: 5416 subscaus of 125 on UT 2002 October 30 aud 10 subscans ou UT 2002 November 2. resulting in a total on-source iutegratiou time of 21 munutes.," The observations were split in 2 sessions: $\times$ 16 subscans of 12s on UT 2002 October 30 and $\times$ 16 subscans on UT 2002 November 2, resulting in a total on-source integration time of 21 minutes."
 We reduced the data with the MOPSI software package1998). including subtraction of the correlated sky noise.," We reduced the data with the MOPSI software package, including subtraction of the correlated sky noise."
" This vields a target flux of Sosucu,=L8dx12 wy.", This yields a target flux of $S_{250\rm GHz}=4.8\pm1.2$ mJy.
 We observed D3 J233013927 with the Westerbork Svuthesis Badio Telescope (WSRT) on several occasious between UT 2001 July 1 aud 2002 September 10 to search for redshitted 221]. «cun (1120.1057. MIIzZ) absorption against the svuchrotrou cussion from the radio source., We observed B3 J2330+3927 with the Westerbork Synthesis Radio Telescope (WSRT) on several occasions between UT 2001 July 1 and 2002 September 10 to search for redshifted 21 cm (1420.4057 MHz) absorption against the synchrotron emission from the radio source.
 Untortunately. a significant fraction of these observations were rendered useless due to external radio frequency interference (REI). or by an unstable ionosphere.," Unfortunately, a significant fraction of these observations were rendered useless due to external radio frequency interference (RFI), or by an unstable ionosphere."
 In the following. we shall therefore ouly use the highest quality observations. with a total iuteeration time of 22 hours.," In the following, we shall therefore only use the highest quality observations, with a total integration time of 22 hours."
 We used the DZB backend with a 10 MIIz bandwidth centered on 317 MIIz and 128 channels eiviug a velocity resolution of ~16 before Tanning simoothing the data., We used the DZB backend with a 10 MHz bandwidth centered on 347 MHz and 128 channels giving a velocity resolution of $\sim 16$ before Hanning smoothing the data.
" We made a line cube using uniform weielting. eivine a resolution of G1""«36"" at PA=0 (north-south)."," We made a line cube using uniform weighting, giving a resolution of $61\arcsec \times 36\arcsec$ at PA=0 (north-south)."
 The noise iu the single channel is ~1.7 wJv/Beam/chamuel (after TlanmineC» simeothine)., The noise in the single channel is $\sim 1.7$ mJy/Beam/channel (after Hanning smoothing).
C» We have also obtained a continuum image of the field., We have also obtained a continuum image of the field.
" At the observed frequeucy aud resolution of the WSRT observations the coutimi chussion of D3 J2330|3927 is unresolved with a peak fiux of [05 τιν. consistent with the 325""mMIIZ WENSS aud5 MIIz Texas flux densities (see Fie. 6))."," At the observed frequency and resolution of the WSRT observations the continuum emission of B3 J2330+3927 is unresolved with a peak flux of 405 mJy, consistent with the 325 MHz WENSS and365 MHz Texas flux densities (see also Fig. \ref{B3SED}) )."
 Figue 2 shows the location of the radio source on the As band nuage., Figure \ref{radioKoverlay} shows the location of the radio source on the $K_S-$ band image.
 The radio source. consisting of 3 cononents with a largest separation of 179. is located exactly in between two objects detected im both the Ro sud As baud nuages.," The radio source, consisting of 3 components with a largest separation of $1\farcs9$ is located exactly in between two objects detected in both the $R-$ and $K_S-$ band images."
 We also detect a resolved COMPOE'oniponuenutut in1 thee ΆνAs baudband imagenuage 37553°55aan xosouthwestvest of ththe radio source. which may be related.," We also detect a resolved component in the $K_S-$ band image 5 southwest of the radio source, which may be related."
 Table 1 lists the on∙∙nd AD Llirometry ob tThese 3 conponents. which WO 6LCL asO.0. aAG 6.," Table \ref{B3astrophotometry} lists the positions and photometry of these 3 components, which we label as, and ."
 The opticalast spectroscopic slit ∙∙∙included objects. aud : ≀∣∙↖↖⇁∐↕↸∖↑↕∐∖∐↸∖⋜∐⋅≓∐⊰↴∖↴↕↕↑∐∐⊳↕∏≼∐∖≺↧∪∐," The optical spectroscopic slit included objects and, while the near-IR slit included only object."
"↕∙↖↽∪↴⋝⋅↿↸∖↸⊳↑∪∙⊡∶↴∙⊾⋯⋅↸∖↴∖↴↓ ∙∙ ⊳ ∙ and 5 show that object. has the classical. spectra . OI:fa type""pe aAGN,eN. showshowing.o narrowarrow οcutission⋅⋅SS1O Ies.ON auddCL aé faint coutinuun enüsson."," Figures \ref{B3Lya2D} and \ref{B3spectra} show that object has the classical spectrum of a type II AGN, showing narrow emission lines and a faint continuum emission."
 We only detect a single. weak enidssousion lineliue iuin objectobiJ (Fig.(Fie | DJ. wh," We only detect a single, weak emission line in object (Fig. \ref{B3Lya2D}) ),"